Nuclear Engineering and Design 197 (2000) 239–247

Simplified analysis of shrinkage in pipe to pipe butt welds�

Chakrapani Basavaraju *Bechtel Corporation, 9801 Washingtonian Bl6d., Gaithersburg, MD 20878, USA

Received 25 August 1999; received in revised form 2 November 1999; accepted 9 November 1999

Abstract

Generally some shrinkage is typical of butt welding of pipes. Shrinkage due to butt welding could be morepronounced and significant in thin wall stainless steel pipes because the thermal expansion coefficient is roughly oneand half times that of carbon steel. An axisymmetric finite element evaluation of hoop shrinkage associated withcircumferential butt welds in thin wall stainless steel pipes was performed. Actual shrinkage data for a larger (24 in.diameter, 0.375 in. wall thickness) pipe and a smaller (4 in. diameter, 0.237 in. wall thickness) pipe were utilized. Theresults indicate that very localized residual stresses in excess of yield strength produced during cooldown of metal inthe weld and heat affected zones cause redistribution of the stresses. A simplified elastic–plastic analysis approachwas developed with adjustments for section modulus and Poisson’s ratio, and the strains due to radial shrinkage werecalculated for inside and outside surfaces of the pipe at the weld center line. From the strain point of view, the strainvalues in the circumferential direction were about 1.4% for the larger size pipe and 3.4% for the smaller size pipe. Thestrain values in the axial direction were 2.5% for the larger pipe and 5.9% for the smaller pipe. It is concluded thatthese levels of strains are not detrimental in nature. However, for the smaller pipe they are on the high side and itis recommended not to use the pipe for elevated temperature service. Residual stresses were also calculated for insideand outside surfaces of the pipe at weld center line using a simplified elastic–plastic approach and a bilinearstress–strain curve and compared with published data indicating a general agreement. © 2000 Elsevier Science S.A.All rights reserved.

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1. Introduction

1.1. Background

Welding is the most commonly used process forjoining structural components, piping, and pres-sure vessels. Even though there are numerousadvantages associated with butt welding such as

being more economical, requiring less space, andproviding a better seal than bolted joints, etc.,there are areas of concern due to residual defor-mations. One of the most difficult problems en-countered in fabrication by welding is distortion.This is caused by concentrated heat input duringthe welding operation and the inherent stiffness ofthe structure itself or external restraints. The de-formations and the associated residual stresses arehighly complex and are influenced by a multitudeof parameters of the weld process such as heat

� ASME Pressure Vessels and Piping Conference (PVPC97)* Tel.: +1-301-417-4426; fax: +1-301-670-0297.E-mail address: cbasavar@bechtel.com (C. Basavaraju)

0029-5493/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved.

PII: S0029 -5493 (99 )00302 -7

C. Basa6araju / Nuclear Engineering and Design 197 (2000) 239–247240

input, number of passes, material properties,torch speed, etc. Generally, some shrinkage istypical of butt welding. Shrinkage due to buttwelding could be more pronounced and signifi-cant in thin wall stainless steel pipes than incarbon steel pipes because of the higher thermalexpansion. Thin wall pipes are more flexible andthe heat affected zone is larger.

Hsu (1977) investigated multi-pass weldingprocess of a 4 in. pipe using finite elementmethod to determine residual stresses and themaximum accumulated plastic strains. Rybickiet al. (1977) correlated residual stresses in girthbutt welded pipes obtained from finite elementanalysis with data from strain gage measure-ments. Mohr (1996) estimated internal surfaceresidual stresses in girth butt welded steel pipe.Michaleris (1996) computed residual stresses forcircumferential girth welds on thin and thickwalled pipes for single and double-V type weldjoints using thermo-elastic–plastic analyses. Dur-ing the welding process, the weld metal and aportion of the parent metal adjacent to it aresubjected to a considerable change in tempera-ture, being raised to molten state and loweredagain to that of the atmosphere. During thecooldown and solidification, the molten materialwill tend to shrink and pull all other materialwith it when shrinking. According to the struc-tural conditions, the parent material will eitherfollow the shrinking movement of the moltenmetal resulting in distortion or shrinkage, or itwill fully or partially resist distortion resultingin residual stresses. After the welding process,tensile residual stresses may develop in the weldsand the heat affected zones (HAZ).

