computational prediction of out-of-plane welding ... · welding tests of a realistic nature to...

Computational prediction of out-of-plane weldingdistortion and experimental investigationD Camilleri, T Comlekci, and T G F Gray*

Department of Mechanical Engineering, University of Strathclyde, Glasgow, Scotland, UK

The MS was received on 19 February 2004 and was accepted after revision for publication on 30 September 2004.

DOI: 10.1243/030932405X7809

Abstract: The main aim of the work was to investigate a simplified finite element simulation ofthe out-of-plane distortion caused by fusion butt welding. The thermal transient part of thesimulation made use of a finite element analysis of the two-dimensional cross-section of theweld joint and the thermoelastic–plastic treatment was based on analytical algorithmsdescribing transverse and longitudinal deformations, leading to predictions of transverseangular deformation and longitudinal contraction force. These results were then applied to anon-linear elastic finite element model to provide predictions of the final angular and overalldeformations of the butt-welded plates. The validity of the simulation was investigated viafull-scale tests on 4m� 1.4m� 5mm steel plates, butt welded using a flux-cored Ar–CO2

metal–inert gas process. Thermography and thermocouple arrays were used to validate thethermal transient computations and out-of-plane deformations were measured usingdisplacement transducers for transient deformations and a laser scanning system to measurethe profiles of the whole plates before and after welding. The results of six full-scale tests aregiven and comparison with the simulations shows that the procedure provides goodprediction of the angular and overall out-of-plane deformations. Prediction accuracy requiresaccount to be taken of initial shape, gravity loading, and support conditions.

Keywords: welding distortion, welding simulation, butt welds, out-of-plane welding deforma-tion, angular deformation

1 INTRODUCTION

1.1 Background

Many industries concerned with the fabrication ofthin-plate structures experience difficulties and highrectification costs related to cutting and weldingthermal distortion. A recent review of a large colla-borative programme, funded by the US Navy Officeof Naval Research [1] states: ‘Severe distortions haveemerged as a major obstacle to the cost-effectivefabrication of such lightweight structures.’ Out-of-plane distortion, in particular, makes it difficult toalign the edges of subassemblies and results in alack of ‘fairness’ in the completed structure. Thegeneral practice in such industries is to base predic-tions of distortion on previous outcomes of particular

cutting, welding, and assembly sequences, but this isnot always successful. A more systematic version ofthis approach has been reported recently [2], basedon neural network software. However, there are fewpredictive tools at present to support design andmanufacturing optimization of such structures withrespect to structural function and manufacturingvariables. Various analytical and computationalapproaches to the problem are possible and havebecome more applicable as computational capabilityincreases, but such strategies have not so far beenwidely used in industries concerned with fabricationof this type, due presumably to complexity and theneed for in-house expertise.

The overall project, of which this study is a part,aims to improve the applicability of computationaldistortion prediction by providing simple and adap-table methodologies, which can be readily validatedthrough experience of application in an industrialcontext. A key factor that underlies this strategy isan uncoupled computational procedure, whereby

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JSA01504 # IMechE 2005 J. Strain Analysis Vol. 40 No. 2

*Corresponding author: Department of Mechanical Engineering,

University of Strathclyde, James Weir Building, 75 Montrose Street,

Glasgow G1 1XJ, UK; email: [email protected]

at Purdue University on May 22, 2015sdj.sagepub.comDownloaded from

http://sdj.sagepub.com/

the thermal transient, thermoelastic–plastic andstructural stages of the thermomechanical deforma-tions induced by fusion welding are treated sepa-rately. The theoretical models and results generatedin the project have been supported at all stages bywelding tests of a realistic nature to maintain confi-dence in the validity and applicability of the treat-ments. This approach has been demonstrated inreference [3] where experimental and computationalresults were given for the welding distortion of a pilottest series of small butt-welded steel plates(0.5m� 0.5m and 6mm thick). The present paperdeals with aspects of a subsequent test series, wherelarge steel plates (nominally 4m� 1.4m and 5mmthick) were butt welded using similar procedures.This scale of test piece is realistic in relation tocommon industrial practice and explores furthercomplexities not present in the smaller models,such as buckling phenomena, the effects of gravityand support positions, and variations in pre-weldingassembly practices.

