integrity of repair weld
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7272019 Integrity of Repair Weld
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HSEHealth amp Safety
Executive
Integrity of Repaired Welds (Phase 1)- Deliverable 5 Summary Report
Prepared by Serco Assurance for the
Health and Safety Executive 2004
RESEARCH REPORT 191
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HSEHealth amp Safety
Executive
Integrity of Repaired Welds (Phase 1)- Deliverable 5 Summary Report
J K Sharples L Gardner
S K Bate R Charles
Serco Assurance
Birchwood Park
Warrington
Cheshire
WA3 6AT
J R Yates
The University of SheffieldSheffield
S1 3JD
M R Goldthorpe
M R Goldthorpe Associates
The Grange
2 Park Vale Road
MacclesfieldCheshire
SK11 8AR
This report summarises work that has been undertaken by Serco Assurance (formerly AEA Technology
Consulting) The University of Sheffield and M R Goldthorpe Associates on behalf of the Health and
Safety Executive It describes Phase 1 of a proposed multi-stage project aimed at
(i) providing general guidance on when welded repairs may or may not be beneficial and
(ii) proposing a suitable engineering procedural method for assessing the integrity of repaired welds on
a case-bycase basis Welds considered are appropriate to ferritic material
This report and the work it describes were funded by the Health and Safety Executive (HSE) Itscontents including any opinions andor conclusions expressed are those of the authors alone and do
not necessarily reflect HSE policy
HSE BOOKS
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copy Crown copyright 2004
First published 2004
ISBN 0 7176 2800 0
All rights reserved No part of this publication may be reproduced stored in a retrieval system or transmitted in any form or by any means (electronic mechanical photocopying recording or otherwise) without the prior written permission of the copyright owner Applications for reproduction should be made in writing to Licensing Division Her Majestys Stationery OfficeSt Clements House 2-16 Colegate Norwich NR3 1BQor by e-mail to hmsolicensingcabinet-officexgsigovuk
ii
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CONTENTS
EXECUTIVE SUMMARY v
INTRODUCTION 1
TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND PREVIOUS
PROBLEMS AND ASSESSMENT OF INFORMATION CONTAINED IN THE
LITERATURE 3
TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF CASES TO CONSIDER 5
TASK 3 ndash WELDSPECIMEN MANUFACTURE 7
TASK 4 ndash MATERIAL CHARACTERISATION TESTS 9
Tensile Tests 9Fracture Tests 9Fatigue Crack Growth Tests 10Metallography And Hardness Testing 10Microstructural Examination 10
TASK 5 ndash RESIDUAL STRESS MEASUREMENTS 12
TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND THERMAL EMISSION METHODS 13
TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS 16
Weld Modelling Technique 16
Material Properties 17Results of Welding Simulations 18 Analyses of Defects In The Simulated Welds 19
TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO MATRIX CASES 21
Edge Defects in the Welded Plate 21Equatorial Defects in the Welded Sphere 24Embedded Defects in the Welded Plate 25
TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE METHODS 28
General Methodology 28
iii
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38
Edge Cracks 29Embedded Cracks 36
TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Practical Issues 38Guidance Resulting From The Finite Element Calculations 39
TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING PROCEDURE METHOD 41
Route for assessing the significance of a flaw in a weld (as-welded PWHT or repaired weld) 41Route for assessing whether repairing a weld Is likely lo be beneficial 41Critical Crack Size Evaluation 41Crack Growth Evaluation 42
TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF PROJECT 44
REFERENCES
FIGURES
APPENDIX 1 ndash LITERATURE REVIEW
APPENDIX 2 ndash MICROSTRUCTURAL EXAMINATION OF WELD SAMPLES
UNDERTAKEN BY SHEFFIELD UNIVERSITY METALS ADVISORY CENTRE (SUMAC)
iv
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EXECUTIVE SUMMARY
This report summarises work that has been undertaken by Serco Assurance (formerly AEA
Technology Consulting) The University of Sheffield and M R Goldthorpe Associates on behalf of
the Health and Safety Executive It describes Phase 1 of a proposed multi-stage project aimed at (i) providing general guidance on when welded repairs may or may not be beneficial and (ii) proposing
a suitable engineering procedural method for assessing the integrity of repaired welds on a case-by-
case basis Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired and
repaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been performed and residual stress profiles
have been evaluated experimentally Metallurgical examination has also has also been carried out in
order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
The report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for Tasks 9
10 11 and 12
v
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1 INTRODUCTION
Repair welds are commonly carried out in industry on components where flaws or defects have been
found in weldments during in-service inspection However in some cases the process may actuallyhave a deleterious effect on the residual lifetime of a component This can be due to metallurgical
changes in the component material in the vicinity of the repair and because of very high residual
stresses which can be introduced in the repaired region
A Serco Assurance (formerly AEA Technology Consulting) led consortium involving (in addition to
Serco Assurance) The University of Sheffield and an independent consultant M R Goldthorpe
Associates has undertaken Phase 1 of a proposed multi-stage project aimed at (i) providing general
guidance on when welded repairs may or may not be beneficial and (ii) proposing a suitable
engineering procedural method for assessing the integrity of repaired welds on a case-by-case basis
Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired andrepaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been perfiormed and residual stress
profiles have been evaluated experimentally Metallurgical examination has also has also been
carried out in order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
1
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The various components (ie Tasks) of the project together with their dependencies are contained in
the flow diagram of Figure 1
Reports constituting Deliverables 1 to 4 have previously been issued that outline the work and
results of Tasks 1 to 8
This report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for
(i) asessment by engineering procedures (Task 9) (ii) provisional guidance on weld repairs (Task 10)
(iii) provisional guidance on weld procedures (Task 11) and (iv) recommendations for future phases
of the project
2
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2 TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND
PREVIOUS PROBLEMS AND ASSESSMENT OF INFORMATION
CONTAINED IN THE LITERATURE
A draft report of the literature review carried out under Task 1 has been previously issued An
updated version of this report is included as Appendix 1
The papers reviewed can be categorised as folllows
Numerical analysis These relate to the prediction of residual stresses in weldments
Case Studies These papers discuss the metallurgical examination of repair welds and the evaluation
of found defects
Weld Repair Procedures and Techniques These papers present weld repair techniques
Performance of Repair Welds An assessment of how various weld repairs have performed in service
The review has indicated that defects in welded structures can occur during the fabrication process
due to lsquoworkmanshiprsquo or in-service due to working conditions During fabrication PD5500 states that
lsquounacceptable imperfections shall be either repaired or deemed not to comply with this standardrsquo
Repair welds have to be carried out to an approved procedure and subjected to the same acceptance
criteria as the original weld Thus all welds have to satisfy the requirements of the design
specification before acceptance by the purchaser or inspecting authority
For defects found in-service there are no standard guidelines available for utilities to use to make adecision on the need to carry out a weld repair An industrial survey carried out by EPRI for utilities
in the United States has shown that utilities will rely on the original manufacturer or outside vendors
to assist on this decision However it is not clear that the assessment procedures used are consistent
or are indeed reliable In the UK the repair of welds appears to rely on in-house experience in the
absence of guidelines to follow However this review showed that re-cracking of repair welds still
occurs due to lack of understanding on why original defects have occurred and how they should be
repaired
Whilst the decision to repair a defect may be aided using an assessment procedure the practical
considerations identified in a paper by Jones could also usefully be considered These show that
repair welds should be considered on a case-by-case behaviour therefore a definitive set of lsquorulesrsquo cannot be given Instead the guidelines need to be produced which provide good practice in assessing
defects in welds and the requirements for carrying out a lsquosafersquo repair
A number of References were found illustrating the capabilities of performing a repair weld without
the need for PWHT This was introduced by the half-bead technique defined in ASME XI primarily
for the nuclear industry This has been superseded by other temperbead techniques which are all
aimed at improving the properties within the weld HAZ whilst saving time and costs by precluding
the time for post-weld heat treatment (PWHT) There is evidence that this method is employed by
other industries in the USA but it is unclear on the use of this practice in the UK
In the references associated with case studies and the performance of weld repairs only a few of them
are related to residual stresses These papers have indicated that the magnitude of residual stresses in
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repair welds can be of yield magnitude The most recent advances in welding simulation were
presented at an e IMechE conference in November 1999 The conference demonstrated the
developments that had been made mainly in the use of finite element analysis to predict residual
stresses Sufficient confidence in numerical analysis needs to be demonstrated by making comparison
with measurement methods
When developing guidelines for the assessment of defects in repair welds sufficient advice needs to
be given to the user as to when residual stresses need to be considered in the assessment Advice also
needs to be provided on when the user should use simple approximations of the residual stress pattern
eg upper bound profiles given in BS7910 or to use finite element analysis techniques to predict the
complex behaviour of the material during welding
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3 TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF
CASES TO CONSIDER
A detailed section on this Task is included in the Deliverable D2 report previously issued (Reference
1)
That section outlines the matrix of analysis cases planned to be undertaken in Task 8 These cases
were developed to illustrate the effect on fatigue life or load margin of either leaving a weld defect
in place or repairing it in-situ Only in-service repairs would be considered Since such comparisons
were only possible by considering the behaviour of defects it was assumed that a defect inadvertently
remains in the weld after ldquorepairrdquo This may or may not grow by fatigue during subsequent service
The double V-preparation weld in plate (Figure 2) used in the experimental work of the project would
be studied in Task 8 It is a relatively simple weld geometry but this would enable a large range of
analysis cases to be considered and so illustrate to non-experts the effects that different parameters
could have on the decision to repair a defective weld
The repair procedure carried out on the test plate in Task 3 is shown in Figure 3 This procedure was
considered to be representative of an in-situ weld repair The repair depth is 15 mm in order to
simulate the grinding out of the weld 2 mm beyond an assumed defect with a depth of 13 mm There
was lower heat input than a shop repair using no pre-heat and smaller electrodes Strong-back plates
were used to simulate the restraint on the surrounding structure and no PWHT was carried out
For Task 8 it was intended to carry out a variety of mainly two-dimensional plane stress finite
element analyses Comparisons would be made between simulations of un-repaired and repaired
situations for a range of different parameters that affect fatigue life or margin on load The intentionwas to illustrate the transition from cases where the defects are best left in place to cases where repair
is required Since comparisons would be made between the un-repaired and repaired situations
simplified two-dimensional plane stress analysis would be capable of illustrating the role of different
parameters in the repair decision
The base case would be a 40 mm thick plate with an alternative thickness of 20 mm
For simplicity defects would be considered to lie in a plane normal to the surface of the plate and
through the middle of the weld The repair evacuation would be symmetrical with respect to the
middle of the weld
The base case for the un-repaired condition would be a surface breaking defect in the weld root as
shown in Figure 4 The defect depth would be equal to one third of the plate thickness Alternative
cases would consider surface breaking weld root defects with different depths covering the range
from the minimum detectable by NDT (about 3 mm) to one half of the plate thickness
Embedded defects in the un-repaired condition (Figure 5) would also be considered The base case
would be an embedded defect having a total height equal to one third of the plate thickness and
symmetrically positioned about the weld throat Alternative cases would consider different defect
heights and position relative to the weld
Figures 6 and 7 show the case of lsquowidersquo and lsquonarrowrsquo excavations that would be studied These were
considered to bound the repair procedure specified in Figure 3
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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8
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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HSEHealth amp Safety
Executive
Integrity of Repaired Welds (Phase 1)- Deliverable 5 Summary Report
J K Sharples L Gardner
S K Bate R Charles
Serco Assurance
Birchwood Park
Warrington
Cheshire
WA3 6AT
J R Yates
The University of SheffieldSheffield
S1 3JD
M R Goldthorpe
M R Goldthorpe Associates
The Grange
2 Park Vale Road
MacclesfieldCheshire
SK11 8AR
This report summarises work that has been undertaken by Serco Assurance (formerly AEA Technology
Consulting) The University of Sheffield and M R Goldthorpe Associates on behalf of the Health and
Safety Executive It describes Phase 1 of a proposed multi-stage project aimed at
(i) providing general guidance on when welded repairs may or may not be beneficial and
(ii) proposing a suitable engineering procedural method for assessing the integrity of repaired welds on
a case-bycase basis Welds considered are appropriate to ferritic material
This report and the work it describes were funded by the Health and Safety Executive (HSE) Itscontents including any opinions andor conclusions expressed are those of the authors alone and do
not necessarily reflect HSE policy
HSE BOOKS
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copy Crown copyright 2004
First published 2004
ISBN 0 7176 2800 0
All rights reserved No part of this publication may be reproduced stored in a retrieval system or transmitted in any form or by any means (electronic mechanical photocopying recording or otherwise) without the prior written permission of the copyright owner Applications for reproduction should be made in writing to Licensing Division Her Majestys Stationery OfficeSt Clements House 2-16 Colegate Norwich NR3 1BQor by e-mail to hmsolicensingcabinet-officexgsigovuk
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CONTENTS
EXECUTIVE SUMMARY v
INTRODUCTION 1
TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND PREVIOUS
PROBLEMS AND ASSESSMENT OF INFORMATION CONTAINED IN THE
LITERATURE 3
TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF CASES TO CONSIDER 5
TASK 3 ndash WELDSPECIMEN MANUFACTURE 7
TASK 4 ndash MATERIAL CHARACTERISATION TESTS 9
Tensile Tests 9Fracture Tests 9Fatigue Crack Growth Tests 10Metallography And Hardness Testing 10Microstructural Examination 10
TASK 5 ndash RESIDUAL STRESS MEASUREMENTS 12
TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND THERMAL EMISSION METHODS 13
TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS 16
Weld Modelling Technique 16
Material Properties 17Results of Welding Simulations 18 Analyses of Defects In The Simulated Welds 19
TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO MATRIX CASES 21
Edge Defects in the Welded Plate 21Equatorial Defects in the Welded Sphere 24Embedded Defects in the Welded Plate 25
TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE METHODS 28
General Methodology 28
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38
Edge Cracks 29Embedded Cracks 36
TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Practical Issues 38Guidance Resulting From The Finite Element Calculations 39
TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING PROCEDURE METHOD 41
Route for assessing the significance of a flaw in a weld (as-welded PWHT or repaired weld) 41Route for assessing whether repairing a weld Is likely lo be beneficial 41Critical Crack Size Evaluation 41Crack Growth Evaluation 42
TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF PROJECT 44
REFERENCES
FIGURES
APPENDIX 1 ndash LITERATURE REVIEW
APPENDIX 2 ndash MICROSTRUCTURAL EXAMINATION OF WELD SAMPLES
UNDERTAKEN BY SHEFFIELD UNIVERSITY METALS ADVISORY CENTRE (SUMAC)
iv
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EXECUTIVE SUMMARY
This report summarises work that has been undertaken by Serco Assurance (formerly AEA
Technology Consulting) The University of Sheffield and M R Goldthorpe Associates on behalf of
the Health and Safety Executive It describes Phase 1 of a proposed multi-stage project aimed at (i) providing general guidance on when welded repairs may or may not be beneficial and (ii) proposing
a suitable engineering procedural method for assessing the integrity of repaired welds on a case-by-
case basis Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired and
repaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been performed and residual stress profiles
have been evaluated experimentally Metallurgical examination has also has also been carried out in
order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
The report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for Tasks 9
10 11 and 12
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1 INTRODUCTION
Repair welds are commonly carried out in industry on components where flaws or defects have been
found in weldments during in-service inspection However in some cases the process may actuallyhave a deleterious effect on the residual lifetime of a component This can be due to metallurgical
changes in the component material in the vicinity of the repair and because of very high residual
stresses which can be introduced in the repaired region
A Serco Assurance (formerly AEA Technology Consulting) led consortium involving (in addition to
Serco Assurance) The University of Sheffield and an independent consultant M R Goldthorpe
Associates has undertaken Phase 1 of a proposed multi-stage project aimed at (i) providing general
guidance on when welded repairs may or may not be beneficial and (ii) proposing a suitable
engineering procedural method for assessing the integrity of repaired welds on a case-by-case basis
Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired andrepaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been perfiormed and residual stress
profiles have been evaluated experimentally Metallurgical examination has also has also been
carried out in order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
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The various components (ie Tasks) of the project together with their dependencies are contained in
the flow diagram of Figure 1
Reports constituting Deliverables 1 to 4 have previously been issued that outline the work and
results of Tasks 1 to 8
This report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for
(i) asessment by engineering procedures (Task 9) (ii) provisional guidance on weld repairs (Task 10)
(iii) provisional guidance on weld procedures (Task 11) and (iv) recommendations for future phases
of the project
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2 TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND
PREVIOUS PROBLEMS AND ASSESSMENT OF INFORMATION
CONTAINED IN THE LITERATURE
A draft report of the literature review carried out under Task 1 has been previously issued An
updated version of this report is included as Appendix 1
The papers reviewed can be categorised as folllows
Numerical analysis These relate to the prediction of residual stresses in weldments
Case Studies These papers discuss the metallurgical examination of repair welds and the evaluation
of found defects
Weld Repair Procedures and Techniques These papers present weld repair techniques
Performance of Repair Welds An assessment of how various weld repairs have performed in service
The review has indicated that defects in welded structures can occur during the fabrication process
due to lsquoworkmanshiprsquo or in-service due to working conditions During fabrication PD5500 states that
lsquounacceptable imperfections shall be either repaired or deemed not to comply with this standardrsquo
Repair welds have to be carried out to an approved procedure and subjected to the same acceptance
criteria as the original weld Thus all welds have to satisfy the requirements of the design
specification before acceptance by the purchaser or inspecting authority
For defects found in-service there are no standard guidelines available for utilities to use to make adecision on the need to carry out a weld repair An industrial survey carried out by EPRI for utilities
in the United States has shown that utilities will rely on the original manufacturer or outside vendors
to assist on this decision However it is not clear that the assessment procedures used are consistent
or are indeed reliable In the UK the repair of welds appears to rely on in-house experience in the
absence of guidelines to follow However this review showed that re-cracking of repair welds still
occurs due to lack of understanding on why original defects have occurred and how they should be
repaired
Whilst the decision to repair a defect may be aided using an assessment procedure the practical
considerations identified in a paper by Jones could also usefully be considered These show that
repair welds should be considered on a case-by-case behaviour therefore a definitive set of lsquorulesrsquo cannot be given Instead the guidelines need to be produced which provide good practice in assessing
defects in welds and the requirements for carrying out a lsquosafersquo repair
A number of References were found illustrating the capabilities of performing a repair weld without
the need for PWHT This was introduced by the half-bead technique defined in ASME XI primarily
for the nuclear industry This has been superseded by other temperbead techniques which are all
aimed at improving the properties within the weld HAZ whilst saving time and costs by precluding
the time for post-weld heat treatment (PWHT) There is evidence that this method is employed by
other industries in the USA but it is unclear on the use of this practice in the UK
In the references associated with case studies and the performance of weld repairs only a few of them
are related to residual stresses These papers have indicated that the magnitude of residual stresses in
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repair welds can be of yield magnitude The most recent advances in welding simulation were
presented at an e IMechE conference in November 1999 The conference demonstrated the
developments that had been made mainly in the use of finite element analysis to predict residual
stresses Sufficient confidence in numerical analysis needs to be demonstrated by making comparison
with measurement methods
When developing guidelines for the assessment of defects in repair welds sufficient advice needs to
be given to the user as to when residual stresses need to be considered in the assessment Advice also
needs to be provided on when the user should use simple approximations of the residual stress pattern
eg upper bound profiles given in BS7910 or to use finite element analysis techniques to predict the
complex behaviour of the material during welding
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3 TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF
CASES TO CONSIDER
A detailed section on this Task is included in the Deliverable D2 report previously issued (Reference
1)
That section outlines the matrix of analysis cases planned to be undertaken in Task 8 These cases
were developed to illustrate the effect on fatigue life or load margin of either leaving a weld defect
in place or repairing it in-situ Only in-service repairs would be considered Since such comparisons
were only possible by considering the behaviour of defects it was assumed that a defect inadvertently
remains in the weld after ldquorepairrdquo This may or may not grow by fatigue during subsequent service
The double V-preparation weld in plate (Figure 2) used in the experimental work of the project would
be studied in Task 8 It is a relatively simple weld geometry but this would enable a large range of
analysis cases to be considered and so illustrate to non-experts the effects that different parameters
could have on the decision to repair a defective weld
The repair procedure carried out on the test plate in Task 3 is shown in Figure 3 This procedure was
considered to be representative of an in-situ weld repair The repair depth is 15 mm in order to
simulate the grinding out of the weld 2 mm beyond an assumed defect with a depth of 13 mm There
was lower heat input than a shop repair using no pre-heat and smaller electrodes Strong-back plates
were used to simulate the restraint on the surrounding structure and no PWHT was carried out
For Task 8 it was intended to carry out a variety of mainly two-dimensional plane stress finite
element analyses Comparisons would be made between simulations of un-repaired and repaired
situations for a range of different parameters that affect fatigue life or margin on load The intentionwas to illustrate the transition from cases where the defects are best left in place to cases where repair
is required Since comparisons would be made between the un-repaired and repaired situations
simplified two-dimensional plane stress analysis would be capable of illustrating the role of different
parameters in the repair decision
The base case would be a 40 mm thick plate with an alternative thickness of 20 mm
For simplicity defects would be considered to lie in a plane normal to the surface of the plate and
through the middle of the weld The repair evacuation would be symmetrical with respect to the
middle of the weld
The base case for the un-repaired condition would be a surface breaking defect in the weld root as
shown in Figure 4 The defect depth would be equal to one third of the plate thickness Alternative
cases would consider surface breaking weld root defects with different depths covering the range
from the minimum detectable by NDT (about 3 mm) to one half of the plate thickness
