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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2907–2917

journa l homepage: www.e lsev ier .com/ locate / jmatprotec

rediction of laser beam welding-induced distortionsnd residual stresses by numerical simulation foreronautic application

uhammad Zain-ul-Abdeina, Daniel Neliasa,∗, Jean-Francois Julliena,ominique Deloisonb

LaMCoS, INSA-Lyon, CNRS UMR5259, F69621, FranceEADS Innovation Works, 12, rue Pasteur, BP 76, 92152 Suresnes Cedex, France

r t i c l e i n f o

rticle history:

eceived 26 March 2008

eceived in revised form

3 June 2008

ccepted 24 June 2008

eywords:

aser beam welding

hermo-mechanical analysis

esidual stress

a b s t r a c t

This paper focuses on the prediction of laser beam welding-induced distortions and residual

stresses through numerical simulation. Fabrication of fuselage panels of latest generation

civil aircraft involves welding of stringers on thin sheets of 6056T4 aluminium alloy. The

efforts are made to exercise better control over the excessive out-of-plane distortions. A

series of experiments have so far been performed using small specimens. One of the test

cases that include single-pass fusion welding on a 6056T4 thin sheet with the industri-

ally used thermal and mechanical boundary and loading conditions is being studied in this

work. Laser beam welding in the keyhole regime is employed. The test plate is maintained

in position with the help of an air suction table made of aluminium. Although a pressure

of 1 bar is used experimentally, yet the possibility of leakage cannot be overruled. Various

magnitudes of pressures are, therefore, introduced during numerical simulation to study

istortion

056T4 aluminium alloy

the effect of each. The effect of contact between test plate and support over thermal and

mechanical results is also integrated. A 3D symmetric model of test plate and support is

incorporated and the comparison between simulation and experimental results is devel-

oped. Finally, a good correlation is found between experimental and simulation results, on

the basis of which residual stress state in the test plate is predicted.

Laser beam welding involves several complex phenom-

. Introduction

aser beam welding is believed to be beneficial in terms ofime saving and weight reduction for the manufacturing of theeronautical structures. Riveting has so far been used industri-lly to assemble the fuselage panels of aircrafts with stiffeners.he laser beam welding, in fact, effectively eliminates the

arge quantity of material added to the aircraft structure inhe form of rivets. However, accompanied with its blessings,elding always brings some inconveniences like distortions

∗ Corresponding author. Tel.: +33 4 72 43 84 90; fax: +33 4 72 43 89 13.E-mail address: daniel.nelias@insa-lyon.fr (D. Nelias).

924-0136/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2008.06.051

© 2008 Elsevier B.V. All rights reserved.

and residual stresses. In the recent years, numerical simula-tion has proven itself to be a useful tool in predicting thesewelding-induced distortions and residual stresses. The knowl-edge of residual stress distribution and distortions may thenlead to the better control over the undesirable aspects of theprocess.

ena like formation of keyhole, weld pool geometry, plasmaformation, etc. Sudnik et al. (2000) discussed the mathemat-ical model of keyhole formation and studied the simulation