1.2 Outline of the uncoupledcomputational approach

The first step in any computation of welding distor-tion is to establish the transient thermal distributionscaused by a given welding process in the geometry ofinterest. This may be achieved in a variety of ways,ranging from the early analytical treatments ofRosenthal [4] to finite-element-based methods, asreviewed recently by Lindgren [5]. In the present

approach, it is argued that the main characteristicsof the thermal transients that drive typical distortionprocesses can be captured through relatively simpletreatments. In particular, it does not appear to benecessary to model the precise details of the thermalpatterns close to the molten weld pool. This is fortu-nate, as the temperature-dependent thermal proper-ties of the materials involved are usually inaccuratelyknown and the thermal outcomes of practicalwelding processes are both difficult to predict andsubject to variation in application. Reference [6]from the earlier pilot study of small plates showedthat a simple thermal transient treatment based on atwo-dimensional cross-section of the weld was suffi-cient to provide accurate temperature distributions,which correlated with experimental data based onthermocouple and thermographic measurements.This approach was carried over to the present testson large plates, where the transients were also checkedexperimentally, as shown in Fig. 1 (the non-dimen-sionalization shown for the transverse positions ofthe thermocouples will be discussed later).

Although a purely computational approach can beused to provide the required thermal information, itis likely that some measure of application-specificmeasurement will usually be required to index thethermal transient calculations to the actual transienttemperature fields during welding operations. Themain driving parameters relevant to thermal transientsare the heat input rate and the material thermal prop-erties, but variations in the process environmentmeanthat a ‘weld efficiency’ factor is usually necessary to

Fig. 1 Comparison of thermocouple results and two-dimensional transient model

162 D Camilleri, T Comlekci, and T G F Gray

J. Strain Analysis Vol. 40 No. 2 JSA01504 # IMechE 2005



relate the calculation to reality. Thermographicimaging, as demonstrated in reference [6], provides apractical approach to determining such correlationsand this tool has now developed to the point whereit is readily applicable to industrial cases.In the second computational stage of the

uncoupled approach, differential strains induced bythe transient thermal gradients are translated intocontraction stresses, which produce mechanicaldistortion. This is the most intractable and complexpart of the whole procedure, not least because therequired high-temperature material properties areusually poorly known and the material also changesstate. The algorithms used in the present treatmentto solve this stage of the process have benefitedfrom the early insights of Okerblom [7]. He notedvarious typical features of the thermomechanicaltransients generated by fast-moving fusion weldingheat sources and made several bold simplificationson the strength of these observations. The availabilityof new computational methods means that some ofthese simplifications are no longer necessary, butothers remain very powerful as ways to avoid theproblematic aspects described above.The main aim of this paper, therefore, is to delineate

the terms of a simplified approach to the thermo-elastic–plastic stage within the welding distortionprocess and to examine critically the main assump-tions in terms of the mechanical behaviour of full-size butt-welded steel plates. Although the validationis specific to this problem andmaterial, the conclusionshould carry over to other situations that can becharacterized by similar thermal transient patterns.

2 SIMPLIFIED ANALYTICAL MODELS OFTHE THERMOMECHANICAL PROCESS

2.1 Longitudinal welding deformations

Okerblom [7] recognized that the major irreversibledeformations responsible for distortion are drivenby the cooling phase of the process in the regionbehind the travelling heat source. The thermal gradi-ents transverse to this line are typically steep, whereasthe gradients parallel to the weld are relativelygradual, as can be deduced from Fig. 1. This factsuggested a simple treatment for longitudinalcontraction, in terms of a transverse plane strainslice, which is passed through the quasi-stationarytemperature field.Further simplification is made by assuming that the

elastic longitudinal stress developed during cooling ata given transverse location will depend in the firstinstance on the maximum thermal strain �Tm gener-ated at that transverse coordinate, irrespective of therelative longitudinal coordinate where that occurs

(Tm is the maximum temperature relative to thereference temperature, taken as zero). The analyticaltreatment arising from this simplification will bedesignated the ‘mismatched thermal strain’ (MTS)algorithm. It can be seen from Fig. 1 that regionsnearer the centre of the slice begin to start to coolbefore adjacent regions further away from thecentre and they cool more rapidly, eventually conver-ging to a common rate. The resulting thermalmismatches develop contraction forces, progressivelyoutwards across the slice. As mismatches are alwayspresent at each point, it is possible that the fullvalues of contraction stress are developed, corre-sponding to the maximum thermal strains at eachpoint (accepting that the yield strength �Y cannotbe exceeded anywhere). Note that this interpretationdiffers from that of Okerblom, in that he attributedthe overall longitudinal contraction to integration ofcompressive plastic strains at each point across thewidth, due to the plane strain suppression of thermalstrain. However, the present formulation in terms ofcontraction forces gives an identical result.