Embedded defects in the un-repaired condition (Figure 5) would also be considered The base case
would be an embedded defect having a total height equal to one third of the plate thickness and
symmetrically positioned about the weld throat Alternative cases would consider different defect
heights and position relative to the weld
Figures 6 and 7 show the case of lsquowidersquo and lsquonarrowrsquo excavations that would be studied These were
considered to bound the repair procedure specified in Figure 3
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
25
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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7272019 Integrity of Repair Weld
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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copy Crown copyright 2004
First published 2004
ISBN 0 7176 2800 0
All rights reserved No part of this publication may be reproduced stored in a retrieval system or transmitted in any form or by any means (electronic mechanical photocopying recording or otherwise) without the prior written permission of the copyright owner Applications for reproduction should be made in writing to Licensing Division Her Majestys Stationery OfficeSt Clements House 2-16 Colegate Norwich NR3 1BQor by e-mail to hmsolicensingcabinet-officexgsigovuk
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CONTENTS
EXECUTIVE SUMMARY v
INTRODUCTION 1
TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND PREVIOUS
PROBLEMS AND ASSESSMENT OF INFORMATION CONTAINED IN THE
LITERATURE 3
TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF CASES TO CONSIDER 5
TASK 3 ndash WELDSPECIMEN MANUFACTURE 7
TASK 4 ndash MATERIAL CHARACTERISATION TESTS 9
Tensile Tests 9Fracture Tests 9Fatigue Crack Growth Tests 10Metallography And Hardness Testing 10Microstructural Examination 10
TASK 5 ndash RESIDUAL STRESS MEASUREMENTS 12
TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND THERMAL EMISSION METHODS 13
TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS 16
Weld Modelling Technique 16
Material Properties 17Results of Welding Simulations 18 Analyses of Defects In The Simulated Welds 19
TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO MATRIX CASES 21
Edge Defects in the Welded Plate 21Equatorial Defects in the Welded Sphere 24Embedded Defects in the Welded Plate 25
TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE METHODS 28
General Methodology 28
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38
Edge Cracks 29Embedded Cracks 36
TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Practical Issues 38Guidance Resulting From The Finite Element Calculations 39
TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING PROCEDURE METHOD 41
Route for assessing the significance of a flaw in a weld (as-welded PWHT or repaired weld) 41Route for assessing whether repairing a weld Is likely lo be beneficial 41Critical Crack Size Evaluation 41Crack Growth Evaluation 42
TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF PROJECT 44
REFERENCES
FIGURES
APPENDIX 1 ndash LITERATURE REVIEW
APPENDIX 2 ndash MICROSTRUCTURAL EXAMINATION OF WELD SAMPLES
UNDERTAKEN BY SHEFFIELD UNIVERSITY METALS ADVISORY CENTRE (SUMAC)
iv
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EXECUTIVE SUMMARY
This report summarises work that has been undertaken by Serco Assurance (formerly AEA
Technology Consulting) The University of Sheffield and M R Goldthorpe Associates on behalf of
the Health and Safety Executive It describes Phase 1 of a proposed multi-stage project aimed at (i) providing general guidance on when welded repairs may or may not be beneficial and (ii) proposing
a suitable engineering procedural method for assessing the integrity of repaired welds on a case-by-
case basis Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired and
repaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been performed and residual stress profiles
have been evaluated experimentally Metallurgical examination has also has also been carried out in
order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
The report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for Tasks 9
10 11 and 12
v
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1 INTRODUCTION
Repair welds are commonly carried out in industry on components where flaws or defects have been
found in weldments during in-service inspection However in some cases the process may actuallyhave a deleterious effect on the residual lifetime of a component This can be due to metallurgical
changes in the component material in the vicinity of the repair and because of very high residual
stresses which can be introduced in the repaired region
A Serco Assurance (formerly AEA Technology Consulting) led consortium involving (in addition to
Serco Assurance) The University of Sheffield and an independent consultant M R Goldthorpe
Associates has undertaken Phase 1 of a proposed multi-stage project aimed at (i) providing general
guidance on when welded repairs may or may not be beneficial and (ii) proposing a suitable
engineering procedural method for assessing the integrity of repaired welds on a case-by-case basis
Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired andrepaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been perfiormed and residual stress
profiles have been evaluated experimentally Metallurgical examination has also has also been
carried out in order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
1
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The various components (ie Tasks) of the project together with their dependencies are contained in
the flow diagram of Figure 1
Reports constituting Deliverables 1 to 4 have previously been issued that outline the work and
results of Tasks 1 to 8
This report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for
(i) asessment by engineering procedures (Task 9) (ii) provisional guidance on weld repairs (Task 10)
(iii) provisional guidance on weld procedures (Task 11) and (iv) recommendations for future phases
of the project
2
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2 TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND
PREVIOUS PROBLEMS AND ASSESSMENT OF INFORMATION
CONTAINED IN THE LITERATURE
A draft report of the literature review carried out under Task 1 has been previously issued An
updated version of this report is included as Appendix 1
The papers reviewed can be categorised as folllows
Numerical analysis These relate to the prediction of residual stresses in weldments
Case Studies These papers discuss the metallurgical examination of repair welds and the evaluation
of found defects
Weld Repair Procedures and Techniques These papers present weld repair techniques
Performance of Repair Welds An assessment of how various weld repairs have performed in service
The review has indicated that defects in welded structures can occur during the fabrication process
due to lsquoworkmanshiprsquo or in-service due to working conditions During fabrication PD5500 states that
lsquounacceptable imperfections shall be either repaired or deemed not to comply with this standardrsquo
Repair welds have to be carried out to an approved procedure and subjected to the same acceptance
criteria as the original weld Thus all welds have to satisfy the requirements of the design
specification before acceptance by the purchaser or inspecting authority
For defects found in-service there are no standard guidelines available for utilities to use to make adecision on the need to carry out a weld repair An industrial survey carried out by EPRI for utilities
in the United States has shown that utilities will rely on the original manufacturer or outside vendors
to assist on this decision However it is not clear that the assessment procedures used are consistent
or are indeed reliable In the UK the repair of welds appears to rely on in-house experience in the
absence of guidelines to follow However this review showed that re-cracking of repair welds still
occurs due to lack of understanding on why original defects have occurred and how they should be
repaired
Whilst the decision to repair a defect may be aided using an assessment procedure the practical
considerations identified in a paper by Jones could also usefully be considered These show that
repair welds should be considered on a case-by-case behaviour therefore a definitive set of lsquorulesrsquo cannot be given Instead the guidelines need to be produced which provide good practice in assessing
defects in welds and the requirements for carrying out a lsquosafersquo repair
A number of References were found illustrating the capabilities of performing a repair weld without
the need for PWHT This was introduced by the half-bead technique defined in ASME XI primarily
for the nuclear industry This has been superseded by other temperbead techniques which are all
aimed at improving the properties within the weld HAZ whilst saving time and costs by precluding
the time for post-weld heat treatment (PWHT) There is evidence that this method is employed by
other industries in the USA but it is unclear on the use of this practice in the UK
In the references associated with case studies and the performance of weld repairs only a few of them
are related to residual stresses These papers have indicated that the magnitude of residual stresses in
3
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repair welds can be of yield magnitude The most recent advances in welding simulation were
presented at an e IMechE conference in November 1999 The conference demonstrated the
developments that had been made mainly in the use of finite element analysis to predict residual
stresses Sufficient confidence in numerical analysis needs to be demonstrated by making comparison
with measurement methods
When developing guidelines for the assessment of defects in repair welds sufficient advice needs to
be given to the user as to when residual stresses need to be considered in the assessment Advice also
needs to be provided on when the user should use simple approximations of the residual stress pattern
eg upper bound profiles given in BS7910 or to use finite element analysis techniques to predict the
complex behaviour of the material during welding
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3 TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF
CASES TO CONSIDER
A detailed section on this Task is included in the Deliverable D2 report previously issued (Reference
1)
That section outlines the matrix of analysis cases planned to be undertaken in Task 8 These cases
were developed to illustrate the effect on fatigue life or load margin of either leaving a weld defect
in place or repairing it in-situ Only in-service repairs would be considered Since such comparisons
were only possible by considering the behaviour of defects it was assumed that a defect inadvertently
remains in the weld after ldquorepairrdquo This may or may not grow by fatigue during subsequent service
The double V-preparation weld in plate (Figure 2) used in the experimental work of the project would
be studied in Task 8 It is a relatively simple weld geometry but this would enable a large range of
analysis cases to be considered and so illustrate to non-experts the effects that different parameters
could have on the decision to repair a defective weld
The repair procedure carried out on the test plate in Task 3 is shown in Figure 3 This procedure was
considered to be representative of an in-situ weld repair The repair depth is 15 mm in order to
simulate the grinding out of the weld 2 mm beyond an assumed defect with a depth of 13 mm There
was lower heat input than a shop repair using no pre-heat and smaller electrodes Strong-back plates
were used to simulate the restraint on the surrounding structure and no PWHT was carried out
For Task 8 it was intended to carry out a variety of mainly two-dimensional plane stress finite
element analyses Comparisons would be made between simulations of un-repaired and repaired
situations for a range of different parameters that affect fatigue life or margin on load The intentionwas to illustrate the transition from cases where the defects are best left in place to cases where repair
is required Since comparisons would be made between the un-repaired and repaired situations
simplified two-dimensional plane stress analysis would be capable of illustrating the role of different
parameters in the repair decision
The base case would be a 40 mm thick plate with an alternative thickness of 20 mm
For simplicity defects would be considered to lie in a plane normal to the surface of the plate and
through the middle of the weld The repair evacuation would be symmetrical with respect to the
middle of the weld
The base case for the un-repaired condition would be a surface breaking defect in the weld root as
shown in Figure 4 The defect depth would be equal to one third of the plate thickness Alternative
cases would consider surface breaking weld root defects with different depths covering the range
from the minimum detectable by NDT (about 3 mm) to one half of the plate thickness
Embedded defects in the un-repaired condition (Figure 5) would also be considered The base case
would be an embedded defect having a total height equal to one third of the plate thickness and
symmetrically positioned about the weld throat Alternative cases would consider different defect
heights and position relative to the weld
Figures 6 and 7 show the case of lsquowidersquo and lsquonarrowrsquo excavations that would be studied These were
considered to bound the repair procedure specified in Figure 3
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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CONTENTS
EXECUTIVE SUMMARY v
INTRODUCTION 1
TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND PREVIOUS
PROBLEMS AND ASSESSMENT OF INFORMATION CONTAINED IN THE
LITERATURE 3
TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF CASES TO CONSIDER 5
TASK 3 ndash WELDSPECIMEN MANUFACTURE 7
TASK 4 ndash MATERIAL CHARACTERISATION TESTS 9
Tensile Tests 9Fracture Tests 9Fatigue Crack Growth Tests 10Metallography And Hardness Testing 10Microstructural Examination 10
TASK 5 ndash RESIDUAL STRESS MEASUREMENTS 12
TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND THERMAL EMISSION METHODS 13
TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS 16
Weld Modelling Technique 16
Material Properties 17Results of Welding Simulations 18 Analyses of Defects In The Simulated Welds 19
TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO MATRIX CASES 21
Edge Defects in the Welded Plate 21Equatorial Defects in the Welded Sphere 24Embedded Defects in the Welded Plate 25
TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE METHODS 28
General Methodology 28
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38
Edge Cracks 29Embedded Cracks 36
TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Practical Issues 38Guidance Resulting From The Finite Element Calculations 39
TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING PROCEDURE METHOD 41
Route for assessing the significance of a flaw in a weld (as-welded PWHT or repaired weld) 41Route for assessing whether repairing a weld Is likely lo be beneficial 41Critical Crack Size Evaluation 41Crack Growth Evaluation 42
TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF PROJECT 44
REFERENCES
FIGURES
APPENDIX 1 ndash LITERATURE REVIEW
APPENDIX 2 ndash MICROSTRUCTURAL EXAMINATION OF WELD SAMPLES
UNDERTAKEN BY SHEFFIELD UNIVERSITY METALS ADVISORY CENTRE (SUMAC)
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EXECUTIVE SUMMARY
This report summarises work that has been undertaken by Serco Assurance (formerly AEA
Technology Consulting) The University of Sheffield and M R Goldthorpe Associates on behalf of
the Health and Safety Executive It describes Phase 1 of a proposed multi-stage project aimed at (i) providing general guidance on when welded repairs may or may not be beneficial and (ii) proposing
a suitable engineering procedural method for assessing the integrity of repaired welds on a case-by-
case basis Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired and
repaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been performed and residual stress profiles
have been evaluated experimentally Metallurgical examination has also has also been carried out in
order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
The report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for Tasks 9
10 11 and 12
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1 INTRODUCTION
Repair welds are commonly carried out in industry on components where flaws or defects have been
found in weldments during in-service inspection However in some cases the process may actuallyhave a deleterious effect on the residual lifetime of a component This can be due to metallurgical
changes in the component material in the vicinity of the repair and because of very high residual
stresses which can be introduced in the repaired region
A Serco Assurance (formerly AEA Technology Consulting) led consortium involving (in addition to
Serco Assurance) The University of Sheffield and an independent consultant M R Goldthorpe
Associates has undertaken Phase 1 of a proposed multi-stage project aimed at (i) providing general
guidance on when welded repairs may or may not be beneficial and (ii) proposing a suitable
engineering procedural method for assessing the integrity of repaired welds on a case-by-case basis
Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired andrepaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been perfiormed and residual stress
profiles have been evaluated experimentally Metallurgical examination has also has also been
carried out in order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
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The various components (ie Tasks) of the project together with their dependencies are contained in
the flow diagram of Figure 1
Reports constituting Deliverables 1 to 4 have previously been issued that outline the work and
results of Tasks 1 to 8
This report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for
(i) asessment by engineering procedures (Task 9) (ii) provisional guidance on weld repairs (Task 10)
(iii) provisional guidance on weld procedures (Task 11) and (iv) recommendations for future phases
of the project
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2 TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND
PREVIOUS PROBLEMS AND ASSESSMENT OF INFORMATION
CONTAINED IN THE LITERATURE
A draft report of the literature review carried out under Task 1 has been previously issued An
updated version of this report is included as Appendix 1
The papers reviewed can be categorised as folllows
Numerical analysis These relate to the prediction of residual stresses in weldments
Case Studies These papers discuss the metallurgical examination of repair welds and the evaluation
of found defects
Weld Repair Procedures and Techniques These papers present weld repair techniques
Performance of Repair Welds An assessment of how various weld repairs have performed in service
The review has indicated that defects in welded structures can occur during the fabrication process
due to lsquoworkmanshiprsquo or in-service due to working conditions During fabrication PD5500 states that
lsquounacceptable imperfections shall be either repaired or deemed not to comply with this standardrsquo
Repair welds have to be carried out to an approved procedure and subjected to the same acceptance
criteria as the original weld Thus all welds have to satisfy the requirements of the design
specification before acceptance by the purchaser or inspecting authority
For defects found in-service there are no standard guidelines available for utilities to use to make adecision on the need to carry out a weld repair An industrial survey carried out by EPRI for utilities
in the United States has shown that utilities will rely on the original manufacturer or outside vendors
to assist on this decision However it is not clear that the assessment procedures used are consistent
or are indeed reliable In the UK the repair of welds appears to rely on in-house experience in the
absence of guidelines to follow However this review showed that re-cracking of repair welds still
occurs due to lack of understanding on why original defects have occurred and how they should be
repaired
Whilst the decision to repair a defect may be aided using an assessment procedure the practical
considerations identified in a paper by Jones could also usefully be considered These show that
repair welds should be considered on a case-by-case behaviour therefore a definitive set of lsquorulesrsquo cannot be given Instead the guidelines need to be produced which provide good practice in assessing
defects in welds and the requirements for carrying out a lsquosafersquo repair
A number of References were found illustrating the capabilities of performing a repair weld without
the need for PWHT This was introduced by the half-bead technique defined in ASME XI primarily
for the nuclear industry This has been superseded by other temperbead techniques which are all
aimed at improving the properties within the weld HAZ whilst saving time and costs by precluding
the time for post-weld heat treatment (PWHT) There is evidence that this method is employed by
other industries in the USA but it is unclear on the use of this practice in the UK
In the references associated with case studies and the performance of weld repairs only a few of them
are related to residual stresses These papers have indicated that the magnitude of residual stresses in
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repair welds can be of yield magnitude The most recent advances in welding simulation were
presented at an e IMechE conference in November 1999 The conference demonstrated the
developments that had been made mainly in the use of finite element analysis to predict residual
stresses Sufficient confidence in numerical analysis needs to be demonstrated by making comparison
with measurement methods
When developing guidelines for the assessment of defects in repair welds sufficient advice needs to
be given to the user as to when residual stresses need to be considered in the assessment Advice also
needs to be provided on when the user should use simple approximations of the residual stress pattern
eg upper bound profiles given in BS7910 or to use finite element analysis techniques to predict the
complex behaviour of the material during welding
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3 TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF
CASES TO CONSIDER
A detailed section on this Task is included in the Deliverable D2 report previously issued (Reference
1)
That section outlines the matrix of analysis cases planned to be undertaken in Task 8 These cases
were developed to illustrate the effect on fatigue life or load margin of either leaving a weld defect
in place or repairing it in-situ Only in-service repairs would be considered Since such comparisons
were only possible by considering the behaviour of defects it was assumed that a defect inadvertently
remains in the weld after ldquorepairrdquo This may or may not grow by fatigue during subsequent service
The double V-preparation weld in plate (Figure 2) used in the experimental work of the project would
be studied in Task 8 It is a relatively simple weld geometry but this would enable a large range of
analysis cases to be considered and so illustrate to non-experts the effects that different parameters
could have on the decision to repair a defective weld
The repair procedure carried out on the test plate in Task 3 is shown in Figure 3 This procedure was
considered to be representative of an in-situ weld repair The repair depth is 15 mm in order to
simulate the grinding out of the weld 2 mm beyond an assumed defect with a depth of 13 mm There
was lower heat input than a shop repair using no pre-heat and smaller electrodes Strong-back plates
were used to simulate the restraint on the surrounding structure and no PWHT was carried out
For Task 8 it was intended to carry out a variety of mainly two-dimensional plane stress finite
element analyses Comparisons would be made between simulations of un-repaired and repaired
situations for a range of different parameters that affect fatigue life or margin on load The intentionwas to illustrate the transition from cases where the defects are best left in place to cases where repair
is required Since comparisons would be made between the un-repaired and repaired situations
simplified two-dimensional plane stress analysis would be capable of illustrating the role of different
parameters in the repair decision
The base case would be a 40 mm thick plate with an alternative thickness of 20 mm
For simplicity defects would be considered to lie in a plane normal to the surface of the plate and
through the middle of the weld The repair evacuation would be symmetrical with respect to the
middle of the weld
The base case for the un-repaired condition would be a surface breaking defect in the weld root as
shown in Figure 4 The defect depth would be equal to one third of the plate thickness Alternative
cases would consider surface breaking weld root defects with different depths covering the range
from the minimum detectable by NDT (about 3 mm) to one half of the plate thickness
Embedded defects in the un-repaired condition (Figure 5) would also be considered The base case
would be an embedded defect having a total height equal to one third of the plate thickness and
symmetrically positioned about the weld throat Alternative cases would consider different defect
heights and position relative to the weld
Figures 6 and 7 show the case of lsquowidersquo and lsquonarrowrsquo excavations that would be studied These were
considered to bound the repair procedure specified in Figure 3
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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38
Edge Cracks 29Embedded Cracks 36
TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Practical Issues 38Guidance Resulting From The Finite Element Calculations 39
TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING PROCEDURE METHOD 41
Route for assessing the significance of a flaw in a weld (as-welded PWHT or repaired weld) 41Route for assessing whether repairing a weld Is likely lo be beneficial 41Critical Crack Size Evaluation 41Crack Growth Evaluation 42
TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF PROJECT 44
REFERENCES
FIGURES
APPENDIX 1 ndash LITERATURE REVIEW
APPENDIX 2 ndash MICROSTRUCTURAL EXAMINATION OF WELD SAMPLES
UNDERTAKEN BY SHEFFIELD UNIVERSITY METALS ADVISORY CENTRE (SUMAC)
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EXECUTIVE SUMMARY
This report summarises work that has been undertaken by Serco Assurance (formerly AEA
Technology Consulting) The University of Sheffield and M R Goldthorpe Associates on behalf of
the Health and Safety Executive It describes Phase 1 of a proposed multi-stage project aimed at (i) providing general guidance on when welded repairs may or may not be beneficial and (ii) proposing
a suitable engineering procedural method for assessing the integrity of repaired welds on a case-by-
case basis Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired and
repaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been performed and residual stress profiles
have been evaluated experimentally Metallurgical examination has also has also been carried out in
order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
The report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for Tasks 9
10 11 and 12
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1 INTRODUCTION
Repair welds are commonly carried out in industry on components where flaws or defects have been
found in weldments during in-service inspection However in some cases the process may actuallyhave a deleterious effect on the residual lifetime of a component This can be due to metallurgical
