4 analysis of residual stresses at weld repairs

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: [email protected] (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.


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).


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).


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.


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 the
original 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 an
essentially 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 simulated
owing 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.



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


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 of
transverse residual stresses along the repair compared

with the initial weld,

(b)
the shorter the repair length the greater the increase in
the 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 of
the repair sharply fall into compression beyond the ends

of the repair, and

(d)
the through-thickness variation within the repair is
influenced 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


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 and
importance 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 be
more 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 models
with 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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4 analysis of residual stresses at weld repairs

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