FE anlaysis of buckling behavior caused by welding in thin plates of high tensile strength steel

FE Analysis of Buckling Behavior Caused by Weldingin Thin Plates of High Tensile Strength Steel

Jiangchao Wang, Sherif Rashed, and Hidekazu Murakawa

(Submitted May 5, 2014; in revised form August 26, 2014)

The target of this study was to investigate buckling behavior during the entire welding process whichconsists of the heating and the cooling processes. For thin plate structures made of high tensile strengthsteel, not only residual buckling during or after cooling down but also transient buckling during heatingmay occur. The thermal elastic plastic FE analysis to investigate welding-induced buckling during the entirewelding process is presented. Because of the high yield stress of high tensile strength steel, larger longi-tudinal compressive thermal stress is produced near the welding line compared with that in the case ofcarbon steel. Therefore, the plate may buckle due to thermal expansion, before the material nears yielding.During cooling down, the longitudinal compressive thermal stress close to the welding line disappears, andlongitudinal tensile residual stress is produced due to contraction. Meanwhile, longitudinal compressiveresidual stress occurs far from the welding line to balance the tensile stress close to the welding line. Thisdistribution of longitudinal residual stress would change the deformed dish shape of transient buckling intoa saddle buckling type when the stress exceeds the critical buckling condition.

Keywords high tensile strength steel, lightweight welded struc-ture, thermal elastic plastic FEM, transient buckling,welding-induced buckling

1. Introduction

For welding engineers and researchers, welding distortion isalways one of difficult problems for welded structure (Ref 1).Generally, welding distortionwill degrade the assembly accuracyand performance capability of welded structures, and whenmitigated, will delay the production schedule and increasefabrication cost. When thin plates are used for assemblinglightweight welded structure such as ship, auto, and train, toimprove its carrying capacity and enhance fuel utilization, notonly the normal welding distortion will be produced, but alsowelding-induced buckling after cooling down may occur.Welding-induced buckling after cooling down is considered tobe the most critical mode of welding distortion compared withother modes of welding distortion. This kind of weldingdistortion not only has the negative influence onwelded structureas normal welding distortion, but also will be very dangerousbecause of its instability and difficulty of straightening (Ref 2).

Until now, many investigations of welding-induced bucklingafter cooling down were conducted by experiment. Masubuchi(Ref 3) conducted experiments of buckling-type deformation ofthin plates caused bywelding, and presented the critical buckling

wave length as influenced by the size of plate and weldingconditions. Watanabe and Satoh (Ref 4) observed welding-induced buckling distortion, the so-called concave-convex orconvex-concave type, in a series of experiments of bead-on-platewelding on thin plates. The critical buckling force and themoment when buckling occurs in welded plates with differentaspect ratio are measured and studied (Ref 5). Terasaki et al. (Ref6, 7) also investigated plate buckling behavior caused bywelding, utilizing experiments, and numerical analyses. Theyhave shown that welding-induced buckling is affected by thewelding conditions, size of plate, and material properties.

Also, using the computational approach in particular FEanalysis, welding-induced buckling is investigated based on thedevelopment of advanced numerical techniques and high perfor-mance computers. Tsai et al. (Ref 8) pointed out that the bifurcationphenomenon of buckling starts during the cooling cycle, and thismay continue to grow until the completion of the cooling process.An integrated experimental and numerical approachwas applied toinvestigate the mechanism of welding-induced buckling evolutionprocess. Meanwhile, eigenvalue analysis using welding longitudi-nal inherent strain distribution and 3D thermal elastic plastic FE(TEP FE) analysis considering large deformation were performedon welded structural models to understand the buckling distortionprocess observed in the experiments.Michaleris (Ref 9) pointed outthat the compressive residual stress parallel to welding linecontributes a loading that eventually results in buckling if thestress exceeds the critical buckling stress of thewelded structure.Hecalled this stress as the applied weld load (AWL), which isdetermined by performing local 3DTEPFE analysis of theweldingprocess. A 2D shell model depicting the actual ship panel using arelatively coarse mesh is then used to perform an eigenvalueanalysis that determines the various buckling modes caused bywelding residual stress. The minimum eigenvalue obtained fromthe analysis is used to evaluate the resistance to buckling. Thisresistance to buckling has been called the critical buckling load(CBL). A comparison of the AWL and the CBL indicates whether

Jiangchao Wang, Department of Mechanical and AerospaceEngineering, Carleton University, Ottawa, Canada; and SherifRashed, and Hidekazu Murakawa, Joining and Welding ResearchInstitute, Osaka University, Osaka, Japan. Contact e-mail:[email protected].

