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Effect of welding conditions on residual stresses due to butt welds

Tso-Liang Tenga,* , Chih-Cheng Linb

aInstitute of System Engineering, Chung Cheng Institute of Technology, Ta-Shi, Tao-Yuan, Taiwan, ROCbTechnical Section, Orderance Readiness and Development Center, Chi-Chi, Nan-Tou, Taiwan, ROC

Received 20 July 1998; accepted 15 August 1998

Abstract

Fusion welding is a joining process in which the coalescence of metals is accomplished by fusion. Owing to localized heating by thewelding process and subsequent rapid cooling, residual stresses can arise in the weld itself and in the base metal. Residual stresses attributedto welding pose significant problems in the accurate fabrication of structures because those stresses heavily induce brittle fracturing anddegrade the buckling strength of welded structures. Therefore, estimating the magnitude and distribution of welding residual stresses andcharacterizing the effects of certain welding conditions on the residual stresses are deemed necessary. In this work, we predict the residualstresses during one-pass arc welding in a steel plate usingansys finite element techniques. The effects of travel speed, specimen size, externalmechanical constraints and preheating on residual stresses are also discussed.q 1998 Elsevier Science Ltd. All rights reserved.

1. Introduction

Fusion welding is a joining process in which the coales-cence of metals is achieved by fusion. This form of weldinghas been widely employed in fabricating structures such asships, offshore structures, steel bridges, and pressurevessels. Owing to localized heating by the welding processand subsequent rapid cooling, residual stresses can arise inthe weld itself and in the base metal. Such stresses areusually of yield point magnitude. Residual stresses attribu-ted to welding pose significant problems in the accuratefabrication of structures because those stresses heavilyinduce brittle fracturing and degrade the buckling strengthof welded structures. Therefore, estimating the magnitudeand distribution of welding residual stresses and character-izing the effects of certain welding conditions on the resi-dual stresses are relevant tasks.

Many investigators have developed analytical and experi-mental methods to predict welding residual stresses.However, with advances in computer technology and suchtechniques as the finite element method, the means ofanalyzing residual stresses in welded structures enhancedeven further. For instance, Norton and Rosenthal [1, 2]measured residual stresses by the X-ray diffraction techni-que. Cheng et al. [3] investigated the residual stresses due tosurface treatment using the compliance method. Thatmethod can measure a rapidly varying compressive stress

under the interface which the X-ray technique would fail todetect. Pange and Pukas [4] presented hole-drilling andstrain gauges to assess residual stresses. Also, Muraki etal. [5] developed elasto-plastic finite-element computerprograms on thermal stresses and metal movement duringwelding. Kuang and Atluri [6] utilized a moving-mesh finiteelement procedure to examine a temperature field due to amoving heat source. Moreover, Shim et al. [7] derived ananalytical method for predicting through-thickness distribu-tion of residual stresses in a thick plate with a multipasswelding process. Chidiac et al. [8] discussed the iterativeprocedure employed for non-linear heat transfer analysis todetermine the thermal cycle for different welding types.Josefson [9] estimated residual stresses in a multi-passweld and in a spot-welded box beam withsolvia andabaqus commercially available FE-codes for non-linearanalyses. Yang and Xiao [10] proposed an analyticalmodel to examine the residual stress distribution acrossthe weld of panels welded with mechanical constraints.Furthermore, Ueda and coworkers [11–13] presented anovel measuring method of three-dimensional residualstresses based on the principle which is simplified by utiliz-ing the characteristics of the distribution of inherent strainsinduced in a long welded joint.

Residual stresses during welding are unavoidable andtheir effects on welded structures cannot be disregarded.Design and fabrication conditions, such as the structurethickness, joint design, welding conditions and weldingsequence, must be altered so that the adverse effects of

International Journal of Pressure Vessels and Piping 75 (1998) 857–864

IPVP 1874

0308-0161/98/$ - see front matterq 1998 Elsevier Science Ltd. All rights reserved.PII: S0308-0161(98)00084-2

* Corresponding author.

residual stresses can be reduced to acceptable levels. In thiswork, we predict the residual stresses during one-pass arcwelding in a steel plate usingansys finite element techni-ques. The effects of travel speed, specimen size, externalmechanical constraints and preheat on residual stresses arealso discussed.

2. Theoretical considerations

Welding residual stress distribution is calculated byansys finite element techniques. Theoretical considerationscan be assessed either by a thermal or a mechanical model.

