4 analysis of residual stresses at weld repairs
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Analysis of residual stresses at weld repairs
P. Donga,*, J.K. Honga, P.J. Bouchardb
aCenter for Welded Structures Research, Battelle Memorial Institute, 505 King Avenue, Columbus, OH 43201, USAbBritish Energy Generation Ltd, Barnwood, Gloucester, UK
Abstract
In contrast to initial fabrication welds, residual stresses associated with finite length weld repairs tend to exhibit some important invariant
features, regardless of actual component configurations, materials, and to some degree, welding procedures. Such invariant features are
associated with the severe restraint conditions present in typical repair welding situations. In this paper, residual stress results from several
weld repair case studies, using both advanced computational modelling procedures and experimental measurement techniques, are presented
and reviewed. From these results, it is evident that weld repairs typically increase the magnitude of transverse residual stresses along the
repair compared with the initial weld and that the shorter the repair length the greater the increase in the transverse stress. Also, beyond the
ends of the repair the transverse stress sharply falls into compression. For selected cases, predicted stresses are compared with detailed
residual stress measurements and the adequacy of finite element simulation procedures is assessed. Welding procedure related parameters
(pass lumping, heat input and inter-pass temperature) appear to be more important in analysing weld repairs than in initial fabrication welds.
Also great care must be taken when employing simplified two-dimensional cross-section finite element models with applied restraint
conditions to simulate the residual stress field at a specific point along the length of a repair.
q 2004 Elsevier Ltd. All rights reserved.
Keywords: Finite element; Residual stress; Pressure vessel and piping
1. Introduction
Over the last decade or so, welding-induced residual
stresses have received increasing attention in the pressure
vessel and piping research community. The driving force for
this interest can be attributed to the fact that application of
modern structural integrity assessment procedures for
defective welded components (e.g., BS7910:1999 [1], R6
[2], and API RP-579, 2000 [3]) require more accurate
information on the weld residual stress state to give a more
realistic assessment. The conventional approach for char-
acterising a weld residual stress profile is to adopt an upper
bound solution. However, as reviewed recently by Bradford
[4], Dong et al. [5], Bouchard and Bradford [6], this
approach not only lacks consistency for the same type of
joints and welding parameters [6], but can either signifi-
cantly over-estimate the residual stress level in some cases
[5,6], or under-estimate it in others [7,8].
0308-0161/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijpvp.2004.08.004
* Corresponding author. Tel.: C1-614-424-6424; fax: C1-614-424-
5263.
E-mail address: dongp@battelle.org (P. Dong).
As weld repairs have increasingly become a structural
integrity concern for aging pressure vessel and piping
components, the need for better characterisation of residual
stresses at repairs has become more evident. Both repair
procedure development and the subsequent safety assess-
ment require a better understanding of the repair welding
effects on structural components [7,9,10]. This is because
weld repair residual stress distributions can be drastically
different from those in original fabrication welds, typically
with the presence of higher tensile residual stresses than in
original fabrication welds [11]. As advanced computational
modelling techniques [12] as well as new and improved
experimental methods have become available over recent
years [13], more accurate residual stress information can
now be obtained for various structural integrity assessment
applications.
As discussed by Dong et al. [10], residual stresses in
weld repairs typically exhibit strong three-dimensional
(3D) features, depending on both component and repair
geometries. As a result, 3D effects should be taken into
account in both experimental measurements and numerical
modelling. However, even with today’s fast computer
International Journal of Pressure Vessels and Piping 82 (2005) 258–269
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P. Dong et al. / International Journal of Pressure Vessels and Piping 82 (2005) 258–269 259
speed and advanced numerical procedures, 3D finite
element (FE) solid element models used in simulations
for multi-pass repairs to realistic component configurations
are very challenging. To date, most residual stress analysis
results for repair welds are based on 2D or axi-symmetric
models with applied restraint conditions. These conditions
may be either assumed [12], or equivalent conditions
derived from a 3D-shell weld model [10], or with time-
dependent generalized plane-strain conditions obtained
from a 3D-shell weld model [14]. An alternative cost
effective approach is to use a composite shell element
model, such as developed by Zhang et al. [15], to capture
some of the 3D global residual stress features in repair
welds. The success of this approach in providing an
adequate resolution scale for through-thickness distri-
butions has been demonstrated for a repair weld in a
35 mm thick pipe, by comparing with deep hole drilling
measurements [10].