JMEPEG �ASM InternationalDOI: 10.1007/s11665-014-1230-2 1059-9495/$19.00

Journal of Materials Engineering and Performance

the welded structure is expected to buckle and what mode ofbuckling is likely to occur. Vanli and Michaleris (Ref 10)considered fillet welded joints with a particular emphasis onwelding-induced buckling instabilities. The effects of stiffenergeometry, welding sequence, welding heat input and mechanicalfixtures on the occurrence of buckling, and the distortion pattern areinvestigated.Michaleris et al. (Ref 11) suggested that themagnitudeof longitudinal residual stress is critical in the prediction of bucklingdistortion. An evaluation of modeling procedures to predictwelding-induced buckling distortion incorporating a moving heatsource, 2D and 3D small deformation analysis, 3D large deforma-tion analysis, and 2D-3D applied plastic strain analyses is carriedout by comparing computed residual stress and distortion withexperimental measurements. Tajima et al. (Ref 12) pointed out thatwelding longitudinal shrinkage (tendon force) produces compres-sive stress in the surroundingplate fields that sometimes cause theseplate fields to buckle. In order to avoid buckling, a series of TEPfinite element analyses are carried out to predict welding tendonforces and transverse shrinkage/bendingwhen utilizing continuousand intermittent welding with different welding specifications. Across-stiffened panel of a car deck of a car carrier is investigated.Bi-directional residual stresses are then evaluated for differentweldingpatterns. The effectiveness ofwelding pattern (continuous, parallel,and zigzag intermittentwelding) in reducingwelding residual stressand preventing buckling is quantified.Wang et al. (Ref 13) focusedon the residual buckling distortion in a test specimen with athickness of 2.28 mm under bead-on-plate welding. Eigenvalueanalysis and elastic FE analysis based on inherent deformationtheory are carried out to investigate the generation mechanism ofresidual buckling in bead-on-plate welded joint. The tendon force(longitudinal inherent shrinkage) is the dominant reason to producebuckling and the disturbance (initial deflection or inherent bending)triggers buckling but does not influence the buckling mode.

These achievements mentioned in above literatures areessential to recognize welding-induced buckling after completedcooling down in lightweight welded structure. However, whenthin plates with high tensile strength steel are used, not onlyresidual buckling during or/and after cooling down but alsotransient buckling during heating may be produced. In addition,due to the instability feature of buckling, transient bucklingduring heating can inversely influence the welding process anddamage the welding equipment. Therefore, the investigation oftransient buckling during heating is also an important researchissue in production of thin plate welded structure.

Thermal buckling of aircraft structure during flying withsupersonic speedwas investigated beforehand. The thermal stresseswhich result from non-uniform temperature distribution producedby aerodynamic heating may have a significant effect on thebuckling of aerodynamic surfaces and aircraft performance. Hel-denfels andRoberts (Ref 14) investigated thermal stresses producedin a flat, rectangular, and aluminum alloy plate by non-uniformheating by experimental and theoretical analysis. The measuredthermal stresses using bonded resistancewire strain gages are foundto be in a good agreement with an approximate theoretical solutionof the problem. Later, Gossard et al. (Ref 15) proposed anapproximate method based on large deflection plate theory tocalculate the deflection of flat or initially imperfect plates subject tothe thermal buckling. The examined object fixed by simplysupported boundary condition is subjected to a tentlike temperaturedistribution over the plate surface. Experimental results for thisparticular panel are in a good agreement with the theoretical resultsfor the range of temperature and deflections considered in the test.Tauchert (Ref 16) presented a survey of investigations concerned

with the response of flat plates to thermal loading. The topic ofbuckling, post-buckling, and largedeformationbehaviors associatedwith elevated temperature and rapid heating is discussed. Further,the influence of plate thickness, support conditions, and materialbehaviors on thermally induced buckling of plate was considered.Thornton (Ref 17) reviewed the research on thermal buckling ofplates and shells. The role of material thermal properties onthickness and spatial temperature gradients is demonstrated.Analytical, computational, and experimental studies are alsodescribed. Governing equations and formulas for critical bucklingtemperatures are presented for several practical applications.