g t e

ab

2908 j o u r n a l o f m a t e r i a l s p r o c e s s i n

of weld pool geometry with keyhole formation and varyingwelding parameters, namely laser beam power and weld-ing speed. According to their findings, there exists a linearrelationship between the length and depth of the weld poolfor laser beam welding experiments with varied laser beampower and constant welding speed; while on the other hand,the weld pool length changes slightly with varying weld-ing speed and constant laser beam power. The experimentalwork presented here uses constant welding speed (8 m min−1)and constant laser beam power (2.3 kW), so as to minimizethe dependency of weld pool geometry over these factors.Jin et al. (2003) focussed upon heat transfer model based onan actual keyhole and discussed the thermal gradient andmelt pool shape around the keyhole on the surface of thetest specimen. Olmedo (2004) also discussed the principalof laser beam welding with special reference to aluminiumalloys used for aeronautical applications. Ferro et al. (2005)proposed a cone-shaped heat source model with an upper andlower sphere to predict the shape of weld pool and thermalgradient around the keyhole formed during electron-beamwelding. Heat source model used in this work also takes care ofkeyhole formation and temperature distribution. Comparisonbetween experimental and simulated results for distortionsis developed by Tsirkas et al. (2003) who used the commer-cial software SYSWELD for simulation. Darcourt et al. (2004)attempted to predict laser beam welding-induced distortionsin a T-joint configuration and suggested that a correct thermalanalysis is mandatory to predict welding-induced distortionsand residual stresses. Josserand et al. (2007) have also triedto predict laser welding-induced distortions for an aeronau-tic aluminium alloy while working on thin test plates. Theyhave suggested that the initial surface profiles of the test platedue to pre-processing, like rolling, etc., play an important rolein defining the distortions level of test plate. In this workthe effort is, therefore, made to predict the residual stressstate and distortion pattern by numerical simulation givingdue care to the factors affecting final result. For instance, thedisplacement field of the test plates is measured in a wayso as to minimize the effect of pre-processing phenomena.Moreover, the industrially employed complex thermal andmechanical boundary conditions are integrated, which havenot previously been taken under consideration for numericalsimulation.

The fuselage panels of aircraft structures are large-thinsheets of an aluminium alloy 6056T4 with stringers weldedupon them. The typical total length of seam reaches 50 mor more. Industrially, these panels are kept in position withthe help of suction force applied through an aluminiumfixture. This is done to avoid out-of-plane displacementsof the panels during welding. However, after the releaseof suction force, i.e. at the end of welding, the out-of-plane deformations dominate. In order to uncouple thecomplexities involved in the process, a step-wise approachhas been adopted for the small-scale experiments thatinclude:

. Fusion welding of test plate without filler material.

. Fusion welding of test plate with filler material.c. T-joint welding of base plate and stiffener with filler mate-

rial.

c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2907–2917

In this work the emphasis is given to the prediction ofout-of-plane displacements and residual stress distributionduring fusion welding of test plate without filler mate-rial.

2. Experimental approach

An instrumented experimental campaign was carried out inorder to have a reference database necessary for numericalsimulation. Various test plates were welded with differ-ent welding parameters and with a variety of thermal andmechanical boundary conditions. The test case presented hereincludes single-pass fusion welding of test plate of material6056T4 and dimensions 200 mm × 300 mm × 2.5 mm with thefollowing welding parameters:

• Power: 2300 W.• Speed: 8 m min−1.

During the experiment, a fusion line was created length-wise in the middle of the test plate and a distance of 5 mm wasleft at both ends. The test plate was held in position with thehelp of an aluminium suction table (25 mm thick). The suctionforce was applied over the entire bottom surface of the testplate. A pressure of 1 bar was maintained during welding andcooling, while after sufficient cooling time the pressure wasreleased to allow the test plate to deform freely. The tempera-ture histories were recorded with the help of thermocouples.A total of nine thermocouples were used to record tempera-tures at various distances from the weld pool. Thermocouplesnamed as TC1, TC2, TC3, TC4 and TC5 were installed on theupper surface, while TC7, TC8 and TC9 were installed on thebottom surface and TC6 was installed in the depth of 0.31 mmbeneath the weld line. The displacement fields were measuredwith the help of 3D image correlation technique applied on theentire upper surface of the test plate, both before and afterwelding. The width and depth of weld pool were measured bymicrography. The geometry of the test plate with thermocou-ple positions and the experimental setup with plate mountedon aluminium suction table are shown in Fig. 1. The red linesin Fig. 1 present the weld line and the red arrows indicate thewelding direction.

Owing to the contact between the test plate and the table,it is believed that some of the heat energy is lost due to thethermal conductance. Moreover, the in-plane displacementsdue to expansion and contraction during welding and cooling,respectively, give rise to the friction at the interface betweenthe test plate and the table.