The overall strain pattern, calculated on the strengthof these assumptions, is shown in Fig. 2. The width ofthe central zone limited by the yield strength is identi-fied by the transverse location where �Tm 5 2"Y. Thiszone consists of two regions. In the inner region A,temperatures exceed the level at which the materialhas significant yield strength and rapid creep obliter-ates compressive elastic stress generated duringheating. In the outer region B, the material retainsstrength throughout, but the strain cycle exceeds 2"Y.In either case, cooling induces a yield-level tensile resi-dual stress. The outer zone D, which remains elasticthroughout the heating and cooling cycle, is definedby �Tm 4 "Y and no contraction stress is generatedin this region. An indication of the physical positionsof these limits in relation to the thermocouplepositionsin the present test welds is given in Fig. 1 in terms of thenon-dimensional parameters. Between these twolimits, in zone C, the tensile elastic residual stress isgiven by Eð�Tm � "YÞ. Thus the total force generatedby contracting material is given by the total shadedarea in Fig. 2 multiplied by Young’s modulus.

Any convenient method can be used to determine arelationship between Tm and the transverse distancey. However the quasi-static analytical treatment ofRosenthal [4] may be used to derive such a relation-ship in the form

Tm ¼ 0:484q

vt

1

c�

1

2y

�1� �y2

2�

�ð1Þ

If the heat dissipation is small, this reduces to theinversely proportional relationship

Tm ¼ 0:242q

vt

1

c�

1

yð2Þ

Out-of-plane welding distortion and experimental investigation 163




This relationship was derived by Okerblom [7] usingthe work of Rykalin and, in reference [8], a correctiondue to Wells [9] for slower-moving heat sources in amaterial of high diffusivity was applied to provide arelationship between the transverse distance y andTm as

Tm ¼ 0:242q

vt

1

c�

1

y� 0:4

�

vð3Þ

The simplest version of these relationships, namelyequation (2), can be integrated over the area toprovide the force as

F ¼ 0:335q

v

�

c�E ð4Þ

This result shows several interesting features. Firstly,the critical controlling parameter on longitudinalcontraction force is shown to be the heat input rate(q=v, in J/m) of the welding source, as is well knownfrom practice. Secondly, the result is independent ofthe yield strength. This is a consequence of the fixedyield strength assumption and the inverse relation-ship between temperature and transverse distancein equation (2). This may not, however, be obtainedin practice if the temperature profile differs fromthe Rosenthal–Rykalin quasi-steady state simpli-fication and the yield strength varies with tempera-ture in the zone of interest. However, this findingsuggests, at least, that the dependence of the contrac-tion force on yield strength is weak, which would bean immensely simplifying factor, if shown to becorrect.The assumption of constant thermal and mechan-

ical properties over a typical range of weld coolingseems at first glance to be an oversimplification.However, using properties typical of C–Mn steel,

such as a yield strength of 405MN/m2, Young’smodulus of 205GN/m2 and an expansivity coefficientof 14� 10�6 8C�1, the boundary temperaturesdefining the width of the inner yielded zone and theouter elastic zone are 282 8C and 141 8C respectively.If the assumption is correct that distortion is drivenmainly by processes occurring in this temperatureband, then the variation in properties may not betoo significant.

2.2 Transverse welding deformations

Okerblom assumed that angular deformation andtransverse contractions are due entirely to thethermal contraction of the fused zone, e.g. the trian-gular zone shown in Fig. 3 of width b and penetrationdepth s in a plate of thickness t.

The implications are that the transverse thermalstrains in the remainder of the cross-section areelastic and that there are no restraints on angulardeformation, other than that provided by theunwelded area below the fusion zone. The two-dimensional treatment here also relies on the findingthat the thermal gradient is small along the length ofthe weld. The simplified treatment arising from thisassumption will be designated the ‘thermal contrac-tion strain’ (TCS) algorithm.

The three diagrams to the right of the weld sketchin Fig. 3 represent the transverse residual stress, themechanical deformations �m induced by compres-sion and bending over the width b and the thermalcontractions �T of the fused zone respectively. Thestarting temperature for the cooling process is Ts

and the ratio k defines the proportion of the surfacethermal contraction absorbed by constrained plasticflow. The residual transverse deformations arisefrom a summation of the mechanical and elastic

Fig. 2 Formulation of total contraction force via MTS





thermal deformations, leading to the formulations

�av ¼P

�e

tð5Þ

� ¼P

�e

Ih ð6Þ

where h is the distance between the centroids of themechanical and thermoelastic deformations and I isthe second moment of the mechanical deformationarea. The total thermoelastic deformation isexpressed from the right-hand diagram in terms ofthe parameter k as