changes in the component material in the vicinity of the repair and because of very high residual
stresses which can be introduced in the repaired region
A Serco Assurance (formerly AEA Technology Consulting) led consortium involving (in addition to
Serco Assurance) The University of Sheffield and an independent consultant M R Goldthorpe
Associates has undertaken Phase 1 of a proposed multi-stage project aimed at (i) providing general
guidance on when welded repairs may or may not be beneficial and (ii) proposing a suitable
engineering procedural method for assessing the integrity of repaired welds on a case-by-case basis
Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired andrepaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been perfiormed and residual stress
profiles have been evaluated experimentally Metallurgical examination has also has also been
carried out in order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
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The various components (ie Tasks) of the project together with their dependencies are contained in
the flow diagram of Figure 1
Reports constituting Deliverables 1 to 4 have previously been issued that outline the work and
results of Tasks 1 to 8
This report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for
(i) asessment by engineering procedures (Task 9) (ii) provisional guidance on weld repairs (Task 10)
(iii) provisional guidance on weld procedures (Task 11) and (iv) recommendations for future phases
of the project
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2 TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND
PREVIOUS PROBLEMS AND ASSESSMENT OF INFORMATION
CONTAINED IN THE LITERATURE
A draft report of the literature review carried out under Task 1 has been previously issued An
updated version of this report is included as Appendix 1
The papers reviewed can be categorised as folllows
Numerical analysis These relate to the prediction of residual stresses in weldments
Case Studies These papers discuss the metallurgical examination of repair welds and the evaluation
of found defects
Weld Repair Procedures and Techniques These papers present weld repair techniques
Performance of Repair Welds An assessment of how various weld repairs have performed in service
The review has indicated that defects in welded structures can occur during the fabrication process
due to lsquoworkmanshiprsquo or in-service due to working conditions During fabrication PD5500 states that
lsquounacceptable imperfections shall be either repaired or deemed not to comply with this standardrsquo
Repair welds have to be carried out to an approved procedure and subjected to the same acceptance
criteria as the original weld Thus all welds have to satisfy the requirements of the design
specification before acceptance by the purchaser or inspecting authority
For defects found in-service there are no standard guidelines available for utilities to use to make adecision on the need to carry out a weld repair An industrial survey carried out by EPRI for utilities
in the United States has shown that utilities will rely on the original manufacturer or outside vendors
to assist on this decision However it is not clear that the assessment procedures used are consistent
or are indeed reliable In the UK the repair of welds appears to rely on in-house experience in the
absence of guidelines to follow However this review showed that re-cracking of repair welds still
occurs due to lack of understanding on why original defects have occurred and how they should be
repaired
Whilst the decision to repair a defect may be aided using an assessment procedure the practical
considerations identified in a paper by Jones could also usefully be considered These show that
repair welds should be considered on a case-by-case behaviour therefore a definitive set of lsquorulesrsquo cannot be given Instead the guidelines need to be produced which provide good practice in assessing
defects in welds and the requirements for carrying out a lsquosafersquo repair
A number of References were found illustrating the capabilities of performing a repair weld without
the need for PWHT This was introduced by the half-bead technique defined in ASME XI primarily
for the nuclear industry This has been superseded by other temperbead techniques which are all
aimed at improving the properties within the weld HAZ whilst saving time and costs by precluding
the time for post-weld heat treatment (PWHT) There is evidence that this method is employed by
other industries in the USA but it is unclear on the use of this practice in the UK
In the references associated with case studies and the performance of weld repairs only a few of them
are related to residual stresses These papers have indicated that the magnitude of residual stresses in
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repair welds can be of yield magnitude The most recent advances in welding simulation were
presented at an e IMechE conference in November 1999 The conference demonstrated the
developments that had been made mainly in the use of finite element analysis to predict residual
stresses Sufficient confidence in numerical analysis needs to be demonstrated by making comparison
with measurement methods
When developing guidelines for the assessment of defects in repair welds sufficient advice needs to
be given to the user as to when residual stresses need to be considered in the assessment Advice also
needs to be provided on when the user should use simple approximations of the residual stress pattern
eg upper bound profiles given in BS7910 or to use finite element analysis techniques to predict the
complex behaviour of the material during welding
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3 TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF
CASES TO CONSIDER
A detailed section on this Task is included in the Deliverable D2 report previously issued (Reference
1)
That section outlines the matrix of analysis cases planned to be undertaken in Task 8 These cases
were developed to illustrate the effect on fatigue life or load margin of either leaving a weld defect
in place or repairing it in-situ Only in-service repairs would be considered Since such comparisons
were only possible by considering the behaviour of defects it was assumed that a defect inadvertently
remains in the weld after ldquorepairrdquo This may or may not grow by fatigue during subsequent service
The double V-preparation weld in plate (Figure 2) used in the experimental work of the project would
be studied in Task 8 It is a relatively simple weld geometry but this would enable a large range of
analysis cases to be considered and so illustrate to non-experts the effects that different parameters
could have on the decision to repair a defective weld
The repair procedure carried out on the test plate in Task 3 is shown in Figure 3 This procedure was
considered to be representative of an in-situ weld repair The repair depth is 15 mm in order to
simulate the grinding out of the weld 2 mm beyond an assumed defect with a depth of 13 mm There
was lower heat input than a shop repair using no pre-heat and smaller electrodes Strong-back plates
were used to simulate the restraint on the surrounding structure and no PWHT was carried out
For Task 8 it was intended to carry out a variety of mainly two-dimensional plane stress finite
element analyses Comparisons would be made between simulations of un-repaired and repaired
situations for a range of different parameters that affect fatigue life or margin on load The intentionwas to illustrate the transition from cases where the defects are best left in place to cases where repair
is required Since comparisons would be made between the un-repaired and repaired situations
simplified two-dimensional plane stress analysis would be capable of illustrating the role of different
parameters in the repair decision
The base case would be a 40 mm thick plate with an alternative thickness of 20 mm
For simplicity defects would be considered to lie in a plane normal to the surface of the plate and
through the middle of the weld The repair evacuation would be symmetrical with respect to the
middle of the weld
The base case for the un-repaired condition would be a surface breaking defect in the weld root as
shown in Figure 4 The defect depth would be equal to one third of the plate thickness Alternative
cases would consider surface breaking weld root defects with different depths covering the range
from the minimum detectable by NDT (about 3 mm) to one half of the plate thickness
Embedded defects in the un-repaired condition (Figure 5) would also be considered The base case
would be an embedded defect having a total height equal to one third of the plate thickness and
symmetrically positioned about the weld throat Alternative cases would consider different defect
heights and position relative to the weld
Figures 6 and 7 show the case of lsquowidersquo and lsquonarrowrsquo excavations that would be studied These were
considered to bound the repair procedure specified in Figure 3
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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EXECUTIVE SUMMARY
This report summarises work that has been undertaken by Serco Assurance (formerly AEA
Technology Consulting) The University of Sheffield and M R Goldthorpe Associates on behalf of
the Health and Safety Executive It describes Phase 1 of a proposed multi-stage project aimed at (i) providing general guidance on when welded repairs may or may not be beneficial and (ii) proposing
a suitable engineering procedural method for assessing the integrity of repaired welds on a case-by-
case basis Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired and
repaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been performed and residual stress profiles
have been evaluated experimentally Metallurgical examination has also has also been carried out in
order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
The report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for Tasks 9
10 11 and 12
v
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1 INTRODUCTION
Repair welds are commonly carried out in industry on components where flaws or defects have been
found in weldments during in-service inspection However in some cases the process may actuallyhave a deleterious effect on the residual lifetime of a component This can be due to metallurgical
changes in the component material in the vicinity of the repair and because of very high residual
stresses which can be introduced in the repaired region
A Serco Assurance (formerly AEA Technology Consulting) led consortium involving (in addition to
Serco Assurance) The University of Sheffield and an independent consultant M R Goldthorpe
Associates has undertaken Phase 1 of a proposed multi-stage project aimed at (i) providing general
guidance on when welded repairs may or may not be beneficial and (ii) proposing a suitable
engineering procedural method for assessing the integrity of repaired welds on a case-by-case basis
Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired andrepaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been perfiormed and residual stress
profiles have been evaluated experimentally Metallurgical examination has also has also been
carried out in order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
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The various components (ie Tasks) of the project together with their dependencies are contained in
the flow diagram of Figure 1
Reports constituting Deliverables 1 to 4 have previously been issued that outline the work and
results of Tasks 1 to 8
This report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for
(i) asessment by engineering procedures (Task 9) (ii) provisional guidance on weld repairs (Task 10)
(iii) provisional guidance on weld procedures (Task 11) and (iv) recommendations for future phases
of the project
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2 TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND
PREVIOUS PROBLEMS AND ASSESSMENT OF INFORMATION
CONTAINED IN THE LITERATURE
A draft report of the literature review carried out under Task 1 has been previously issued An
updated version of this report is included as Appendix 1
The papers reviewed can be categorised as folllows
Numerical analysis These relate to the prediction of residual stresses in weldments
Case Studies These papers discuss the metallurgical examination of repair welds and the evaluation
of found defects
Weld Repair Procedures and Techniques These papers present weld repair techniques
Performance of Repair Welds An assessment of how various weld repairs have performed in service
The review has indicated that defects in welded structures can occur during the fabrication process
due to lsquoworkmanshiprsquo or in-service due to working conditions During fabrication PD5500 states that
lsquounacceptable imperfections shall be either repaired or deemed not to comply with this standardrsquo
Repair welds have to be carried out to an approved procedure and subjected to the same acceptance
criteria as the original weld Thus all welds have to satisfy the requirements of the design
specification before acceptance by the purchaser or inspecting authority
For defects found in-service there are no standard guidelines available for utilities to use to make adecision on the need to carry out a weld repair An industrial survey carried out by EPRI for utilities
in the United States has shown that utilities will rely on the original manufacturer or outside vendors
to assist on this decision However it is not clear that the assessment procedures used are consistent
or are indeed reliable In the UK the repair of welds appears to rely on in-house experience in the
absence of guidelines to follow However this review showed that re-cracking of repair welds still
occurs due to lack of understanding on why original defects have occurred and how they should be
repaired
Whilst the decision to repair a defect may be aided using an assessment procedure the practical
considerations identified in a paper by Jones could also usefully be considered These show that
repair welds should be considered on a case-by-case behaviour therefore a definitive set of lsquorulesrsquo cannot be given Instead the guidelines need to be produced which provide good practice in assessing
defects in welds and the requirements for carrying out a lsquosafersquo repair
A number of References were found illustrating the capabilities of performing a repair weld without
the need for PWHT This was introduced by the half-bead technique defined in ASME XI primarily
for the nuclear industry This has been superseded by other temperbead techniques which are all
aimed at improving the properties within the weld HAZ whilst saving time and costs by precluding
the time for post-weld heat treatment (PWHT) There is evidence that this method is employed by
other industries in the USA but it is unclear on the use of this practice in the UK
In the references associated with case studies and the performance of weld repairs only a few of them
are related to residual stresses These papers have indicated that the magnitude of residual stresses in
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repair welds can be of yield magnitude The most recent advances in welding simulation were
presented at an e IMechE conference in November 1999 The conference demonstrated the
developments that had been made mainly in the use of finite element analysis to predict residual
stresses Sufficient confidence in numerical analysis needs to be demonstrated by making comparison
with measurement methods
When developing guidelines for the assessment of defects in repair welds sufficient advice needs to
be given to the user as to when residual stresses need to be considered in the assessment Advice also
needs to be provided on when the user should use simple approximations of the residual stress pattern
eg upper bound profiles given in BS7910 or to use finite element analysis techniques to predict the
complex behaviour of the material during welding
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3 TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF
CASES TO CONSIDER
A detailed section on this Task is included in the Deliverable D2 report previously issued (Reference
1)
That section outlines the matrix of analysis cases planned to be undertaken in Task 8 These cases
were developed to illustrate the effect on fatigue life or load margin of either leaving a weld defect
in place or repairing it in-situ Only in-service repairs would be considered Since such comparisons
were only possible by considering the behaviour of defects it was assumed that a defect inadvertently
remains in the weld after ldquorepairrdquo This may or may not grow by fatigue during subsequent service
The double V-preparation weld in plate (Figure 2) used in the experimental work of the project would
be studied in Task 8 It is a relatively simple weld geometry but this would enable a large range of
analysis cases to be considered and so illustrate to non-experts the effects that different parameters
could have on the decision to repair a defective weld
The repair procedure carried out on the test plate in Task 3 is shown in Figure 3 This procedure was
considered to be representative of an in-situ weld repair The repair depth is 15 mm in order to
simulate the grinding out of the weld 2 mm beyond an assumed defect with a depth of 13 mm There
was lower heat input than a shop repair using no pre-heat and smaller electrodes Strong-back plates
were used to simulate the restraint on the surrounding structure and no PWHT was carried out
For Task 8 it was intended to carry out a variety of mainly two-dimensional plane stress finite
element analyses Comparisons would be made between simulations of un-repaired and repaired
situations for a range of different parameters that affect fatigue life or margin on load The intentionwas to illustrate the transition from cases where the defects are best left in place to cases where repair
is required Since comparisons would be made between the un-repaired and repaired situations
simplified two-dimensional plane stress analysis would be capable of illustrating the role of different
parameters in the repair decision
The base case would be a 40 mm thick plate with an alternative thickness of 20 mm
For simplicity defects would be considered to lie in a plane normal to the surface of the plate and
through the middle of the weld The repair evacuation would be symmetrical with respect to the
middle of the weld
The base case for the un-repaired condition would be a surface breaking defect in the weld root as
shown in Figure 4 The defect depth would be equal to one third of the plate thickness Alternative
cases would consider surface breaking weld root defects with different depths covering the range
from the minimum detectable by NDT (about 3 mm) to one half of the plate thickness
Embedded defects in the un-repaired condition (Figure 5) would also be considered The base case
would be an embedded defect having a total height equal to one third of the plate thickness and
symmetrically positioned about the weld throat Alternative cases would consider different defect
heights and position relative to the weld
Figures 6 and 7 show the case of lsquowidersquo and lsquonarrowrsquo excavations that would be studied These were
considered to bound the repair procedure specified in Figure 3
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
25
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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7272019 Integrity of Repair Weld
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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1 INTRODUCTION
Repair welds are commonly carried out in industry on components where flaws or defects have been
found in weldments during in-service inspection However in some cases the process may actuallyhave a deleterious effect on the residual lifetime of a component This can be due to metallurgical
changes in the component material in the vicinity of the repair and because of very high residual
stresses which can be introduced in the repaired region
A Serco Assurance (formerly AEA Technology Consulting) led consortium involving (in addition to
Serco Assurance) The University of Sheffield and an independent consultant M R Goldthorpe
Associates has undertaken Phase 1 of a proposed multi-stage project aimed at (i) providing general
guidance on when welded repairs may or may not be beneficial and (ii) proposing a suitable
engineering procedural method for assessing the integrity of repaired welds on a case-by-case basis
Welds considered are appropriate to ferritic material
The project has centred on detailed finite element modelling of a matrix of relevant un-repaired andrepaired weld configurations Development and validation of the finite element models have been
undertaken by way of mechanical testing involving photoelastic coating and thermal emission
methods A number of material characterisation tests have been perfiormed and residual stress
profiles have been evaluated experimentally Metallurgical examination has also has also been
carried out in order to examine the changes in microstructure resulting from the welding process
The project has involved the following tasks
Task 1 ndash Review of current industrial practices and previous problems and assessment of
information contained in the literature
Task 2 - Scoping calculations to establish a matrix of cases to consider
Task 3 ndash Weldspecimen manufacture
Task 4 ndash Material characterisation tests
Task 5 ndash Residual stress measurements
Task 6 ndash Tests involving photoelastic coating and thermal emission methods
Task 7 ndash Development of finite element models
Task 8 ndash Application of finite element models to matrix cases
Task 9 ndash Assessment by engineering procedure methods
Task 10 ndash Provisional guidance on weld repairs
Task 11 ndash Provisional guidance on engineering procedure method
Task 12 ndash Recommendations for future phases of project
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The various components (ie Tasks) of the project together with their dependencies are contained in
the flow diagram of Figure 1
Reports constituting Deliverables 1 to 4 have previously been issued that outline the work and
results of Tasks 1 to 8
This report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for
(i) asessment by engineering procedures (Task 9) (ii) provisional guidance on weld repairs (Task 10)
(iii) provisional guidance on weld procedures (Task 11) and (iv) recommendations for future phases
of the project
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2 TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND
PREVIOUS PROBLEMS AND ASSESSMENT OF INFORMATION
CONTAINED IN THE LITERATURE
A draft report of the literature review carried out under Task 1 has been previously issued An
updated version of this report is included as Appendix 1
The papers reviewed can be categorised as folllows
Numerical analysis These relate to the prediction of residual stresses in weldments
Case Studies These papers discuss the metallurgical examination of repair welds and the evaluation
of found defects
Weld Repair Procedures and Techniques These papers present weld repair techniques
Performance of Repair Welds An assessment of how various weld repairs have performed in service
The review has indicated that defects in welded structures can occur during the fabrication process
due to lsquoworkmanshiprsquo or in-service due to working conditions During fabrication PD5500 states that
lsquounacceptable imperfections shall be either repaired or deemed not to comply with this standardrsquo
Repair welds have to be carried out to an approved procedure and subjected to the same acceptance
criteria as the original weld Thus all welds have to satisfy the requirements of the design
specification before acceptance by the purchaser or inspecting authority
For defects found in-service there are no standard guidelines available for utilities to use to make adecision on the need to carry out a weld repair An industrial survey carried out by EPRI for utilities
in the United States has shown that utilities will rely on the original manufacturer or outside vendors
to assist on this decision However it is not clear that the assessment procedures used are consistent
or are indeed reliable In the UK the repair of welds appears to rely on in-house experience in the
absence of guidelines to follow However this review showed that re-cracking of repair welds still
occurs due to lack of understanding on why original defects have occurred and how they should be
repaired
Whilst the decision to repair a defect may be aided using an assessment procedure the practical
considerations identified in a paper by Jones could also usefully be considered These show that
repair welds should be considered on a case-by-case behaviour therefore a definitive set of lsquorulesrsquo cannot be given Instead the guidelines need to be produced which provide good practice in assessing
defects in welds and the requirements for carrying out a lsquosafersquo repair
A number of References were found illustrating the capabilities of performing a repair weld without
the need for PWHT This was introduced by the half-bead technique defined in ASME XI primarily
for the nuclear industry This has been superseded by other temperbead techniques which are all
aimed at improving the properties within the weld HAZ whilst saving time and costs by precluding
the time for post-weld heat treatment (PWHT) There is evidence that this method is employed by
other industries in the USA but it is unclear on the use of this practice in the UK
In the references associated with case studies and the performance of weld repairs only a few of them
are related to residual stresses These papers have indicated that the magnitude of residual stresses in
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repair welds can be of yield magnitude The most recent advances in welding simulation were
presented at an e IMechE conference in November 1999 The conference demonstrated the
developments that had been made mainly in the use of finite element analysis to predict residual
stresses Sufficient confidence in numerical analysis needs to be demonstrated by making comparison
with measurement methods
When developing guidelines for the assessment of defects in repair welds sufficient advice needs to
be given to the user as to when residual stresses need to be considered in the assessment Advice also
needs to be provided on when the user should use simple approximations of the residual stress pattern
eg upper bound profiles given in BS7910 or to use finite element analysis techniques to predict the
complex behaviour of the material during welding
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3 TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF
CASES TO CONSIDER
A detailed section on this Task is included in the Deliverable D2 report previously issued (Reference
1)
That section outlines the matrix of analysis cases planned to be undertaken in Task 8 These cases
were developed to illustrate the effect on fatigue life or load margin of either leaving a weld defect
in place or repairing it in-situ Only in-service repairs would be considered Since such comparisons
were only possible by considering the behaviour of defects it was assumed that a defect inadvertently
remains in the weld after ldquorepairrdquo This may or may not grow by fatigue during subsequent service
The double V-preparation weld in plate (Figure 2) used in the experimental work of the project would
be studied in Task 8 It is a relatively simple weld geometry but this would enable a large range of
analysis cases to be considered and so illustrate to non-experts the effects that different parameters
