weldon-porto-paper06-unott-residual stresses in welded p91 pipes -a0406.0402

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5th International Conference on Mechanics and Materials in Design

Chapter IV: Welds at High Temperature (WELDON) in Design 1

REF: A0406.0402

SIMULATION OF RESIDUAL STRESSES IN WELDED P91 PIPES

A. Yaghi1

, T.H. Hyde1

, A.A. Becker1*

, W. Sun1

,J.A. Williams2, and B. Pathiraj3 1School of Mechanical, Materials & Manufacturing EngineeringUniversity of Nottingham, Nottingham NG7 2RD, UK 2Independent Consultant, East Leake, Leicester LE12 6LJ, UK

3METSEARCH B.V., Netherlands

Email:(*)

[email protected]

SYNOPSIS

Residual stresses can be responsible for altering the performance of their engineering

components; therefore it is important to be able to predict such stresses. In this study the FEmethod has been applied to simulate residual axial and hoop stresses generated in the weld

region and heat affected zone (HAZ) of a P91 steel welded pipe. Both the pipe and

circumferential butt-weld are assumed to be axisymmetric. The outer diameter of the pipe is

145mm and its wall thickness is 50mm, the weld having 50 beads. The FE simulation

consists of a thermal analysis, revealing the temperature history of the FE model, followed by

a sequentially-coupled structural analysis, giving residual stress results. A user subroutine

within the ABAQUS FE code adjusts the temperature history of the FE model to match

certain welding conditions.

The thermal analysis has revealed temperature contours which indicate the size of the weld

region and the heat affected zone (HAZ). Residual axial and hoop stresses obtained from the

analysis are shown in the form of stress contours through the pipe wall thickness and stress

curves at the outside surface of the pipe. Trends of behaviour of residual stresses have

emerged for the set of preliminary material properties implemented in the FE analysis.

NOTATION

С specific heat capacity (kJ/kgK)

DFLUX distributed heat flux (W/m3)

E elastic modulus (Pa)

h heat transfer coefficient (W/m2K)

HAZ heat affected zoneI current (A)

PM parent metal

Q net line energy (J/m)

R i pipe inside radius (mm)

T pipe wall thickness (mm) or temperature (oC)

TSOFT softening temperature (oC)

U voltage (V)

v weld electrode speed (m/s)

V weld pass volume (m3)

WCL weld centre line

WM weld metalα coefficient of linear thermal expansion (1/K)



Porto-Portugal, 24-26 July 2006

Editors: J.F. Silva Gomes and Shaker A. Meguid 2

∆t duration of the triangular time function (s)

η arc efficiency

λ thermal conductivity (W/mK)

ν Poisson's ratio

σy yield stress (Pa)

1 INTRODUCTION

The process of welding is an integral manufacturing procedure in the production of many

engineering and structural components, having a direct influence on the integrity of the

components and their thermal and mechanical behaviour during service. Due to the high

temperatures introduced during welding and the subsequent cooling of the welded metal,

welding can produce undesirable residual stresses and deformations. Such stresses can be

simulated for the process of welding to delineate the ensuing residual stresses and

deformations and for use in the prediction of the behaviour of welded structures.Welded structures are an essential part of many buildings, bridges, ships, pipes, pressure

vessels, nuclear reactors and other engineering structures [1, 2]. Circumferentially welded

pipes are often used in oil transport systems and steam piping for conventional and nuclear

systems. Residual stresses are important in the consideration of cracking and fracture

problems in welded structures. Their evaluation can help resolve problems, for example,

related to intergranular stress corrosion cracking, hydrogen-induced cracking, stress relief

cracking and, to some extent, fatigue strength.

The numerical simulation of the process of welding can take place in two alternative ways [3].