Since welding process is well known as a high non-linerphysical phenomenon, extreme non-uniform temperature dis-tribution produced by rapid heating in narrow region duringheating will generate thermal expansion, in particular whichmay induce transient buckling (thermal buckling duringheating). When transient buckling occurs in production of hightensile strength welded structure, it is difficult to clarify thedetail behaviors of transient buckling using the direct exper-imental observation. The FE analysis has its unique advantagesto visually investigate the detail behaviors and clarify thegeneration mechanism of transient bucking during heating.

In this study, transient buckling and residual buckling in thinplates of high tensile strength steel are investigated by FEanalysis. They are first reproduced by TEP FE analysis for a thinplate with bead-on-plate welding. Influential factors affectingwelding-induced buckling, in particular transient bucklingduring heating such as large deformation theory and materialyield stress, are investigated using above-mentioned TEP FEanalysis. The cause of occurrence of transient buckling duringheating and different modes of transient/residual buckling areclarified using theoretical explanation and computed longitudinalinherent deformation (longitudinal transient/residual stresses).

2. Fundamental Theory and Method

With the development of high performance computer andadvanced numerical techniques, FE analysis is widely acceptedand considered as a practical and effective research tool toinvestigate the welding such as buckling behavior caused bywelding. The fundamental theory and method of FE analysisemploying in this study are introduced as follows.

2.1 Mechanical Failure Behavior of Material/Structure

Based on the theory of plate mechanics under uniaxial force,it is well known that the material will yield when the externalloading Fload exceeds the yield stress regardless the compres-sive or tensile case. Equation 1 shows the fundamentalmechanism of yield behavior of plastic material. For a platefixed by simply support boundary condition under a uniformuniaxial compressive force, the buckling will occur when theexternal compressive loading exceeds the critical stress givenby Eq 2, which not only depends on the material properties butalso influences by dimensions of considered plate.

Yield case:Fload

A¼ r>rY ¼ Eetotal ðEq 1Þ

Buckling Case:Fload

A¼ r>rE ¼

k

12

p2E

1� m2t

b

� �2; ðEq 2Þ

where rY and rcr mean the yield stress and critical bucklingstress, respectively; A means the area of cross section; E and


m are the material properties such as Young�s modules andPoisson�s ratio; t and b are the thickness and width of plate;and the k is a numerical factor which determined by ratio oflength/width.

Generally, the welded structure is assembled by thick plates;the yield behavior and its resulting plastic deformation are thedominant issue of welding mechanics. However, when the hightensile strength materials and its alloy are employed, the weldedstructure can be designed and fabricated using thin plates. Forthis case, the buckling behavior will become the criticalproblem for the thin plate welded structures.

2.2 Theory of Plasticity

When welded structures are subjected to excessively com-pressive thermal stress due to arc heating,weld jointsmayundergoplastic strain and plastic deformation. Plastic deformation iscaused by the motion of dislocations, and dislocations are mainlydriven by shear stress, and hydrostatic pressure does not influenceits motion; thus, the yield condition of a metal is independent onhydrostatic pressure unless it is extremely large. Theory ofplasticity with incremental form for stress-strain relation has beenemployed to solve problems involving unloading in most finiteelementmethods. Theprimary researchfields of plasticity areflowtheory, yield condition, and strain hardening rule, which will bediscussed respectively in the following.

2.2.1 J2 Flow Theory. As mentioned above, the flowtheory is superior to the deformation theory for numerical analysisof practical problems. In this study, J2 flow theory is employed forFE computation, and its details are discussed in follows.