In the case of girth welded pipes, distortionand the residual stresses are affected by the pipediameter, the pipe thickness, and the size of theweld bead. Girth welds generally lead to hightensile residual stresses on the inside surface ofthe pipe, (Ando, 1980; Fox, 1980). Tensile resid-ual stresses are known to be a contributing fac-tor for stress corrosion cracking in chemicalrefinery pressure equipment and power piping(Boswell and Kim, 1996). Rybicki et al. (1982)showed that thicker pipes generally have lesstensile or compressive residual stresses on the

inside surface of the pipe. In the case of residualstresses, the major concerns are linked to struc-tural performance (i.e. fracture, fatigue, creep,corrosion, stress corrosion cracking, etc.) (Gor-don, 1996)). Hou et al. (1996) stated that athorough understanding of the effects of weldinduced residual stresses on the near-tip fields ofcracks in welds and HAZ is critical for thestrength and life expectancy of the welded struc-tures. Intergranular stress corrosion cracking(IGSCC) is also influenced by the presence ofhigh tensile stresses.

1.2. Input data

Considering the shrinkage data for the buttwelded stainless steel pipes to be somewhat ex-cessive, the field requested an engineering assess-ment of two different sizes of girth butt weldedpipes for disposition. The measured contours ofweld shrinkage were supplied by the field fortwo different pipe sizes. The pipe sizes were 24in. Sch 20 butt welded to 24 in. Sch 20 pipeand 4 in. Sch 40 butt welded to 4 in. Sch 40.The pipes were butt welded using two passesutilizing arc welding process. Preheating was60–120°F if below 32°F and there was no postweld heat treatment done. Radial shrinkageswere measured using contour gage. The dataconsisted of contours along the axis of the pipe.For each axial location, the shrinkage measure-ments were made at eight circumferential loca-tions (45° apart) for 24 in. pipe and fourcircumferential locations (90° apart, 12, 3, 6 and9 O’ Clock positions) for 4 in. diameter pipe.The shrinkage is maximum at the weld centerline and decays as the axial distance from theweld center line increases. Within the toleranceof measurement accuracy (91/48 in.), the read-ings around the circumference are uniform al-lowing us to use an axisymmetric assumptionfor shrinkage. A schematic of butt welded pipewith radial shrinkage around the weld region isshown in Fig. 1. The pipe parameters and the(average value of four or eight measured cir-cumferential readings) radial shrinkage (d) atthe center line of the weld are presented inTable 1.

C. Basa6araju / Nuclear Engineering and Design 197 (2000) 239–247 241

1.3. Approach

The strain values were computed for buttwelded stainless steel pipes at the center line of theweld based on a simplified elastic–plastic ap-proach, incorporating the measured shrinkagedata at the center line based on a paper byBasavaraju (1997). The computed inelastic strainvalues are compared with the criteria presented inASME Code case N-47 (ASME, 1995a) for ac-ceptability. ASME Code case N-47 is used herefor guidance. Utilizing a simplified elastic–plasticanalysis and a bilinear approximation for thestress–strain curve of the material, the residualstresses at the center line of the butt weld wereestimated. The residual stresses were comparedwith published results. The approach outlined inthis paper is only applicable to stresses and strainsin thin wall pipes with approximately axisymmet-ric shrinkage.

2. Elastic analysis

2.1. Simplifications

The subject of weld residual stresses and strainsis extremely complex and hence some simplifica-tions, approximations and assumptions are to bemade. Since the measured maximum radialshrinkage is at the center line of the butt weld, thestresses and strains are postulated to be maximumat this location. Tensile residual stresses areknown to be a contributing factor for stress cor-rosion cracking and failure of pressure equipmentand piping. Therefore, the primary interest andarea for focus of this paper is the weld center line.A commonly made assumption is that the residualstresses and deflections of girth welded pipes areaxisymmetric. The shrinkage data shows that theradial shrinkage is not perfectly axisymmetric butis fairly close to being axisymmetric.

