Materials Science and Engineering A 527 (2010) 30253039

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Experim siminduce in

Muhamm is Jua Universite deb EADS, 12 Rue

a r t i c l

Article history:Received 25 MReceived in reAccepted 18 Ja

Keywords:Laser beam weFinite elementResidual stressDistortion

nd itof AAuratiog indrmedbenchmercGauss undmate

hardening behaviour (von Mises plasticity model). A comparison between the experimental and simula-tion results shows a good agreement. Finally, the residual stress and strain states in a T-joint are predicted.

2010 Elsevier B.V. All rights reserved.

1. Introdu

Fabricatlaser beamconventionrial to be adrequired; this a very hstructures ototal lengthally, thesea suction tasides of thevery natureresidual strnumerical sing these wof residualbetter cont

CorresponAvenue Albertfax: +33 4 72 4

E-mail add

0921-5093/$ doi:10.1016/j.ction

ing the fuselage panels of aircraft structures with thewelding (LBW) technique has a twofold advantage overal riveting, the rst being weight reduction, since mate-ded as rivets and overlap of metal sheets is no longere second being the high production rate, since LBW

igh speed process. The fuselage panels are large thinf AA 6056-T4 with stiffeners welded upon them. Theof weld seam per panel reaches 50m or so. Industri-

fuselage panels are held in position with the help ofble. LBW is employed in a keyhole regime from bothstiffener in a T-joint conguration. However, by theof the process, welding induces highly non-uniform

esses and distortions in the structure. In recent years,imulationhas proven itself to be a useful tool in predict-elding induced distortions and stresses. The knowledgestress distribution and distortions may then lead torol over undesirable aspects of the fabrication process,

ding author at: LaMCoS, INSA-Lyon, Btiment J. Jacquard (302), 20Einstein, 69621 Villeurbanne Cedex, France. Tel.: +33 4 72 43 84 90;3 89 13.ress: daniel.nelias@insa-lyon.fr (D. Nlias).

which include dimensional inaccuracies and distorted shapes dueto bending/buckling of the structure.

LBW involves several complex phenomena like the formationof a keyhole, ionization and vaporization of material, circulation ofmoltenmetalwithin theweld pool due to buoyancy andMarangoniforces [13], solidication at the liquid-solid interface, etc. Varioussimplications are, however, admissible in numerical simulationof welding, with minimal loss in accuracy [4,5]. For instance, thethermoelasto-plastic welding process can be uncoupled into athermal transient analysis and an elasto-plastic structural anal-ysis. Some research [6,7] has been dedicated entirely to thermalanalysis and heat source modelling while other authors [8,9] havefocussed upon welding induced stresses. With special referenceto llet-welded stiffeners, Camilleri et al. [10,11] have suggestedthat the out-of-plane displacements can be efciently predicted bycomputational means. Other workers [12,13] have predicted theresidual stress state in friction stir welded panels and found thatthe collapse behaviour is less sensitive to advanced process effectsthan initial buckling of the panel. Spina et al. [14] and Darcourt etal. [15] attempted to predict LBW induced distortions in thin platesand T-joints of aluminium alloys and suggested that a correct ther-mal analysis is mandatory to predict welding induced distortionsand residual stresses. Josserand et al. [16] concluded that the initialsurface proles of a test plate due to pre-processing actions suchas rolling, play an important role in dening the nal distortion

see front matter 2010 Elsevier B.V. All rights reserved.msea.2010.01.054ental investigation and nite elementd residual stresses and distortions in th

ad Zain-ul-abdeina, Daniel Nliasa,, Jean-FrancoLyon, CNRS, INSA-Lyon, LaMCoS UMR5259, F69621, FrancePasteur, BP 76, 92152 Suresnes Cedex, France

e i n f o

ay 2009vised form 17 January 2010nuary 2010

ldingsimulation

a b s t r a c t

Laser beam welding has recently foufuselage panels, made of thin sheetsthe same material in a T-joint congresidual stresses and distortions usinditions. Various measurements perfoexperimental results that serves as asimulation is performed with the comencoding a conical heat source withtemperaturedisplacement analysis iperature and displacement elds. Them/locate /msea

ulation of laser beam weldingsheets of AA 6056-T4

lliena, Dominique Deloisonb

s application in the fabrication of aircraft structures where6056-T4 (an aluminium alloy), are welded with stiffeners ofn. The present work simulates laser beam welding inducedustrially employed thermal and mechanical boundary con-on small-scale welded test specimens provide a database ofmark for qualication of the simulation results. The weldingial nite element software Abaqus and a Fortran programmesian volumetric distribution of ux. A sequentially coupledertaken to simulate the weld pool geometry, transient tem-rial is assumed to follow an elasto-plastic law with isotropic

3026 M. Zain-ul-abdein et al. / Materials Science and Engineering A 527 (2010) 30253039

Table 1Chemical composition of AA 6056-T4 by wt%.