Since hydrostatic component of the stress tensor has noeffect on the yielding and the plastic deformation of thematerial, the plastic phenomenon is governed only by devia-toric stress Sij, which is defined by

Sij ¼ rij � p

p ¼ r11 þ r22 þ r33

3

ðEq 3Þ

When the isotropic material is considered, the plasticphenomenon can be described by the three invariants, whichare independent of directions, of the deviatoric stress Sij. Theseinvariants J1, J2, and J3 are defined as

J1 ¼ S11 þ S22 þ S33

J2 ¼ S11S22 þ S22S33 þ S33S11 � S12S21 � S23S32 � S31S13

J3 ¼ detðSijÞðEq 4Þ

Among the above invariants, the second invariants J2 playan important role in the flow theory. Meanwhile, the J2 can berearranged by stress tensor in the following form:

J2 ¼1

6

�ðr11 � r22Þ2 þ ðr22 � r33Þ2 þ ðr33 � r11Þ2

þ6ðr212 þ r2

23 þ r231Þ)

ðEq 5Þ

2.2.2 Yield Condition. Various yield conditions havebeen proposed for different materials. For example, Misesand Tresca yield conditions are well known. In case of J2 flowtheory, Mises yield condition is employed, and the equivalentstress is defined as

r ¼ ð3J2Þ12 ðEq 6Þ

So material will yield when the following condition is satis-fied.

r ¼ ð3J2Þ12 ¼ ryield; ðEq 7Þ

where ryield is the current (after arbitrary plastic deformation)yield stress of the material.

In other words, material yields when the equivalent stress rresearches the yielding stress given by the one dimensionalstress-strain curve.

2.2.3 Strain Hardening Rule. Strain hardening or workhardening is a process by which the material grows stronger asit is deformed. In other words, yield stress after plasticdeformation increases with the plastic strain. For a strainhardening material, the size and shape of the yield surfacedepend on the total history of deformation. Two approaches todescribe the way that a material yields are isotropic hardeningand kinematic hardening.

For isotropic hardening, the yield surface expands during plasticflow, and this expansion is uniform in all directions about the originin stress space. Thus, initial shape and orientation are maintained.For kinematic hardening, the yield surface retains its original size,shape, and orientation with respect to the origin of the stress space,but the yield surface is assumed to undergo translation in the stressspace. Kinematic hardening theory takes into account the Bausch-inger effect and considers thematerial as a non-isotropic continuum.In reality, the hardening process often involves simultaneoustranslation and expansion of the yield surface, combining theisotropic hardening andnon-linear kinematic hardening approaches.

2.3 Large Deformation Theory

The equation relating the strain and displacement is essential todescribe the buckling behavior. If small deformation is assumed,strains are given as linear functions of displacements. When thedeformation is large, Green-Lagrange strain, which is a non-linearfunction of displacements, must be used. Equation 8 shows theGreen-Lagrange strain. From the expressionof strain, thefirst-orderterm represents the linear response, and the second-order term isessential to the non-linear behavior under large deformation.

ex ¼@u

@xþ 1

2

@u

@x

� �2

þ @v

@x

� �2

þ @w

@x

� �2( )

ey ¼@v

@yþ 1

2

@u

@y

� �2

þ @v

@y

� �2

þ @w

@y

� �2( )

ez ¼@w

@zþ 1

2

@u

@z

� �2

þ @v

@z

� �2

þ @w

@z

� �2( )

cxy ¼@u

@yþ @v@xþ @u

@x

� �@u

@y

� �þ @v

@x

� �@v

@y

� �þ @w

@x

� �@w

@y

� ��

cyz ¼@v

@zþ @w@yþ @u

@y

� �@u

@z

� �þ @v

@y

� �@v

@z

� �þ @w

@y

� �@w

@z

� ��

cxz ¼@u

@zþ @w@xþ @u

@x

� �@u

@z

� �þ @v

@x

� �@v

@z

� �þ @w

@x

� �@w

@z

� �� ;

ðEq 8Þ

where ex, ey, and ez are the normal Green-Lagrange strain inx, y, and z directions; cxy, cyz, and cxz are the shear Green-La-grange strain on the x-y, y-z, and z-x planes; and u, v, and w arethe displacement in the x, y, and z directions, respectively.