Fig. 1. Schematic showing shrinkage in butt welded pipe.

Table 1Pipe parameters and maximum radial shrinkage at weld center line

Do (in.) d/td (in.)Do/tMaterial R (in.)Pipe size t (in.)

0.16936411.81250.375 0.45152424 in. Sch 20A312 TP 3042.1315 19A312 TP 304 0.07294 in. Sch 40 0.30764.5 0.237

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Table 2Material properties for A312 TP304 stainless steel

E=28.3×106Young’s modulus of elasticitypsi

Poisson’s ratio for elastic analysis m=0.3Yield strength Sy=30 ksi

Su=75 ksiTensile strength=35%% Elongation(longitudinal)ou=0.3525% (transverse)ou=0.25m=0.5Poisson’s ratio for elastic–plastic analysis

(based on constancy of volumecondition)

Fig. 2. Concentrated axisymmetric load on a long thin walledcylinder (p lb in.−1 of circumference).

imum radial shrinkage) of d at the center line ofweld (Fig. 2). The expressions for circumferential(hoop) and longitudinal stresses and strains at thecenter line of the weld for inside and outsidesurfaces of the pipe based on formulations fromcase c15 table c29 of Young (1989) are shownin Table 3. The strain results from the elasticformulation are adjusted for plasticity effects anda simplified elastic–plastic approach wasdeveloped.

3. Simplified elastic–plastic analysis

3.1. Plastic strains

Since the elastic analysis showed that thestresses exceeding yield stress are attained due to

2.2. Finite element analysis

As an initial effort, an axisymmetric finite ele-ment model using ANSYS (1989) STIF11 shellelement was constructed for 24 in. Sch 20 pipe.The room temperature material properties for A312 TP 304 were extracted from ASTM (1995),ASME (1995a,b,c) and are shown in Table 2. Themeasured displacement profile of the radialshrinkage for a distance of 3 in. on either side ofthe center line of butt weld was applied to themodel and a linear elastic static analysis wasperformed. The model was 24.5 in. long axiallyand consisted of 77 nodes and 76 elements. Meanradius is R=11.8125 in. and wall thickness ist=0.375 in. The maximum shrinkage applied atthe center line of the weld is 0.1693 in. radiallyinward at the midlength of the model. The in-plane rotation applied at the center line of theweld is zero. One end of the model is fixed in theaxial direction.

2.3. Elastic strains

The results of this preliminary elastic finite ele-ment analysis showed that elastically calculatedstresses reached values of several thousand psiwhich simply indicates that plastic deformationhas occurred. The strains and elastic stresses atthe center line of the weld matched the results fora cylinder with axisymmetric concentrated radialload with the required load magnitude p (lb in.−1

of circumference) to produce a deflection (=max-

Table 3Expressions for stress and strain (elastic basis) at weld centerlinea

Bending strainMembrane strain

oum=−d/Ri oub=0ououm=−d/R oub=0o

iom omm=m d/R omb=+(d/R)[3(1−m2)]omb=−(d/R)[3(1−m2)]omm=m d/Ro

Bending stressMembrane stress

i sum=−Ed/R sub=+(Emd/R)[3/(1−m2)]suo sum=−Ed/R sub=−(Emd/R)[3/(1−m2)]

smb=+(Ed/R)[3/(1−m2)]smm=0ism

o smm=0 smb=−(Ed/R)[3/(1−m2)]

a i, Inside surface at center line of weld; o, outside surface atcenter line of weld; su, ou, stress, strain in the hoop orcircumferential or transverse direction; sm, om, stress, strain inthe axial or longitudinal or meridional direction; Poisson’sratio m=0.3.