X�e ¼ 1

2sb�Ts � 1

2sbk2�Ts ¼ 1

2sb�Tsð1� k2Þ

leading to

�av ¼1

2

s

tb�Tsð1� k2Þ ð7Þ

� ¼ s

t

b

t�Ts

�3ð1� k2Þ � 2

s

tð1� k3Þ

�ð8Þ

Noting also that �t þ "Yb ¼ ð1� kÞ�Tsb and�t ¼ �av þ �t=2, these values may be substituted inequations (7) and (8), to solve for k in terms of s=tand "Y=�Ts as shown in Fig. 4. A starting temperatureTs of 1000 8C was chosen for the present applicationto steel, following the example given by Okerblom,who justified this choice through comparison withtests. However, it may also be observed that thisrepresents an upper bound on the temperature atwhich steel starts to develop some mechanicalstrength. In the case of the remaining parameters,the centre curve embodies thermal and mechanicalproperties appropriate to the present case, as definedin section 2.1.

Note that, when the fusion zone penetrates toapproximately 60 per cent of the overall section thick-ness, the value of k drops to zero and the values fromequations (7) and (8) reduce to a case where thefusion zone simply contracts in proportion to itsshape from the starting temperature. It is difficult tosee that the choice of 1000 8C starting temperatureis realistic for such cases, as thermal contractions atthe higher temperatures could be restrained easilyby rather small forces, including self-weight andweld joint tacks. This point therefore requires specialattention when considering the experimental results.

A similar approach can be applied to other typicalfusion zone shapes, such as parabolic and rectan-gular, as shown in Fig. 5. This confirms practicalexperience of the effects of weld preparation andfusion zone shape on angular distortion. As angulardistortion triggers out-of-plane distortion by dis-placing the longitudinal contraction force from theneutral axis of the cross-section, it can be understoodthat fusion zone shape has a profound effect on theoverall out-of-plane deformations.

3 FINITE ELEMENT IMPLEMENTATION

3.1 Thermal transients

The transient temperature profiles in the present studywere determined computationally, as outlined in sec-tion 1.2, rather than through the analytical treatmentsdescribed in section 2.1. Conduction has the maineffect on the thermal history of the plates duringwelding, but convection and radiation effects werealsomodelled, following the scheme described in refer-ence [6]. Non-linear conduction properties were intro-duced through standard conductivity and enthalpy

Fig. 3 Schematic diagram of transverse deformation





data (data obtained in a study on C–Mn plate steelby S. Wen, 2003, personal communication) coveringtemperatures in the range from ambient to 2000 8C.This approach takes into account phase changes. Alter-native computations were carried out using twodifferent configurations of volumetric heat input. Inthefirst, the thermal energywas applied to a fully pene-trated V preparation and, in the second, a 0.5mmunpenetrated root was simulated. The temperature

difference Tm between the two models was no greaterthan 5 8C at 20mm distance from the weld centre-line.

3.2 Thermomechanical algorithm

The MTS and TCS formulations from Okerblom’streatment, as described in section 2, were used toimpose longitudinal and transverse strains on elasticfinite element models of the large plate assemblies.

Fig. 4 Relation between k, s=t, and "Y=�Ts for a triangular fusion zone. (After reference [7])

Fig. 5 Relation between k and s=t for various fusion zone shapes. (After reference [7])





Introducing an ambient temperatureTa, the overalllongitudinal contraction in the structural model canbe found by applying a ‘load’ profile correspondingto an artificial temperature reduction equal to�½TlðyÞ � Ta� at points y across the width of theplane strain strip. The magnitude of TlðyÞ is sufficientto develop contraction strain corresponding to �"Yin regions A and B of Fig. 2 and zero strain in regionD. The limiting node positions y1 and y2 for theseregions are such that Tmðy1Þ ¼ 2"Y=�þ Ta andTmðy2Þ ¼ "Y=�þ Ta. In region C, a further simplifica-tion was adopted to reduce the element budget andthe corresponding computation time. The tempera-ture profile was assumed to follow an inverserelationship with respect to the transverse distance[equation (2)] such that the ‘load’ temperaturescould be defined in terms of a constant At, derivedfrom the computational thermal analysis. Hence,the artificial temperature drop was given by

TlðyÞ ¼ 2Ta þ"Y�

� At

yð9Þ

In the case of the transverse contractions, the pene-tration of the fusion zone profiles in the test weldsexceeded the values where the correction parameterk would have been applicable. Hence, the fusionzone was simply defined by the points correspondingto the ‘start of cooling’ temperature of 1000 8C, thesebeing nearer the centre-line of the weld joint thanthe points y1 defining the width of the yielded zone.Orthotropic coefficients of expansion were used to

enable the artificial temperature loads at a givenpoint to generate the required simulated thermome-chanical strains in the finite element implementation.In the longitudinal axis, the actual coefficient ofexpansion was used but, in the transverse and thick-ness directions, the coefficient was set to zero, apartfrom in the fusion zone, where it was set to a value�T given by