Al Mg Si Cu Mn Fe Zn

Balance

level after wpredict weljoint. Schenupon the wstrong inution can bethe clampin

Metallurstudied thestir weldingaphysicallyfor the precvarious nucanalysis of ftemper statwith that evhot crackinstudied the

The worcal simulatifrom AA 60percentageidate the simof increasin

(a) Fusion p(b) Filler pa(c) T-joint w

Results fin Zain-ul-aimental wo(Cases 02 a

2. Experim

Since thwelding wafusion passwere perforrial, respectsimultaneousing two wof an alumito integrateary conditiospecimensCase 01Case 02Case 03

The laseYAG with amountedontrol. The bediameter bwith a nearcal arrangeused togetheral prelim

Table 2Laser beam welding parameters.

Welding parameters Case 01 Case 02 Case 03

eer (Wding sl lengl spotl poineigh l

ireerateeter

tionleance f

ing garetionrate

leance fm)

etersmpleed w.weldspecnwictiontes. Aunt

re (2llowointsng dn thearatioishength

ype tres avariasurewas created with white and black paints to quantify the

ld out-of-plane and in-plane displacements using a digitalcorrelation (DIC) technique. An infra-red camerawas used toe the evolution of the weld pool surface temperature duringg. Micrography of welded joints was performed to measureensions of the fusion zone (FZ). Welding at least 5 spec-

for each test case ensured reproducibility of experimental.geometry, layout plan of instrumentation and experimentalor the T-jointwelding (Case 03) are shown in Fig. 1. A total ofthermocouples (TC1TC11) were located on T-joint assem-hile nine thermocouples (TC1TC9) were installed on the

ates (Case 02). Table 3 presents the coordinate positions ofrmocouples. Since the stiffeners were not included in Cases02, the geometry and instrumentation of test plates (Cases02) were identical to those of the base plates of T-joints3). Pairs of LVDTs 1 and 2 and LVDTs 3 and 4, were placed0.71 0.87 0.67 0.62 0.07 0.18

elding. Similarly, Zaeem et al. [17] have also tried toding buckling distortion in a thin walled aluminium T-k et al. [18] studied the inuence of clamping deviceselding distortions. Their ndings show that there is aence of clamps on the distortion, and that the distor-controlled to some extent by appropriate selection ofg conditions.gical aspects have also beenexamined.Gallais et al. [19]microstructural evolution inAA6056 alloy after frictionfrom two initial conditions (T4 and T78) and suggestedbasedmodel forprecipitationandhardening toaccountipitation of a quaternary (Q) phase and the existence ofleation sites. Olea et al. [20] performed sub-structuralriction stir welded joints in AA 6056 alloy for T4 and T6es and compared the microstructure in the base metalolving in the weld zone. Cicala et al. [21] focussed upong in laser beam welded butt joints of AA 6056-T4 andeffects of operating parameters.k presented here describes measurements and numeri-ons of laser beam welded test plates and T-joints made56-T4 (see Table 1 for the chemical composition byweight). The experimental observations are used to val-ulation results in a three-step approachwith test cases

g complexity:

ass welding of test plate Case 01.ss welding of test plate Case 02.elding of base plate and stiffener Case 03.

rom therst step (Case01) have alreadybeenpresentedbdein et al. [22]. This paper focuses ondescribing exper-rk and numerical predictions for the next two stepsnd 03) and comparing results from the various cases.

ental work

in sheets of thickness 2.5mm were used, single passs employed for all the cases. As the name suggests,welding (Case 01) and ller pass welding (Case 02)med without and with the addition of ller wire mate-ively. T-jointwelding (Case 03)was performedwith theus addition of ller wire on both sides of the stiffenerelding heads. The ller wire material used was made

nium alloy 4047 (diameter: 1mm). Efforts were madethe industrially used thermal and mechanical bound-ns using small-scale specimens. The dimensions of the

are as follows:Test plate: 300mm200mm2.5mmTest plate: 300mm200mm2.5mmBase plate: 300mm200mm2.5mmStiffener: 300mm100mm2.5mm

r used for this work was a continuous wave Nd:maximum beam power of 3.5 kW. The assembly wasa four-axis displacementmachinewithnumerical con-

am was carried to the target surface through a 400mreoptic cable. The laser spot exhibited a circular shape

-uniform intensity prole deriving from a classical opti-

LaserTypPowWelFocaFocaFocaRayl

Filler wTypFeedDiamPosiAngDist

ShieldNatuPosiFlowAngDist

(m

paramthat conalizTable 2

Theof thepositioThe suthe placoolingperatuas to athe T-jclampically oits sepand nbead le