2.4 Introduction of In-house Code for TEP FE Analysis

The in-house program suit Joining and Welding ResearchInstitute ANalysis (JWRIAN) was developed by the researchgroup of mathematical modeling and computational analysis,JWRI, Osaka University. This in-house program suit consists ofa TEP FE analysis, using solid elements models.

In the TEP FE analysis, two processes are considered, thethermal process and themechanical process.Despite the fact that thethermal process has a decisive effect on the mechanical process, themechanical process has only a small influence on the thermalprocess, and a coupled thermalmechanical analysis is not necessary.Therefore, thermal-mechanical behavior duringwelding is analyzedusing uncoupled thermal/mechanical formulation. This uncoupledformulation considers the contribution of the transient temperaturefield to stress through thermal expansion as well as temperature-dependent thermal-physical and mechanical properties. The solu-tion procedure consists of two steps. First, the temperaturedistribution history is computed using heat transfer analysis. Thenthe obtained transient temperature distribution is employed as athermal load in the subsequent mechanical analysis, in whichresidual stresses, plastic strains, and displacements are computed.

The main TEP computational model for transient thermaland stress analysis is described as follows:

2.4.1 Thermal Analysis. A welding employs a movinglocal high intensity power source to the part which generates asharp thermal profile in the weld pool, heat-affected zone(HAZ), and base metal. The 3D transient temperature isbasically determined by solving the partial differential equationfor the conservation of energy on a domain defined by a FEMmesh in a Lagrangian formulation._hþr � qþ Q ¼ 0

q ¼ �jrT

_h ¼ qcdT

dt;

ðEq 9Þ

where h is the specific enthalpy, the super-imposed dot de-notes the derivative with respect to time, T is the temperature,,T is the temperature gradient, Q is the power per unit vol-ume or the power density distribution, k is the thermal con-ductivity, c is thermal capacity, and q is density. Thesematerial properties are usually temperature dependent.

In this analysis, the initial temperature is often assumed tobe room temperature, and body heat source with uniform powerdensity Q (w/m3: welding arc energy/volume of body heatsource) is employed to model the heat source of welding arc.

Besides considering the moving heating source, heat lossesdue to convection and radiation are also taken into account inthe finite element model. A combined convection and radiationboundary condition generates a boundary flux q (w/m2) on allexternal surfaces. This flux is determined by heat convectionand radiation together from the following equations:

q ¼ qc þ qr

¼ hðT � TambientÞ þ eC½ðT þ 273Þ4 � ðTambient þ 273Þ4�¼ ½hþ eC½ðT þ 273Þ2 þ ðTambient þ 273Þ2�½ðT þ 273Þþ ðTambient þ 273Þ��ðT � TambientÞ;

ðEq 10Þ

where qc and qr are heat convection and radiation, respec-tively, h is coefficient of heat convection, e is emissivity ofthe object which will be equal to 1 for ideal radiator, and Cis the Stefan-Boltzmann constant.

Meanwhile, the FEM domain is dynamic, which will changewith filler metal adding to the welding pass in each time stepduring welding. After welding pass is completed, the time steplength was increased exponentially until sum of computed timereaches a defined maximum examined time, and the analysishalts.

2.4.2 Stress Analysis. Given the density q, the fourth-order elastic plastic tensor D as a 69 6 matrix, the body forceb, and the Green-Lagrange strain e, and stress analysis solvesthe conservation of momentum equation at the end of each timestep that can be written in the form of Eq 11 in which inertialforces are neglected.

r � rþ b ¼ 0

r ¼ De

e ¼ ruþ ðruÞT þ ðruÞTru2

ðEq 11Þ

The initial stress often is assumed to be stress free. Thesystem is solved using a time marching scheme with time steplengths with certain magnitude during welding; usually, anexponentially increasing time step length after welding hasstopped. In terms of boundary conditions, the part is free todeform, but rigid body motion is fixed as constraint.

3. Computation of Welding-Induced Buckling

A rectangular plate with bead-on-plate welding, whose sizeis 3009 2009 2.28 (mm), is selected as research object. Thisthin plate bead-on-plate welded joint is made of high tensilestrength steel (HT950). The TEP FE analysis is carried out toinvestigate the buckling behavior in this thin plate welded jointthroughout the entire welding process.