�T ¼�

Ta � Ts

Ta � "Y=�

�� ð10Þ

The flow chart for the ‘simultaneous’ algorithm,whereby transverse and longitudinal temperature‘loads’ were applied together is given in Fig. 6. The algo-rithm for the alternative ‘sequential’ implementationwas given in reference [3]. In this case the transversedeformations are applied first and the resulting plateshape, which is distorted angularly along the wholelength of the plate, provides the starting point for simu-lation of the longitudinal deformation process.

3.3 Other computational features

The flow chart (Fig. 6) also shows that the computa-tion can be carried out alternatively in terms of a

plate assembly which is initially perfectly flat, or onewhere the initial out-of-plane shape has beenmeasured and is used as the starting point for thesimulation. The ‘initial shape’ sub-algorithm isshown in Fig. 7. This algorithm made use ofsmoothing procedures detailed in reference [10].

The weight of the plate assembly was supported, asin the real case, at a number of specified points.ANSYS LINK 10 elements, consisting of two-nodeelements having three translational degrees offreedom per node, were used at the support points.The elements were set to exhibit stiffness undercompressive loads but to assume zero stiffness intension. Non-linear geometry capability was speci-fied, together with the Newton–Raphson line-searchsparse-direct equation solver. Figure 8 shows thefinite element model, including boundary conditions.Various effects related to choice of Poisson’s ratio,coefficient of expansion, fusion zone shape, andload-stepping strategies were investigated to opti-mize the computational process. The application ofthe artificial strains within a one-load step analysissignificantly reduced the computational time. Typi-cally the simulations required between 2 and 3h,when performed on a dual-processor workstationwith 2.2GHz central processing unit and 1Gbyterandom-access memory.

Figure 9 shows a sample computed result using the‘simultaneous’ algorithm. This assumed that the platewas flat initially but supported at specific points, asdescribed in the next section, so that the weight ofthe plate generated small out-of-plane deformations.These ripples are magnified by the longitudinaltension in the welding simulation and this is accom-panied by an angular distortion of 1.058.

4 FULL-SCALE WELDING EXPERIMENTS

4.1 Equipment and test assemblies

The full-scale tests were carried out using a purpose-built rig (Fig. 10) consisting of several integratedsystems with automatic data capture, to carry outthe following functions:

(a) to complete a single-pass full-penetration auto-matic metal–inert gas (MIG) weld with Ar–CO2

shielding and flux-cored wire, the voltage,current, and travel speed being monitoredcontinuously;

(b) to measure temperatures continuously duringwelding and cooling, using thermocouples infixed locations on the plate and a thermographiccamera for whole-field recording;

(c) to measure overall out-of-plane transient defor-mations during welding and cooling, using





linear variable displacement transducers (LVDTs)in a fixed array (Fig. 11);

(d) to measure out-of-plane deformations over thewhole plate, before and after welding and cooling,using a laser scanning system.

The C–Mn steel plates (BS4360 grade 50D) weresupported on an array of height-adjustable point

supports, fixed to a moving frame in the layoutshown in Fig. 11. This frame was traversed at therequired welding speed under the welding head andthermographic camera which were mounted in afixed position. The relative deformation data acquiredby the LVDTs were processed to measure the angulardistortions and longitudinal profiles over the platearea spanned by the array.

Fig. 6 Thermoelastic ‘simultaneous’ algorithm





The MIG weld was applied to a 608 included angle Vpreparation. A ceramic backing strip was used toprevent burn-through, as there was some variation inthe root gap. Welding conditions were 26V, 210–225A,and 5.75mm/s travel speed, giving a nominal grossheat input of 950 J/mm. Correlation with the thermo-couple data indicated a weld energy input efficiencyof 70 per cent.The plate specimens were shot blasted, primed,

and laser cut to size by the industrial partner in theproject, in order to embody commercially realisticpractice in the trials. Typical variations in fit-up andweld tacking procedure were also permitted, to givesome indication of sensitivity to such variations.The plates, when offered up for assembly and tacking,proved not to be ideally flat and it was not alwayspossible to align both sides of the joint to acommon plane. Likewise, the initial aim to have atight butt joint with no gap was not achievedthroughout and in some cases a gap of 1–2mmresulted.Different tack weld assembly strategies were

applied, in the light of known variations in industrialprocedures and continuously developing evidencefrom the test welds. In all cases, the run-on–off tabswere fillet welded first, as illustrated in Fig. 10.