With the development of improved residual stress
measurement techniques [13] such as neutron diffraction
and deep hole drilling, more comprehensive and reliable
experimental data are becoming available, for example [11].
These data allow a more discriminative assessment of weld
residual stress simulations including the adequacy of
simplified models and the relative importance of different
weld modelling parameters.
Before modelling or measuring a weld residual stress
field, it is of fundamental importance to understand what kind
of residual stress field to expect so that an effective numerical
modelling scheme or experimental method can be devised to
capture it. This paper reviews residual stress results from
several weld repair case studies using both advanced
computational modelling procedures and experimental
measurement techniques. From these results general charac-
teristics of repair weld residual stress fields are then inferred.
This is followed by a detailed discussion of a simplified 2D
cross-section analysis for a weld repair using equivalent
applied restraint conditions to account for 3D effects. For
selected cases, predicted stresses are compared with detailed
residual stress measurements and from this the adequacy of
FE simulation procedures used is assessed.
2. Case studies
2.1. Repaired aluminium alloy butt weld
This case study illustrates important differences between
the residual stress field associated with an initial fabrication
weld and that subsequently introduced by finite length weld
repairs.
Dong et al. [14] have studied the influence of introducing
a repair into a butt-welded aluminium alloy (Al–Li)
cryogenic space shuttle tank mock-up, see Fig. 1a. In this
investigation, a special 3D shell element model [15] was
used to simulate the welding process for the initial butt weld
joining two 610!152!5 mm3 panels. The two-pass weld
was modelled with a moving heat source model [15]. Fig. 1b
shows that the predicted distribution of longitudinal residual
stress was reasonably uniform along the weld length, except
near the welding torch start and stop positions. The peak
value of tensile stress exceeded the material yield strength
(414 MPa). In contrast, the transverse residual stress
component showed a significant variation along the weld,
see Fig. 1c, ranging from a tensile value of 138 MPa around
50–100 mm from the stop position to a compressive value of
about K276 MPa at the stop position. X-ray residual stress
measurements in the heat-affected zone (HAZ) confirmed
such a variation along the weld direction, as shown in
Fig. 1d. These results illustrate how in initial fabrication
welds, the longitudinal component of residual stress (i.e.
that parallel to the direction of welding) is the dominant
component, often reaching and exceeding the magnitude of
the tensile yield strength of the material. The transverse
component of residual stress typically exhibits lower
residual stress magnitudes, with a distribution that is
strongly dependent upon welding procedures and restraint
conditions specific to the component of concern.
When a short length weld repair was introduced at the
mid-length of the initial butt-weld in the same specimen
(Fig. 1a), this resulted in a strongly varying pattern of
transverse residual stress surrounding the repair, as seen in
Fig. 2a. The magnitude of transverse tensile residual stresses
in the region of the repair was high and approached that of
the longitudinal stress component (Fig. 2b). Moreover, the
transverse residual stress field had a long sphere of influence
in the transverse direction. Immediately beyond the repair
start and stop positions, two distinct compressive zones of
transverse stress were predicted. Less marked compressive
zones are also evident in the predicted distribution of
longitudinal stresses, but the overall distribution was
broadly similar to that of the initial butt weld, compare
Fig. 2b with Fig. 1b.
2.2. Repaired carbon steel vessel
A recent fitness-for-service assessment for a series of
high level radioactive waste tanks (radius to thickness ratio
of about 800) containing weld repairs employed finite
element methods to estimate residual stresses for various
repair weld conditions. The storage tanks were made of
ASME Div. 2 A285 carbon steel. The girth welds and local
weld repairs were made by shielded metal arc welding
(SMAW) processes with E6010 electrodes. A majority of
stress corrosion cracks found in these tanks by remote non-
destructive inspection techniques were seen around weld
repairs. However, detailed repair weld information such as
the pass sequence, repair depths, and repair lengths were not
available at the time of the evaluation. Several approxi-
mations in the weld simulation procedure were adopted in
order to provide conservative estimates of overall residual
stress distributions for fitness-for-service assessments of
Fig. 1. Residual stresses in an initial longitudinal butt weld of a long aluminium alloy test panel: (a) specimen geometry and dimensions (b) predicted transverse
residual stress, (c) predicted longitudinal residual stress, and (d) comparison of predicted with measured residual stresses in the HAZ adjacent to the initial butt
weld.