Firstly, the complex fluid and thermo-dynamics local to the weld pool are modelled by

looking at the weld pool and the heat affected zone (HAZ). The conservation of mass,momentum and heat together with the latent heat and surface tension boundary conditions are

equated to represent the physical phenomena of the molten weld pool and thermal behaviour

of the HAZ. Secondly, the solid mechanics approach is adopted by modelling the global

thermo-mechanical behaviour of the weld structure, paying special attention to the heat

source. A variety of simplified heat source models can be used in the simulation of welding,

the accuracy of which relying on the theoretical and empirical parameters describing the weld

pool size and shape.

In their brief review of weld simulation, Teng and Chang [1] state that a thermomechanical

model was developed by Friedman [4] using the FE method to calculate temperatures, stresses

and distortions during welding; that elastoplastic FE computer programs were developed by

Muraki et al [5] to monitor welding thermal stresses and metal movement; that residual

stresses were estimated by Josefson [6] in a multi-pass weld and in a spot-welded box beam

with SOLVIA and ABAQUS, which are commercially available FE codes for non-linear

analyses; and that temperatures and stresses were analysed by Karlsson [7] and Karlsson and

Josefson [8] in single-pass girth butt welding of carbon-manganese pipe using the FE codes

ADINAT and ADINA.

Brickstad and Josefson [9] simulate residual stresses due to welding using the ABAQUS FE

code consisting of two main parts, thermal and structural. They use a technique called

‘element birth’ to represent the laying of weld beads to avoid any displacement or strain

mismatch at the nodes connecting the weld elements to those of the base material. Fanous et

al [10] have introduced another technique for metal deposition using element movement.Temperature dependency of material properties is taken into account in the latter two papers.





Dong [11] performed FE analyses on stainless steel and carbon steel welded pipes with

different geometries, obtaining a range of through-thickness residual stresses. He has

conducted a careful parametric investigation using his research results and other data

published in literature to find characteristic trends for through-thickness residual stresses due

to welding.This paper describes the numerical methodology for obtaining residual stresses in a multi-pass

butt-welded P91 steel pipe using the techniques as described in references [12] and [9],

starting with an FE thermal analysis and ending with an FE structural analysis, sequentially

coupled and modified by a user’s subroutine to manipulate the temperature field in the

material. The results are then presented in the form of temperature contours and residual axial

and hoop stresses throughout the pipe thickness. A specific set of preliminary material

properties have been generated for P91 steel. Although in reality welding is a three-

dimensional procedure, it is often considered sufficient to represent a pipe weld using an

axisymmetric FE model, which has been adopted throughout this work.

2 FINITE ELEMENT ANALYSIS

FE weld simulation in principle consists of a thermal analysis, which represents the thermal

process during welding culminating in revealing the temperature contours associated with

welding, followed by a structural analysis which is based on the thermal findings. The

structural analysis takes the temperature contours, made available by the thermal simulation,

and uses them as input data to calculate a range of stress contours at the end of the analysis

which remain in the modelled component as residual stresses. To conduct this type of FE

analysis, a sequentially coupled thermal-stress analysis is adopted since the stress or

displacement solution is dependent on a temperature field with no inverse dependency [13].

For accurate simulation of the temperature history it is important to use a user subroutine, anABAQUS FORTRAN program, to adjust the temperature values at certain times and

locations before being utilised in the structural analysis.

2.1 Model Geometry

The simulation of the process of welding has been performed on P91 steel pipes with outer

diameter of 145mm and wall thickness of 50mm, the weld having 50 beads. The modelled

weldment consists of two P91 steel pipes circumferentially welded with P91 weld metal with

slightly different material properties. The types of welding which have been modelled using

the FE technique are the gas tungsten arc welding (GTAW) for weld beads 1 to 7 and the

shielded metal arc welding (SMAW) for weld beads 8 to 50. The sequence of laying the weld passes is shown in Figure 1, which has been drawn by the welder. The welding specifications

are provided in Table 1. In the FE simulation, the root bead (first bead) protrudes by 1mm

and the last layer of beads (weld crown) protrudes by 5mm.