Then, in the first three specimens, longitudinal weldtacks were applied consecutively on the undersideof the joint at 250mm pitch, beginning at the startingedge of the intended weld run. The disadvantage ofthis procedure was that it proved to be difficult toforce the weld preparation edges level, particularlytowards the end of the joint. Two measures wereapplied to deal with this. In specimens 3–6, the tackspacing was increased to 307mm pitch (this alsoreflected advice on typical practice from the indus-trial partner). Also, for specimens 4 to 6, a sym-metrical tacking strategy was adopted, starting atthe centre of the weld run and working outwards,towards both ends. This procedure resulted in anincreased tendency to angular distortion in the initialplate shape, but less force was required to bring thesespecimens into alignment. Eventually, in the two finaltests, small mismatches in plate height were simplytolerated, in order to reduce further any ‘locked-in’bending moments due to forced levelling and tackingprocedures, as applied in specimens 1 to 4.

The initial out-of-plane deformation patterns of theassembled plates mounted on the rig could fairly bedescribed as unstable, as relatively small out-of-plane forces on the surface of the assembled platescould flip the initial shape from one configuration

Fig. 7 Initial shape subalgorithm





to another. This is relevant to the outcomes of eachtest, as will be noted later.

4.2 Results and discussion

The measured deformation behaviour of the largebutt-welded plates was found to be complex.

Variations between different test specimens wereidentified, due to initial shape imperfections, effectsrelated to initial assembly and weld tacking pro-cedures, transient mechanical variations in boundarysupport conditions, and variations in the weldingconditions. These variations led to inconsistencies inmeasured distortions between the different tests.

Fig. 8 Finite element modelling of butt welds

Fig. 9 Computed out-of-plane deformation of an initially flat plate





These effects are nevertheless encountered normallyin industrial practice and therefore represent a realisticchallenge for the simulation of welding. The experi-mental programme highlighted the fact that most ofthe final out-of-plane movement takes place longafter the weld has been completed. This findingimplies that detailed knowledge of high-temperaturematerial properties may not be crucial to the simu-lation process (as it would be for welding processsimulation of metallurgy-dependent phenomena).The net out-of-plane deformations (final minus

initial deformations) varied substantially for eachspecimen in the series. Test specimens 2 and 4 wereparticularly eccentric, as the final 0.5m of these plateassemblies flipped from positive to negative angulardeformation, leaving a severe transverse fold at thetransition point (as shown in Fig. 12). It should benoted that, in this figure, the zero coordinate on the‘length’ axis corresponds to the start-of-weld position.The reasons for this behaviour will be discussed later.Aside from these two cases, the deformation

patterns were characterized largely as magnificationsof the initial deformations and these were simulatedreasonably by the computational model. Figure 13

shows a direct comparison between the test resultfor specimen 6 and the corresponding ‘simultaneous’computation. This is one of the most accurate resultsand, although the computation underestimates thedeformations a little, it replicates the complex patternwell.

The capability of the computational method tomodel angular deformation is particularly important,as the resulting cross-sectional shape drives the longi-tudinal behaviour. Figure 14 shows overall contourmaps of angular deformation in specimen 5 and againindicates good comparison. The overall root-mean-square (r.m.s.) values of experimental and calculatedangular deformations are almost identical, althoughsuch a measure allows differences at each point, asobserved. It is also noteworthy that the angular defor-mations in the experimental case are highly concen-trated in the fusion zone, as assumed in the simpleOkerblom model for transverse deformation.

However, there were discrepancies between theexperimental and calculated deformation patterns,not least for specimens 2 and 4, and it is of interestto determine the reasons. Figure 15 shows thedevelopment of angular deformation and curvature

Fig. 10 Schematic diagram of welding rig

Fig. 11 Layout of supports and LVDTs





Fig. 12 Net out-of-plane deformation: specimen 4

Fig. 13 Experimental and calculated deformations: specimen 6





Fig. 14 Experimental and calculated angular deformations: specimen 5

Fig. 15 Dynamic distortion results: specimen 5





during test 5, in the region covered by the measure-ment system (see Fig. 11). As the heat source passes,the assembly deforms quickly into a V-shape andcontinues to do so more slowly until the whole platehas cooled to ambient temperature over a longperiod. The step changes in angular deformation,which can be seen in the trace, are found in all thetests and correspond exactly to the points wheretack welds were fused, as the heat source passed.This event releases the plates to the influence of thetransverse contraction forces in the trailing region ofthe weld. In the case of longitudinal curvatures (nega-tive curvature implies ‘hogging’ of the plate) there areminor variations during welding, but most of theeventual curvature in this region takes place duringthe long period of cooling to ambient temperature.The changes in curvature rate and direction duringwelding coincide with the points where the heatsource crosses the transverse axis of each supportpair, implying that the plate is lifting off varioussupports, as indeed was observed. Also note thatsagging curvature is promoted when the heat sourcepasses through the monitored region. This isexpected, as a consequence of the V-shape and therelative expansion of the weld zone during thisinterval.The pattern of dynamic deformation behaviour in