P. Dong et al. / International Journal of Pressure Vessels and Piping 82 (2005) 258–269260
Fig. 2. Predicted residual stresses in aluminium test panel (Fig. 1a) after introducing a repair weld: (a) transverse residual stress, (b) longitudinal residual stress.
P. Dong et al. / International Journal of Pressure Vessels and Piping 82 (2005) 258–269 261
potential crack growth at repair locations. A lumped-pass
weld simulation technique was used, that is without
considering moving-arc weld metal deposition effects. The
heat transfer analysis procedures were tuned to achieve the
same size of HAZ as a moving arc weld. As discussed in
[16], such a simplification tends to over-estimate the overall
residual stresses in weld repairs but ignores localized stress
concentration features associated with a moving-arc
[10,16]. Solid state phase transformation effects were not
modelled since they were judged to contribute to higher
Fig. 3. Predicted residual stresses transverse to the welding direction in a 16 mm th
repair depths 1/4t and 1/2t and repair lengths 152 mm and 305 mm (only 1/2-rep
order perturbations of the underlying residual stress
distribution [12] that are of less structural significance.
These simplifications were adopted to avoid employing a
much more refined 3D finite element mesh, given that the
intent of the investigation was to provide a conservative
estimate of the effects of repair depth, length, and width on
the overall residual stress distributions.
Predicted distributions of transverse residual stresses
introduced by a low heat input repair are shown in Fig. 3 and
illustrate some of the important residual stress features
ick and 5000 mm diameter carbon steel vessel, for repair widths w and 2w,
air weld length with stop position shown).
P. Dong et al. / International Journal of Pressure Vessels and Piping 82 (2005) 258–269262
associated with repair welds. The contour plots show a
through-wall tension-compression-tension distribution
along the length of the repair, but with significantly
increased tension on the repair side of the surface (i.e. the
outer surface) compared with the initial weld when
the repair length is relatively small (Cases 1–3 in Fig. 3).
As the repair depth increases from 1/4t (t is the base plate
thickness) to 1/2t (Case 1 versus Case 3), the difference in
the transverse residual stresses is mostly seen in the through-
thickness distributions. As the repair weld width increases
from 1 to 2w (Case 2 versus Case 3), the area subjected to
tensile residual stresses area is significantly increased,
where w represents the initial weld width. It is of interest to
note that the compressive zone beneath the repair starts to
disappear when the repair width, w, or repair depth is
increased. This is largely due to fact that an overall through-
thickness structural reaction induced by the increased repair
weld metal shrinkage force starts to dominate the residual
stress distribution. If the repair length is doubled from 152
to 305 mm (Case 2 versus Case 4), a marked change in the
transverse residual stress distributions can be seen, with
significantly reduced levels of tensile stress along the repair.
Further discussion on repair length effects is given in a later
section of this paper.
2.3. Repaired stainless steel pipe girth weld (35 mm thick)
Residual stresses introduced by finite length repairs to an
AISI Type 316H stainless steel pipe girth weld (35 mm
thick and 541 mm outer diameter) have been studied using
Fig. 4. Composite shell finite element model for multi-pass repair weldi
the composite shell modelling procedures described in
[15,16]. Three repairs of varying lengths, all symmetrically
positioned on the original girth weld centre-line, with a
repair depth 75% of the wall thickness from the outer
surface were analyzed, see Fig. 4. A moving-arc weld metal
deposition analysis for each of four lumped-bead passes was
employed with an assumed inter-pass temperature in the
range 170–200 8C. The direction of welding was alternated
between passes. The predicted variations in axial
(i.e. transverse) residual stress around one-half of the
circumference at the weld centre-line on the inner and outer
surfaces are shown in Fig. 5a and b. The repair weld lengths
(angular arc) are also marked on these graphs. The
magnitudes of the original girth weld residual stresses are
evident at circumferential positions far from the ends of the
20 and 558 arc-length repairs, that is about 230 MPa at the
OD and about 200 MPa at the ID surface. All the repairs
increase the axial residual stress levels within the repair
length. Beyond the ends of each repair, the stress falls
rapidly into compression before approaching the stress state
corresponding to the initial weld. Fig. 5a shows that the
shorter the repair the higher are the tensile residual stresses
at the outer surface along the length of the repair.