2.1. Thermal model analysis

2.1.1. Governing equationsWhen a volume is bounded by an arbitrary surfaceS, the

balance relation of the heat flow is expressed by

22Rx

2x1

2Ry

2y1

2Rz

2z

� �1 Q�x; y; z; t�

� rC2T�x; y; z; t�

2t�1�

whereRx, Ry, Rz are the rates of heat flow per unit area,T�x; y; z; t� is the current temperature,Q�x; y; z; t� is therate of internal heat generation,r is the density,C is thespecific heat andt is the time.

The model can then be completed by introducing theFourier heat flow as

Rx � 2kx2T2x

�2a�

Ry � 2ky2T2y

�2b�

Rz � 2kz2T2z

�2c�

wherekx, ky, kz are the thermal conductivities in the x, y andz directions respectively.

By considering that the process in the material non-linear,the parameterskx, ky, kz, r , C are a function of temperature.Inserting eqns (2a), (2b), (2c) into eqn (1) yields

2

2xkx

2T2x

� �1

2

2yky

2T2y

� �1

2

2zkz

2T2z

� �1 Q� rC

2T2t�3�

eqn (3) is the differential equation governing heat conduc-tion in a solid body. The general solution is obtained byaccepting the initial and boundary conditions:initial condition

T�x; y; z; 0� � T0�x; y; z� �4�

boundary condition

kx2T2x

Nx 1 ky2T2y

Ny 1 kz2T2z

Nz

� �1 qs

1 hc�T 2 T∞�1 hr�T 2 Tr� � 0 �5�whereNx, Ny, Nz are the direction cosines of the outwarddrawn normal to the boundary,hc is the convection heattransfer coefficient,hr is the radiation heat transfer coeffi-cient, qs is the boundary heat flux,T∞ is the surroundingtemperature andTr is the temperature of the radiation heatsource.

The radiation heat transfer coefficient is expressed as

hr � s1F�T2 1 T2r ��T 1 Tr� �6�

in whichs is the Stefan–Boltzmann constant,1 is the effec-tive emissivity andF is a configuration factor.

2.1.2. Material propertiesSince welding processes undergo a high temperature

cycle and exhibit material properties that are temperaturedependent, the transient temperature can be calculated by anextrapolation method with a two-time interval as

T�t� � T�t 2 Dt�1t

Dt�T�t 2 Dt�2 T�t 2 2Dt�� 7�

Let g denote the temperature-dependent material coefficient,i.e. the function ofT(t). The material coefficient at timetcan be expressed as

g� 1Dt

Zt

t 2Dtg�T�t�� dt �8�

2.2. Mechanical model analysis

2.2.1. Mechanical equationsTwo basic sets of equations relating to the mechanical

model, the equilibrium equations and the constitutive equa-tions, are considered as follows.(a) Equations of equilibrium

sij ;j 1 rbi � 0 �9a�and

sij � sji �9b�wheres ij is the stress tensor andbi is the body force.(b) Constitutive equations for a thermal elasto-plasticmaterial

The thermal elasto-plastic material model, based on thevon Mises yield criterion and the isotropic strain hardeningrule, is considered. Stress–strain relations can be written as

�ds� � �Dep��d1�2 �Cth� dT �10�and

�Dep� � �De�1 �Dp� �11�where [De] is the elastic stiffness matrix, [Dp] is the plastic

T.L. Teng, C.C. Lin / International Journal of Pressure Vessels and Piping 75 (1998) 857–864858

stiffness matrix, [Cth] is the thermal stiffness matrix, ds isthe stress increment, d1 is the strain increment and dT is thetemperature increment.

2.2.2. IterationSince thermal elasto-plastic analysis is a non-linear

problem, the incremental calculation is employed herein.

In this study, incremental stress is obtained by the fullNewton–Raphson method.

3. Estimation of welding residual stresses

3.1. Analyzed model

Fig. 1 depicts the specimen in this study. Analysis isperformed on two long plates of 300 mm length and100 mm width by butt welding. The magnitude of heatinput is characterized by a welding currentI � 110 A,voltage V � 20 V, welding speedv � 5 mm s21 and theefficiency of heat-inputEff � 0.7.

Fig. 2 displays the material’s thermal and mechanicalproperties. Evaluating the three-dimensional residual stres-ses may require a considerable amount of computationaltime and cost. Herein, a two-dimensional axisymmetricmodel was designed to calculate the residual stress of theplate by theansys finite element code. Four-node thermal-structure couple elements were also used.

3.2. Results and discussion

A stress acting parallel to the direction of the weld bead isknown as a longitudinal stress, denoted by the terms y. Fig.3 depicts the distributions of longitudinal residual stressalong thex direction. High tensile stresses occur in regions

T.L. Teng, C.C. Lin / International Journal of Pressure Vessels and Piping 75 (1998) 857–864 859

Fig. 1. Geometry of butt-welded plates.

Fig. 2. Mechanical properties of welded plates.