test 2, which was unstable, is shown in Fig. 16. Thecurvature changes are much more exaggerated butalso relate to the support positions. In this case, theimplication is that changes in curvature after weldcompletion have been enough to raise the plate off

the final pair of supports and the cantileveredweight of overhanging plate has triggered an unstablereversal of angular deformation and curvature step atthe 2479 s marker.

The variation in tacking procedure is probably alsoan important factor leading to divergent behaviour inthe tests, as the action of aligning the plate edges willgenerate initial transverse moments which are bothvariable and impracticable to incorporate in themodel. It is probably significant that the two resultsthat were best simulated were from the tests whereno clamping was applied.

In the case of these two abnormal test outcomes,improved simulation might be achieved by steppingthe artificial thermal load, thereby allowing the varia-tion in support conditions to influence the bucklingmodes of the plate assemblies. Similar measureswould be necessary to take account of in-built edgemoments due to initial misfitting of the butt edges,which were forced into alignment and tacked.

Overall comparison of calculated and test results isdifficult to characterize in the light of these variationsbut Table 1 provides a measure of comparisonthrough r.m.s. values. The values in the error columnsrepresent the r.m.s. differences between experimentaland calculated values at discrete points on themeasurement grid and the remaining data representthe r.m.s. values of all deformations in the plates.(In the case of specimens 2 and 4, the data from theend sections of the plates, which flipped to the oppo-site angular deformation state were missed out fromthe r.m.s. determination.)

Fig. 16 Dynamic distortion results: specimen 2





5 CONCLUSIONS AND SUMMARY

The main aim of this study was to investigate asimplified finite element simulation of out-of-planedistortion, caused by the process of fusion buttwelding. The key simplifications in this approachare embodied in analytical treatments of the angularand longitudinal deformations through the TCS andMTS algorithms respectively.From the computational viewpoint, the problem

has been reduced to an elastic finite element struc-tural model, with an artificial temperature loading,applied in a single load step. This was relativelysimple to implement and solved quickly. The ‘sequen-tial’ and ‘simultaneous’ alternative formulations ofthe interacting angular and longitudinal deforma-tions gave slightly different results, the latter probablybeing the more realistic.Comparison between the results of the simulations

and the out-of-plane deformations measured wasgood, bearing in mind the substantial variationsfound in practice, as discussed in section 4.2. Overallshape comparisons were good, except for twospecimens where other factors intervened. Themagnitudes of angular deformations and overallout-of-plane deformations were predicted wellenough to be useful as a guide to what wouldhappen in a practical case. If anything, the simula-tions slightly underpredicted the real deformations.The principal value of the simulation process there-

fore is that it provides a background prediction, whichgives insight into the causes of distortion and a tool toformulate possible remedies. For example, it is clearthat initial shape imperfections are crucial to theprocess of prediction, as also are in-built edgemoments and support conditions, especially for flex-ible plates subject to gravitational out-of-plane forces.The thermal simulation aspect of the programme

has not been discussed in detail, but it is worthnoting that a relatively simple two-dimensional treat-ment was effective in terms of describing the thermaltransients, at least to the extent necessary to provideinput values to the thermoelastic simulation. The

prediction accuracy does depend, however, on somemeans of correlating the overall simulated heatinput to the actual weld power.

Summarizing, the following conclusions can bedrawn:

1. A finite element computational procedure forsimulating the process of industrial-scale fusionbutt welding has been demonstrated, wherebythe thermoelastic–plastic part of the computationis replaced by simple analytical algorithms. Non-linear structural behaviour arises in this type ofthin flat geometry and a non-linear displacementanalysis capability is essential.

2. The thermal part of the simulation scheme wasbased on simplified two-dimensional finite elementmodelling. The thermocouple and thermographicmeasurements of temperature confirmed that thisapproach was adequate for the test cases, whichinvolved high-power fast-moving heat sources.

3. The simulation results for out-of-plane deforma-tions compared well with full-scale welding trials,in terms of both overall shape characterizationand magnitudes of angular and overall deforma-tions.