Since it was observed with the help of 3D image correlationtechnique that the test plate is not perfectly straight ratherthere exists an initial curvature in the test plate, the differ-ence between initial (before welding) and final (after welding)state is taken as standard to be compared later with numer-ical simulation results. The surface profiles before and afterwelding taken from the upper surface of the test plate are

shown in Fig. 2. Here, ‘after welding’ means after completecooling and release of the pressure from the suction table. Itis observed from the difference profile (Fig. 3) that the maxi-mum out-of-plane displacements/vertical displacements are

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2907–2917 2909

Fig. 1 – Geometry of test plate with thermocouple positions (left); experimental setup (right).

ight

pmTtsrfdamu

Fig. 2 – Initial (left) and final (r

resent towards the center of the test plate, while the mini-um values are at the start and stop ends of the weld seam.

he probable reason being the pre-bended/buckled state ofhe test plate. Moreover, during welding the in-plane expan-ion and contraction of the central regions of the test plate areestricted by their adjacent regions and hence to compensateor these expansion and contraction occurrences the test plate

eform more in the out-of-plane direction at the center thant the weld start and stop edges. These out-of-plane displace-ents reach up to 1.05 mm at the middle of the test plate and

p to 0.89 mm at the edges, thereby defining the range for max-

Fig. 3 – Maximum and minimum

) surface profiles of test plate.

imum and minimum values; the numerical simulation resultswill be compared in this range.

Fig. 3 shows the maximum and minimum vertical displace-ments as a function of the distance across the weld joint,obtained from the difference profile shown on the right. Themaximum and minimum values are noted at the intersec-tion of test plate and a cutting plane passing through the test

plate across the welding direction and moving in the weldingdirection.

Assuming weld joint an axis of symmetry, the vertical dis-placements of right half of the test plate will be considered

out-of-plane displacements.

g t e

2910 j o u r n a l o f m a t e r i a l s p r o c e s s i n

only. In addition to the specimen’s geometry and thermo-mechanical properties of the material, it is assumed that themagnitude of vertical displacement is influenced by the fol-lowing three factors:

• The amount of heat energy absorbed by the test plate duringwelding which has a direct influence on the geometry of theweld pool and the temperature fields in the vicinity of theweld joint.

• The friction coefficient present at the interface of the testplate and the support.

• The actual suction pressure present at the bottom surface ofthe test plate; as there is a possibility of air leakage from theboundary of the test plate which is, in fact, simply placedon the suction table with a very fine rubber joint to avoidleakage. Yet during welding the leakage is observed due toin- and out-of-plane expansion and contraction of the testplate.

These factors are given emphasis in this work and are beingstudied for the first time with reference to friction coefficientand suction pressure. Different friction coefficients and suc-tion pressure values will be used to analyze the affect of eachon the final distortion level.

3. Finite element model

Numerical simulation has been performed using the commer-cial finite element code Abaqus/Standard. The finite element(FE) model of the test plate and support consist of contin-uum solid three-dimensional linear elements. The test plate

mesh consists mostly of 8-nodes brick elements (type: DC3D8,C3D8R) completed by some 6-nodes prism elements (type:DC3D6, C3D6), for 58,000 nodes and 50,000 elements; whilethat of mesh of support consists only of 8-nodes brick ele-

Fig. 4 – Plate and support mesh with dimensions

c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2907–2917

ments with a relatively coarse mesh size. Taking the weldline as an axis of symmetry, a symmetric model is assumedin order to minimize the degrees of freedom and conse-quently the calculation time. Due to the high thermal gradientin the fusion and heat-affected zones the mesh in theseregions is considerably fine where mostly brick elementsare used. The dimensions of the smallest brick element are0.5 mm × 0.3 mm × 0.31 mm (Fig. 4). As the temperature gradi-ent is considerably low outside the heat-affected zone (HAZ), arelatively coarser mesh is deemed sufficient for analysis. Thesize of the mesh increases progressively away from the axisof symmetry, i.e. fusion line. To compensate for the increasein size of brick elements prism elements are used selectively.Lengthwise, there are 600 elements at the fusion line whichthen reduce to only 30 at the far end of the test plate; whilethickness-wise there are 8 elements at the fusion line whichfinally reduce to 2 at the far end. The model is shown inFig. 4.

An uncoupled thermo-mechanical analysis approach isemployed, where the thermal analysis is first performed inde-pendently in order to adjust the heat source parameters andincorporate the complex thermal boundary conditions includ-ing free and forced convection and thermal contact resistancebetween the test plate and the support. Temperature histo-ries calculated during thermal analysis are then used as apredefined field for mechanical analysis. Other mechanicalboundary conditions and loadings are applied during mechan-ical analysis.