C. Basa6araju / Nuclear Engineering and Design 197 (2000) 239–247 243

weld shrinkage, a simplified elastic–plastic analy-sis is undertaken. Again, it should be noted thatthis approximate elastic–plastic analysis is to esti-mate the residual stresses and strains based onaxisymmetric distribution approximation on theinside and outside surface of the pipe at the centerline of the weld. The strain expressions, derivedfrom Roark for an axisymmetric concentratedload to produce radial deflection equal to themeasured radial shrinkage at the center line of theweld were adapted with the following adjustmentsto account for plastic deformation.� In the elastic deformation, from experiments it

is known that the Poisson’s ratio m is in theneighborhood of 0.25–0.35 for most of thematerials and hence a value of 0.3 is commonlyused. During plastic deformation, it can beshown experimentally that materials can beconsidered incompressible, i.e. volumetricchange is zero signifying the volume constancycondition (Nadai, 1950; Johnson and Mellor,1962). From the simple example of a bar oflength L and cross section W×T in tensionand experiencing plastic flow, it can be shownanalytically that Poisson’s ratio m=0.5. Forplasticity effects, the Poisson’s ratio (m) is ad-justed to 0.5 based on the volume constancy(incompressibility) condition that prevails inplastic deformation as opposed to m=0.3 typi-cally used in elastic analysis.

� The numerical coefficient of three to be notedfrom Table 3 in meridional bending strain elas-

tic (omb=9 (d/R)[3(1−m2)]) expression isadjusted to two (see Table 4, meridional bend-ing strain plastic: omb=9 (d/R)[2(1−m2)])to account for plasticity considerations as ex-plained below. Weld shrinkage is generally as-sociated with prevalence of plasticdeformation.

For a rectangular strip of cross section withunit (1) width in circumferential direction andthickness (t): the term t2/6 in elastic sectionmodulus expression changes to t2/4 in plasticsection modulus expression; and the elastic mo-ment of inertia expression t3/[12(1−m2)]changes to t3/[8(1−m2)] which is an expressionanalogous to plastic moment of inertia. Thus,it can be noted that the ratio of plastic–elasticsection modulus (also plastic–elastic momentof inertia) is 3:2. Hence, the numerical coeffi-cient of three in Table 3 is replaced by two asshown in Table 4.

� The term d/R (ratio of radial shrinkage d atcenter line of weld to mean radius of pipe R) inthe strain expressions remains unchanged.Incorporating these adjustments, the strain ex-

pressions at the center line of the weld from thesimplified elastic–plastic analysis are shown inTable 4.

3.2. Residual stresses

The stresses at the center line of the weld areestimated from the calculated strains using a bilin-

Table 4Expressions for stress and strain (simplified elastic–plastic basis) at weld center linea

Membrane strain Total strainBending strain

oub=0oum=−d/RI ou=−d/Rououm=−d/Ro ou=−d/Roub=0

om= (d/R)[m+2(1−m2)]omb=+(d/R)[2(1−m2)]omm=m×d/Riom

om= (d/R)[m−2(1−m2)]omb=−(d/R)[2(1−m2)]omm=m×d/Ros=Sy+[(o−oy)/(ou−oy)](Su−Sy)su=30+[(ou−0.001)/(0.250−0.001)](75−30) ksism=30+[(om−0.001)/(0.350−0.001)](75−30) ksi

a i, Inside surface at center line of weld; o, outside surface at center line of weld; su, ou: stress, strain in the hoop or circumferentialor transverse direction; sm, om, stress, strain in the axial or longitudinal or meridional direction; su includes circumferential bendingstress to inhibit circumferential bending strain of m×omb; Poisson’s ratio m=0.5.

C. Basa6araju / Nuclear Engineering and Design 197 (2000) 239–247244

Fig. 3. Schematic of a bilinear stress–strain curve.

su=30+� (ou−0.001)

(0.250−0.001)n

(75−30) ksi

sm=30+� (om−0.001)

(0.350−0.001)n

(75−30) ksi

4. Results and discussion

4.1. Strain results

The calculated strains based on the simplifiedelastic–plastic analysis as explained in the Section3 for 4 and 24 in. diameter butt welded stainlesssteel pipes at the inner and outer surfaces of weldcenter line are shown in Table 5. Radial shrinkagecreates a compressive membrane strain in thehoop direction and a compressive bending strainon the outer surface and a tensile bending strainon the inner surface in the axial direction.