Although in reality welding is a three-dimensional procedure, it is often considered sufficient

to represent a pipe weld with an axisymmetric FE model [8, 9, 14]. In addition, two-

dimensional simulations are much faster and easier to perform; therefore the methodology

described here is based on an axisymmetric model. The corresponding FE mesh is shown in

Figure 2.

The process of welding includes the melting of metal and then allowing it to cool down and

solidify to form beads in the weld region connecting both parts of the steel pipe. Each bead in

this work is considered to be a pass, so that the number of passes in the FE model is equal to

the number of beads in the simulated weld. It is also stated to be acceptable sometimes to





simplify the model and assume that a pass can represent more than one bead [8, 9].

The FE mesh models a welded pipe which has the weld crown machined off at the end of the

welding process. This is represented in the numerical simulation by removing the FE

elements which make up the weld crown at the end of the FE structural analysis. This results

in the residual stresses redistributing in order to allow for such a geometric change.

Table 1 Welding Process Specifications (*see sketch of weld sequence in Figure 1)

Figure 1-Weld sequence sketch of modelled single-U multi-pass butt-weld of a P91

steel pipe, supplied by the welder .

Figure 2-Axisymmetric FE mesh of the modelled single-U multi-pass butt-weld of a P91 steel pipe





2.2 Material Properties

Detailed thermal and mechanical property data are needed for the material cast being

considered, the weld metal and any structures deemed important within the weldment. As

these data had not been available at the inception of this FE study for the P91 pipes, a general

P91 parent metal data base has been generated from the available literature and, where

possible, has been modified to take some account of any material data for the actual cast and

the weld metal. For this work, a two material weldment model has been assumed, namely

weld metal, WM, and parent metal, PM, only. The analysis method also allows for a HAZ

region, but no allowance has been made for properties in this region. The basic parent metal

data have been generated as described in a previous publication [12].

To make some allowance for the actual material mechanical properties, the basic P91 strength

curves have been proportioned using the cast certificate data for the parent material and using

the manufacturer’s data for the weld metal over the complete temperature range. Although

not an ideal method, this does give a reasonable view of the data for the actual cast and a

minimum correction for the weld metal data. The latter is a lower estimate as there is aminimum strength requirement for the weld metal, whereas the actual weld metal value is

generally higher.

A set of mechanical and thermal material property data is shown in Figure 3. It should be

noted that properties are quoted for temperatures in excess of the melting point of

approximately 1500oC; the low strength values are generally to allow efficient operation of

the FE analysis.

Figure 3 Mechanical and thermal material properties, for the parent and weld materials, against temperature,used in the FE analysis of the P91 steel pipe

No explicit account is taken of any phase transformation that will occur other than the effect

that will be incorporated within the coefficient of thermal expansion values where a non

linearity occurs near the expected transformation temperature.

In addition to the properties given in Figure 3, a latent heat capacity of 260 kJ/kg has been

assumed together with a solidus temperature of 1420oC and a liquidus temperature of 1500oC.

The type of hardening in the ABAQUS input file for the structural analysis has been specified

to be KINEMATIC, which has been used throughout the FE analysis. The applied ratio of the

hardening modulus to the elastic modulus for the temperature range 20oC to 650oC is 0.018

and it is 3.0×10-4 for the temperature range 650oC to 2000oC. The density of the material has been assumed to be constant at a value of 7770 kg/m3.

0

1

2

3

4

5

6

0 500 1000 1500 2000

Temperature (oC)

M a t e r i a l p r o p e r t i e s f o r P 9 1

E (1.0E+11 Pa)

σy(PM) (1.0E+8 Pa)

σy(WM) (1.0E+8 Pa)

α (1.0E-5 /K)

ν (1.0E-1)

λ (1.0E+1 W/mK)

С (kJ/kgK)