4. Thermal analysis

The thermal analysis was performed using temperaturedependent thermal material properties. The transient temper-ature field T in time (t) and space (x, y, z) is acquired by solving

(mm) of brick elements in the fusion zone.

t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2907–2917 2911

t

Hpttg

imGsbeiaFdeeaeisifiataoouw

fii

Fs

j o u r n a l o f m a t e r i a l s p r o c e s s i n g

he following heat transfer equation:

∂

∂x

(k(T)

∂T

∂x

)+ ∂

∂y

(k(T)

∂T

∂y

)+ ∂

∂z

(k(T)

∂T

∂z

)+ Qint

= �(T)Cp(T)(

∂T

∂t

)(1)

ere, k(T) is the thermal conductivity as a function of tem-erature in W m−1 K−1, �(T) is the density as a function ofemperature in kg m−3, Cp(T) is the specific heat as a func-ion of temperature in J kg−1 K−1 and Qint is the internal heateneration rate in W m−3.

The heat source modeling is considered to be the mostmportant aspect of the welding thermal analysis. Various

odels including cone-shaped volumetric heat source withaussian distribution and double-ellipsoidal volumetric heatource in accordance with Goldak et al. (1984) exist that maye employed for a variety of welding processes like TIG, MIG,lectron-beam welding, laser beam welding, etc. The choices, however, largely dependant upon the size of the weld poolnd the temperature field recorded in or near the weld pool.or instance, Lundback and Runnemalm (2005) used Goldak’souble ellipsoid with double elliptic cone to simulate thelectron-beam welding process with keyhole. Similarly, Ferrot al. (2005) used conical distribution of heat flux with an uppernd lower sphere to incorporate the keyhole phenomenon oflectron-beam welding process. A similar kind of heat sources also integrated in this work. Cone-shaped volumetric heatource with Gaussian distribution and an upper hollow spheres used to attain the required weld pool size and temperatureelds. In practice, the laser beam penetrates the test plate cre-ting a capillary-shaped keyhole to a required depth, whilehe impingement zone experiences material evaporation andcomparatively wider fusion zone appears. The conical part

f the heat source is, therefore, meant to capture the effectf keyhole formation due to laser beam penetration; and thepper hollow sphere is incorporated to achieve the desiredidth of fusion zone. The heat source model is shown in Fig. 5.

Eq. (2) gives the combined heat source model where therst part represents the Gaussian distribution of the heat flux

n the cone and the second part corresponds to a linear distri-

ig. 5 – Conical Heat source model with an upper hollowphere.

Fig. 6 – Schematic diagram of thermal boundary conditions.

bution of the heat flux in a hollow sphere.

Qv = 9�P · f

�(1 − e−3)· 1

(ze − zi)(r2e + reri + r2

i )

·exp

(−3r2

r2c

)+ 3�P · (1 − f )

4�(res − ris)3· ds (2)

where

rc = ri + (re − ri)z − zi

ze − zi

Here, Qv is the total volumetric heat flux in W m−3, P is thelaser beam power in W, � is the efficiency of the process, f isthe fraction of the heat flux attributed to conical section, r isthe current radius as a function of Cartesian coordinates x andy, rc is the flux distribution parameter for the cone as a func-tion of depth (z), ds is the flux distribution parameter for thehollow sphere such that its value is 1 at inner radius of sphere(ris) and 0 at outer radius of sphere (res). re and ri are largerand smaller radii of the cone, respectively. Similarly, ze and zi

are upper and lower z-coordinates of the cone, respectively.The parameters are also shown in Fig. 5. An efficiency (�) of37% is used for the thermal analysis with power (P) of 2300 W.The remaining parameters are adjusted to obtain the requiredweld pool geometry. A latent heat of fusion of 4 × 105 J kg−1 isused between the solidus and liquidus temperature of 587 ◦Cand 644 ◦C, respectively.