Review of the strain results in Table 5 indicatesthat for 24 in. pipe, the circumferential strain is1.43% at the inner as well as outside surface of theweld center line and axial strain is 2.48% at theinner surface and 1.04% at the outer surface. Thestrain values for 4 in. pipe are significantly higherwith the hoop or circumferential strain of 3.42%and axial strain of 5.89% at the inner surface. TheASME Code (ASME, 1995a) indirectly limits theradial shrinkage requiring no further evaluationwhen d/t ratio is less than or equal to 0.25 bystating that the piping stress indices for girth buttwelds for nuclear class 1 piping application are

ear stress–strain curve utilizing the data fromASTM and ASME as shown in Fig. 3 (schematicview of bilinear stress–strain curve).

The strain corresponding to yield point is usedas oy=0.001 in stead of 0.2% as Sy/E=30 000/28.3×106=0.001. The strain corresponding toultimate strength is ou=0.35 for longitudinal di-rection and ou=0.25 for transverse direction.Sy=30 ksi, Su=75 ksi. The stress (s) corre-sponding to a strain of (o) is calculated as follows.

s=Sy+� (o−oy)

(ou−oy)n

(Su−Sy)

Table 5Strains from simplified elastic–plastic analysis

Membrane strain Bending strain Total strain

4 in. Pipe, R=2.1315 in., d=0.0729 in., m=0.5 ou=−0.03420oum=−0.0342iouo oum=−0.0342 0 ou=−0.0342

omb=+0.0419om om=+0.0589i omm=+0.01714 in. Pipe, R=2.1315 in., d=0.0729 in., m=0.5omb=−0.0419 om=−0.0248o omm=+0.0171

ou=−0.01430oum=−0.014324 in. Pipe, R=11.8125 in., d=0.1693 in., m=0.5 iou0 ou=−0.0143o oum=−0.0143

om om=+0.024824 in. Pipe, R=11.8125 in., d=0.1693 in., m=0.5 omb=+0.0176omm=+0.0072iom=−0.0104omb=−0.0176omm=+0.0072o

C. Basa6araju / Nuclear Engineering and Design 197 (2000) 239–247 245

Table 6Estimated stresses from simplified elastic–plastic analysisa

Stress (ksi)

i4 in. Pipe, R=2.1315 in., d=0.0729 in., m=0.5, ou=0.25 su=−32.2= (−1.07 Sy)suo su=−39.8= (−1.33 Sy)

4 in. Pipe, R=2.1315 in., d=0.0729 in., m=0.5, ou=0.35 ism sm=+37.4= (+1.25 Sy)o sm=−33.1= (−1.10 Sy)

su24 in. Pipe, R=11.8125 in., d=0.1693 in., m=0.5, ou=0.25 i su=−30.8= (−1.03 Sy)o su=−34.0= (−1.13 Sy)ism sm=+33.1= (+1.10 Sy)24 in. Pipe, R=11.8125 in., d=0.1693 in., m=0.5, ou=0.35o sm=−31.2= (−1.04 Sy)

a su Includes circumferential bending stress to inhibit circumferential bending strain of m×omb.

applicable only when d/t50.25. In this evalua-tion, d/t ratio exceeded 0.25 for butt welds on 4 aswell as 24 in. pipe. Hsu (1977) calculated accumu-lated plastic strains of up to 6.4% for 4 in. stain-less steel pipe based on transient thermal andtime-independent elastic–plastic finite elementanalysis which is in close agreement with 5.89%strain calculated in this paper using a simplifiedelastic–plastic analysis.

4.2. Stress results

The above strain values are used in the follow-ing expression representing a bilinear approxima-tion to stress–strain curve to estimate the residualstresses at the inside and outside surfaces of theweld center line.

s=Sy+� (o−oy)

(ou−oy)n

(Su−Sy)

su=30+� (ou−0.001)

(0.250−0.001)n

(75−30) ksi

sm=30+� (om−0.001)

(0.350−0.001)n

(75−30) ksi

The results are presented in Table 6. The Tablealso shows the stress results as a multiple of Sy.