2.3 Thermal Analysis

In the thermal analysis, the welding process is primarily simulated by applying a distributed

heat flux to the weld elements and is a triangular function of heat per unit volume against

time. The heat flux is assumed to reach its peak value from zero in a straight line during the

up-ramp of the triangular time function, followed by a straight line from its peak value back

to zero, producing the shape of an isosceles triangle as the down-ramp reaches zero, as

detailed in section 3.2. From that point in time the heat flux remains zero until the end of the

particular weld pass 360o cycle, during which time the weld is allowed to cool down, until the

next weld pass cycle begins. Once the last pass has been laid enough time is prescribed for

the weld to cool down to ambient temperature. Then the whole model is gradually heated up

to a desired service temperature by applying a constant distributed heat flux to all the

elements of the model. The distributed heat flux, DFLUX, is given by

DFLUX = U⋅I⋅η/V (1)

where U is the voltage, I is the current, η is the arc efficiency and V is the weld pass volume.

The triangular time variation of the heat flux corresponds to the approach and passing of the

welding torch. The weld pass volume, V, which is a three-dimensional parameter, is related

to the duration ∆t of the triangular time function by assuming that ∆t is equal to the time taken

by the weld electrode to move around volume V, causing it to melt, as it travels around the

circumference at speed v. The net line energy is given by

Q = U⋅I⋅η/v (2)

From equations (1) and (2), the distributed heat flux is given by

DFLUX = Q⋅v/V (3)

The value of V can only be estimated, since it relates to the effective volume of weld material

directly influenced by the heat flux in the axisymmetric simulation. As a guideline, Brickstad

and Josefson [9] suggest that a fraction of the circumference equal to 1/16 to 1/2 of a radian

can be used to estimate V. A provisional simulation is performed with a first estimation for

DFLUX. The temperature results are then checked after the thermal analysis to verify that the

molten zones throughout the analysis are realistic and the temperatures reached in the heat

affected zone (HAZ) are reasonable. The HAZ is typically 2 to 4mm from the weld metal.

Another important indication which is used to modify DFLUX is the distance of penetration

of the weld metal into the parent material. This is assumed to be 1mm which is confirmed bythe welder. If the temperature results are not satisfactory, the value of the heat flux is adjusted

accordingly. For any set of DFLUX values for the weld passes produced by the same welding

process, the area under the heat flux triangular function must remain constant (DFLUX⋅∆t/2),

signifying a constant total amount of thermal input energy per unit volume.

In addition to the use of latent heat properties to describe heat effects relevant to the molten

metal of the weld pool, thermal conductivity for molten metal is doubled to allow for its

convective stirring effect [9]. The thermal boundary conditions are taken into consideration

by allowing for convection and radiation and their combined effect to be represented by

specifying an equation for the temperature-dependent heat transfer coefficient [9].

One of the most prominent features of the current FE simulation is the use of a techniquecalled “element birth”, which allows the structural analysis to be conducted without





incompatibility problems. The thermal aspect of the element birth technique is to change the

thermal conductivity of the relevant part of the FE mesh corresponding to the weld passes that

have not been laid yet. In the thermal analysis, the elements which correspond to the weld

passes before being laid are given a value for thermal conductivity equivalent to that of air.

At the time of application of each weld pass, the thermal conductivity is made to change fromair value to that of steel.

The other material properties relevant to the thermal analysis are the density of the metal, the

specific heat capacity, the latent heat capacity and the solidus and liquidus temperatures. The

thermal conductivity and thermal heat capacity are usually temperature dependent. The FE

continuum solid element type used in the thermal analysis is an 8-node quadratic

axisymmetric diffusive heat transfer quadrilateral. The FE mesh also contains 6-node

quadratic axisymmetric diffusive heat transfer triangular elements for geometric reasons.

The weld simulation consists of a set of time steps, each STEP representing the application of

a weld pass. The application of each pass includes a series of time increments. The

maximum allowable change in temperature in an increment has been set at 40o

C.The final set of values for DFLUX for the FE model is shown in Figure 4, the time on the x-

axis being the time from the beginning of each weld application for every weld pass. The

area under any one of the triangular curves is constant as long as the type of welding remains

the same. The triangular curves correspond to two different types of welding process, which

is reflected in the constant triangular area for the GTAW of the first seven weld beads and

another constant area for the SMAW of the remaining 43 weld beads.