4. The success of the simulation process clearlydepends on the quality of input data and it wasfound, not surprisingly, that input information onthe initial shape of the test pieces was crucial toaccurate prediction. It was also clear that deforma-tions due to self-weight were important, both inthe initial state and transiently during the weldingand cooling process. An advantage of the simplifica-tion inherent in the procedure is that the availablecomputing power can be directed to modelling ofthe structural features which have a powerful influ-ence on the deformation behaviour.

ACKNOWLEDGEMENTS

The project has been supported by the Engineeringand Physical Sciences Research Council and BAE

Table 1 Comparison of test results and calculations (r.m.s. basis)

Specimen

Experimentalout-of-planedeformation(mm)

Simulationout-of-planedeformation(mm)

Error(mm)

Experimentalangulardeformation(deg)

Simulationangulardeformation(deg)

Error(deg)

1 7.16 5.18 5.88 1.23 1.30 0.822 n/a* 5.11 n/a* n/a 1.28 n/a3 8.20 5.14 7.59 1.42 1.33 0.924 n/a* 6.00 n/a* n/a 1.46 n/a5 7.11 5.55 3.9 1.38 1.39 0.496 8.83 6.55 3.20 1.45 1.18 0.57

n/a, not available.*See text.





Systems Marine. The authors gratefully acknowledgethe participation in the project of Dr NormanMacPherson of BAE Systems and colleagues at theUniversity of Strathclyde, Alex Galloway, Dr CheeKong Lee, and Henry Tan.

REFERENCES

1 Huang, T. D., Dong, P., DeCan, L. A., and Harwig, D. D.Residual stresses and distortions in lightweight shippanel structures, Northrop Grumman. Technol. Rev. J.,2003, 11(1), 1–26.

2 Bruce, G. J., Yuliadi, M. Z., and Shahab, A. S. Towards apractical means of predicting weld distortion. SNAME J.Ship Prod., May 2001, 17(2), 62–68.

3 Camilleri, D., Comlekci, T., and Gray, T. G. F. Out-of-plane distortion of CMn steel plates during flux-coredCO2/Ar automatic butt welding. In Proceedings of theInternational Conference on Metal Fabrication andWelding Technology (METFAB-2003), September 2003,pp. 117–127.

4 Rosenthal, D. The theory of moving sources of heat andits application to metal treatments. Trans. Am. Soc.Mech. Engrs, 1946, 68(8), 849–866.

5 Lindgren, L. E. Finite element modeling and simulationof welding. Part 1: increased complexity. J. ThermalStresses, 2001, 24, 141–192.

6 Camilleri, D., Comlekci, T., Lee, C. K., Tan, H., andGray, T. G. F. Investigation of temperature transientsduring flux-cored CO2/Ar butt welding of CMn steelplates. In Proceedings of the International Conferenceon Metal Fabrication and Welding Technology(METFAB-2003), September 2003, pp. 107–116.

7 Okerblom, N. O. The Calculations of Deformations ofWelded Metal Structures, 1958 (Her Majesty’s StationeryOffice, London).

8 Wickramasinghe, D. M. G., and Gray, T. G. F. A simpletreatment of welding distortion. Weld. Res. Int., 1978,8(5), 409–422.

9 Wells, A. A. Heat flow in welding. Weld. J., Weld. Res.Suppl., 1952, 31, 263s–267s.

10 Comlekci, T., Camilleri, D., and Gray T. G. F. Finiteelement representation of experimental surface defor-mation data from fusion welded plates. In Proceedingsof the 11th Annual Conference of the Association forComputational Mechanics in Engineering, Glasgow,2003, pp. 33–36.

APPENDIX

Notation

At temperature distribution coefficient [seeequation (9)]

b fusion zone width (see Fig. 3)c specific heatE Young’s modulush centroid offset (see Fig. 3)I transverse second moment of area (see Fig. 3)k angular contraction parameter (see Fig. 3)s penetration depth (see Fig. 3)t plate thicknessTa ambient temperatureTl cooling temperature for a longitudinal artificial

loadTm maximum temperature at the y coordinate from

thermal analysisTs starting temperature for the angular

deformation processv weld travel speedx‚ y longitudinal and transverse coordinates

respectively in the plate

� expansivity�T artificial expansivity for transverse

deformations� coefficient of loss of temperature�av average transverse mechanical deformation

(see Fig. 3)�c transverse mechanical deformation

(compressive) (see Fig. 3)�e transverse elastic deformation in the weld (see

Fig. 3)�m transverse mechanical deformation (see Fig. 3)�t transverse mechanical deformation (tensile)

(see Fig. 3)�T thermal deformation (see Fig. 3)"Y yield strain� angular deformation (see Fig. 3)� thermal diffusivity� density�Y yield strength





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