Owing to the complex nature of thermal boundary condi-tions at the bottom surface of the test plate forced convectionand thermal contact resistance are used. Forced convection isassumed to be present due to air suction through suction tableand leakage at the boundaries of the test plate. Similarly, astest plate comes in contact with aluminium suction table dueto air suction, thermal conductance as a function of pressureis also introduced at the interface of test plate and suctiontable. Free convection and radiation to atmosphere are usedat all the remaining surfaces except the symmetric plane. Aschematic sketch of thermal boundary conditions is shownin Fig. 6, where free convection and radiation is assumed tobe present at all the surfaces of the plate except the bottomsurface, while at the bottom surface it is assumed that forcedconvection is present due to air suction and leakage and ther-mal conductance is present at the interface of the test plateand aluminium support.

Eqs. (3)–(5) define qconv+rad, qth cond and qforced conv as generalboundary conditions.

4 4

q conv+rad = hfree conv(T − T0) + �ε((T − Tabs) − (T0 − Tabs) )

(3)

qforced conv = hforced conv(T − T0) (4)

2912 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2907–2917

sion

Fig. 7 – Comparison of the weld fu

qth cond = hth cond(Ts − T) (5)

where, T, T0, Tabs and Ts are the temperature of the testplate, ambient temperature, absolute zero and tempera-ture of the support, respectively. The values used for theheat transfer coefficients and radiation constants are asfollows:

• Convective heat transfer coefficient of air, hfree conv =15 W K−1 m−2.

• Emissivity of aluminium surface, ε = 0.08.• Emissivity of speckle pattern, ε = 0.71.• Stefan–Boltzmann constant, � = 5.68 × 10−8 J K−4 m−2 s−1.• Convective heat transfer coefficient for air suction,

hforced conv = 200 W K−1 m−2.• Heat transfer coefficient at the interface of the test plate

and support, hth cond = 50 W K−1 m−2 at 0 bar, 84 W K−1 m−2

at 1 bar.

A volumetric heat flux Qv, as defined in Eq. (2), is intro-duced in the Abaqus model through a user subroutine DFLUXprogrammed in FORTRAN. The heat source parameters areadjusted in order to achieve the experimentally observed

Fig. 8 – Time–temperature curves at TC1, TC2 and T

zone, experiment vs simulation.

weld pool geometry. Fig. 7 compares the weld pool geometryobserved experimentally and numerically.

The physical phenomena occurring at the level of weld poollike formation of keyhole, ionization and vaporization of mate-rial, circulation of molten material within the weld pool dueto electromagnetic and buoyancy forces, solidification at theliquid–solid interface, etc. are difficult to model. Various sim-plifications are, therefore, required to be assumed. In this workthe weld pool is treated as a solid phase for calculating thetemperature fields only. The temperature histories recorded inthe vicinity of the weld pool during experimentation are thencompared with the numerically simulated time–temperaturecurves at positions TC1 to TC9 (Fig. 1). Figs. 8 and 9 presentthis comparison of temperature histories at the upper andlower surface and in-depth beneath the fusion line, respec-tively.

A good accordance is found between experimental andsimulation results. The disagreement between peak tem-peratures at some of the thermocouple positions, however,may be attributed to some inaccuracies in heat flux

distribution—assumed constant in the model, some impreci-sion in the thermocouple locations with respect to the fusionline, relatively coarser mesh away from the fusion zone, andthe simplifications assumed during numerical simulation.

C3 (upper surface); experiment vs simulation.

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h

F(

5

Htme(o

f

a

ε

Hoptppyε

wsa

a

F

ig. 9 – Time–temperature curves at TC6, TC7 and TC9lower surface); experiment vs simulation.

. Mechanical analysis

aving obtained the result of the thermal analysis, theemperature fields are used as predefined field for the

echanical analysis. The material assumes rate-dependentlasto-viscoplastic behavior with isotropic hardening lawMises plasticity model). The three-dimensional formulationf viscoplastic strain states:

(�, T, Hiso) < 0 (6)

nd

˙vp = 32

pS

�eff, where p =

( 〈f 〉�

)n

and �eff =√

32

S : S (7)

ere, f is the yield function that defines the limit of the regionf purely elastic response, Hiso shows isotropic hardeningarameters, T is the temperature, �eff is the Von Mises effec-ive stress, S is the deviatoric stress and � and n are viscosityarameters is the viscoplastic strain rate and is the cumulativelastic strain rate. The term rate-dependent implies that theield strength, �y = �y(εp, εp, T). The effect of plastic strain rate,