Figure 4 - DFLUX against time for five weld pass depositions, time being depicted from the

beginning of each weld pass application

As for the boundary conditions during the thermal analysis, convection and radiation are both

taken into consideration and their combined effect is represented in the following two

equations [9] for the temperature-dependent heat transfer coefficient, h.

h = 0.0668⋅T (W/m2 oC) when 0 ≤ T ≤ 500oC (4)

h = 0.231⋅T – 82.1 (W/m2 oC) when T ≥ 500oC (5)

The time duration of each STEP is controlled in order to keep the interpass temperature

within the practical temperature range between 250 and 300o

C. The interpass temperature has been checked for each STEP and confirmed to fall within this temperature range.

D F L U X ( W / m 3 )

0.0E+00

1.0E+10

2.0E+10

3.0E+10

4.0E+10

5.0E+10

0 2 4 6 8 10 12 14 16

Time (s)

Pass 1

Pass 2

Pass 7

Pass 10

Pass 45





2.4 Structural Analysis

The thermal analysis processes DFLUX as the input data and delivers a set of temperature

contours as the output file. The structural analysis uses the temperature distributions obtained

from the thermal analysis as input data. They are read by the structural input file and then

sent to a user subroutine for amendment before being processed to finally provide a structural

output file containing the required residual stresses, strains and deformations.

The element birth technique has been utilised in the structural analysis to avoid the

incompatibility which would be introduced due to the thermal analysis producing strains in

the parent material which would not be compatible with the strain-free weld elements during

their application to bring them to existence in the structural analysis. The incompatibility

would be due to the weld material being applied in the structural analysis to a region which

had already experienced significant strain caused by high temperatures. In order to avoid this,

the FE mesh including all the elements are generated before the FE analysis is carried out, and

then the weld elements are kept at an assumed softening temperature, TSOFT, until the

moment of weld application in the structural analysis. At TSOFT, the Young’s Modulus andthe yield stress of the material are so low that the weld can be applied without suffering from

any stresses. The formation of stresses begins only when the material starts to cool down.

The FE continuum solid element type used in the structural analysis is an 8-node biquadratic

axisymmetric stress/displacement quadrilateral with reduced integration. A 6-node quadratic

axisymmetric stress/displacement continuum triangular element has also be used in certain

parts of the mesh for geometric reasons.

3 FINITE ELEMENT RESULTS

3.1 Temperature Contours

The temperature contours should be examined at the time of peak temperature, or just after,

occurring in every time step representing each weld pass. The temperature contours indicate

the region experiencing melting and the zones which are heat affected.

In this section, typical examples of temperature contours are presented. The temperature

contours are shown in the FE model when peak temperatures are reached in weld beads 1, 15,

35 and 50 in Figures 5, 6, 7 and 8 respectively. Penetration into the parent metal causing its

boundary near the HAZ to melt can be seen in the figures, which demonstrate that the

penetration distance is consistent with a realistic expectation of around 1mm.

The HAZ is assumed to experience at least a temperature between 800oC and 900oC for the

P91 steel material in consideration, as pointed out in a previous publication [12], but it can

reach significantly higher temperatures in certain parts.

The peak temperatures in the HAZ in the FE model are within the wider range of 800 –

1200oC and are mainly between 800oC and 900oC as has been suggested before [12], but they

reach higher values at certain nodal points, as would be realistically expected in a typical

welding experience, particularly at the outer and inner surface positions.

The volume of the weld beads is not entirely constant. The metal volume surrounding the

weld beads, which acts as a heat sink, is also not constant. This is true particularly towards

the beginning and end of the welding procedure. In addition, the distance between the beads

and the defined HAZ line is variable. These geometric and thermal considerations contributeto the variable nature of the peak temperatures in the HAZ.