could have on the decision to repair a defective weld
The repair procedure carried out on the test plate in Task 3 is shown in Figure 3 This procedure was
considered to be representative of an in-situ weld repair The repair depth is 15 mm in order to
simulate the grinding out of the weld 2 mm beyond an assumed defect with a depth of 13 mm There
was lower heat input than a shop repair using no pre-heat and smaller electrodes Strong-back plates
were used to simulate the restraint on the surrounding structure and no PWHT was carried out
For Task 8 it was intended to carry out a variety of mainly two-dimensional plane stress finite
element analyses Comparisons would be made between simulations of un-repaired and repaired
situations for a range of different parameters that affect fatigue life or margin on load The intentionwas to illustrate the transition from cases where the defects are best left in place to cases where repair
is required Since comparisons would be made between the un-repaired and repaired situations
simplified two-dimensional plane stress analysis would be capable of illustrating the role of different
parameters in the repair decision
The base case would be a 40 mm thick plate with an alternative thickness of 20 mm
For simplicity defects would be considered to lie in a plane normal to the surface of the plate and
through the middle of the weld The repair evacuation would be symmetrical with respect to the
middle of the weld
The base case for the un-repaired condition would be a surface breaking defect in the weld root as
shown in Figure 4 The defect depth would be equal to one third of the plate thickness Alternative
cases would consider surface breaking weld root defects with different depths covering the range
from the minimum detectable by NDT (about 3 mm) to one half of the plate thickness
Embedded defects in the un-repaired condition (Figure 5) would also be considered The base case
would be an embedded defect having a total height equal to one third of the plate thickness and
symmetrically positioned about the weld throat Alternative cases would consider different defect
heights and position relative to the weld
Figures 6 and 7 show the case of lsquowidersquo and lsquonarrowrsquo excavations that would be studied These were
considered to bound the repair procedure specified in Figure 3
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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The various components (ie Tasks) of the project together with their dependencies are contained in
the flow diagram of Figure 1
Reports constituting Deliverables 1 to 4 have previously been issued that outline the work and
results of Tasks 1 to 8
This report constitutes the final deliverable (Deliverable 5) of this phase 1 project The main results of
Deliverables 1 to 4 are summarised and the outline of the work and results are presented for
(i) asessment by engineering procedures (Task 9) (ii) provisional guidance on weld repairs (Task 10)
(iii) provisional guidance on weld procedures (Task 11) and (iv) recommendations for future phases
of the project
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2 TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND
PREVIOUS PROBLEMS AND ASSESSMENT OF INFORMATION
CONTAINED IN THE LITERATURE
A draft report of the literature review carried out under Task 1 has been previously issued An
updated version of this report is included as Appendix 1
The papers reviewed can be categorised as folllows
Numerical analysis These relate to the prediction of residual stresses in weldments
Case Studies These papers discuss the metallurgical examination of repair welds and the evaluation
of found defects
Weld Repair Procedures and Techniques These papers present weld repair techniques
Performance of Repair Welds An assessment of how various weld repairs have performed in service
The review has indicated that defects in welded structures can occur during the fabrication process
due to lsquoworkmanshiprsquo or in-service due to working conditions During fabrication PD5500 states that
lsquounacceptable imperfections shall be either repaired or deemed not to comply with this standardrsquo
Repair welds have to be carried out to an approved procedure and subjected to the same acceptance
criteria as the original weld Thus all welds have to satisfy the requirements of the design
specification before acceptance by the purchaser or inspecting authority
For defects found in-service there are no standard guidelines available for utilities to use to make adecision on the need to carry out a weld repair An industrial survey carried out by EPRI for utilities
in the United States has shown that utilities will rely on the original manufacturer or outside vendors
to assist on this decision However it is not clear that the assessment procedures used are consistent
or are indeed reliable In the UK the repair of welds appears to rely on in-house experience in the
absence of guidelines to follow However this review showed that re-cracking of repair welds still
occurs due to lack of understanding on why original defects have occurred and how they should be
repaired
Whilst the decision to repair a defect may be aided using an assessment procedure the practical
considerations identified in a paper by Jones could also usefully be considered These show that
repair welds should be considered on a case-by-case behaviour therefore a definitive set of lsquorulesrsquo cannot be given Instead the guidelines need to be produced which provide good practice in assessing
defects in welds and the requirements for carrying out a lsquosafersquo repair
A number of References were found illustrating the capabilities of performing a repair weld without
the need for PWHT This was introduced by the half-bead technique defined in ASME XI primarily
for the nuclear industry This has been superseded by other temperbead techniques which are all
aimed at improving the properties within the weld HAZ whilst saving time and costs by precluding
the time for post-weld heat treatment (PWHT) There is evidence that this method is employed by
other industries in the USA but it is unclear on the use of this practice in the UK
In the references associated with case studies and the performance of weld repairs only a few of them
are related to residual stresses These papers have indicated that the magnitude of residual stresses in
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repair welds can be of yield magnitude The most recent advances in welding simulation were
presented at an e IMechE conference in November 1999 The conference demonstrated the
developments that had been made mainly in the use of finite element analysis to predict residual
stresses Sufficient confidence in numerical analysis needs to be demonstrated by making comparison
with measurement methods
When developing guidelines for the assessment of defects in repair welds sufficient advice needs to
be given to the user as to when residual stresses need to be considered in the assessment Advice also
needs to be provided on when the user should use simple approximations of the residual stress pattern
eg upper bound profiles given in BS7910 or to use finite element analysis techniques to predict the
complex behaviour of the material during welding
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3 TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF
CASES TO CONSIDER
A detailed section on this Task is included in the Deliverable D2 report previously issued (Reference
1)
That section outlines the matrix of analysis cases planned to be undertaken in Task 8 These cases
were developed to illustrate the effect on fatigue life or load margin of either leaving a weld defect
in place or repairing it in-situ Only in-service repairs would be considered Since such comparisons
were only possible by considering the behaviour of defects it was assumed that a defect inadvertently
remains in the weld after ldquorepairrdquo This may or may not grow by fatigue during subsequent service
The double V-preparation weld in plate (Figure 2) used in the experimental work of the project would
be studied in Task 8 It is a relatively simple weld geometry but this would enable a large range of
analysis cases to be considered and so illustrate to non-experts the effects that different parameters
could have on the decision to repair a defective weld
The repair procedure carried out on the test plate in Task 3 is shown in Figure 3 This procedure was
considered to be representative of an in-situ weld repair The repair depth is 15 mm in order to
simulate the grinding out of the weld 2 mm beyond an assumed defect with a depth of 13 mm There
was lower heat input than a shop repair using no pre-heat and smaller electrodes Strong-back plates
were used to simulate the restraint on the surrounding structure and no PWHT was carried out
For Task 8 it was intended to carry out a variety of mainly two-dimensional plane stress finite
element analyses Comparisons would be made between simulations of un-repaired and repaired
situations for a range of different parameters that affect fatigue life or margin on load The intentionwas to illustrate the transition from cases where the defects are best left in place to cases where repair
is required Since comparisons would be made between the un-repaired and repaired situations
simplified two-dimensional plane stress analysis would be capable of illustrating the role of different
parameters in the repair decision
The base case would be a 40 mm thick plate with an alternative thickness of 20 mm
For simplicity defects would be considered to lie in a plane normal to the surface of the plate and
through the middle of the weld The repair evacuation would be symmetrical with respect to the
middle of the weld
The base case for the un-repaired condition would be a surface breaking defect in the weld root as
shown in Figure 4 The defect depth would be equal to one third of the plate thickness Alternative
cases would consider surface breaking weld root defects with different depths covering the range
from the minimum detectable by NDT (about 3 mm) to one half of the plate thickness
Embedded defects in the un-repaired condition (Figure 5) would also be considered The base case
would be an embedded defect having a total height equal to one third of the plate thickness and
symmetrically positioned about the weld throat Alternative cases would consider different defect
heights and position relative to the weld
Figures 6 and 7 show the case of lsquowidersquo and lsquonarrowrsquo excavations that would be studied These were
considered to bound the repair procedure specified in Figure 3
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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2 TASK 1 ndash REVIEW OF CURRENT INDUSTRIAL PRACTICES AND
PREVIOUS PROBLEMS AND ASSESSMENT OF INFORMATION
CONTAINED IN THE LITERATURE
A draft report of the literature review carried out under Task 1 has been previously issued An
updated version of this report is included as Appendix 1
The papers reviewed can be categorised as folllows
Numerical analysis These relate to the prediction of residual stresses in weldments
Case Studies These papers discuss the metallurgical examination of repair welds and the evaluation
of found defects
Weld Repair Procedures and Techniques These papers present weld repair techniques
Performance of Repair Welds An assessment of how various weld repairs have performed in service
The review has indicated that defects in welded structures can occur during the fabrication process
due to lsquoworkmanshiprsquo or in-service due to working conditions During fabrication PD5500 states that
lsquounacceptable imperfections shall be either repaired or deemed not to comply with this standardrsquo
Repair welds have to be carried out to an approved procedure and subjected to the same acceptance
criteria as the original weld Thus all welds have to satisfy the requirements of the design
specification before acceptance by the purchaser or inspecting authority
For defects found in-service there are no standard guidelines available for utilities to use to make adecision on the need to carry out a weld repair An industrial survey carried out by EPRI for utilities
in the United States has shown that utilities will rely on the original manufacturer or outside vendors
to assist on this decision However it is not clear that the assessment procedures used are consistent
or are indeed reliable In the UK the repair of welds appears to rely on in-house experience in the
absence of guidelines to follow However this review showed that re-cracking of repair welds still
occurs due to lack of understanding on why original defects have occurred and how they should be
repaired
Whilst the decision to repair a defect may be aided using an assessment procedure the practical
considerations identified in a paper by Jones could also usefully be considered These show that
repair welds should be considered on a case-by-case behaviour therefore a definitive set of lsquorulesrsquo cannot be given Instead the guidelines need to be produced which provide good practice in assessing
defects in welds and the requirements for carrying out a lsquosafersquo repair
A number of References were found illustrating the capabilities of performing a repair weld without
the need for PWHT This was introduced by the half-bead technique defined in ASME XI primarily
for the nuclear industry This has been superseded by other temperbead techniques which are all
aimed at improving the properties within the weld HAZ whilst saving time and costs by precluding
the time for post-weld heat treatment (PWHT) There is evidence that this method is employed by
other industries in the USA but it is unclear on the use of this practice in the UK
In the references associated with case studies and the performance of weld repairs only a few of them
are related to residual stresses These papers have indicated that the magnitude of residual stresses in
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repair welds can be of yield magnitude The most recent advances in welding simulation were
presented at an e IMechE conference in November 1999 The conference demonstrated the
developments that had been made mainly in the use of finite element analysis to predict residual
stresses Sufficient confidence in numerical analysis needs to be demonstrated by making comparison
with measurement methods
When developing guidelines for the assessment of defects in repair welds sufficient advice needs to
be given to the user as to when residual stresses need to be considered in the assessment Advice also
needs to be provided on when the user should use simple approximations of the residual stress pattern
eg upper bound profiles given in BS7910 or to use finite element analysis techniques to predict the
complex behaviour of the material during welding
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3 TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF
CASES TO CONSIDER
A detailed section on this Task is included in the Deliverable D2 report previously issued (Reference
1)
That section outlines the matrix of analysis cases planned to be undertaken in Task 8 These cases
were developed to illustrate the effect on fatigue life or load margin of either leaving a weld defect
in place or repairing it in-situ Only in-service repairs would be considered Since such comparisons
were only possible by considering the behaviour of defects it was assumed that a defect inadvertently
remains in the weld after ldquorepairrdquo This may or may not grow by fatigue during subsequent service
The double V-preparation weld in plate (Figure 2) used in the experimental work of the project would
be studied in Task 8 It is a relatively simple weld geometry but this would enable a large range of
analysis cases to be considered and so illustrate to non-experts the effects that different parameters
could have on the decision to repair a defective weld
The repair procedure carried out on the test plate in Task 3 is shown in Figure 3 This procedure was
considered to be representative of an in-situ weld repair The repair depth is 15 mm in order to
simulate the grinding out of the weld 2 mm beyond an assumed defect with a depth of 13 mm There
was lower heat input than a shop repair using no pre-heat and smaller electrodes Strong-back plates
were used to simulate the restraint on the surrounding structure and no PWHT was carried out
For Task 8 it was intended to carry out a variety of mainly two-dimensional plane stress finite
element analyses Comparisons would be made between simulations of un-repaired and repaired
situations for a range of different parameters that affect fatigue life or margin on load The intentionwas to illustrate the transition from cases where the defects are best left in place to cases where repair
is required Since comparisons would be made between the un-repaired and repaired situations
simplified two-dimensional plane stress analysis would be capable of illustrating the role of different
parameters in the repair decision
The base case would be a 40 mm thick plate with an alternative thickness of 20 mm
For simplicity defects would be considered to lie in a plane normal to the surface of the plate and
through the middle of the weld The repair evacuation would be symmetrical with respect to the
middle of the weld
The base case for the un-repaired condition would be a surface breaking defect in the weld root as
shown in Figure 4 The defect depth would be equal to one third of the plate thickness Alternative
cases would consider surface breaking weld root defects with different depths covering the range
from the minimum detectable by NDT (about 3 mm) to one half of the plate thickness
Embedded defects in the un-repaired condition (Figure 5) would also be considered The base case
would be an embedded defect having a total height equal to one third of the plate thickness and
symmetrically positioned about the weld throat Alternative cases would consider different defect
heights and position relative to the weld
Figures 6 and 7 show the case of lsquowidersquo and lsquonarrowrsquo excavations that would be studied These were
considered to bound the repair procedure specified in Figure 3
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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repair welds can be of yield magnitude The most recent advances in welding simulation were
presented at an e IMechE conference in November 1999 The conference demonstrated the
developments that had been made mainly in the use of finite element analysis to predict residual
stresses Sufficient confidence in numerical analysis needs to be demonstrated by making comparison
with measurement methods
When developing guidelines for the assessment of defects in repair welds sufficient advice needs to
be given to the user as to when residual stresses need to be considered in the assessment Advice also
needs to be provided on when the user should use simple approximations of the residual stress pattern
eg upper bound profiles given in BS7910 or to use finite element analysis techniques to predict the
complex behaviour of the material during welding
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3 TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF
CASES TO CONSIDER
A detailed section on this Task is included in the Deliverable D2 report previously issued (Reference
1)
That section outlines the matrix of analysis cases planned to be undertaken in Task 8 These cases
were developed to illustrate the effect on fatigue life or load margin of either leaving a weld defect
in place or repairing it in-situ Only in-service repairs would be considered Since such comparisons
were only possible by considering the behaviour of defects it was assumed that a defect inadvertently
remains in the weld after ldquorepairrdquo This may or may not grow by fatigue during subsequent service
The double V-preparation weld in plate (Figure 2) used in the experimental work of the project would
be studied in Task 8 It is a relatively simple weld geometry but this would enable a large range of
analysis cases to be considered and so illustrate to non-experts the effects that different parameters
could have on the decision to repair a defective weld
The repair procedure carried out on the test plate in Task 3 is shown in Figure 3 This procedure was
considered to be representative of an in-situ weld repair The repair depth is 15 mm in order to
simulate the grinding out of the weld 2 mm beyond an assumed defect with a depth of 13 mm There
was lower heat input than a shop repair using no pre-heat and smaller electrodes Strong-back plates
were used to simulate the restraint on the surrounding structure and no PWHT was carried out
For Task 8 it was intended to carry out a variety of mainly two-dimensional plane stress finite
element analyses Comparisons would be made between simulations of un-repaired and repaired
situations for a range of different parameters that affect fatigue life or margin on load The intentionwas to illustrate the transition from cases where the defects are best left in place to cases where repair
is required Since comparisons would be made between the un-repaired and repaired situations
simplified two-dimensional plane stress analysis would be capable of illustrating the role of different
parameters in the repair decision
The base case would be a 40 mm thick plate with an alternative thickness of 20 mm
For simplicity defects would be considered to lie in a plane normal to the surface of the plate and
through the middle of the weld The repair evacuation would be symmetrical with respect to the
middle of the weld
The base case for the un-repaired condition would be a surface breaking defect in the weld root as
shown in Figure 4 The defect depth would be equal to one third of the plate thickness Alternative
cases would consider surface breaking weld root defects with different depths covering the range
from the minimum detectable by NDT (about 3 mm) to one half of the plate thickness
Embedded defects in the un-repaired condition (Figure 5) would also be considered The base case
would be an embedded defect having a total height equal to one third of the plate thickness and
symmetrically positioned about the weld throat Alternative cases would consider different defect
heights and position relative to the weld
Figures 6 and 7 show the case of lsquowidersquo and lsquonarrowrsquo excavations that would be studied These were
considered to bound the repair procedure specified in Figure 3
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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3 TASK 2 ndash SCOPING CALCULATIONS TO ESTABLISH MATRIX OF
CASES TO CONSIDER
A detailed section on this Task is included in the Deliverable D2 report previously issued (Reference
1)
That section outlines the matrix of analysis cases planned to be undertaken in Task 8 These cases
were developed to illustrate the effect on fatigue life or load margin of either leaving a weld defect
in place or repairing it in-situ Only in-service repairs would be considered Since such comparisons
were only possible by considering the behaviour of defects it was assumed that a defect inadvertently
remains in the weld after ldquorepairrdquo This may or may not grow by fatigue during subsequent service
The double V-preparation weld in plate (Figure 2) used in the experimental work of the project would
be studied in Task 8 It is a relatively simple weld geometry but this would enable a large range of
analysis cases to be considered and so illustrate to non-experts the effects that different parameters
could have on the decision to repair a defective weld
The repair procedure carried out on the test plate in Task 3 is shown in Figure 3 This procedure was
considered to be representative of an in-situ weld repair The repair depth is 15 mm in order to
simulate the grinding out of the weld 2 mm beyond an assumed defect with a depth of 13 mm There
was lower heat input than a shop repair using no pre-heat and smaller electrodes Strong-back plates
were used to simulate the restraint on the surrounding structure and no PWHT was carried out
For Task 8 it was intended to carry out a variety of mainly two-dimensional plane stress finite
element analyses Comparisons would be made between simulations of un-repaired and repaired
situations for a range of different parameters that affect fatigue life or margin on load The intentionwas to illustrate the transition from cases where the defects are best left in place to cases where repair
is required Since comparisons would be made between the un-repaired and repaired situations
simplified two-dimensional plane stress analysis would be capable of illustrating the role of different
parameters in the repair decision
The base case would be a 40 mm thick plate with an alternative thickness of 20 mm
For simplicity defects would be considered to lie in a plane normal to the surface of the plate and
through the middle of the weld The repair evacuation would be symmetrical with respect to the
middle of the weld
The base case for the un-repaired condition would be a surface breaking defect in the weld root as
shown in Figure 4 The defect depth would be equal to one third of the plate thickness Alternative
cases would consider surface breaking weld root defects with different depths covering the range
from the minimum detectable by NDT (about 3 mm) to one half of the plate thickness
Embedded defects in the un-repaired condition (Figure 5) would also be considered The base case
would be an embedded defect having a total height equal to one third of the plate thickness and
symmetrically positioned about the weld throat Alternative cases would consider different defect
heights and position relative to the weld
Figures 6 and 7 show the case of lsquowidersquo and lsquonarrowrsquo excavations that would be studied These were
considered to bound the repair procedure specified in Figure 3
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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Various defects remaining after the repair would be studied Generally these defects would be
smaller in height than those in the un-repaired condition The base case for repaired weld defects
would be an embedded one caused by incomplete excavation as indicated in Figures 6 or 7 Various
defect heights would be considered ranging from a minimum of 3 mm to a maximum smaller than the
un-repaired size
Alternative analysis cases for the repaired condition would consider different surface defects
remaining after improper repair of pre-existing surface defects (Figure 8) and embedded defects
resulting from improper repair of embedded defects (Figure 9) Although in practice the former are
likely to be weld toe cracks the analyses would consider cracks situated in the middle of the weld
Figures 10 to 12 show the different defect configurations it was intended to analyse for the 40 mm
thick plate and Figures 13 to 15 show the defects for the 20 mm thick plate Table 1 gives a summary
of the un-repaired and repaired defect sizes with a code for each case The finite element
computations would actually consider a large range of defect sizes in order that calculations of fatigue
crack growth could be undertaken
In addition to the geometrical parameters referred to above the planned matrix of cases contained
variations in tensile properties fracture toughness residual stresses and service stresses (service
stresses would be simulated in the plate geometry by applying a tensile stress transverse to the weld)
The variations in these parameters are included in Table 1
As will be seen in Section 9 the finite element analysis covered a good selection of the cases
described above that were proposed under Task 2
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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7272019 Integrity of Repair Weld
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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4 TASK 3 ndash WELDSPECIMEN MANUFACTURE