˙p, is essential to take care of viscous behaviour of material,hich is generally more pronounced at high temperatures,

pecially in fusion and heat-affected zones. This may, in turn,ffect the final residual stress state of test plate.

ig. 10 – Maximum and minimum out-of-plane displacements fo

n o l o g y 2 0 9 ( 2 0 0 9 ) 2907–2917 2913

As already mentioned, a suction pressure of 1 bar is appliedat the bottom surface of the test plate through an aluminiumsuction table to avoid out-of-plane distortions during weldingand cooling; yet the in-plane distortions due to expansion andcontraction of the test plate are not restricted which, in turn,give rise to friction at the interface of the test plate and thesuction table. Moreover, the suction pressure may also reduceto certain extent due to the leakage at the fine rubber joint ofthe support and the test plate. The subsequent discussion is,therefore, developed from two perspectives:

. Effect of various friction coefficient values on the out-of-plane displacements while keeping the suction pressureconstant.

b. Effect of various pressure values, provided the friction coef-ficient is constant.

5.1. Out-of-plane displacements

5.1.1. Effect of friction coefficientFrom literary sources (Beardmore, 2007), the value of the fric-tion coefficient between two aluminium surfaces could beapproximated to 0.57 when one of the surfaces is moving whilethe other is static. To observe the effect of various coefficientvalues, a separate simulation was run while maintaining thepressure equals to 1 bar. The following values were used:

• Friction coefficient, � = 0.4, 0.57, 0.8 and 1.0.

Simulation results are compiled and compared with theexperimental ones for out-of-plane displacements and arepresented in Fig. 10. It is to be noted that, due to the symmetryof the test plate, only the results of the out-of-plane displace-ments for the right half of test plate are shown. Moreover, allthe displacements are set to zero at a distance of 5 mm fromthe center of the test plate. This is because the experimen-tal results for displacement measures are not available in thefusion and heat-affected zones.

It can be observed from Fig. 10 that in spite of using

different friction coefficients, the simulation results for theout-of-plane displacements are least affected. The probablereason for this observation is that the mean contact pressure– of the order of 1 bar, i.e. 0.1 MPa – and the surface shear stress

r different friction coefficients; experiment vs simulation.

2914 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2907–2917

Fig. 11 – Maximum and minimum out-of-plane displacements at different pressures; experiment vs simulation.

The in-plane displacements, Uy, in the direction transverseto the fusion zone as measured with the image correlationtechnique are shown in comparison with the simulated valuesin the middle of the test plate in Fig. 13. A good correlation is

during welding and cooling are too less to cause any signifi-cant effect over the final distortion level. The choice for theadequate value of the friction coefficient is, therefore, madeat this stage and a value of 0.57 is taken as a standard; as thesame is suggested in literary sources (Beardmore, 2007) for thecase of a sliding-static interface which is actually the situationunder discussion.

5.1.2. Effect of suction pressureHaving established the friction coefficient value of 0.57, theeffect of various suction pressures is observed over the out-of-plane displacements. The possibility of leakage is presentat the rubber joint, which provides seal between the test plateand the suction table. This means that the overall pressurepresent at the bottom surface of the test plate is less than1 bar. Simulations are, therefore, run for the following pressurevalues to include the leakage effect:

• Pressure, p = 1 bar, 0.8 bar, 0.6 bar and 0.4 bar.

Comparison of all these simulations and experimentalresults is presented in Fig. 11. It is found that despite thelarge variations in pressure values the effect over the out-of-plane displacement values is less. Nevertheless this effectis quite systematic; the lesser the pressure the larger thedisplacement. It can also be observed that the experimentalresults lie somewhere in between the simulation results at1 bar and 0.8 bar. This means that in spite of leakage at therubber joint the effective pressure value is more than 80% ofthe applied pressure. The locations for maximum and mini-mum displacement values on the test plate are also shown inFig. 11.