Fig. 3. The longitudinal stress along thex direction.

Fig. 4. The transverse stress along they direction.


Fig. 5. The effect of specimen length on transverse residual stresses.

Fig. 6. The effect of specimen thickness on longitudinal residual stresses.

near the weld due to a resistance contraction of the materialas cooling commences. Also, for self-equilibratingpurposes, compressive stresses occur in regions removedfrom the weld. The maximum stress value is as high asthe material’s yield stress.

A stress acting normal to the direction of the weld bead, isknown as a transverse stress, denoted by the terms x. Fig. 4illustrates the distributions of transverse residual stresss x

along they direction. As this figure reveals, the stress distri-butions are symmetrical at the middle of the plate. Thetensile stresses occur at the middle of the plate, and thecompressive stresses occur at the ends of the weld. Further-more, the magnitude of compressive stresses exceeds thetensile stresses.

4. The effects of welding conditions on residual stresses

In welded structures, reducing the residual stresses duringan early stage of design and fabrication is of priorityconcern. For this reason, the effects of certain weldingconditions on the residual stresses are characterized in thefollowing.

4.1. Effects of specimen length

A butt-welded plate joint of thin plate is considered as amodel for analysis under the welding conditions mentionedearlier. The specimen’s width is assumed to be 200 mm, andthe length of specimen varies as 50 mm, 100 mm, 200 mmand 400 mm. Fig. 5 summarizes the effect of specimenlength on transverse residual stresses. This figure indicatesthat the transverse residual stresses are tensile in the centralareas and compressive in the areas near the plate ends.Notably, the high tensile stresses in the central regiondecrease with increasing length of the specimen.

4.2. Effects of specimen thickness

Welds were made with some heat input. Fig. 6 presentsthe distributions of longitudinal residual stresses at the topsurface with various specimen thicknesses, i.e. 5 mm,8 mm, 12 mm, in the weld metal of a butt joint. The tensilestress always appears only in the areas near the fusion zone.The fact that the absorption energy per unit volume in a thinweldment exceeds that in thick ones accounts for why theresidual stresses increased with decreasing specimenthickness.


Fig. 7. The effect of travel speed on transverse residual stresses.

4.3. Effects of travel speed

Approximately the same weld size was produced withvarious travel speeds of 3.33 mm s21, 7 mm s21 and10 mm s21. A higher welding speed not only reduces theamount of adjacent material affected by the heat of thearc, but also progressively decreases the residual stresses,as shown in Fig. 7. The important difference lies in the factthat the higher speed welding technique produced a slightlynarrower isotherm. This isotherm’s width influences thetransverse shrinkage of butt welds, accounting for whyfaster welding speeds generally result in less residualstresses.

4.4. Effects of external mechanical constraints

The thermal and mechanical behavior of weldmentscould be readily manipulated through external constraints.For a circumstance in which the lateral contraction of thejoint is restrained by an external constraint, Fig. 8 depictsthe distribution of transverse residual stresses. Moreover,the fact that the degree of the transverse shrinkage of arestrained joint is reduced accounts for why the magnitudeof the residual stresses with a restrained joint is larger thanthat estimated with an unrestrained joint.

4.5. Effects of preheating

The residual stresses depend on the final equilibriumtemperature of the temperature–stress cycle. Preheating treat-ments are used primarily to influence the time at temperatureand cooling rates within the weldment, thereby reducing theresidual stresses. Herein, the specimen was preheated homo-geneously up to 2008C, 3008C and 4008C. Fig. 9 summarizesthose results and shows that transverse residual stressessignificantly reduce after applying the preheating treatment.

5. Conclusions

Based on the above discussion, we can conclude thefollowing.

(1) For the residual stresses distribution in a butt weld, themiddle weld bead is in tension and the magnitude of thisstress equals the yield stress. The ends of the weld are incompression.

(2) The peak transverse residual stresses in the centralregion decrease with an increasing specimen length.

(3) The tensile residual stresses in the region near thefusion zone increase with a decreasing specimen thickness.

(4) A higher welding speed reduces the amount of


Fig. 8. The effect of mechanical constraint on transverse residual stresses.

adjacent material affected by the heat of the arc and progres-sively decreases the residual stresses.

(5) The magnitude of the residual stresses with a restrainedjoint is larger than that estimated with an unrestrained joint.

(6) Owing to the preheating treatment, the weldmentsignificantly reduces the residual stresses.

References

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[11] Ueda Y, Fukuda K, Tanigawa M. New measuring method of threedimensional residual stresses based on theory of inherent strain.Transactions of JWRI 1979;8(2):89–96.

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Fig. 9. The effect of preheating treatment on transverse residual stresses.