Figure 1 shows the solid elements model of theconsidered thin plate welded joint. This solid elements modelhas 17,956 nodes and 13,200 elements. Boundary conditionsto prevent rigid body motion are adopted as shown in Fig. 1.In order to investigate transient buckling and residualbuckling, the six points shown in Fig. 1 are selected tomonitor the real-time record of out-of-plane weldingdistortion. Welding condition of this bead-on-plate weldingis assumed as given in Table 1. Welding heat is assumed touniformly penetrate the full thickness of the plate, andthe influence of bending deformation (angular distortion)caused by temperature gradient in thickness direction isignored.

3.1 Welding-Induced Buckling During the Entire WeldingProcess

In Fig. 2, the distributions of out-of-plane weldingdistortion at different times during the entire welding processare presented. As may be seen from the figures, the platedeforms in a dish shape during heating and in a saddle shapeafter cooling down. This difference in deformation shapes(buckling modes) can be explained as the response to thedifferent distributions of compressive stress during heatingand after cooling down as discussed in the followingsections.


3.2 Transient Buckling During Heating

Because the investigations of residual buckling after coolingdown were already presented in lots of literatures, the followingstudy topic is focused on transient buckling during heating.

To understand the behavior at the time when transientbuckling occurs during heating, temperature distribution andlongitudinal transient stress distribution are presented in Fig. 3,in which compressive transient stresses in the longitudinal andtransverse direction are produced around the welding line. Asmay be seen from Fig. 3(b), for the high tensile strength weldedstructure with the high yield stress, longitudinal compressivestress will largely increase where welding arc torch is passing,and if it exceeds the buckling stress, transient buckling occurs.

3.3 Tendency of Out-of-plane Welding Distortion DuringWelding

To closely examine the buckling behavior caused by bead-on-plate welding in thin plate, out-of-plane displacements at the sixselected points shown in Fig. 1 are plotted in Fig. 4 from the startof welding to the completion of cooling down. As maybe seefrom the figure, the magnitude of deflection increases duringheating and increases in the opposite direction during coolingdown. Noting that no bending deformation can be produced bythe resulting temperature gradient in thickness direction as shownin Fig. 3(a), it may be concluded that the observed deflection isproduced by buckling. The buckling occurs during heating isdefined as transient buckling, and buckling after completedcooling down is defined as residual buckling. Point A shown inFig. 4 means that the transient bucking starts to develop, andpoint B means after the completion of cooling down.

4. Influential Factors of Welding-Induced Buck-ling

Through TEP FE analysis, it has been shown that when thematerial of the plate is high tensile strength steel, buckling may

happen both during heating and after completion of coolingdown. To confirm buckling and the influence of yield stress ofthe plate, computations assuming small deformation andassuming carbon steel are carried out and presented in thissection.

4.1 Out-of-plane Welding Distortion under SmallDeformation

In order to confirm transient buckling during heating, thesmall deformation theory is employed to analyze the same

1

2

3

4

5

6

200mm

300mm

XY

Z

Fixed DOF

Nodes: 17956Elements: 13200Thickness: 2.28mm

Fig. 1 Solid elements model of considered thin plate welded joint

Table 1 Welding condition

Current Voltage Velocity Efficiency

175-185 (A) 14-16 (V) 3.6 mm/s 0.7-0.8

8.0+00

6.4+00

4.8+00

3.2+00

1.6+00

0.0+00

-1.6+00

-3.2+00

-4.8+00

-6.4+00

-8.0+00

Component [mm] Max MinZ-Direction Displacement 0.0000 0.0000

XY

Z

(a)

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

-1.0

XY

Z

Component [mm] Max MinZ-Direction Displacement 7.400 0.004(b)

(c)

8.0

6.0

4.0

2.0

0.0

-2.0

-4.0

-6.0

-8.0

Component [mm] Max MinZ-Direction Displacement 7.186 -6.36

XY

Z

Fig. 2 Out-of-plane welding distortion during entire welding pro-cess. (a) Out-of-plane displacement before welding (b) Transientbuckling during heating (c) Residual buckling after cooling


problem, and the computed out-of-plane welding distortion isshown in Fig. 5.