Fig. 6 shows the predicted through-thickness axial
residual stress distributions at the weld centre-line and
near the fusion line of the repair. The distributions are
highly non-linear due to multi-pass deposition effects and
very sensitive to axial position relative to the weld. The
profiles at both locations exhibit a membrane stress
(i.e. the uniformly distributed stress giving the same
ng simulation in a 35 mm thick, 541 mm OD stainless steel pipe.
Fig. 5. Comparison of predicted axial residual stress distributions along the
original/repair weld centre-line for three repair lengths (short—208,
medium—558, and long—1108 arc-lengths) in a 35 mm thick, 541 mm
OD stainless steel pipe (Fig. 4).
Fig. 6. Comparison of predicted through-thickness axial residual stress
distributions at repair mid-length for three repair lengths (short—208,
medium—558, and long—1108) in a 35 mm thick, 541 mm OD stainless
steel pipe (Fig. 4); (a) at Point A (HAZ), and (b) at Point B (weld centre-
line).
P. Dong et al. / International Journal of Pressure Vessels and Piping 82 (2005) 258–269 263
integrated force) that decreases as the repair length
becomes longer, and an overall bending character that is
tensile at the outer surface. Residual stress measurements
have been performed on a mock-up of the repaired pipe
[17] using the deep hole drilling technique. The measured
results for the through-thickness distribution at Point B in
Fig. 6 are shown in Fig. 7. The overall agreement between
the measured and predicted stresses is good despite the
limitations of the composite shell element model with
lumped-bead weld passes.
2.4. Repaired stainless steel pipe girth weld (19 mm thick)
Recently, high quality residual stress measurement data
for a 19.6 mm thick, 432 mm OD pipe girth weld mock-up
containing offset weld repairs have become available [11].
Prior to fabrication of this mock-up and the measurements
programme, residual stresses in this type of repaired
component were investigated using a 3D shell FE weld
simulation model by Dong et al. [10,18] using assumed
repair welding conditions. A model for a 19 mm thick,
541 mm OD pipe with a girth weld was constructed using
special composite shell elements having four layers (Fig. 8).
This allowed three layers to be used to simulate the
deposition of lumped-bead repair weld passes to a depth of
75% of the shell thickness. Structural symmetry along the
weld centre-line was assumed to simplify the analysis (i.e.
the repair offset was ignored). The pipe original girth weld
residual stress field, from a 2D FE simulation model,
was first mapped onto the 3D shell model giving an initial
axi-symmetric distribution of as-welded residual stress.
Local excavation of the repair groove process was then
represented using a layer activation/deactivation scheme;
this resulted in a re-distribution of the original weld residual
stresses. The repair weld simulation involved two steps; an
analytical thermal analysis to predict moving weld-arc
transient temperatures for the three consecutively deposited
lumped-beads, followed by an ABAQUS mechanical
analysis based on the temperature history. The direction of
welding was alternated between the three lumped-bead
repair passes. The analysis employed temperature depen-
dent material properties, annealing of historical plastic
strains on melting and isotropic hardening behaviour.
Fig. 7. Predicted through-wall residual stress distributions in the HAZ
(Point B in Fig. 6) at mid-length of a short (z208 arc-length) weld repair to
a 35 mm thick, 541 mm OD stainless steel pipe girth weld, compared with
measured stresses for centrally embedded 75% wall-thickness weld repair
to a 37 mm thick, 432 mm OD stainless steel pipe mock-up; (a) axial
residual stress, and (b) hoop residual stress.
P. Dong et al. / International Journal of Pressure Vessels and Piping 82 (2005) 258–269264
Predicted axial residual stresses on the outer surface of
the pipe are shown in Fig. 9 for three repair weld lengths.