A detailed section on this Task is included in the Deliverable D2 report of Reference 1
Motherwell Bridge Group was contracted to prepare a suitable welded steel plate using materials and
weldingrepair processes typical of current industrial practice They used available steel plate of
thickness 40mm to BS1501 490 LT50 The weld procedure qualification record is shown in Figure 2
An asymmetric double ldquoVrdquo preparation was used with the weld root positioned 23 of the plate
thickness from the surface of side 1 which was filled first Typical pre-heat and interpass
temperatures were used of 75degC and 250degC respectively No PWHT was carried out Visual
inspection Magnetic Particle Inspection (MPI) and ultrasonic testing confirmed that there were no
detectable defects after welding
The test plate is shown in Figure 16 and comprised two 40 mm thick plates with length 4000 mm and
width 500 mm welded together at the long edges Half of the welded plate (ie a 2000 mm length)was cut into five sections as shown to provide as-welded material for the experimental work under
project Tasks 4 (material characterisation) 5 (residual stress measurements) and 6 (photoelastic and
thermal emission experiments) along with two blanks for manufacture of further test specimens in a
later phase of the project Motherwell Bridge Group retained the remaining half of the test plate for
repair weld processing described below
Strong back plates made from the same material as the test plate were used to restrain out of plane
bending during welding The strong-back plates formed 40 mm thick ribs 400 mm high running
across the full 1000 mm width of the test plate on the opposite side to that being welded Each
strong-back plate was attached to the test plate by fillet welds which extended for 300 mm from each
end A central 150 mm cut out was formed to accommodate pre-heaters in the case of the originalweld only Eight strong-back plates were used for the original welding of the 4000 mm long test
plate placed at 500mm intervals commencing 250 mm from the end The strong-back plates were
fixed to test plate side 2 whilst welding side 1 and vice versa
The weld repair process carried out on the second 2000 mm length of test plate (Figure 16) was
designed to simulate the site repair of a central root defect in the original weld This involved typical
grinding out from the narrower side of the weld (side 2) to a depth of 17 mm to ensure removal of a
defect in the original weld root at a depth of 135 mm The weld procedure qualification record for
the repair weld is shown in Figure 3
To simulate a repair process being applied to a structure on site rather than under ideal workshop
conditions some modifications were agreed to the weld procedure Welding under more difficultaccess conditions was simulated by use of smaller electrodes and more rapid passes with less ldquoweaverdquo
than was the case for the original weld This process (known as ldquostringer beadrdquo technique) resulted in
a lower heat input than for the original weld This was exacerbated by the omission of pre-heat for
the repair simulating a site situation where pre-heat could be difficult to apply effectively Lower
heat input results in more rapid cooling of the weld metal which can lead to changes in the material
properties No PWHT was carried out following the repair welding Visual inspection MPI and
ultrasonic testing confirmed that there were no detectable defects after repair
For the repair weld four strong-back plates of the type used for the original weld were attached to
simulate structural restraint These were set at 500 mm spacing on the 2000 mm long test plate fixed
to side 1 only as the repair was single sided
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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5 TASK 4 ndash MATERIAL CHARACTERISATION TESTS
A detailed section on this Task is included in the Deliverable D2 report of Reference 1 Initialmaterial characterisation tests covered in Reference 1 were those to determine tensile fracture and
fatigue crack growth properties The results of metallography and hardness testing are also presented
in Reference 1 Narrow bands of high hardness were measured in the heat affected zone (HAZ) of the
samples (see below) To provide an understanding of the formation of these it was decided to carry
out a more detailed microstructural examination of the welded regions in samples for both the as-
welded and weld repair specimens
Results of all the material characterisation tests are summarised as follows
51 TENSILE TESTS
Tensile properties of the weld material in both as-welded and repair-welded conditions at roomtemperature were obtained from tests on 35 mm diameter round bar specimens
The tensile test results are listed in Table 2 True stresstrue strain data are given in Reference 1
The results show that in the as-welded state the weld was overmatched by 46 based on the 02
proof stress (PS) values of approximately 512 MPa and 350 MPa for weld and parent plate
respectively The parent material exhibited typical upper and lower yield point behaviour which was
not present in the weld metal results The ultimate tensile stress (UTS) for the weld was 18 higher
than that for the parent material with average values of 622 MPa and 527 MPa respectively
For the repair weld material higher values of 02PS were obtained compared to the as-weldedcondition The near surface average value for repair weld was 540 MPa compared to 512MPa for the
as-welded condition (5 increase) whilst the near root average value for repair weld was 580MPa
(13 increase) The UTS value obtained from near surface repair weld was similar to that for the as-
welded condition (628 MPa against 622 MPa respectively) whilst the value for near root repair weld
was 670 MPa (approximately 13 increase on as-welded) It should be noted that a spurious result
was obtained from repair weld specimen WI12 due to failure outside the gauge length and this has
therefore been discounted
52 FRACTURE TESTS
Fracture toughness J resistance curves at room temperature were obtained from single edge notch
bend (SENB) side grooved unloading compliance specimens to BS 7448 Part 4 for the original weldand the repair weld Two specimens were tested in each condition The specimen notch was aligned
centrally in the through-thickness direction The specimen orientation was selected and the initial
crack length after fatigue pre-cracking adjusted within the standard limits to ensure that the crack tip
lay in original weld or repair weld as desired
The results are shown in the crack growth resistance curves of Figures 17 and 18 for as-welded and
repair-welded material respectively The results showed that the fracture toughness behaviour was
similar in both the as-welded and repair-welded specimens with initiation toughness J02 values of-2
approximately 105 kJm-2
and 102 kJm respectively (allowing for blunting J02BL of approximately-2116kJm-2 and 119kJm respectively)
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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53 FATIGUE CRACK GROWTH TESTS
Fatigue crack growth properties at room temperature were obtained for the original weld and the
repair weld using Compact Tension (CT) specimens in accordance with ASTM E647 The specimen
notch was aligned centrally in the weld in the through-thickness direction The specimen orientation
was selected and the initial crack length adjusted within the standard limits to ensure that crack
growth was obtained in original weld or repair weld as desired
The results of the fatigue crack growth tests on weld metal are shown in the Paris Law plots of Figure
19 The data indicate that similar fatigue crack growth behaviour was obtained with both the as-
welded and repair-welded material The slopes of the Paris Law plots are very similar with some
offset giving slightly higher growth rates with the as-welded material The valid region of stress
intensity factor range 983108K was from approximately 25 MPaOumlm to 60 MPaOumlm
54 METALLOGRAPHY AND HARDNESS TESTING
Sections from the weld in the as-welded and repaired states were polished and etched to reveal the
welds macro photographs taken and hardness testing carried out In addition to examination oftransverse sections the edges of the samples (ie the surface of the test plate) were also prepared by
polishing down to the level of the plate surface Surface hardness measurements were taken to
compare with the sub-surface values obtained from the transverse sections The Vickers Hardness
surveys (Hv 10kg load) of the parent materials welds and HAZs were carried out according to BS EN
288-3
The original welds had typical well-defined runs with HAZs in the order of 2-3mm wide The area
of weld repair had a less well-defined weld run structure due to the larger number of smaller beads
The Vickers Hardness survey according to BS EN 288-3 showed no significant hard spots in any of
the samples for the transverse sections The hardness values in the unaffected parent material were in
the region of approximately Hv140 to Hv180 The highest hardness values were recorded in the
HAZ as expected The HAZ on the repair weld was slightly harder than the original weld with
maximum recorded values of Hv331 and Hv268 respectively These levels are below the maximum
permitted hardness value of Hv350 stated in BS EN 288-3 for this class of material
The results for the surface measurements show a similar but less pronounced variation in hardness to
that recorded for the transverse sections The maximum HAZ hardness values recorded were Hv258
and Hv284 for the as-welded and repair-welded conditions respectively This gives some confidence
that increased hardness could be indicated by measurements on the accessible surface of a structure
but suggests that small isolated areas of peak hardness may not be detected since they may occur sub-
surface
55 MICROSTRUCTURAL EXAMINATION
The more detailed microstructural examination was carried out by the Sheffield University Metals
Advisory Centre (SUMAC) The details of this are given in Appendix 2 The SUMAC work
consisted of examinations on both as-welded and repair-welded samples in terms of microstructural
observations standard hardness tests microhardness surveys and microanalysis using dispersive x-
rays
It was shown that the HAZ microstructure followed the typical pattern of a multi-pass weld with a
zone of grain growth at the fusion line backed by a band of recrystallization followed by a
spheroidizedtempered zone before the unaffected matrix Each weld pass imposed a further HAZ on
the underlying weld (and itrsquos HAZ) leading to a refined microstructure at the overlap The grain
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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growth and recrystallization zones had a microstructure of grain boundary and Widmanstatten ferrite
(the amount depending on the local austentising temperature and subsequent cooling rate) in a
transformed matrix In carbon and low alloy steels of this type the matrix can be a mixture of the
phases ferrite pearlite bainite and martensite The root run area was completely refined and tempered
and contained no ldquohard spotsrdquo The macro and micro-hardness testing indicated that the HAZ of the
lsquotoersquo welds in weld 2 (the smallest weld on the side containing the repair weld) of both the as-welded
and repair-welded samples had higher hardness values than elsewhere The microstructure whilst not
exhibiting defined lsquopoolsrsquo of hard phase did show structural refinement and reductions in pro-
eutectoid ferrite that could explain the increased hardness
The study concluded that both the as-welded and repair-welded samples passed the hardness
requirement and some potentially high hardness values obtained by microhardness should not detract
from this particularly as they were in areas where this might be expected and were not found
elsewhere in the weld
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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6 TASK 5 ndash RESIDUAL STRESS MEASUREMENTS
The destructive technique of block removal splitting and layering was used to determine the throughthickness residual stress distribution in the as-welded and repair-welded specimens Further details of
the procedure and the measured results are contained in Reference 1
The residual stress results for the as-welded condition are shown in Figures 20 and 21 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The
stresses in the Y direction are self-balancing through the thickness with tensile values near the
surfaces and compressive values in the central area The stresses in the X direction are tensile
throughout the thickness The distributions are asymmetric as expected considering the asymmetric
weld preparation with minimum values occurring at a depth of approximately 25 mm from weld side
1 which corresponds to the location of the weld root Stress maximum values occur at depths of
approximately 5 mm and 35 mm The peak tensile stress in the Y-direction (perpendicular to the
weld) is ~220-350 MPa and in the X-direction (parallel to the weld) ~500-580 MPa
The residual stress results for the repair-welded condition are shown in Figures 22 and 23 for the
Y direction (perpendicular to the weld) and X direction (parallel to the weld) respectively The form
of the stress distributions is basically the same as for the as-welded condition (Figures 20 and 21)
The stress minimum values are of similar magnitude to the as-welded but occur closer to the centre of
the plate corresponding to the location of the repair weld root Also the stress maximum values at
depth of 5 mm show a noticeable increase over the as-welded for both the Y and X directions whilst
the maximum values at depth of 35mm remain at similar levels The increase in peak tensile residual
stress therefore occurs on the side remote from the weld repair rather than on the repaired side The
peak tensile values at depth of 35 mm are 600 MPa and 750 MPa for Y and X directions respectively
the latter being in excess of the weld metal yield stress measured in the tensile tests The reason forthis high peak is not clear but the two sets of strain measurements taken in the X direction gave very
similar results which suggests that it is not due to an experimental error or test equipment fault
As a further check on the residual stress levels at the surfaces measurements were made using the
shallow hole drilling technique This technique involves using a trepanning air-abrasive jet drilling
technique which has been shown to introduce practically no residual stresses into the component
under test The technique involves the drilling of a small blind hole (typically 18 mm diameter x 18
mm deep) in the centre of a special three-element strain gauge rosette Local strain relaxation is
related to the initial stress state in the specimen and calibration using a known (usually uniform) stress
field allows residual stresses to be calculated
The surface stresses evaluated from the shallow hole drilling technique are as follows
(13 weld side) (23 weld side)
As-Welded Perpendicular Stress (MPa) -94 365 368
As-Welded Parallel Stress (MPa) 225 138 181
Repair-Welded Perpendicular Stress (MPa) 34 280 386
Repair-Welded Parallel Stress (MPa) 181 -27 -162
These values have been included in the residual stress distribution plots of Figures 20 to 23 It can be
seen that the surface stresses obtained from the hole drilling method are generally consistent with the
near-surface stress distributions evaluated from the block removal splitting and layering technique
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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7 TASK 6 ndash TESTS INVOLVING PHOTOELASTIC COATING AND
THERMAL EMISSION METHODS
Detailed information on this Task is contained in Reference 2 The Task focused on (i) quantifyingthe fatigue crack propagation rate in welded and repair welded steel plate (ii) investigating the use of
a full field photoelasticity technique to measure residual stresses in the plates and (iii) investigating
the use of a thermoelasticity technique to measure the true crack tip driving force (ie stress intensity
factor) in the two types of weld
The specimens used for testing were obtained from the initial test plate as described in Section 4 The
specimens tested were identical for both original and repair welds The geometry used for the study of
fatigue crack growth was a tension specimen 415 mm wide (W ) and 12 mm thick (t ) with a 4 mm
initial edge notch (a) spark machined in the side of the original or repair weld as appropriate
(Figure 24)
Stress intensity factors were calculated using the following equation
K I 983108 Y 983108983155 983101 a983152 (1)
where2 3 4
Y 2310121 ccedil983270 983085983101 a
5510 ccedil983270 divide983083 ouml
adivide ouml 7221 ccedil983270 983085
adivide ouml
3930 ccedil983270 983083 a
divide ouml (2)egrave W 983288 egrave W 983288 egrave W 983288 egrave W 983288
Such values are referred to as lsquo983108K I Theoryrsquo so as to distinguish them from values determined by
thermoelastic measurement
The tests carried out consisted of analysing the crack growth for a tensile edge cracked specimen
using thermoelastic stress analysis The machine used for this purpose was an ESH 100kN servo-
hydraulic machine which allows the application of a cyclic load to the specimen at the frequency and
load convenient for the thermoelastic test
Seven fatigue tests were carried out for different load conditions as detailed below
Identifier Load range
kN
R ratio Comments
AEA1 324 013 Original weld
AEA2 40 01 Original weld 30kN range at R=01 applied for 800000cycles with no growth
AEA3 330 013 Repair weld
AEA4 396 01 Repair weld Subsequently used for J test
AEA_F2 369 028 Repair weld Test run to fracture of specimen
AEA_F3 376 058 Original weld
AEA_F1 376 058 Repair weld
Images at different number of cycles during the tests were taken At the same time for every picture
captured the number of cycles and the crack length were noted A vernier microscope was used to
measure the rate at which the crack length had grown between different images
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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A non-standard J test was carried out by loading in four-point bending one of the edge cracked tensile
specimen used for crack growth analysis The results obtained were found to be similar to those
previously obtained that are presented in Figure 17 In addition one of the fatigue tests was run until
failure The loads at fracture were Pmin = 164 kN Pmax = 516 kN the final crack length being
3493 mm including the initial 4 mm slit Failure occurred after 536770 cycles
The stress intensity factor ranges were plotted against the crack length for different R values and for
different specimens (original and repair welds) An example is shown in Figure 25 for the R = 013
case of the repaired weld specimen AEA3 ldquoRATrdquo and ldquoFGDrdquo referred to in Figure 25 are the initials
of the two different operators who processed the results In all cases experimental results were
compared to the range of stress intensity factor calculated by Equations 1 and 2 It was observed that
all experimental data lay below the theoretical values when the crack length is long enough This is
thought to be due primarily to the crack closure effect (see below) but other factors may also be
influential In particular the large displacement of the crack at high stress intensity factors may well
mean that the published stress intensity factor calibrations are erroneous at these levels
At the same time using information from the tests the crack growth rate against the stress intensity
factor was plotted for the different experiments Figure 26 is an example of such a plot whereby theParis law is presented using experimental values for the stress intensity factor (identified as
lsquoDeltatherm datarsquo in the Figure) and values predicted from Equations 1 and 2 and the crack growth
rates obtained from experimental measurement The ldquoAEAT growth equationrdquo curve included in
Figure 26 has been derived from the data presented in Figure 19
Finally an estimate of the closure level was made from the difference between the theoretical 983108K I and
the value measured using Deltatherm The values are shown in Figure 27 plotted against the crack
length
In considering crack closure effects it has previously been observed that non-linear crack opening
behaviour results in a region of residual tensile deformation in the ldquowakerdquo of a fatigue crack Theresulting permanent contact between the two crack faces results in a lowering of the crack opening
displacement and consequently lower driving force for fatigue crack advancement
A large amount of research has been carried out on this topic during the last few years and the
mechanisms involved have been described These mechanisms suggest that several types of closure
affect the rate of fatigue crack advance The possible sources of crack closure are the following
983085 Plasticity induced crack closure due to residual stress in the wake of the crack
983085 Oxide induced crack closure due to the oxide layers formed inside the fatigue crack
983085 Roughness induced crack closure due to the roughness of the fatigue fracture surface
983085 Viscous induced crack closure due to the penetration of viscous fluids inside of the crack
983085 Transformation induced crack closure due to phase deformations at the crack tip caused by stress
or strain
In addition the presence of non-uniform residual stresses in a structure will contribute to the crack tip
driving force in addition to primary loads These complex stresses may increase the stress intensity
factor above that estimated from the external loading or may decrease it thereby having a similar
effect on crack closure
Looking ahead to Figures 37 and 38 which present the finite element determined values of stress
intensity factor for the residual stress fields (refer to section 91) it is evident that the K I values are
positive for all crack sizes considered (crack depth a ranging from just over 2 mm to 20 mm) Crack
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
25
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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opening as opposed to crack closure would therefore be expected to occur from the residual stress
distribution
Some tests were undertaken using reflection photoelasticity with the intention of measuring residual
stress in welds Two different specimens were used from the original and the repair welds The
photoelastic results confirmed the previous measurements referred to in Section 6 whereby very little
difference was observed between the residual stresses in the as-welded and repaired weld conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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7272019 Integrity of Repair Weld
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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8 TASK 7 ndash DEVELOPMENT OF FINITE ELEMENT MODELS
Detailed finite element modelling of a matrix of relevant un-repaired and repaired weld configurations
has formed a major part of the project The work was mainly focussed on the modelling of a plategeometry but a spherical vessel geometry was also considered This work (covering Tasks 7 and 8) is
fully described in Reference 3 and summarised in the following sub-sections
81 WELD MODELLING TECHNIQUE
In terms of the development of the finite element models a weld bead lumping approach was used to
model weldments in which a small number of lumped beads was modelled in both original and repair
welds A non-linear analysis of the welding process was carried out using a simplified ABAQUS
finite element model of the parent plate and weld In this analysis the original weld was built up by
the addition of each lumped weld bead in an incremental manner
A thermal transient analysis was first conducted in order to establish the temperature history of each point in the plate or sphere due to the addition of each weld bead A subsequent elastic-plastic
analysis used an almost identical finite element model to simulate the addition of the weld beads
This mechanical model was loaded by imposing at each time increment the temperature of each node
from the above thermal transient analysis Like the thermal analysis the mechanical model was
necessarily simplified so the complex behaviour of the weld and parent metal near melting point was
not considered However approximate temperature dependent mechanical properties were used
Low values of yield stress and perfectly plastic properties were used at temperatures near the melting
point to reduce the loading on adjacent material However this did incur the penalty of producing
unrealistically large plastic strains that cannot be annealed
After adding the final lumped bead of the original weld the current state of the mechanical model(displacements stresses elastic and plastic strains etc) was saved for subsequent restarts Following
this the elements in the repaired areas were removed and the lumped beads of the repair were added
The required state of the model was again saved for subsequent restarts
Figure 28 shows a part of the finite element mesh used to model a though-thickness section of the
welded test plate in the region of the weld For convenience the mesh is shown rotated by 90o with
respect to Figures 2 and 3 The plate thickness was 40 mm measured in the horizontal direction in
Figure 28 The depth of the repair weld was 15 mm this being slightly smaller than the 17 mm
actually excavated in the real plate weld The original weld comprised nine lumped beads and the
repair weld had four The weld caps were not modelled The plate width was measured in the vertical
direction in Figure 28 Due to symmetry about the centre of the weld only one half of the 1000 mm
plate width was modelled
To make allowance for later generalisation the finite element mesh was actually three-dimensional
but only a single element thickness was used in the plate height direction perpendicular to the plane of
Figure 28 The strong back plates used during the actual welding were modelled as beam elements
with equivalent section modulus running vertically along the appropriate side of the mesh in Figure
28
A sphere was modelled with 40 mm thickness and 20 m diameter The weld was considered to be a
fully equatorial one with dimensions and bead lumping exactly as modelled in the plate weld The
repair lay on the outside of the sphere Figure 29 shows the axisymmetric finite element mesh used
Again due to symmetry about the centre of the weld only one half of the sphere was modelled No
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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this study values of toughness were considered that ranged from 160 MPaOumlm down to significantly
lower levels of about 30 MPaOumlm in the as-repaired condition As discussed later such low values of
fracture toughness can result in repair welds due to a variety of circumstances
The properties used for the weld simulation thermal analysis and the creep properties used in the
simulation of the intermediate post-weld heat treatment are described in Reference 3
83 RESULTS OF WELDING SIMULATIONS
Figures 32(a-b) compare the through-thickness stress distributions at the middle of the weld with the
measured results presented in Figures 20 to 23 It should be noted that in these and subsequent
similar Figures the through-thickness distance is always measured from the non-repaired side 1 The
experimental results are shown as solid lines and the predicted results are dashed lines The stresses
produced by the original weld are shown in blue those caused by the repair weld are in red Predicted
results are in general agreement with the measurements with tension near the plate surface and
compression at mid-thickness However the numerical simulation was unable to predict the precise