These observations are, however, valid with respect to themaximum out-of-plane displacement values. The minimumout-of-plane displacement values recorded experimentallyare considerably different from the ones found during simu-

lation. The probable reason for this difference is the complexgrooved and drilled shape of suction table. The suction is cre-ated through these grooves and drilled-holes and it is likelythat the distribution of pressure at the bottom surface of thetest plate during the experiment is non-uniform, while duringsimulation a constant pressure is assumed to be present overthe entire bottom surface.

Subsequent comparison for out-of-plane displacements,Uz, with a suction pressure of 0.8 bar and a friction coeffi-cient of 0.57 is shown in Fig. 12. A good agreement may beobserved between experimental and simulated results. Dis-placement values are set to the scale of experimental valuesshown earlier in Fig. 3.

5.2. In-plane displacements

Fig. 12 – Maximum and minimum out-of-planedisplacements; experiment vs simulation.

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2907–2917 2915

ents

om‘io

5

Wfiattorwsicebsr

Fig. 13 – In-plane displacem

bserved on each side of the test plate. Due to the symmetricodel of the test plate, the displacement values for the part

not included’ in the numerical model are taken as a mirrormage of the values calculated in the meshed region with anpposite sign convention.

.3. Residual stress distribution

elding is characterized by highly non-uniform temperatureeld and high heat input. The stresses induced during weldingre, therefore, highly heterogeneous. In the molten weld poolhe stresses are released and can be assumed to zero. However,he expansion of the fusion zone exerts compressive stressesn the regions immediately adjacent to it. Once the mate-ial starts to solidify shrinkage takes place in the weld zone,hich then exerts stresses on the surrounding HAZ. These

tresses reside in the material after welding and may result

n unwanted distortions. The applied mechanical boundaryonditions may further increase the level of stresses; how-ver some of the stresses may be released by relaxing theseoundary conditions at the end of welding. The self-balancedtresses remaining without any external load are known asesidual stresses.

Fig. 14 – Longitudinal (left) and transverse (right) residua

; experiment vs simulation.

The 2 major components, viz. longitudinal and transversestress, of the residual stress tensor for the case under study arepresented in Fig. 14. The residual stress distribution profilesare presented for the upper surface of the test plate. It can beestablished from the residual stress profiles that the stressesin the direction of welding, �xx, will have the strongest influ-ence over the distortion and/or failure of the material. Theselongitudinal residual stresses are largely tensile in nature.Three distinct regions are demarcated in Fig. 15 as fusion zone,HAZ and base metal. The graph is reproduced from the stressprofiles of �xx, �yy and �zz on the upper surface and in themiddle of the test plate lengthwise. It is to be noted that thedistinction between HAZ and base metal is merely arbitraryand based on the assumption that base metal has zero levelof stresses. Moreover, nodal stress values are presented in thisgraph, which are actually the values extrapolated from thestress values calculated at corresponding Gauss integrationpoints.

The comparison between �xx, �yy and �zz is also presentedin Fig. 15. It is observed that maximum stresses are present in

the HAZ both in the case of longitudinal residual stresses �xx

and transverse residual stresses �yy; the longitudinal stressesare, however, approximately 5 times more than the transverseones. Moreover, the longitudinal stresses, �xx, are entirely ten-

l stress field on the upper surface of the test plate.

2916 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 2907–2917

s a f

r

Fig. 15 – Residual Stresses �xx, �yy and �zz a

sile in nature; while the transverse stresses are compressive inthe fusion zone and tensile in the HAZ. The through-thicknessstresses, �zz, have insignificant magnitude, yet the non-zerovalue can be attributed to the approximations in interpolatingthe stress values from Gauss integration points to the surfacenodes. Similarly, all the remaining stress components viz. �xy,�xz and �yz, being negligible in magnitude, will have least effectover the entire distortion of the test plate.

6. Conclusion

An uncoupled thermo-mechanical analysis has been per-formed to predict the distortions and residual stresses for asingle-pass fusion welded thin test plate. A comparative studyof experimental and simulation results has also been carriedout. Following conclusions are inferred:

1. Comparison of weld pool geometry with simulated fusionzone (Fig. 7) justifies the heat source model with an upperhollow sphere and a subsurface cone, which are actuallymeant to achieve the required width and penetration ofthe fusion zone, respectively. Likewise, the applied heatflux and thermal boundary conditions are well integratedso as to calculate the resultant temperature fields in closeapproximation to the experimentally recorded thermal his-tories (Figs. 8 and 9). A few discrepancies may be attributedto the simplifications assumed during simulation.