The plots illustrate the general pattern of stress associated
with repair welds which is similar to that described above
for the repaired aluminium plate butt weld. For the repair
case with a z208 angular span, the overall distribution is
essentially the same as the one shown in Fig. 2a. As the
repair length increases, the high tensile axial (i.e. transverse)
residual stresses are predicted to become more concentrated
towards the repair ends with peak values occurring in
the area near the stop position. However, such stress
Fig. 8. Details of composite shell finite element models (3-pass and 6-pass)
used for simulating multi-pass repairs in a 19 mm thick, 541 mm OD
stainless steel pipe girth weld.
concentration end effects have not been observed in residual
stress measurements from the long (z608 angular span)
weld repair in the 19.6 mm thick, 432 mm OD pipe mock-
up [11]. It is open to debate as to whether the predicted end
effects are artefacts of the analysis procedure or whether a
more complete mapping of measured residual stress on a
circumferential-radial cross-section of the repair weld might
reveal a more complex pattern of stress.
Comparisons between the measured [11] and predicted
through-thickness distributions of hoop and axial stress in
the HAZ at mid-length of a short (z208 angular span) repair
are shown in Fig. 10. It is evident that both deep hole
drilling and neutron diffraction techniques provided
remarkably consistent measurements for the through-
thickness stress distributions. As for the pre-measurement
3D special shell model predictions, the agreement with the
measured data seems to be poor, at first glance. However,
the predicted membrane stress levels are similar and within
the repair depth (i.e. outer 2/3rd of the pipe thickness), the
overall trends between the predicted and measured can be
viewed as consistent, even though the magnitudes differ
significantly. A careful examination of the mock-up
fabrication conditions, measurement data, and the earlier
3D shell element study assumptions [10,18] was carried out.
The following are believed to contribute the discrepancies
shown in Fig. 10:
(a)
The actual weld repair was axially offset from theoriginal girth weld centre-line by 12 mm (see Fig. 10
inset), whereas the modelled repair was assumed to be
symmetrically aligned with the girth weld centre-line.
(b)
The repair weld passes were performed in anessentially continuous manner, only leaving enough
time for removing slag in between passes. This would
have resulted in the development of inter-pass
temperatures well above room temperature. In the
3D shell element model, each lumped-bead pass was
deposited when the previous pass had cooled down to
room temperature. Here it is worth noting that in the
35 mm thick pipe repair case discussed earlier, an
inter-pass temperature of 170–200 8C was simulated
and this resulted in a bending dominant type of
through-wall residual stress distribution near the
fusion line (see Figs. 6 and 7).
(c)
The actual welding conditions were not simulatedowing to the use of three lumped-bead weld passes in
the 3D shell FE model (instead of 12 passes actually
used). In general, lumped-bead weld simulation pro-
cedures inherently over-estimate the actual heat input
per unit time to a weldment.
To investigate observations (b) and (c), a sensitivity FE
analysis was performed by defining a 6-pass configuration
(see Fig. 8) in the same 3D shell element model [10,18] and
depositing each of the passes simultaneously, that is using
a lumped-pass procedure without moving-arc effects.
Fig. 9. Predicted repair weld axial residual stresses (from 3-pass model) on the outer surface of a 19 mm thick, 541 mm OD stainless steel pipe girth weld for
three repair lengths (short—208, medium—578, and long—1148 arc-lengths).
Fig. 10. Comparison of predicted through-wall residual stresses in the HAZ at mid-length of a short (208 arc-length) weld repair to a 19 mm thick 541 mm OD
pipe (see Figs. 8 and 9) with measured residual stresses in the HAZ (see inset) at mid-length of a short (z208 arc-length) weld repair in a 19.6 mm thick,
432 mm OD stainless steel pipe mock-up; (a) axial residual stress, and (b) hoop residual stress.
P. Dong et al. / International Journal of Pressure Vessels and Piping 82 (2005) 258–269 265
P. Dong et al. / International Journal of Pressure Vessels and Piping 82 (2005) 258–269266
This was achieved by depositing each of the 6 lumped-passes
at the melting temperature with a hold time corresponding to
the time for the weld torch to travel from end to end of the
short repair. This approximate procedure did not accurately
model the effective heat input of the repair passes, but was
adopted as a pragmatic approach. Each of the deposited
passes was allowed to cool down to 200 8C before the
deposition of the next pass. The new 3D shell model results
show a much closer correlation with the experimental
measurements, see Fig. 10. This finding demonstrates how
the predicted through-wall residual stress distribution at a
repair weld is highly sensitive to the details of the repair weld
simulation procedure, that is the number of passes, the
welding heat input and the assumed inter-pass temperature.