Because the heat is assumed to uniformly penetrate theconsidered thin plate during welding, there is almost no

temperature gradient in thickness direction, therefore, weldingbending distortion cannot be produced. When the smalldeformation theory is employed, buckling-type welding distor-tion cannot be predicted. As expected, out-of-plane weldingdistortion is not observed except the local deformation of thewelding bead, which is produced by accumulation of in-planeshrinkage that is predicted no matter whether the computationis large deformation or small deformation. Once, it can beconcluded that the out-of-plane welding distortion shown inFig. 2 is produced by buckling not by bending deformation.

4.2 Buckling of a Carbon Steel Plate

Assuming that the material of the plate is carbon steel(SM490), welding distortion is analyzed assuming the samewelding condition. Figure 6 shows the out-of-plane weldingdistortion at the six selected points during heating andsubsequent cooling down. As may be seen from the figure,there is almost no out-of-plane welding distortion duringheating. And it is interesting to notice that out-of-plane weldingdistortion observed after cooling down is as large as that in thecase of high tensile strength steel. As for the buckling mode,the thin plate has deformed in a saddle shape, the same as in thecase of high tensile strength steel. This comes from the fact thatbuckling in the cooling stage is caused by the longitudinal

7.0+02

6.0+02

5.0+02

4.0+02

3.0+02

2.0+02

1.0+02

0.0+00

-1.0+02

-2.0+02

-3.0+02

-4.0+02

-5.0+02

-6.0+02

XY

Z

Component [MPa] Max MinX-Direction Stress 693.6 -575.8

(b)

1.6+03

1.4+03

1.2+03

1.0+03

0.8+03

0.6+03

0.4+03

0.2+03

0.0+03

Temperature Max Min 1500°C 20°C

(a)

XY

Z

Fig. 3 Computed results of thermal/mechanical analysis when tran-sient buckling occurs. (a) Transient temperature distribution (b) Dis-tribution of longitudinal transient stress

-8

-6

-4

-2

0

2

4

0 100 200 300 400 500 600

Point 1Point 2Point 3Point 4Point 5Point 6

Dis

plac

emen

t in

Z d

irec

tion

(m

m)

Time (sec)

weldingcompleted

A

B

Fig. 4 Real-time record of out-of-plane welding distortion duringthe entire welding process (high tensile strength steel)

0.15

0.10

0.05

0.00

-0.05

-0.10

-0.15

-0.20

XY

Z

Fig. 5 Out-of-plane welding distortion after completed coolingdown under small deformation

-8

-6

-4

-2

0

2

4

0 100 200 300 400 500 600

Point 1Point 2Point 3Point 4Point 5Point 6

Dis

plac

emen

t in

Z d

irec

tion

(m

m)

Time (sec)

weldingcompleted

Fig. 6 Real-time record of out-of-plane welding distortion duringthe entire welding process (carbon steel)


residual compressive stress, which is produced in the regionaway from the welding line to balance the longitudinal residualtensile stress close to the welding line (Fig. 7). Noting that thelongitudinal residual tensile stress is mostly dependent on theheat input and less sensitive to the yield stress of the material, itmay be seen that the longitudinal residual compressive stress incarbon steel plate and high tensile strength steel plate are nearlyequal.

5. Results and Discussions

In order to understand the above-presented computedresults, a theoretical clarification is first proposed. During theheating of welding, the region of welding line where thewelding torch is passing will be heated and then elongate due tothe thermal expansion with no constraint. However, because ofthe high non-uniform heating with moving welding torch, themetal away from the heated region of welding line will keeproom temperature and prevent the thermal expansion ofwelding line in longitudinal direction. Then the longitudinalcompressive thermal stress is generated. When this longitudinalcompressive thermal stress exceeds the yield stress of consid-ered material, the welding line will yield, and longitudinalcompressive plastic strain occurs. For the high tensile strengthsteel, a relatively larger longitudinal compressive thermal stressis required to make the welding line yield compared with that incase of carbon steel. On the other hand, when the consideredplate of high tensile strength steel is thin enough, the criticalbuckling stress may less than yield stress, and consequently,transient buckling during heating will occur before the materialnears yielding due to the longitudinal compressive thermalstress produced by welding. This is the reason for the behaviorthat transient buckling with dish shape will be observed only inthe thin plate of high tensile strength steel.