magnitudes and positions of stress peaks and troughs This is not surprising given the simplifications
and approximations involved It should also be noted that the predictions and measurements agree thata higher transverse stress occurs in the repaired weld but on the un-repaired side 1 Both
measurements and predictions show a similar magnitude of peak transverse stress on the repaired side
2
In Figures 33(a-b) comparisons are made for through-thickness distributions of transverse and
longitudinal stress across the middle of the weld between the four different numerical simulations
These cases are
(i) as originally welded (blue diamonds)
(ii) as originally welded followed by post-weld heat treatment (green diamonds)
(iii) as originally welded followed by partial weld removal and repair welding (red circles)
(iv) as originally welded followed by post-weld heat treatment partial weld removal and finally
repair welding (orange circles)
In case (ii) the effect of heat treating the original weld is apparent with a large reduction of both
components of stress compared with the as-welded case (i) In Figure 33(a) it is seen that the through-
thickness transverse stresses in the weld for the two repair cases (iii) and (iv) are similar The repair
of the PWHT weld thus re-establishes a pattern of stress as if the original PHWT had not been carried
out Furthermore close to the surface of the un-repaired side 1 the repair causes an increase in
transverse stress to a higher peak level than the un-heat treated original weld (compare the orangewith blue curves) Figure 33(b) shows that the longitudinal stress is affected by repair mainly on the
repaired side 2 itself
Figures 34(a-b) compare the predicted residual stress results for the four simulation cases carried out
on the sphere The general pattern of results is similar to that of the plate in Figures 33(a-b)
Figure 35(a) compares transverse stresses for cases (ii) and (iv) between the plate (open symbols) and
sphere (filled symbols) For case (ii) the original PWHT weld shown in green the peak transverse
tensile stresses predicted in the sphere are about half those in the plate on the last welded side 2 This
situation is reversed on the first welded side 1 The sphere therefore appears to have a component of
through-wall bending stress For case (iv) repaired stresses shown in orange the sphere has higher
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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values than the plate at the un-repaired side Figure 35(b) showing longitudinal stresses also
illustrates slightly lower predictions in the sphere than the plate in respect of the PWHT original weld
case (ii)
Comparisons of residual stresses for lsquodeeprsquo and lsquoshallowrsquo repairs in the sphere are shown in Figures
36(a-b) These graphs show results for the original PWHT weld the standard simulated repair of
depth 15 mm and also for the shallower repair with a depth of 66 mm On the repaired side of the
weld the shallow repair promotes peak values of transverse and longitudinal stress similar to the
deeper repair On the un-repaired side of the weld the shallow repair gives peak stresses lying
between the un-repaired PWHT cases and the deep repair case Thus shallow weld repairs can
promote high local residual stresses if the component is not heat treated
84 ANALYSES OF DEFECTS IN THE SIMULATED WELDS
Crack-like defects were inserted into the plate and sphere weld cases (ii) and (iv) of the previous
section Additional loads were applied to the models to give stresses on the defective section
typically experienced by engineering structures and crack driving forces (CDFs) were calculated
These parameters were then used to determine limiting or critical defect sizes for various values ofweld fracture toughness in the two welded states Comparisons were made between limiting defect
sizes for defects in these heat treated and as-repaired situations
Using the CDFs fatigue crack growth calculations were also carried out to determine the number of
loading cycles required to reach the limiting condition for a range of initial defect sizes Comparisons
were made between fatigue lives of defects in the heat treated and as-repaired states for a range of
initial defect sizes and fracture toughness
Some modelling simplifications were made in these analyses of defects in welds and these are
explained in Reference 3
Defects were inserted into the plate model on the plane through the middle of the weld The two
configurations considered in the welded plate are actually those shown in Figures 4 and 5 In Figure 4
a surface defect of depth a is shown in the weld In some cases the tip reaches into the original weld
(for the weld repair cases) In Figure 5 an embedded or internal defect is considered in the weld In
some of the weld repair cases this also reached into the original weld As for the surface defect this
defect was also considered as fully extended along the whole length of the weld The defect is
characterised by its depth 2a and the distance of its nearest tip from the repaired surface p
In the welded sphere surface defects were considered in the middle of the repair weld like Figure 4
Since the repair was considered to lie on the outside of the sphere (Figure 29) and the finite element
model was axisymmetric this corresponds to a fully extended outer surface defect of depth a along an
equatorial weld
Modelling of the defects was accomplished by removing the symmetry boundary conditions along the
line of the defect These restraints were replaced by equivalent forces that were reduced to zero in
several subsequent elastic-plastic increments of the analysis The created defect usually opened
under the influence of the residual stress field In some circumstances however the defect closed over
at least part of its depth due to a predominantly compressive residual stress In such cases the contact
of the opposing faces of the defect was not modelled so the defect was allowed to lsquoover-closersquo
Simultaneous introduction of the entire crack surface is mechanistically different to the modelling of
slow sub-critical crack growth where the crack is introduced progressively In the former a zone of
plastic deformation appears at the crack tip(s) only In the latter a wake of plastic deformation
develops on the crack flanks as (each) crack tip moves forward
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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7272019 Integrity of Repair Weld
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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In terms of the primary loading a remote uniformly distributed tensile load was applied to the top of
the modelled plate 500 mm away from the defect plane This represents loading in the weld
transverse direction normal to the plane of the defect causing it to open further or to open if closed in
the residual stress field acting alone Various magnitudes of remote membrane load were applied
with a maximum of 225 MPa This load was considered to be the occasional lsquooverloadrsquo condition for
which the possibility of ductile crack initiation or cleavage fracture was assessed A remote load of
180 MPa was considered to be the cyclic lsquooperatingrsquo load that causes fatigue crack growth This value
of nominal stress is about 50 of the 02 proof stress and 34 of the UTS of the parent plate and
so is typical of an engineering structure
An internal pressure was applied to the sphere This results in an equi-biaxial stress in the spherical
shell that acts to open the defect Various magnitudes of pressure were applied with a maximum of
18 MPa corresponding to a meridional stress of 225 MPa according to thin shell theory Again this
was considered as the overload condition The operating condition was a repeatedly applied pressure
of 144 MPa causing a nominal stress of 180 MPa in the shell
Crack driving force was evaluated in terms of stress intensity factor This parameter was evaluated
both elastically (designated K) and from an elastic-plastic analysis (designated K J) Because of thecomplexity of the finite element analyses the conventional J-contour integral option with ABAQUS
could not be accurately employed to evaluate K and K J The primary reason for this is that the
contour integral calculation of J requires that significant unloading of the material does not take place
This was not the case in the present finite element analyses that simulated welding heat treatment
material removal and repair welding An alternative calibration approach based on the crack opening
displacements at the node immediately behind the crack tip was therefore used as a proxy for J Full
details of this calibration procedure are contained in Reference 3 It may be noted that J was05
converted to K by the usual equation K = [(EJ)(1-983150 2 )] where E is Youngrsquos modulus (taken as 200
GPa and 983150 is Poissonrsquos ratio (taken as 03)
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
25
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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7272019 Integrity of Repair Weld
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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9 TASK 8 ndash APPLICATION OF FINITE ELEMENT MODELS TO
MATRIX CASES
This Task is associated with applying the finite element models and methodology referred to in
Section 8 above to a matrix of cases It should be noted that because of previously unforeseen
complexities of the analyses (eg the requirement to develop the calibration method used to evaluate
crack driving force) it was not possible to include all the cases that had originally been suggested
under Task 2 (Section 3) A good selection of the cases was included in the analyses however
91 EDGE DEFECTS IN THE WELDED PLATE
Figures 37(a-b) show results for elastic stress intensity factor K for various defect depths and levels of
primary load in the welded plate in the un-repaired heat treated and the as-repaired states
respectively The magnitude of primary load is indicated in the legends 0 MPa corresponds to
residual stress only The stress intensity factors for the defect in the repaired weld are obviously larger
than in the un-repaired PWHT case The two curves for residual stress only show a tendency to rise
with increasing defect depth and then gradually fall reaching a maximum K for about 11 mm defect
depth This is a consequence of the residual stress fields presented in Figure 33(a) whereby the
stresses are shown to start decreasing in magnitude after reaching tensile peak values at a distance of
about 10 mm from the appropriate side of the plate The other curves simply show that the additional
stress intensity factor is proportional to the primary load applied
Figures 38(a-b) show results for K J calculated from J obtained from elastic-plastic analyses The
curves for zero primary load are unchanged from Figures 37(a-b) With increasing crack depth and
load the value of K J becomes larger than the corresponding value of K in Figure 37 due to plasticity
effects The K J results in the as-repaired state are higher than in the PWHT state particularly forintermediate defect depths and loads For deeper defects and higher loads the residual thermal strains
arising from welding are reduced by the mechanical plastic strains and so the difference in CDFs
between the two welded states is reduced
Repeated loading and unloading between zero and 180 MPa was considered Fatigue crack growth
predictions are made using the Paris law Equation 3 but with the more representative parameter
983108 K J =K Jmax-K Jmin used in preference to 983108 K Here K Jmin is the crack driving force for the appropriate
residual stress acting alone and K Jmax is the total CDF for combined residual stress plus 180 MPa
applied stress Both these parameters are available in Figures 38(a-b) For each updated crack depth
the value of K J for an occasional 225 MPa applied stress was also available This K J was required to
assess when the critical crack size had been reached during the fatigue crack growth calculations (ie
fatigue crack growth was based on an applied stress range of 180 MPa and critical crack size was
based on an overload stress of 225 MPa)
Results of fatigue crack growth predictions are illustrated in Figures 39(a-b) These graphs show
crack depth a as a function of the number of loading cycles N between zero and 180 MPa for the
different initial defect depths indicated in the legends Defects in the as-repaired weld Figure 39(b)
need fewer cycles to grow to a given depth compared with the PWHT state Figure 39(a) since the
value of 983108 K J is generally lower for the PWHT state (Figure 38)
Ductile crack initiation or cleavage failure in the ductile-to-brittle transition region of ferritic steels
is considered to occur when K J is equal to a given fracture toughness K Jc No differentiation is drawn
between these types of failure and the term lsquolimiting conditionrsquo is used hereafter In Figures 40(a-b)
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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results are presented for fracture toughness K Jc versus the number of 0-180 MPa loading cycles N f
required to cause the limiting condition due to an occasional 225 MPa overload Curves are shown for
different initial defect depths A comparison of the two graphs shows that for a given fracture
toughness and initial defect fewer cycles are required to grow to the limiting condition in the as-
repaired weld
Figure 41 shows the relationship between critical defect depth ac at the limiting condition and
fracture toughness in the two weld states For a given toughness the critical defect depth is smaller in
the as-repaired weld The difference in critical defect depth between the two welds depends on
toughness For example for a weld toughness of 160 MPaOumlm the critical defect depth is about 175
mm in the PWHT weld and 167 mm in the as-repaired case This difference in depth is not
significant However for a lower fracture toughness of 100 MPaOumlm the respective critical defect
sizes are about 135 mm and 95 mm This difference is more significant
Figure 42 shows curves of the ratio of the number of loading cycles to the limiting condition for a
defect in the repair N f (repaired) to the number of cycles in the un-repaired PWHT state N f (un-
repaired) These curves assume the same initial defect depth in both weld states Each curve
represents a different fracture toughness that is also assumed to be the same in both welds So in thisgraph a comparison is made of the fatigue life of the same size defect and same fracture toughness in
the repaired and un-repaired welds Values less than unity imply a worse life for the repair Of course
in the majority of cases this is the case due to the higher repair residual stresses Some results are
greater than unity for initial defects between 8 mm and 14 mm deep for high toughness This occurs
because of high values of K J at zero load in the as-repaired state Figure 38(b) giving lower values of
983108 K J in the as-repaired weld compared with un-repaired and so reduced fatigue crack growth rates
The series of graphs in Figures 43(a-e) also illustrate the ratio of operating cycles required to reach
the limiting condition for repaired and un-repaired cases These take account of different initial defect
depths and fracture toughness in the two weld states The scenarios are either an edge defect is left in
the (un-repaired) weld or a repair is carried out that leaves the same size or shallower edge defectlocated in material with the same or reduced local fracture toughness The trade-off is thus explored
between introducing the same or shallower defect in the repair and higher levels of residual stress and
lower fracture toughness in that weld
Firstly Figure 43(a) shows comparisons between leaving un-repaired a 5 mm deep edge defect and
inadvertently introducing either 5 mm 42 mm or 33 mm deep defects in the as-repaired weld Curves
are shown of the ratio of operating cycles to reach the limiting condition in the repaired and un-
repaired weld versus the percentage reduction in repaired fracture toughness from the original PHWT
value Each curve represents a combination of repair defect depth and original toughness The highest
values of PWHT fracture toughness are represented by blue curves and the lowest by red For
example the blue squares show the effect of leaving in the repair the same size 5 mm deep defect for
an original PWHT fracture toughness of 160 MPaOumlm slightly greater than the initiation toughness of
the plate test welds The operating life of the repair is always lower than the un-repaired life (ratio of
cycles to the limiting condition is less than unity) Repair life gets comparatively worse as the
repaired toughness reduces So a 40 reduction of the repaired toughness compared with the
original PWHT value leads to a halving of the repaired life compared with the life if left un-repaired
The open blue diamonds show the effect of introducing into the repair a 42 mm defect compared with
leaving un-repaired the PWHT weld containing a 5 mm defect The repaired life slightly exceeds the
un-repaired life by only a small margin though if the repaired toughness drops more than 20 below
the original 160 MPaOumlm the life of the repair becomes less than the un-repaired life The blue
triangles show the comparison between having a 33 mm defect in the repair and leaving un-repaired
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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the 5 mm defect The repaired exceeds the un-repaired life until the repaired toughness drops below
about 43 of the PWHT level
There are more interesting consequences for lower PWHT fracture toughness Consider a toughness
of 100 MPaOumlm in the PWHT state the three sets of orange curves and symbols in Figure 43(a) A
defect in the repair having a depth of either 5 mm or 42 mm always has a shorter operating life thanthe 5 mm deep defect in the PWHT weld A 33 mm deep repair defect shown by orange triangles
gives a slightly longer life than the un-repaired 5 mm case for no reduction of toughness However a
mere 10 or so reduction of toughness due to the repair results in a shorter operating life For the
lowest 80 MPaOumlm PWHT toughness (red curves and symbols) all repaired defects from 33 mm to 5
mm depth imply an inferior fatigue life even if the repaired toughness does not change These results
therefore demonstrate that repairing a shallow surface defect by re-welding is likely to result in a
shorter operating life if it leaves a defect and reduces the fracture toughness This is particularly
apparent for materials with low original toughness Although the repair surface defects considered
here could be detected visually or by Magnetic Particle Inspection it is considered that a defect about
3 mm deep cannot be sized accurately by Ultrasonic Techniques
Figure 43(b) shows similar sets of predictions for a 67 mm deep original defect Here a defect ofdepth 67 mm 5 mm or 33 mm is considered left in the repair The trend of the predictions is similar
to the 5 mm case discussed above but a larger reduction of toughness is needed to obtain a shorter life
in the repaired situation For example the orange triangles show that for 100 MPaOumlm toughness in the
PWHT weld a 45 reduction due to repair is required to give a shorter life for a 33 mm deep repair
defect
Figures 43(c-e) however provide more support for repairing deeper surface defects Figure 43(c)
compares an un-repaired 92 mm defect with repaired defects of 67 mm 5 mm or 33 mm Note that
not all symbols in the legend are seen on the graph because some initial defecttoughness
combinations considered meet the limiting condition and so imply zero operating life (see Figure 41)
or the repair life exceeds twice the un-repaired The steeper angle of the curves suggests that for thesedeeper initial defects the effect of toughness reductions due to repair can be more severe For
example the red diamonds compare the un-repaired 92 mm defect with 5 mm in the repair for a low
PWHT toughness of 80 MPaOumlm If the toughness reduces by up to 10 the life of the repair is still
over twice the life if un-repaired However a toughness reduction of 30 due to repair causes the
repaired life to drop drastically to about one quarter of that if the weld was left un-repaired
Figure 43(d) shows a comparison of the 108 mm deep un-repaired defect with 92 mm 67 mm or 5
mm defects in the repair Since it is unlikely that a 92 mm defect is left in a repaired weld the
shallower depths are perhaps more feasible Considering 160 MPaOumlm PWHT toughness and a 5 mm
defect in the repair (blue triangles) then a 60 toughness reduction due to repair (down to about 64
MPaOumlm) is required to obtain a shorter fatigue life in the repair If the PWHT weld has a lower 80
MPaOumlm toughness (red triangles) then only a 30 reduction down to about 56 MPa Oumlm will give a
worse or even no repair life
Finally Figure 43(e) compares the un-repaired 133 mm deep defect with 92 mm 67 mm or 5 mm in
the repair Many of the ratios are zero or unreported because there is no un-repaired or repaired life
the initial defect is at or beyond the limiting condition Obviously this original 133 mm defect is
more likely to warrant repair than the shallow ones discussed above However onerous welding
conditions giving the likelihood of poor toughness and a remaining defect can result is a worse life
Leaving a mere 5 mm deep defect and reducing an original toughness of 100 MPa Oumlm (orange dotted
curve) by 45 will lead to little or no life of the repair It will reach the limiting condition on first
overload As seen in Figure 41 a 5 mm deep defect with a toughness of about 60 MPaOumlm is near the
limiting condition in the repair weld
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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92 EQUATORIAL DEFECTS IN THE WELDED SPHERE
The stress intensity factors for primary load alone are in good agreement with standard results for
extended edge defects in spheres Figures 44(a-b) give the results for the parameter K J from the
welded sphere simulations It is apparent that the crack driving forces are lower in this geometry than
previously seen for the plate Due to algebraically more compressive residual stress at the defective
side 2 of the PWHT sphere weld (Figure 35a) the crack driving forces are negative for the shallowest
and also for the deepest defects in the absence of primary load as seen in Figure 44(a)
Repeated loading and unloading between nominal biaxial stresses of zero and 180 MPa was again
considered with fatigue crack growth predictions made using Equation 3 and 983108 K J =K Jmax-K Jmin Only
the range over which K Jmin is positive contributes to fatigue since the crack is actually closed if K Jmin is
negative according to Figure 44(b) The value of K J was calculated for an assumed overloading to a
nominal stress of 225 MPa at each crack depth and associated number of cycles Fatigue crack growth
predictions are shown in Figures 45(a-b) As seen in the welded plate case earlier defects in the as-
repaired state need fewer cycles to grow to a given depth compared with the PWHT state
Figures 46(a-b) show results for fracture toughness versus the number of loading cycles required to
cause the limiting condition at the 225 MPa load As with the welded plate fewer cycles are required
in the as-repaired sphere weld to grow the defect to the limiting condition Note that the range of
toughness is shifted to lower values compared with the welded plate because of the lower crack
driving forces in the sphere
Figure 47 plots critical defect depth at the limiting condition as a function of fracture toughness in the
two weld states Again for a given toughness the critical defect depth is smaller in the as-repaired
weld However the difference between the two cases is more significant due to the generally lower
levels of toughness illustrated For example for a weld toughness of 100 MPaOumlm the critical defect
depth is about 19 mm in the PWHT weld and 105 mm in the as-repaired case The respective criticaldepths for the welded plate (Figure 41) are about 135 mm and 95 mm Thus the difference between
critical depths in the welded sphere is clearly more significant than for the plate The green curve in
Figure 47 suggests that for PWHT toughness close to 60 MPaOumlm there is a large change in critical
crack depth This is due to the flat or falling CDF in Figure 44(a) arising from compressive PWHT
residual stress at distances from side 2 greater than about 10 mm see Figure 35(a)
Figure 48 compares the fatigue life of the same initial size defect and fracture toughness in the
repaired and un-repaired welds Results are always less than unity implying a worse life for defects in
the repair
Figures 49(a-e) illustrate for edge defects in the welded sphere the trade-off between introducing the
same or shallower defect in the repair and higher residual stress and lower toughness there Thesegraphs are similar to Figures 43(a-e) for the welded plate discussed earlier with the exception that the
maximum toughness examined here is lower due to smaller crack driving forces in the sphere
Figure 49(a) contrasts leaving un-repaired a 5 mm deep defect with introducing either 5 mm 42 mm
or 33 mm deep defects in the as-repaired weld With few exceptions the operating life of the repair is
always lower than the un-repaired life for PWHT fracture toughness up to 110 MPaOumlm Repairing a
long 5 mm deep surface defect in this weld geometry by re-welding without heat treatment is not
beneficial if it is likely that a mere 3 mm or so deep surface defect can remain undetected after repair
The probability that the toughness will be reduced by a non-heat treated repair reinforces this
conclusion
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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Figure 49(b) shows comparisons between leaving un-repaired a 67 mm deep defect and introducing
67 mm 5 mm or 33 mm deep defects in the repair For the highest PWHT toughness of 110 MPaOumlm
and the smallest repair defect of 33 mm (blue triangles) the defective repair has a longer life unless
the repair causes a toughness reduction of about 35 to 72 MPaOumlm For the lowest PWHT toughness
examined of 70 MPaOumlm a mere 12 toughness reduction will give a lower life for a 33 mm deep
defect in the repair (red triangles)
Looking ahead to Figure 49(d) compares leaving un-repaired a 108 mm deep defect in the PWHT
weld with having 92 mm 67 mm or 5 mm defects in the as-repaired state For 110 MPaOumlm PWHT
toughness and leaving the 5 mm defect after repair (blue triangles) a lower life is achieved by the
repair should the toughness fall by more than 35 to about 72 MPa Oumlm For the lowest considered
PWHT toughness of 70 MPaOumlm only a 12 or so reduction in toughness will give a lower fatigue
life for the 5 mm repair defect (red triangles)
Finally Figure 49(e) compares a 133 mm un-repaired defect with 92 mm 67 mm and 5 mm defects
in the repair For 110 MPaOumlm PWHT toughness and a 5 mm defect in the repair (blue triangles) then
about 43 toughness reduction to 63 MPaOuml m is required to obtain a shorter life in the repair
93 EMBEDDED DEFECTS IN THE WELDED PLATE
This section explores the behaviour of embedded defects in both the un-repaired and repaired weld in
the plate Two initial types of defect configuration were considered In the first labelled lsquo p+2a=167
mmrsquo the upper defect tip closest to side 1 (see Figure 5) lies at a depth of 167 mm from the repaired
side 2 of the plate Various initial defect heights 2a were examined In the second configuration
lsquo p+2a=108 mmrsquo the upper defect tip is 108 mm from side 2 Again various initial defect heights
were studied In all cases examined here only the lower tip of the defect closest to repaired side 2
was considered This necessary simplification meant that fatigue crack growth was not considered at
the upper tip closest to side 1 This is not as approximate as it might at first appear particularly for