3. 2D cross-sectional FE models for repairs
The examples presented above illustrate that repair welds
introduce complex three-dimensional distributions of
residual stress. Nonetheless, if the important features of the
residual stress field for a specific repair scenario can be
identified then it is possible, and desirable, to tailor the finite
element analysis approach that is adopted to quantify the
stress conditions of interest. For example, if the overall
residual stress distribution is of interest, then simplified
analysis procedures using 2D cross-section or axi-symmetric
assumptions can be used with equivalent restraint conditions
applied to account for three-dimensional effects. However,
such 2D repair weld models only provide a residual stress
solution at a given location along the repair weld length.
Some of the issues associated with such simplified
approaches are clarified in the following case study.
Fig. 11. 2D cross-section finite element model under generalized plane strain condi
test panel shown in Fig. 1.
3.1. Case study:-repaired aluminium alloy butt weld
In the repaired aluminium alloy butt weld example
discussed in Section 2.1 above, a 3D special shell element
was used to capture the overall in-plane residual stress
characteristics (see Fig. 2). The corresponding local residual
stress distributions were analyzed using a 2D cross-section
model under generalized plane strain conditions, as
discussed in [16]. The 2D cross-section model is shown in
Fig. 11 for the repair weld. In this analysis, the cross-section
model was intended to approximate the residual stress state
corresponding to a unit slice from the mid-length of the
weld repair in Fig. 2.
The following assumptions were introduced. The line
corresponding to the point at the right end of the 2D model
in Fig. 11a remains as a line during welding, allowing
translation in both x and y directions. In this case, it was
convenient to use one element in the through thickness
direction and to introduce a triangular element for imposing
the displacement boundary conditions (see Fig. 11a) in the
form ux(t), uy(t), where t is the time from start of welding.
Secondly, a plane corresponding to the x–y plane of the 2D
model remains as plane, i.e. uzðtÞZaðtÞxCbðtÞyCcðtÞ;
where a(t), b(t), and c(t) signify the time-dependency of
these coefficients during welding and measure rotations of
the plane with respect to the x and y axes, and translation in
z, respectively. To obtain ux(t), uy(t), and uz(t), the special
shell element model [15], as used for generating the 3D
residual stress results shown in Fig. 2 [14] is particularly
effective. For the case shown in Fig. 2, ux(t), uy(t)
were obtained at a boundary node of the shell model at
the mid-length of the specimen. Note that in this process
tions and its relationship to a 3D shell element model of the aluminium alloy
P. Dong et al. / International Journal of Pressure Vessels and Piping 82 (2005) 258–269 267
the rotational term from the shell element model at the node
can be ignored for most applications. Otherwise, significant
mesh refinements in 2D cross-section models are typically
required in order to capture such rotation-induced shear
within the vicinity of the boundary. The function uz(t) was
obtained as relative displacements between two adjacent
planes (two parallel lines with a unit distance in between)
transverse to the weld direction in the shell model. After a
series of parametric studies was performed [19], it was
found that ux(t), uy(t), and uz(t) could be treated in the 2D
cross-section model as constants that correspond to the final
values from the welding simulation of the shell model. It is
worth noting that axi-symmetric conditions can be recov-
ered as one specific case in such a generalized cross-section
model by imposing an appropriate uz(t).
With the above approach, both the initial weld (Fig. 1a)
and the repair weld (Fig. 2) were analyzed using the 2D
cross-section model depicted in Fig. 11b. The residual stress
results are compared with X-ray measurements in Fig. 12
along the same cross section that was modelled. The
measured and predicted residual stresses on the top surface
of the specimen are plotted with respect to the distance
measured from the weld centre-line. The measured and
predicted longitudinal residual stresses compare reasonably
well with each other (Fig. 12a). The rapid reduction in the
predicted longitudinal residual stresses across the fusion
Fig. 12. Comparison of X-ray residual stress measurements and finite
element predictions using a 2D cross-section model (Fig. 11) with applied
restraint conditions derived from a 3D model: (a) longitudinal residual
stresses, and (b) transverse residual stresses.
boundary and inside the weld metal is due to the use of
under-matched filler metal (about 50% lower in yield
strength [14]). The discrepancies within this region can be
attributed to the resolution scale in the X-ray measurement
techniques and surface conditions due to the presence of the
weld bead profile. The effects of repair on the longitudinal
residual stress magnitude are not significant. As discussed
earlier, restraint conditions for the longitudinal residual
stress development are already high even under initial
welding conditions.