Figure 5 Temperature contours (oC) for the FE model during the laying of the first weld pass.

Figure 6 Temperature contours (oC) for the FE model during the laying of the fifteenth weld pass.

Figure 7 Temperature contours (oC) for the FE model during the laying of the thirty fifth weld pass.





Figure 8 Temperature contours (

o

C) for the FE model during the laying of the fiftieth weld pass.

3.2 Residual Stress Contours

Residual stresses obtained from the structural analysis have been plotted to show sections of

the FE models, at the weld region, exhibiting the most relevant stresses. Figures 9 and 10

depict residual axial and hoop stress contours respectively. Both these are tensile at the

outside surface and compressive at the inside surface in the weld region and HAZ. The crown

part of the weld has been effectively removed at the end of the FE structural analysis to

simulate the case of the weld crown being machined off once the process of welding had been

completed. Although the corresponding part of the FE mesh is still shown in Figures 9 and

10, in the numerical simulation no material exists in the weld crown at the end of the FEanalysis.

Figure 9 Residual axial stress contours (N/m2) at the FE weld region and HAZ.





Figure 10 Residual hoop stress contours (N/m2) at the FE weld region and HAZ.

3.3 Values of Residual Stresses

Figures 11 and 12 present residual axial and hoop stresses, respectively, plotted along a

straight line on the outer surface in the axial direction, the midpoint of which coincides with

the weld centre line (WCL). The stresses shown are those after the weld crown has beenremoved. The length of the line along which the residual stresses are plotted is just over three

times the width of the weld at the outside surface. It is also equal to the width of the mesh

along the outside surface of the pipe shown in Figures 2, 9 and 10.

The residual axial stress curve in Figure 11 shows that, at the outside surface of the pipe, the

weld region has areas with a tensile stress magnitude significantly higher than that occurring

in the parent metal also on the outside surface of the pipe. The stress is tensile with the

exception of a moderate dip in the compressive range only at the interface between the weld

metal and the parent material.

The residual hoop stress curve in Figure 12 shows that, at the outside surface of the pipe,

except at the interface between the weld metal and parent material, the weld region has a hoopstress which is significantly higher than that found in the parent metal on the outside surface

of the pipe in the pipe section shown in the figure. In addition, the surface stresses are all

tensile.

4 DISCUSSION

Residual stresses have been numerically calculated for an axisymmetric single-U butt-weld

having 50 beads in a P91 steel pipe. For the purpose of being used in the FE analysis, a

general P91 parent metal data base has been generated from the available literature and, where

possible, has been modified to take some account of any material data for the actual cast andthe weld metal.The temperature contours have been checked during the deposition of every





weld bead and typical examples have been shown in Figures 5-8. The molten zones, weld

penetration distance into the parent metal and the temperature range at the HAZ have all been

checked and they comply with general thermal expectations. The residual axial and hoop

stresses are depicted through the pipe wall thickness (Figures 9 & 10) and on the outside

surface at the weld region and the HAZ (Figures 10 & 11), where both residual stresses aretensile at the outside surface and compressive at the bore.

Figure 11-Residual axial stress curves (N/m2) for the FE model against distance (m), alonga straight line on the outside surface in the axial direction, the midpoint of which coincides

with the WCL, after removing the weld crown.

Figure 12-Residual hoop stress curves (N/m2) for the FE model against distance (m), along a

straight line on the outside surface in the axial direction, the midpoint of which coincides with

the WCL, after removing the weld crown.





Before discussing the specific results obtained here, it is helpful to briefly consider effects of

residual stress on weld performance; thereby allowing a structured view of the calculated

stress effects.

The influence of residual stress on integrity is a complex problem. For example, the effects of

residual stress are generally more critical when they are linked with metallurgical features

such as low ductility or with processes/mechanisms that contribute to ductility reductions.