p+2a=167 mm since the upper tip lies far from side 1 and generally experiences lower crack drivingforces (and ranges) than the lower tip of the defect Given the power law dependence of the Paris law
Equation 3 this leads to much lower rates of fatigue crack growth than experienced by the lower tip
Figures 50(a-b) gives some K J crack driving force results for increasing height of an embedded defect
in the un-repaired and repaired weld These relate to the case p+2a=167 mm A comparison of
Figures 50(a-b) and Figures 38(a-b) shows that for the same defect heightdepth the CDFs for the
embedded cases are comparable to the edge cases particularly for higherdeeper defects At first
sight this appears to be inconsistent with what is generally understood that edge cracks have higher
CDFs than embedded cracks of the same depth However the embedded defect tip is developing
towards the repaired surface and so experiencing an increasing tensile nominal stress field By
contrast the edge defect results relate to the (only) tip of the defect in the lsquodeeprsquo position which
develops towards a more compressive stress field at plate mid-thickness Should the 2a=14 mm high
embedded defect break through the 27 mm remaining ligament to the repaired surface it is re-
characterised as a 167 mm edge defect In both PWHT and as-repaired welds the CDF will increase
at the 220 MPa maximum applied load plotted compare Figures 38(a-b) for a=167 mm with Figures
50(a-b) for 2a=14 mm
Figures 51(a-b) plot fracture toughness versus number of loading cycles to the limiting condition for
the case p+2a=167 mm As expected for the same toughness fewer cycles are achieved in the as-
repaired weld Figures 52 and 53 compare critical crack depths for un-repaired PWHT and as-repaired
welds for the two embedded cases p+2a=167 mm and p+2a=108 mm respectively A lower range
of toughness is displayed in these cases compared with the edge defects (Figure 41) consistent with
the generally smaller crack driving forces obtained The rapid change of critical defect height with
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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7272019 Integrity of Repair Weld
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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toughness in Figure 53 compared with Figure 52 is due to the defect tip in question being closer to
and so more sensitive to the tensile part of the residual stress field near the plate surface
Figure 54 plots the ratio of cycles to limiting condition in the as-repaired weld to cycles in the un-
repaired condition as a function of toughness and initial defect height for the case p+2a=167 mm
This shows that for the same initial defect size and toughness in both welds a shorter life is generally
obtained in the repair A longer repair life is however seen for the very short initial defects examined
This behaviour is due to the defect tip of interest lying in the compressive part of the repair residual
stress field resulting in low rates of fatigue crack growth compared to the un-repaired case Results
for the case p+2a=108 mm are seen in Figure 55 There is a more restricted range of toughness to
show here due to the low CDFs for this shorter defect
Figure 56(a) contrasts leaving un-repaired a 5 mm high defect with introducing either 5 mm 42 mm
or 33 mm high defects in the as-repaired weld for p+2a=167 mm The squares show the effect of
having the same size 5mm deep defect in the repair Obviously the repaired life is always lower than
the un-repaired life and gets comparatively worse as the repaired toughness reduces If the repaired
defect is 42 mm high (diamonds) a reduction in toughness is needed to get a worse life out of the
repair The triangular symbols for the shallow 3 mm high defect in the repair are well over unity dueto a large life of that repair This is due to the defect tip in question lying well inside the compressive
region of the repair residual stress field giving low initial crack growth rates However the fatigue
lives are generally very long for this un-repaired defect (see rightmost curve in Figure 51(a) Leaving
un-repaired small height defects near the middle of the plate is therefore likely to be a reasonable
course of action
Results comparing a 67mm high defect in the un-repaired weld with 67 mm 5 mm or 42 mm high in
the repair are illustrated in Figure 56(b) The diamonds show that introducing a smaller 5 mm defect
in the repair always gives a shorter life The triangles start to appear showing the smallest repaired
defect of 417 mm where the fatigue life ratios remain well above unity
Figure 56(c) compares the 92 mm high un-repaired defect with 92 mm 67 mm or 5 mm in the
repair The diamonds have moved up slightly compared with the previous graph but the squares have
shifted downwards This is an interaction between tip position and the associated residual stress field
The defect tip is growing towards the repaired surface so initially higher (longer) defects experience
more strongly the tensile region of the residual stress near the repair surface
In Figure 56(d) a 108 mm high un-repaired defect is compared with smaller 92 mm 67 mm or 5
mm defects in the repair Leaving the same size in the repair (squares) always gives a shorter
operating life particularly for lower toughness The 67 mm repair defect (diamonds) needs a large
reduction in toughness to give shorter life than the un-repaired 108 mm defect
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
42
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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The final graphs Figures 57(a-b) show similar comparisons for the embedded cases in which
p+2a=108 mm There is a more restricted range of defect heights and toughness to consider and so
fewer points are plotted than in Figure 56 Also the growing defect tip of interest lies at a
comparatively shallow depth in the repair so it tends to experience more tensile repair residual
stresses and so has a comparatively shorter fatigue life In Figure 57(a) the life ratio of many of the
triangular symbols is below unity indicating that repairing the 5 mm high defect but leaving a 33 mm
one gives a shorter life The highest 60 MPaOumlm PWHT toughness considered needs only 16
reduction in the repair to give a shorter life As noted earlier the defect tip considered is now shifted
towards the tensile part of the repair residual stress so the repair has a relatively shorter life In fact
for a large range of toughness the initial repair is at a limiting condition with respect to the overload
considered so the repair life is zero cycles Figure 57(b) compares a 67 mm high un-repaired defect
with 67 mm 5 mm or 42 mm repaired Many repaired cases have no life for the range of toughness
considered The triangles show that having a 42 mm defect in the repair gives a lower life than the
un-repaired 67 mm defect if repair causes a modest reduction in toughness
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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10 TASK 9 ndash ASSESSMENT BY ENGINEERING PROCEDURE
METHODS
101 GENERAL METHODOLOGY
British Standard BS 79101999 Guide on Methods for Assessing the Acceptability of Flaws in
Metallic Structures (Reference 4) contains three levels for the assessment of fracture resistance
The materials involved the input data available and the conservatism required are the factors which
determine the chosen level For the purpose of the calculations carried out in this task Level 2 the
normal assessment route was applied This involves values of the plastic collapse parameter Lr and
fracture mechanics parameter K r to be evaluated and plotted on the appropriate fracture assessment
diagram (FAD)
Three residual stress conditions were assumed They were (i) as-welded (ii) as-welded followed by
post weld heat treatment (PWHT) and (iii) weld repair In case (i) the transverse residual stress
distribution shown in Figure Q1(a) of BS 7910 was considered It was judged that this distribution
could be approximately represented by a through-wall bending stress equal to the material yield stress
Case (ii) assumed the residual stresses to be a membrane stress equal to 20 of the yield stress
(Section 7242 of BS 7910) In case (iii) the transverse residual stress distribution shown in Figure
Q1(d) of BS 7910 was considered It was judged that this distribution could be approximately
represented by a membrane stress equal to the material yield stress In these calculations the yield
stress was taken as the lowest value of 02 proof stress given in Table 2 (ie 345 MPa) To
summarise therefore the residual stress conditions assumed were
(i) As-welded condition ndash through-wall bending stress (+ 345 MPa at the surfaces)
(ii) As-welded followed by PWHT condition ndash membrane stress of 69 MPa(iii) Weld repair condition ndash membrane stress of 345 MPa
The term 983154 is included in the evaluation of K r in order to cover interaction between the primary and
secondary stress systems The procedure used to determine 983154 was as detailed in Annex R2 of BS
7910 as follows
a) Determine K Is the linear elastic stress intensity factor for the flaw size of interest using the
elastically-calculated secondary stresses K Is is positive when it tends to open the crack
If K Is is negative or zero then 983154 is set to zero and the remainder of this procedure does not
apply
b) Determine the ratio K I pLr
s sc) Determine K I (K I
pLr ) from the result of a) and b) If K I (K I
pLr ) gt 4 then Annex R3 of BS
7910 should be used to evaluate 983154983086 This is a more detailed procedure for calculating 983154 and the
steps involved are
si Calculate the parameters K I
s and K p Advice on determining the effective (elastic-
plastic) stress intensity factor K ps
is given in Annex R4 of BS 7910 In these
calculations K ps was evaluated by the route given in Annex R43 of BS 7910 which is
based on the small-scale yielding correction to K Is
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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sii Determine the ratio K p (K I
pLr ) where K I
p and Lr are calculated as in Sections 73 and
74 of BS 7910
iii Obtain the parameter 983161 from the table in Annex R1 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) calculated in step (II) Linear interpolation should be used for
s
values not given in the table If K ps
= K I then 983154 is set equal to 983161 and the remainder ofthis annex does not apply
iv Obtain the parameter 983146 from the table in Annex R2 of BS 7910 in terms of Lr and thes
parameter K p (K I pLr ) from step (II) Linear interpolation should be used for values not
given in the table
v Determine 983154 from the following equation
K s ouml983270 I 983085 1 983154 983085983129983101 983146 ccedilccedil
egrave dividedivide 983288 K
s
P
If this results in a negative value for 983154983084 then 983154 is re-defined to be zero
The detailed procedure described above for the determination of 983154 was automated in thes
calculation if K I (K I pLr ) gt 4 A visual basic program was used to search two tables to find
s sappropriate values of 983161 and 983146 as functions of K p (K I
pLr ) and Lr where K p is as described in
sAnnex R43 of the procedures If K I (K I
pLr ) lt 4 983154 was evaluated following the simplistic
route of steps d) and e) below
a) Determine 9831541 from Figure R1 of BS 7910
b) Determine 983154983086
983154 983101 983154983089 Lr lt= 08
983154 983101 983092983154983089(105 - Lr ) 08 lt Lr lt 105
983154 983101 0 105 lt= Lr
102 EDGE CRACKS
1021 Available Solutions
and 983155
In the case of an edge crack two possible solutions are available in BS 7910 for the calculation of K I
Reference Figures M6 and M10 of BS 7910 show a long surface flaw and an edge flaw geometryrespectively The solutions described for the long surface flaw geometry Figure M6 of BS 7910
were used rather than those for the edge crack flaw geometry The reason for this is that the axis of
the plane of bending (as required for the residual stress case (i) ) is not correct in the case of the edge
flaw geometry
However two K I solutions were calculated to compare the difference between the two crack
geometries for just membrane loading This clearly showed that there was a negligible difference
between the two solutions
The stress intensity factor solution (Eq M1 of BS 7910) is
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
30
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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K I 983101983080Y 983155 983081 983152 awhere for Level 2 assessments
Y 983155 983101983080Y 983155 983081 p 983083983080Y 983155 983081 s (Eq M4 of BS 7910)
where 983080Y 983155 983081 p and 983080Y 983155 983081 s represent contributions from primary and secondary stresses respectively
They are calculated as follows
983080Y 983155 983081 p 983101Mf 983131k M M P 983083k M M 983163 P 983083983080k m 9830851983081 P m983165983133 (Eq M5 of BS 7910)w tm km m m tb kb b b
983080Y 983155 983081 s 983101M 983083 QM b (Eq M6 of BS 7910)mQm b
where for the case under consideration M k tm M km k tb M kb f w = 1 and M m and M b are given below
for aB lt= 06 (Section M33 of BS 7910)
4M m = 112 - 023(aB) + 106(aB)
2 - 217(aB)3 + 304(aB)
4M b = 112 - 139(aB) + 732(aB)2 - 131(aB)3 + 14(aB)
The reference stress for a long surface flaw in flat plates is as follows (Section P32 of BS 7910
assuming normal bending restraint)
50
P 983083983131 P b29830839 P 2 9830801 983085 a 983081 2 983133b m
983155 983101ref 298308013 983085 a 983081 where a = aB
1022 Results
Figure 58 contains values of crack depth versus number of fatigue cycles for initial crack depths of
333 mm 10 mm and 1667 mm in the plate subjected to 180 MPa cyclic primary stress for the un-
repaired PWHT case The calculated values using the BS 7910 K solutions are compared to the FE
solutions of Figure 39(a) As has been explained previously the FE calculations were carried out in
terms of the elastic-plastic 983108K J as opposed to the elastic 983108K Since the BS 7910 calculations were
evaluated in terms of 983108K such evaluations have also been carried out based on the FE K solutions
(using the data given in Figure 37) and the results of these have been included in Figure 58 It should
be noted that since K min in the 983108K calculations is based on the weld residual stress alone and K max is
based on the primary stress plus the residual stress then the actual value of the residual stress is not
sensitive to such calculations It can be seen from Figure 58 that the BS 7910 based crack depth vs
cycles results are very similar to those based on the FE elastic solutions This implies of course that
the BS 7910 K values were very similar to those of the elastic FE K values This aspect is considered
further in section 1023 below
Figure 59 contains the same type of information as for Figure 58 but for the as-repaired condition
Again the BS 7910 based crack depth vs cycles results are shown to be very similar to those based on
the FE elastic solutions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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Figure 60 contains fracture toughness vs critical crack depth curve evaluated by BS 7910 for the
weldment material states (ie residual stresses) (i) (ii) and (iii) The calculations have been carried
out for a 225 MPa overload stress along with the various residual stress assumptions As would be
expected the PWHT state results in the largest critical crack depth sizes (the residual stress being 69
MPa membrane) the as-welded state results in the second largest values (the residual stress being 345
MPa through-wall bending) and the PWHT state results in the lowest values (the residual stress being
345 MPa membrane)
Figure 61 shows comparisons of the BS7910 evaluated and FE calculated values of critical crack
depth for the un-repaired PWHT condition It can be seen that the critical crack depths based on the
BS 7910 calculations are somewhat lower than those obtained by the FE analysis This aspect is
considered further in section 1023 below
Figure 62 contains the same type of information as for Figure 61 but for the as-repaired condition
For this state the critical crack depths based on the BS 7910 calculations are seen to be significantly
lower than those obtained by the FE analysis Again this is further considered in section 1023
1023 Refined Calculations
In the previous sub-section with reference to Figures 61 and 62 it was shown that the critical crack
sizes based on the BS 7910 calculations were lower than those obtained by the FE analysis It was
considered that the differences in residual stress distributions between those of the BS 7910 document
and those evaluated by finite elements was likely to be the main reason for these differences in critical
crack sizes The residual stress distributions evaluated by the finite element techniques were
therefore considered in refined BS 7910 calculations Since the residual stress fields are of a
sinusoidal nature and since no solutions are available in BS 7910 for evaluating stress intensity factor
(K I) solutions for such stress distributions alternative K solutions were employed as follows
K I for an edge crack in a plate or a cylinder can be represented (Reference 5) as05 2 3
KI = (983152a) [F0 A0 + 2(at)983152 F1 A1 + (at) 2 F2 A2 + 4(at) (3983152) F3 A3] (4)
where a is crack depth and t is wall thickness
A0 to A3 are constants in the cubic polynomial equation representing the through-wall stress
distribution 983155 over the depth (a) of the crack (but prior to the presence of the crack) ie
2 3983155 = A0 + A1(xt) + A2(xt) + A3(xt)
x is the distance into the plate thickness
For a flat plate the Fn functions are given by
F0 = [1148 ndash 09913 at + 3076(at)2] [1 ndash at]
F1 = [1077 ndash 08345 at + 1543(at)2] [1 ndash at]
F2 = [1007 ndash 07007 at + 0781(at)2] [1 ndash at]
F3 = [1015 ndash 07296 at + 0446(at)2] [1 ndash at]
Solutions for Fn at the deepest point of the crack are also available for cylinders
It is evident that for applied membrane loading only the first term in Equation 4 will be required
since 983155 = A0
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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For through-wall bending the first two terms in Equation 4 are required since 983155=A0+A1at where A1=-
2A0 with A0 being the stress at the surface
The above equations were used to evaluate values of K I for the various residual stress distributions
modelled in the finite element analyses of Tasks 7 and 8 In preliminary calculations the ldquotruerdquo finiteelement calculated distributions were considered However since these generally consisted of
compressive stresses at the surface of the plate where the crack was situated the calculational route
described above resulted in compressive values of K I ie crack closure for all lengths of crack A
study of all the residual stress distributions (a As-welded b As-welded and Repair c As-welded and
PWHT d As-welded and PWHT and Repair) indicated that the peak tensile stress occurred at a
distance of approximately 71 mm from the surface As a compromise in modelling the residual stress
distributions to evaluate K I it was assumed that the peak tensile stress occurred over the first 71 mm
of the plate These modified residual stress distributions are shown in Figure 63 over approximately
one half of the plate ie for distances of up to approximately 20 mm from one side of the plate
When evaluating K I for these stress distributions different cubic polynomial equations were fitted for
different crack sizes since it was not possible for one equation to accurately represent all crack sizesin the range being considered (ie 0 to 20 mm) Once values of K I had been evaluated for the
different crack sizes a cubic polynomial equation was fitted for each of the four residual stress cases
represented by the equation
2 3KI = C0 + C1a + C2 a + C3 a
where a is crack depth (in mm) and K I is in MPaOumlm
For completeness values of K I were also obtained for a sinusoidal distribution (tensile at both
surfaces and compression in the middle region of the plate) and for membrane and bending (tensile
stress on one side of the plate and compressive stress on the other) Values for C0 to C3 for thedifferent stress cases considered are as follows
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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Stress Case C0 C1 C2 C3
As-Welded
(Stress = 3125 MPa for a = 0 to 71 mm)
49282 11388 -05382 0008
As-Welded then Repair
(Stress = 3162 MPa for a = 0 to 71 mm)
45909 11788 -05944 0013
As-Welded then PWHT
(Stress = 1103 MPa for a = 0 to 71 mm)
33661 3495 -01406 00012
As-Welded then PWHT then Repair
(Stress = 3176 MPa for a = 0 to 71 mm)
97278 10043 -04285 00085
Sinusoidal Distribution
(Stress peaks at 1103 MPa at Surfaces)
19775 40770 -03384 000773
Sinusoidal Distribution
(Stress peaks at 3176 MPa at Surfaces)
56939 11740 -09744 002226
Bending
(Stress = 1103 MPa to ndash1103 MPa)
22364 35034 -02544 0009
Bending
(Stress = 3176 MPa to ndash3176 MPa)
64394 100877 -07327 00259
Membrane
(Stress = 1103 MPa)
18927 40597 -02658 00128
Membrane
(Stress = 3176 MPa)
54498 116897 -07655 00368
Values of K I plotted against crack depth are presented in Figures 64 to 66
Figure 64 contains the evaluated K I distributions for the As-welded As-welded-Repair As-welded-
PWHT and As-welded-PWHT-Repair cases As would be expected by consideration of the stress
distributions given in Figure 63 the As-welded-PWHT-Repair case gives the highest K I values and
the As-welded-PWHT case gives the lowest
Figure 65 contains the evaluated K I distributions for the As-welded-PWHT case together with the
evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 1103 MPa
at the surface) the bending stress distribution case (stress = 1103 MPa on one surface and ndash1103
MPa on the other surface) and the membrane stress case (=1103 MPa) As would be expected by
consideration of the respective stress distributions the K I distribution for the As-welded-PWHT case
is similar to that for the membrane case for crack depths of up to approximately 7 mm after which the
K I values for the latter increase significantly It may be noted that for the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT case was taken to be 69
MPa membrane The K I vs crack depth curve for this distribution would therefore lie some 40
lower than the membrane curve shown in Figure 65 (see below with reference to Figure 68)
Figure 66 contains the evaluated K I distributions for the As-welded-PWHT-Repair case together with
the evaluated K I distributions for the sinusoidal stress distribution case (the stress peaking at 3176
MPa at the surface) the bending stress distribution case (stress = 3176 MPa on one surface and ndash
3176 MPa on the other surface) and the membrane stress case (=3176 MPa) Again as would be
expected by consideration of the respective stress distributions the K I distribution for the As-welded-
PWHT-Repair case is similar to that for the membrane case for crack depths of up to approximately 7
mm after which the K I values for the latter increase significantly For the BS 7910 calculations
covered in section 1022 the stress distribution for the As-welded-PWHT-Repair case was taken to
be 345 MPa membrane The K I vs crack depth curve for this distribution would therefore lie just
about 10 above the membrane curve shown in Figure 66 (see below with reference to Figure 69)
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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Figure 67 contains a comparison of the various K I solutions considered in this work for an edge
cracked plate subjected to a membrane stress of 220 MPa The ldquohandbookrdquo solutions of Rooke and
Cartwright (Reference 6) for both restrained and un-restrained bending have also been included It
can be seen that the values obtained from the BS 7910 finite element Sharples et al solutions
(Reference 5) described above and the Rooke and Cartwright un-restrained bending solutions are all
very similar to one another with the FE values lying slightly below the others The Rooke and
Cartwright restrained bending solution values lie significantly below those of the other solutions
This confirms that the solutions considered in this work are relevant to the un-restrained bending case
Such conditions are relevant for application to the applied membrane stress case However since
residual stresses arise from a displacement control mechanism restrained bending conditions may be
more appropriate when evaluating values of K I for such stresses The use of the BS 7910 and
Sharples et al solutions may therefore result in over-estimates of K I values for residual stresses
Figure 68 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT residual stress case The BS 7910 and Rooke and Cartwright values are for a
membrane stress of 69 MPa For completeness the Rooke and Cartwright restrained bending values
have been included Again the BS 7910 and Rooke and Cartwright un-restrained bending values are
identical to one another As suggested above with reference to Figure 65 the Sharples et al solutionvalues are somewhat higher than the BS 7910 (and Rooke and Cartwright un-restrained bending)
solution values up to a crack depth of just under 15 mm The finite element solution values are fairly
close to the BS 7910 values up to a crack depth of approximately 10 mm after which they start to
diverge and become considerably lower
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 61 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are actually lower than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 68 between the BS 7910 and Sharples et
al values of K I for the residual stress Although such calculations have not been performed it is
evident from Figure 68 that critical crack depth values closer to those obtained from the finite elementanalysis may be obtained by using the Rooke and Cartwright restrained bending solutions for
modelling the residual stress field as 69 MPa membrane
Figure 69 contains a comparison of the K I values evaluated from the various solutions for the As-
welded-PWHT-Repaired residual stress case The BS 7910 and Rooke and Cartwright values are for
a membrane stress of 345 MPa Again for completeness the Rooke and Cartwright restrained
bending values have been included The BS 7910 and Rooke and Cartwright un-restrained bending
values are of course identical to one another As suggested above with reference to Figure 66 the
Sharples et al solution values are higher than the BS 7910 (and Rooke and Cartwright un-restrained
bending) solution values It is also interesting to note that the Sharples et al solution values are very
similar to those of the Rooke and Cartwright restrained bending solution The finite element solution
values are significantly lower than the other values
Values of critical crack depth obtained by using the Sharples et al residual stress K I solutions have
been included in Figure 62 (referred to as ldquoBS 7910 refinedrdquo) It can be seen that the critical crack
depth values for this case are slightly higher than those of the original BS 7910 calculations This of
course can be explained by the difference shown in Figure 69 between the BS 7910 and Sharples et
al values of K I for the residual stress This time it is evident that even using the Rooke and
Cartwright restrained bending solutions for modelling the residual stress field as 345 MPa membrane
would not result in critical crack depth values closer to those obtained from the finite element
analysis
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
35
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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The significance of the BS 7910 calculation results in terms of the fatigue life for the repaired
condition compared to the fatigue life for the un-repaired (ie as-welded-PWHT state) condition can