2. FE simulation results of mechanical analysis comparedwith experimental results for out-of-plane (Figs. 10–12) andin-plane (Fig. 13) displacements are found in good agree-ment with each other, for a suction pressure of 0.8 bar anda friction coefficient of 0.57. This, in turn, establishes thereliability of the mechanical model, material properties,constitutive laws and mechanical boundary conditions. It is

also noticed that the out-of-plane displacements are insen-sitive to change in friction coefficient; however, variation insuction pressure may impart a systematic change in theirmagnitude, yet the effect is little.

unction of the distance from the weld line.

3. The longitudinal residual stresses, �xx, have values as highas the yield strength of the material. Compared to all otherstress components, they will have considerable influenceover the distortion level and failure of the material.

4. The transverse residual stresses, �yy, are around 20% of theyield strength in the fusion zone and are even lesser in theHAZ. Moreover, they are tensile in the HAZ and compres-sive in the fusion zone.

5. The through-thickness residual stresses, �zz, and otherstress components, namely �xy, �xz and �yz have negligi-ble magnitudes and, hence, do not contribute significantlyto the distortions.

6. Laser beam welding with keyhole formation is char-acterised by a more pronounced dominance of thelongitudinal residual stresses over the transverse residualstresses. In the present analysis the former is found 5 timeshigher than the latter.

7. Three-dimensional elements with linear interpolationbetween the nodes are used both for thermal and mechan-ical analyses. Improvement in results may also be expectedwith quadratic interpolation between nodes for mechani-cal analysis.

Acknowledgments

The author would like to acknowledge the financial supportprovided by EADS, AREVA-NP, EDF-SEPTEN, ESI Group andRhône-Alpes Région through the research program INZAT4.

e f e r e n c e s

Beardmore, R., 2007. Tribology index, friction coefficients. On lineavailable from: http://www.roymech.co.uk/Useful Tables/

Tribology/co of frict.htm (accessed 4 April 2007).

Darcourt, C., Roelandt, J.-M., Rachik, M., Deloison, D., Journet, B.,2004. Thermomechanical analysis applied to the laser beamwelding simulation of aeronautical structures. J. Phys. IV 120,785–792.

t e c h

F

G

J

J

j o u r n a l o f m a t e r i a l s p r o c e s s i n g

erro, P., Zambon, A., Bonollo, F., 2005. Investigation ofelectron-beam welding in wrought Inconel 706—experimentaland numerical analysis. Mater. Sci. Eng. A 392, 94–105.

oldak, J., Chakravarti, A., Bibby, M., 1984. A new finite elementmodel for welding heat sources. Metall. Trans. 15B,299–305.

in, X., Li, L., Zhang, Y., 2003. A heat transfer model for deep

penetration laser welding. Int. J. Heat Mass Transfer 46, 15–22.

osserand, E., Jullien, J.F., Nelias, D., Deloison, D., 2007. Numericalsimulation of welding-induced distortions taking into accountindustrial clamping conditions. Math. Modell. Weld Phenom.8, 1105–1124.

n o l o g y 2 0 9 ( 2 0 0 9 ) 2907–2917 2917

Lundback, A., Runnemalm, H., 2005. Validation ofthree-dimensional finite element model for electron beamwelding of Inconel 718. Sci. Technol. Weld. Joining 10 (6),717–724 (8).

Olmedo, M., 2004. Soudage laser en aluminium. PhD Thesis.ENISE France.

Sudnik, W., Radaj, D., Breitschwerdt, S., Eroeew, W., 2000.

Numerical simulation of weld pool geometry in laser beamwelding. J. Phys. D: Appl. Phys. 33, 662–671.

Tsirkas, S.A., Papanikos, P., Kermanidis, Th., 2003. Numericalsimulation of the laser welding process in butt-jointspecimens. J. Mater. Proc. Technol. 134, 59–69.