This would seem to be intuitively correct as the locked in elastic strains which generate the

residual stresses will be of the order of the yield strains as a maximum. Furthermore, failure

will be initiated when the total strain exceeds the local ductility, if a ductility criterion for

failure is used, and thus interaction of these stresses with the low ductility or embrittled

regions will give the largest effects. In addition, cracks/damage will tend to be driven by

stresses normal to the maximum stress axis, and thus crack orientations will often identify the

form and orientation of the driving stresses.

Two typical examples of mechanisms can be identified that are residual stress sensitive

although others will exist. These examples are outlined below.

• Residual stresses in welds will be present after the initial fabrication and, in addition, the

HAZ structures will be in an un-tempered state with a lower ductility. Before use, the

welds are normally post weld heat treated, PWHT, to both relax the residual stress by creep

and to temper the HAZ structures to improve the local ductility. However, there are certain

materials which, when welded, generate very low ductility structures within the HAZ

which can initiate damage during the fabrication and the early stages of PWHT. Examples

are the stress relief cracking can occur in ferritic CrMoV welds welded with ferritic

2.25Cr1Mo weld metal, [14] and to a lesser extent in P91 welds and hydrogen cracking in

P91 weldments. Other examples exist in, for example, AISI 347 austenitic stainless steel

welds, [15] although others exist.• The former effects are the formation of low ductility coarse grained un-tempered Bainite in

the HAZ [14], or coarse grained regions adjacent to the weld metal interface but in the

weld metal which had been poorly post weld heat treated [14]. Thus, residual stress can be

a contributing factor for the nucleation of damage in the low ductility regions of the weld.

This damage can then grow during service under the action of the operational stresses, for

example pressure and system. Thus, the position of the maximum stresses relative to the

outer surfaces will be important as this can influence the nucleation of damage and the ease

of detection, for example outer surface damage is always easier to detect than that on the

bore, and the orientation, hoop or axial stress driven.

With this in mind, the residual stresses shown in Figures 9-12 can be considered and thelocation of the peak tensile stresses can be observed to try to correlate it to any field data

about cracked or damaged P91 pipes in power plants. The peak residual tensile stresses

appear at the outside surface for both axial and hoop stresses suggesting that any low ductility

regions within the weld metal will be sensitive to cracking during post weld heat treatment,

PWHT, and any cracking will generally occur towards the outer surface. Similar effects could

be expected within the HAZ region based on these calculations although the HAZ properties

are not specifically included within the FE analysis. This could make the detection of cracks

or damage a more achievable field task, since the outside surface seems to be the area at the

highest risk of damage.

The above inference has been made by assuming that solid-state phase transformation (SSPT)is not required to be explicitly included in the FE simulation of the welded pipe although this





transformation effect is implicitly included within the coefficient of thermal expansion term.

However, it has been demonstrated that the residual stress field can be significantly

influenced by explicitly allowing for SSPT during the numerical simulation of a multi-pass

butt-welded modified 9Cr-1Mo steel pipe [16], in which residual axial and hoop stresses both

have kept their general shape but the magnitude of their tensile stresses have substantially been reduced, at some peak locations even changing from tensile to compressive.

Although this current study provides a clear description of numerically predicted residual

stresses in welded P91 steel pipes, it is important for completion to explicitly allow for SSPT

in the FE analysis, which will be the subject of a future publication.

5 CONCLUSIONS

• The FE study described here presents the methodology of numerically simulating residual

stresses in an axisymmetric single-U multi-pass butt-weld of a P91 steel pipe, predicting

residual stresses through the pipe wall thickness, taking temperature dependency of material properties into consideration but without explicitly allowing for solid-state phase

transformation.

• Residual axial and hoop stresses in the P91 pipe weld are tensile on the outside surface and

compressive on the inside surface of the pipe. The peak residual stresses are close in

magnitude to the yield stress values for the relevant materials as expected.

Acknowledgements:

The authors wish to acknowledge the EU financial support through a WELDON project

(GRD2-2000-30363).

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