be understood from the information presented in Table 3 This table gives values of NrepairedNun-repaired
for initial crack depths (in both the repaired and un-repaired conditions) of 333 mm 10 mm and
N
1667 mm for fracture toughness values (K IC) ranging from 60 to 160 MPaOumlm The values in the table
have been compiled from the crack depth versus number of cycles N data presented in Figures 58and 59 and from the fracture toughness versus critical crack depth data of Figures 60 and 61 The
finite element values based on K J given in Table 3 are of course those plotted in Figure 48 An
explanation of the values shown in brackets in Table 3 is given in the next paragraph With the
exception of four cases It can be seen that the finite element NrepairedNun-repaired values based on elastic
K are somewhat higher than those based on elastic-plastic K J It can also be seen that the BS 7910
refined calculation values are somewhat higher than the BS 7910 original calculation values It is also
noticeable that for the lower fracture toughness values of 100 and 120 MPaOumlm the BS 7910
repairedNun-repaired values are considerably lower than the finite element values However for the higher
fracture toughness values of 140 and 160 MPaOumlm the BS 7910 NrepairedNun-repaired values are closer to
the finite element values Where direct comparisons between the BS 7910 and the finite element
results are available within Table 3 the same trends are shown for both methods ie that the fatigue
life for the repaired state is lower than that for the un-repaired state It is shown however that thefinite element margins of NrepairedNun-repaired are not produced by the BS 7910 calculations
The values contained in brackets in Table 3 have been derived as follows
The Paris Law equation as in Equation 3 is of the form
dNda 983101C983108K m (5)
Rearranging this equation gives the incremental cycle dN as
dadN 983101 (6)
C983108K m
daor dN micro (7)
983108K m
50983080 Now 983108Kmicro 983152983155983108 a983081 (8)
and since in the work being considered here 983155983108 for the repaired case is taken to be the same as that
for the un-repaired case then
983108Kmicroa 50(9)
For the increment cycle being considered in these calculations crack depth a grows from the initial
size aI to the limiting size aL It is reasonable to assume therefore that the average value of a
(ie (aI+aL)2) can be used in Equation 9 Therefore
50983270 a 983083a ouml
983108K micro ccedil i L divide (10)egrave 2 983288
Setting da to (aL-a
I) and the value of m to 277 (Equation 3) and substituting Equation 10 into
Equation 7 results in
35
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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a 983085 adN micro
L i (11)3851983080ai 983083a 983081L
dN
3851
repaired 983080a
L983085 a
i 983081repaired 983080a
i983083a
L 983081unrepairedor 983101 (12)3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081repaired
The values in brackets in Table 3 were therefore obtained from Equation 12
It can be seen from Table 3 that these values are very close to those (without the brackets) obtained
from the detailed fatigue crack growth calculations for when the elastic Krsquos are used in the
calculations As may have been expected the values are not as close to those when the inelastic Krsquos
(ie K Jrsquos) are used in the calculations
Based on the elastic route therefore Equation 12 seems to be a reliable and relatively easy route for
determining values of NrepairedNun-repaired values once the critical or limiting crack length aL has beenevaluated for both the repaired and un-repaired cases
103 EMBEDDED CRACKS
1031 Available Solutions
In the case of an embedded crack a solution is available appropriate to Figure M1 of BS 7910 for the
calculation of K I and 983155Reference The geometry for this solution again presented problems in that the axis
of the plane of bending is not appropriate for this particular case and it assumes that the crack is in the
centre of a flat plate
Another solution appropriate to Figure M7 of BS 7910 was then considered In this case the crack
geometry does not satisfy conditions set The geometry is not identical to the embedded crack case in
that Figure M7 has an elliptical crack of length 2c whereas the problem has a crack length of the
same magnitude as the width of the specimen W Therefore 2cW gt 05 and not lt 05 as specified in
the conditions
After considering the two representations as described above It was decided that the geometry in
Figure M1 and associated K I (section M31 of BS 7910) and 983155Reference (section P31 of BS 7910)
solutions should be used even though it was not exactly like the embedded through-wall crack case in
question
Membrane stress could be represented in the normal way
Bending stress (actually not used in the current calculations) could be represented by specifying a
relevant component of membrane stress and a relevant component of bending stress to allow for the
fact that the crack is not in the centre of the plate specimen
1032 Results
Some comparisons were made between the BS 7910 calculated stress intensity factor values and those
obtained from the finite element analyses These comparisons are presented in Figures 70 to 72 (for
the position of the crack p+2a being 167 mm)
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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Figure 70 compares the K I values for an applied membrane stress of 220 MPa Values obtained from
the appropriate Rooke and Cartwright (Reference 6) solutions have also been included as a check
These solutions are shown to be almost identical to those of BS 7910 The finite element values are
shown to be very close to those of the BS 7910 calculations up to a crack depth (2a) of approximately
8 mm For crack depths greater than 8 mm the FE values then increasingly become higher than the
BS 7910 values Fatigue crack growth calculations have not been performed using the BS 7910 K Isolutions for the embedded crack cases However the K I comparisons of Figure 70 tend to suggest
that fatigue crack growth evaluations for the BS 7910 K I solutions would be identical to those of the
FE solutions up to a crack depth of 8 mm after which the former solutions would show a reduced
crack growth rate Based on just these considerations therefore the comparisons would tend to
suggest that the BS 7910 K I solutions may be non-conservative for fatigue crack growth for the
particular case being considered
Figure 71 compares the BS 7910 and FE K I values for the As-welded-PWHT residual stress case As
well as the elastic FE values (denoted K) the elastic-plastic FE values (denoted KJ) have also been
included in the figure It can be seen that there is practically no difference between the elastic and
elastic-plastic FE values The BS 7910 values (based on a membrane stress of 69 MPa) are shown to be higher than the FE values up to a crack depth of approximately 11 mm after which the opposite is
true Critical crack calculations have not been performed using the BS 7910 K I solutions for the
embedded crack cases However the information contained in Figures 70 and 71 suggests that the
critical crack sizes (for different fracture toughness value assumptions) for the as-welded-PWHT case
would be underestimated (compared to the FE calculated values) for crack depths up to approximately
8 mm For higher crack depths the critical crack sizes may be overestimated which is non-
conservative The BS 7910 critical crack height curve could therefore be on the right of the
corresponding FE curve presented in Figure 52
Figure 72 compares the BS 7910 and FE K I values for the As-welded-PWHT-Repair residual stress
case This time the elastic-plastic FE values start to diverge from the elastic FE values at a crackdepth of approximately 8 mm The BS 7910 values (based on a membrane stress of 345 MPa) are
shown to be higher than the FE elastic values by margins greater than 20 MPa Oumlm The information
contained in Figures 70 and 72 suggests that the critical crack sizes (for different fracture toughness
value assumptions) for the As-welded-PWHT-Repair case would be underestimated (compared to the
FE calculated values) for all crack depths considered with the possible exception of the largest cracks
(ie possibly overestimated for 2a = 12 mm to 14 mm say) The BS 7910 critical crack height curve
would therefore likely be on the left (for crack sizes up to approximately 12 mm) of the corresponding
FE curve presented in Figure 52
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
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12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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11 TASK 10 ndash PROVISIONAL GUIDANCE ON WELD REPAIRS
Under this Task provisional guidance on weld repairs has been developed The resulting guidance
firstly focuses on practical issues that have been highlighted from the review carried out under Task 1and from other relevant information Secondly guidance resulting from the finite element
calculations of the matrix of cases considered is presented
111 PRACTICAL ISSUES
Types of Defect
Weld defects can be categorised as follows
983223 Category 1 - cracks or crack-like defects (planar discontinuities) such as incomplete fusion or
penetration
983223 Category 2 - geometric defects including undercut misalignment and incorrect weld profile
983223 Category 3 - slag and porosity they are the most innocuous type of weld defect but the most
frequently repaired
Causes of Defects
During fabrication defects may arise due to problems with the fabrication procedure which must be
addressed quickly Poor joint design and weld misalignment are frequent causes of fabrication
defects During service the cause and nature of the cracking must be investigated and action must be
taken to prevent recurrence Otherwise the same type of defect may develop Incorrect joint design
and unforeseen service conditions are commonly cited causes of defect development
Significance of Defects
Many repairs can be unnecessary and sometimes reduce the integrity of the structure This is because
there is a gap between the high integrity resulting from the weld quality associated with workmanship
standards and the often much lower level of quality required to satisfy a fitness-for purpose
assessment
Necessity of Repair Welding
Repair welding is not always necessary particularly for shallow defects that may be removed by analternative method for example by grinding out
Problems Associated with Repair Welding
There are several problems associated with repair welding which may lead to a reduction of the
structural integrity of a weld compared with its original defective condition These include
983223 inadequate removal of the original defect for example incomplete excavation of a crack
983223 introduction of new defects hydrogen cracking is a likely source of new defects in repair welds
38
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
39
7272019 Integrity of Repair Weld
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
40
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4750
12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
7272019 Integrity of Repair Weld
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
42
7272019 Integrity of Repair Weld
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3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
43
7272019 Integrity of Repair Weld
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
7272019 Integrity of Repair Weld
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983223 unfavourable site conditions for re-welding including poor access the inability to apply
sufficient preheat and poor weld positioning
983223 unfavourable conditions for inspection and testing of the repaired weld
983223 repairs of restrained welds in structures may have a higher risk increased residual stress ordistortion
983223 post-weld heat treatment of a site repair is often unfeasible giving a higher probability of
increased residual stress and lower toughness
In this regard repairing a weld can lead to inferior or inappropriate properties of the repair due to a
degraded microstructure Poor fracture toughness is of particular concern Inappropriate properties
can arise from a number of different reasons including
983085 inappropriate welding consumables
983085 insufficient pre-heat
983085 inappropriate (usually too low) heat input since a different welding process may be used in the
repair compared with the original fabrication site (repair welds are invariably made manually but
the original fabrication weld may have been an automatic process)
983085 inappropriate composition and weldability of the local parent material if a repair is being carried
out in a previously unwelded region of a component
In terms of fracture toughness there is strong evidence to suggest that too high or too low heat input
can have a deleterious effect on toughness Reductions of CTOD toughness in Heat Affected Zones
(HAZ) by a factor of between 5 and 8 have been reported for carbon and carbon-manganese steelwelds (corresponding to reductions in K J toughness by factors of approximately 22 and 28) On the
other hand high preheat and inter-pass temperatures and post-weld heat treatment help to increase
HAZ toughness These latter improvements are unlikely to be obtained in difficult on-site working
conditions however For carbon-manganese steel welds lower bound CTOD toughness of the HAZ
can be increased by PWHT by a factor of 10 compared with as-welded toughness Mean CTOD
toughness of the HAZ can increase by a factor of 5 It should be noted though that in some modern
thermo mechanically rolled or TMCP steel HAZ toughness may not improve or actually reduce due
to PWHT To summarise In standard carbon and carbon-manganese steels PWHT obviously
improves the toughness of HAZ in particular This combined with the benefit derived from using
proper pre-heat correct heat input a satisfactory welding position and other factors must mean that
on-site repairs are likely to be produce lower values of fracture toughness than original shop welds
112 GUIDANCE RESULTING FROM THE FINITE ELEMENT CALCULATIONS
In this study of crack-like defects in welds comparisons have been made between the behaviour of
various sizes of defects in a heat treated weld and in a non-heat treated repaired weld The main
parameters considered are those that are quantifiable and can be used within a fracture mechanics
framework These are weld residual stress pattern defect depth or height and local fracture
toughness The initial defects in the two weld cases are assumed to grow by fatigue due to a cyclic
operating load Occasional overloads at each resulting defect depth or height are assessed to see
whether this causes a limiting condition for given values of fracture toughness Of course it seems
rather pessimistic to consider that a defect always remains after repair and it is difficult to place
39
7272019 Integrity of Repair Weld
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limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
40
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4750
12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
7272019 Integrity of Repair Weld
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For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
42
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4950
3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
43
7272019 Integrity of Repair Weld
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13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4650
limits on its possible size However limits of sizing in ultrasonic testing provide a useful lower bound
to the repair defect position and height
The main findings are as follows
983223 For a given fracture toughness the critical defect depth at the limiting condition is smaller in theas-repaired weld than the PWHT weld As the fracture toughness reduces the relative difference
in critical defect size between the two cases becomes more significant This phenomenon is
particularly apparent for the welded sphere studied
983223 Predictions of fatigue crack growth in both the plate and the sphere show more rapid rates of
crack growth in the repair compared with the original PWHT weld Fewer loading cycles are
required in the repair to cause a limiting condition for the same initial defect size and fracture
toughness
983223 A graphical framework is presented to compare fatigue lives of defects in original heat treated
welds with the same or shallower defects in as-repaired welds (Figures 42 43 48 49 54 55 and
56) From this information it can be concluded that
983085 Weld repairing shallow defects and low toughness parent or weld materials is more likely to
give a shorter fatigue life than leaving the weld un-repaired
983085 A relatively shorter fatigue life of the weld repair compared with leaving un-repaired is more
likely in the sphere than the plate The welded sphere geometry is more sensitive to reductions
in fracture toughness in both PWHT and conditions
983085 For embedded defects in double lsquoVrsquo preparation butt welds the case for whether to repair or
not depends on the depth and height of the defect
983085 Short embedded defects near the middle of the plate are likely to experience low or
compressive levels of compressive stress and so low crack driving forces and relatively long
fatigue lives The best course of action is likely to be to leave these defects in place
40
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4750
12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4850
For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
42
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4950
3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
43
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 5050
13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4750
12 TASK 11 ndash PROVISIONAL GUIDANCE ON ENGINEERING
PROCEDURE METHOD
Section 10 above has reported on Task 9 of the project dealing with assessment by engineeringmethods This task has focused on the BS 7910 methodology From the experience gained in
undertaking Task 9 provisional recommendations are now made on the use of this methodology to
firstly assess the significance of flaws in weldments (as-welded PWHT or repaired weld) on a case-
by-case basis and secondly to assess as to whether repairing a weld is likely to be beneficial or not
These provisional recommendations are derived from the work relating to the edge-cracked plate
configuration considered in this study However many of the aspects given below may be applied in
a generic sense
121 ROUTE FOR ASSESSING THE SIGNIFICANCE OF A FLAW IN A WELD (AS-
WELDED PWHT OR REPAIRED WELD)
The significance of a flaw known or postulated to occur in a weldment (or indeed in parent material)
can be evaluated from the following three steps
1 Evaluate the critical crack size
2 Evaluate the operating time or cycles to grow (eg by fatigue) the flaw to the critical crack
size
3 Use the information obtained from 2 to decide as to whether continued operation in the
current state is possible what the future inspection frequency should be or plan for repair or
replacement
122 ROUTE FOR ASSESSING WHETHER REPAIRING A WELD IS LIKELY TO BE
BENEFICIAL
Assessing whether repairing a weld is likely to be beneficial or not can be evaluated from the
following four routes
1 Evaluate the critical crack sizes for the un-repaired weld and for the repaired weld states
2 For the un-repaired weld state evaluate the operating time or cycles for the known flaw to
grow (eg by fatigue) to the critical crack size
3 For the repaired weld evaluate the operating time or cycles for the maximum size of flaw
that could be missed by the relevant detection techniques to grow (eg by fatigue) to the
critical crack size
4 Compare the results of 2 and 3 to conclude as to whether it is likely to be beneficial or
detrimental to go ahead with the weld repair
123 CRITICAL CRACK SIZE EVALUATION
It is recommended that critical crack size should be evaluated by following the Level 2 procedures of
BS 7910 section 7 (Assessment for Fracture Resistance)
For the edge crack plate configuration under consideration here the stress intensity factor (K I) and
reference stress (983155ref ) for the primary Stress (membrane) should be evaluated from BS 7910 with
reference to Figures M6 and M10 of that BS
41
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4850
For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
42
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4950
3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
43
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 5050
13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4850
For the secondary residual stresses ideally elastic FE solutions for K I of the appropriate residual
stress profile should be obtained (as for the FE calculations presented above) In practice though
such solutions are usually not available and the time and effort required to produce them is likely to
be restrictive The guidance given in BS7910 is therefore likely to produce conservative (ie under-
estimates) values of critical crack size (Figures 61 and 62) whereby residual stress for the various
conditions can be represented as follows
As-welded - + 02 proof stress Through-wall Bending
PWHT - 20 of 02 proof stress Membrane
Weld Repair - 02 proof stress Membrane
K I solutions for the membrane residual stress assumptions can be evaluated with reference to Figure
M6 and M10 BS 7910 K I solutions for the residual stress assumption of through-wall bending can
be evaluated with reference to Figure M6 of the BS
(Note the refined calculations referred to in section 1023 for evaluating K I from a simplified
distribution of the FE residual stress profiles were shown to produce only a marginal benefit from
those of the BS 7910 route as described above)
It is important that the tensile and fracture toughness materials properties relevant to the appropriate
weld state are taken into account in the calculations This is particularly true in calculations for
assessing whether repairing a weldment may be beneficial since the fracture toughness in the repaired
state may be significantly different from that in the un-repaired state due to different heat treatments
being evident between the two cases
124 CRACK GROWTH EVALUATION
If fatigue crack growth is the relevant mechanism then the procedures of BS 7910 section 8
(Assessment for Fatigue) should be employed It may be noted that other likely crack growth
mechanisms are corrosion fatigue (covered to a certain extent in section 8 of BS7910) creep (covered
in section 9 of BS7910) stress corrosion cracking (mentioned in section 10 of BS7910 but essentially
a specialist topic) and creepfatigue (combined procedures of sections 8 and 9 of BS7910 but
essentially a specialist topic)
In the simplified fatigue crack growth route considered here the R ratio (defined in BS7910 as
minimum stressmaximum stress but in reality is minimum K Imaximum K I) has not been taken into
account and therefore only the primary stress needs to be considered in the fatigue crack growth
calculations More accurate fatigue crack growth calculations can be obtained by taking the R ratio
into account in the Paris Law relationship as outlined in BS7910 together with threshold
considerations The use of the R ratio would necessitate the residual stresses to be taken into account
Furthermore in line with R5 procedures (Reference 7) inelastic values of K (ie K J) instead ofelastic values should really be used for evaluating 983108K as was done in the calculations reported in
section 9 above
For assessing whether repairing a weld is likely to be beneficial for a flawed component subjected to
fatigue loading the route described in the relevant sub-section above together with the considerations
described in the paragraph above should ideally be pursued
However as has been shown in section 1023 above the use of equation 12 ie
42
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4950
3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
43
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 5050
13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 4950
3851dN repaired
983080aL 983085 ai 983081repaired983080ai 983083aL 983081
unrepaired983101
3851dN unrepaired 983080aL 983085 ai 983081unrepaired 983080ai 983083aL 983081
repaired
is a reasonable approximation to establish whether repairing a defect is beneficial or not in terms ofimproved fatigue life It may be noted that the verification of this equation has been undertaken
(Table 3) by considering initial defect size (ai) to be the same in both the un-repaired and repaired
states However there is no reason why the relationship should not be equally valid when aI for the
repaired state is different (usually smaller) than for the un-repaired state
43
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 5050
13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
7272019 Integrity of Repair Weld
httpslidepdfcomreaderfullintegrity-of-repair-weld 5050
13 TASK 12 ndash RECOMMENDATIONS FOR FUTURE PHASES OF
PROJECT
Recommendations for work to undertake in future phases of this project are given below
1 Repair Length This first phase of the project has focussed on a weld repair configuration
extending along the full width of the plate (ie the original wide plate used for the experimental
programme) and the geometry has been simplified to a two-dimensional situation (ie an edge-
cracked or through-cracked plate) In reality though the length of a defective weld and hence
the subsequent repair weld is likely to be more limited It is therefore important to study the
influence on repair length on the residual stress distribution as well as depth At the same time
it is necessary to consider realistic semi-elliptical surface or elliptical embedded cracks as
opposed to the simpler edge or through-wall cracks considered here
2 Defect Position in Weld For simplicity the flaws in this initial study have been assumed to
occur at the centre of the weld In reality however it is common for flaws to occur in the HAZ
Further phases of the programme should therefore address HAZ flaws and their subsequent
repair
3 Development of Defect In this study fatigue crack growth has been simulated as a post-
processing operation that is gradual growth of the crack tip is not explicitly simulated in the FE
models Other studies have concluded that crack driving forces can be reduced due to the build-
up of the plastic wake behind of the growing crack This is an effect that has been examined
experimentally in Task 6 It could also be usefully explored in future numerical models
4 Residual stress relief due to mechanical loading (either operation or proof testing) has not beentaken into account in the present study but it could be incorporated in future developments
5 Fatigue Simulation The load-unload-reload sequence is likely to be predominantly elastic That
is due to strain hardening there is unlikely to be an effect of reverse plastic straining in real
defective structures Thus crack driving force ranges may be over-estimated in the calculation
of fatigue crack growth rates This aspect could usefully be investigated further
6 Other Sub-Critical Crack Growth Mechanisms Alternative forms of crack growth could be
considered using the crack driving forces obtained in this work Stress corrosion cracking is a
common sub-critical mechanism that can be strongly affected by welding residual stress Given
material properties it would be a relatively simple task to make alternative predictions of
operating life in un-repaired and repaired situations
7 Effect of Weld Process Control on Fracture Toughness Guidance is required on how the various
welding parameters (eg heat input) effect the material fracture toughness
8 Residual Stress Distributions Improvements need to be made on providing more realistic
residual stress distributions for as-welded PWHT and repaired conditions
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