4.3. Discussion

In order to determine the acceptability of thesecalculated strain values shown in Table 5, guid-ance is taken from ASME Code Case N-47 whichsuggests local inelastic strain to be limited to 5%

except at welds where a 2.5% strain limit wassuggested. Since the calculated strains are localvalues at the weld center line, 2.5% limit shouldbe used. The 24 in. pipe weld shrinkage meets the2.5% strain limit whereas 4 in. pipe weld shrink-age exceeds 2.5% strain limit. Since ASME Codecase N-47 is for components in elevated tempera-ture service (T\750°F), it is recommended thateither the service temperature for operation for 4in. pipe be less than 750°F, or some post weldheat treatment be performed to relieve the resid-ual stresses and strains. It is also suggested toreview the shrinkage from flow requirements andpressure drop considerations.

For the 4 in. diameter pipe, the axial stress atthe inside surface of weld center line reached 1.25Sy tensile, and hoop stresses at outside surfacereached 1.33 Sy compressive. For the 24 in. di-ameter pipe, the axial stress at the inside surfaceof weld center line reached 1.1 Sy tensile and hoopstress reached 1.08 Sy compressive. Comparingthese residual stress results with published datareported by Mohr (1996), Michaleris (1996) wherethere was significant scatter in the published dataranging from 1.2 to −0.6 Sy, it can be concludedthat there is a good general agreement with theresults presented in this paper.

5. Summary and conclusions

5.1. Summary

The residual stresses and strains at the weldcenter line due to shrinkage in butt welded pipes

C. Basa6araju / Nuclear Engineering and Design 197 (2000) 239–247246

were evaluated utilizing measured radial shrink-age at the weld center line. Two different pipesizes 4 in. Sch 40 and 24 in. Sch 20 were investi-gated. The pipes were made of A312 TP 304stainless steel. Shrinkage was assumed to beaxisymmetric. A simplified elastic–plasticmethodology was developed. The available ex-pressions for strain formulation for axisymmetricconcentrated load on a thin wall cylinder areadjusted for plasticity considerations. A bilinearapproximation to the stress–strain curve wasutilized.

5.2. Conclusions

� The calculated residual plastic strains, based onsimplified elastic–plastic analysis were com-pared with published data and good agreementwas found.

� The residual stresses are 1.3 Sy for 4 in. buttwelded pipe and 1.1 Sy for 24 in. butt weldedpipe studied here.

� The residual stresses and strains at the centerline of the butt weld at the inside surface aretensile in the meridional (axial) direction.The rest of the stresses and strains at thecenter line of the butt weld are compressive. Itshould be noted that this paper does notaddress the HAZ where the nature and distri-bution of stresses and strains could be differ-ent.

� The calculated plastic strains at weld centerline were compared with inelastic strain limitsproposed in ASME code case N-47 for compo-nents in elevated temperature service for ac-ceptability. Residual strains due to shrinkageof butt welds in 4 in. diameter stainless steelpipe exceeded code case N-47 strain limits andhence is considered to be unacceptable for ele-vated temperature (\750°F) use.

� The simplified elastic–plastic analysis approachoutlined in this paper is easy to apply and isconsidered to be applicable for evaluation ofresidual stresses and strains at the weld centerline due to axisymmetric radial shrinkages as-sociated with butt welding.

Acknowledgements

The author wishes to express his gratitude toE.W. Thomas of Bechtel Corporation for his sup-port and encouragement.

Appendix A. Nomenclature

Do outside diameter of the pipeE Young’s modulus of elasticityi inside surface

outside surfaceOmean radius of the pipeRyield stressSy

tensile strengthSu

wall thickness of the pipeTd maximum radial shrinkage at the

center line of the butt weldo strain

ultimate strain (elongation)ou

Poisson’s ratiom

stresss

Subscriptsm meridionalmb meridional bending

meridional membranemmultimateuyieldycircumferentialu

ub circumferential bendingcircumferential membraneum

S.I. metricequi6alents

1 in. 2.54×10−2 m1 lbf 4.448222 N

6.894757×103 N m−21 psi1 ksi 6.894757×106 N m−2

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