The predicted and measured transverse residual stresses
in the initial weld (see Fig. 12b) are of low magnitude
relative to the peak longitudinal stresses. The overall
agreement between the predicted and measured results is
evident. The cross-section model predicted that the
introduction of a repair significantly increased the trans-
verse residual stresses. However, it is worth noting here that
the measured transverse residual stresses tend to be higher
than the predicted values, but with an overall trend being
consistent with the predicted one. This suggests that the 2D
cross-section model tends to under-estimate the transverse
residual stresses in this case due to the inherent assumptions
at the boundary associated with the definitions of ux(t), uy(t),
and uz(t) discussed earlier. Examination of the aluminium
alloy butt weld specimens showed noticeable out-of-plane
deformations that were not captured by the linear defor-
mation assumptions described above. However, for thicker
sections such discrepancies are expected to be less
significant.
4. Discussion
Regardless of the overall component geometry (e.g. plate
structures versus pipes or vessels) and materials (aluminum
alloys versus stainless steels or carbon steels), the overall
distribution of residual stress distribution associated with
finite length weld repairs share the following invariant
features:
(a)
weld repairs increase the magnitude and importance oftransverse residual stresses along the repair compared
with the initial weld,
(b)
the shorter the repair length the greater the increase inthe transverse stresses, but for very long repairs the
transverse residual stresses within the central region of
the repair length approaches that of the initial weld,
(c)
tensile transverse residual stresses along the length ofthe repair sharply fall into compression beyond the ends
of the repair, and
(d)
the through-thickness variation within the repair isinfluenced by the repair width, repair length, heat input
per pass, and inter-pass temperature.
The above observations are based on either numerical
predictions or systematic measurements from a range of
P. Dong et al. / International Journal of Pressure Vessels and Piping 82 (2005) 258–269268
different applications. These important common features are
governed by the high restraint conditions typically associ-
ated with repair welding. Any deviations from these general
features can be attributed to the change in restraint
conditions associated with specific weld repair applications.
From the case studies presented in Sections 2 and 3, it has
been inferred that the welding thermal conditions (e.g.
number of passes, heat input and inter-pass temperature) are
important parameters in repair weld residual stress analyses.
This is because the mechanical restraint conditions between
passes can be altered noticeably and this should be
accounted for in performing residual stress analysis. For
example, Fig. 10 shows how the through-wall bending
component of stress is significantly changed by the assumed
welding conditions. Such sensitivity is typically not seen in
analyzing initial fabrication welds. Further investigations
are needed to establish appropriate pass lumping procedures
and their implications on an equivalent heat input for repair
applications.
5. Concluding remarks
Residual stress results from several weld repair case
studies have been presented and the important general
features of the repair residual stress fields identified. For
selected cases, predicted stresses have been compared
with detailed residual stress measurements and the
adequacy of the finite element simulation procedures
assessed. The following general conclusions can be
drawn.
1.
Finite length weld repairs increase the magnitude andimportance of transverse residual stresses along the
repair compared with the initial weld. Beyond the
ends of the repair the transverse stress sharply falls
into compression. The shorter the repair length the
greater the increase in the transverse stresses, but for
very long repairs the transverse residual stress within
the central region of the repair length approaches that
of the initial weld.
2.
Welding procedure related parameters appear to bemore important in analysing repair welds than in
initial fabrication welds. These include bead and pass
lumping, heat content of lumped-beads, inter-pass
temperature, as well as pass sequencing. This is not
surprising since the high restraint conditions typical
to repair welds can be altered by some of these
parameters, resulting in significant changes to the
through-thickness distribution of residual stress.
3.
Simplified 2D cross-section finite element modelswith applied restraint conditions can be used to
capture the general stress field at a specific point
along the length of a repair, but great care must be
taken with assigning the boundary conditions.
Acknowledgements
The authors acknowledge funding by British Energy for
some of the repair case studies on Type 316 stainless steel
girth welds. This paper is published with the permission of
British Energy Generation Ltd.
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