After completed cooling, the above-mentioned longitudinalcompressive thermal stress in the welding line will disappear,and an amount of longitudinal compressive plastic strain isgenerated. Also, longitudinal tensile residual stress is produceddue to the contraction of welding line, and longitudinalcompressive residual stress occurs far away from the weldingline to balance the longitudinal tensile residual stress close to

welding line. This kind of residual stress distribution wouldchange the deformed dish shape of transient buckling into asaddle buckling type when the longitudinal compressiveresidual stress exceeds the critical buckling stress.

To closely examine the stress distribution just beforetransient buckling starts to develop, the stress distributions ofthe carbon steel plate and the high tensile strength steel plateare compared at time A as shown in Fig. 4, when the heatsource is close to the end of welding line. Figure 8 shows thedistribution of the longitudinal transient stress on the middlecross section (at the heat source). As may be seen from thefigure, in the case of high tensile steel, compressive stressobserved in the area adjacent to the welding line is larger thanthat in the case of carbon steel. This explains why transientbuckling during heating is likely to occur when the yield stressof the material is high.

Figure 9 shows the distributions of longitudinal transientstress in the case of high tensile strength steel at times A and B

Component Max MinZ-displacement 3.6593 -6.38

4.0

3.0

2.0

1.0

0.0

-1.0

-2.0

-3.0

-4.0

-5.0

-6.0

-7.0

XY

Z

Fig. 7 Buckling distortion of plate after completed cooling down(carbon steel)

-600

-400

-200

0

200

400

0 50 100 150 200

High tensile strength steelCarbon steel

Tra

nsie

nt s

tres

s (M

Pa)

Coordinate in transverse direction (mm)

Fig. 8 Comparison of transient longitudinal stresses in the cases ofhigh tensile strength steel and carbon steel

-600

-400

-200

0

200

400

600

800

1000

0 50 100 150 200

During heaing processAfter cooling down

Tra

nsie

nt/R

esid

ual s

tres

s (M

Pa)

Coordinate in transverse direction (mm)

Fig. 9 Comparison of longitudinal transient stress and longitudinalresidual stress caused by welding


in Fig. 4 when transient buckling is about to happen and aftercooling down. After cooling down, the typical longitudinalresidual stress distribution with a strong narrow tension band atthe welding line and compressive stress away from the weldingline are observed. Because of these different longitudinal stressdistributions, dish-type buckling is promoted during heating,and saddle-type buckling is promoted after cooling.

6. Conclusions

Using TEP FE analysis, buckling behavior caused by bead-on-plate welding in a thin plate of high tensile strength steel isinvestigated. It is found that the plate may buckle both during andafter welding. The modes of buckling during the heating and aftercoolingdown inwelding are dish typemodeand saddle typemode.Both types of buckling mode are produced by the compressivestress associated with the transient thermal stress or the residualstress, respectively. The following conclusions also can be drawn:

(1) In case of a high tensile strength steel plate 3009 20092.28 mm in length, width, and thickness and yield stressequals to 950 MPa, transient buckling occurs duringwelding. On cooling down, residual buckling occurs.

(2) During heating, because of the high yield stress, com-pared with carbon steel, larger compressive thermalstress is produced near the welding line. Therefore, thinplate structures made of high tensile strength steel maybuckle due to thermal expansion during welding.

(3) During cooling down, the compressive thermal stress inthe region close to the welding line disappears, andtherefore, transient buckling also disappears. Meanwhile,tensile residual stress is produced in and around thewelding line due to contraction. Compressive residualstress is then produced away from the welding line tobalance the tensile stress in and around the welding line.This compressive residual stress, when it exceeds thecritical buckling condition, will change the deformedshape to a saddle buckling type.

(4) With development of advanced high strength materials,transient buckling caused by welding becomes an impor-tant issue that needs more investigation.

References

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FE anlaysis of buckling behavior caused by welding in thin plates of high tensile strength steel

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