K-tperatulinearto meapatternfull eimageobservweldinthe dimimensresults

Thesetup felevenblies; wtest plthe the01 and01 and(Case 0ment. A collimating lens of 200mm focal length waser with a focusing lens of 200mm focal length. Sev-

inary weld runs were carried out to adjust the welding

in line withnience, theand 4 Set BNd: YAG Nd: YAG Nd: YAG) 2300 3000 22500peed (m/min) 8 8 5th (mm) 200 200 150size (m) 400 400 450t position (m) 0 0 0ength (mm) 118.105 118.105 149.477

4047 4047(m/min) 5 3(mm) 1 1

Ahead Ahead 30 25

rom interaction point 1.5mm ahead 1.5mm ahead

sArgon Argon ArgonBehind Behind Behind

(l/min) 20 20 2035 35 35

rom interaction point 13 13 13

(beam power, welding speed, focal spot, etc.) suchte penetration of the weld bead could be avoided. The

elding parameters for different test cases are shown in

ing operation was performed lengthwise in the middleimens, while maintaining the test plates/base plates inth thehelp of an aluminiumsuction table (25mmthick).force was applied over the entire bottom surface ofpressure of 1bar was maintained during welding and

il the temperature of the specimens reached room tem-0 C). The pressure was released at the end of cooling sofree deformation of the test specimens. In the case of, stiffeners were placed in position with an additionalevice. Two forces of 50N each were also applied verti-stiffener through the clamping device, in order to avoidn from the base plate during welding. The weld started

d at 5mm from each end of the plate giving a total weldof 290mm.

hermocouples (TCs) were installed to record the tem-t specic positions near the fusion zone (FZ), whileble differential transformer (LVDT) sensors were placedthe in-plane displacements during welding. A speckleeach other perpendicular to the weld bead. For conve-pair of LVDTs 1 and 2 will be called Set A and LVDTs 3. To perform image correlation, a speckle pattern was

M. Zain-ul-abdein et al. / Materials Science and Engineering A 527 (2010) 30253039 3027

Case

created oneach side of

Some qmental resumeasuremelater.

2.1. Micros

AA 6056Dissolutionhowever, sstart appeartemperaturevents are r

GP zone d precip precipi

cipit

Table 3Coordinate po

Case

02xyz

03xyzFig. 1. Geometry, layout plan of instrumentation and experimental setup

the top surface of the plates over a width of 85mm on Q pre

the weld joint.

ualitative observations with respect to the experi-lts are presented here. Quantitative comparisons ofnts with numerical simulation results are discussed

copic observations

exhibits Guinier-Preston (GP) zones in the T4 state.of GP zones takes place with increase in temperature;ome new hardening precipitates like , , and Qingat certainhigher temperatures.Dependingupon thee attained, the following dissolution and precipitationeported in the literature [19]:

issolution around 30150 C;itation around 240/250 C;tation from 250 up to 320 C;

precipit Q dissolu dissolu

Opticalmtinct zones,In Fig. 2, thresulting frhigh tempecoarse precQ, and

neprecipito conductithe fusion zing; as no the solidicsuggests thLBW, a lle

sitions of thermocouples (dimensions in mm).

TC1 TC2 TC3 TC4 TC5 TC6

75 75 75 225 225 753 6 9 3 6 00 0 0 0 0 2.2

75 75 75 225 225 753.5 7 10 4 7 00 0 0 0 0 2.003 (dimensions in mm; not drawn on scale).

ation from 290 up to 350 C;

ation around 450 C;tion in the 400500 C range;tion around 550 C.

icroscopyofCase01 (fusionwelding) revealed twodis-the fusion zone (FZ) and the heat-affected zone (HAZ).e HAZ presents elongated grains of the base materialom the rolling of sheets prior to welding. Owing to therature range (550150 C) in the HAZ, the relativelyipitates dispersed in the parentmatrix are likely to be oftypes. The fusion zone, on the other hand, contains verytates resulting fromrapid coolingof themoltenpool dueve heat loss in the surrounding base metal. Moreover,one contains hairline cracks resulting from hot crack-ller wire was provided in this case to compensate foration shrinkage of the molten metal. This observationat in order to obtain a quality weld on AA 6056 usingr wire must be supplied during welding.

TC7 TC8 TC9 TC10 TC11

75 93 94 6 0 3

2.5 2.5 2.5

93 93 75 75 2250 4 1.25 1.25 1.25

2.5 2.5 4 7 4

3028 M. Zain-ul-abdein et al. / Materials Science and Engineering A 527 (2010) 30253039

2.2. Temper

In his wshould be ually, his ninertia withpossible diagradient doof the TC mworkpiecespot-welde

Since thwelded testpresentedthermocouptemperaturtivity is 41involvedduspot-weldespot-weldelaser beamwelding, that a temperlm of plastion but alsapplicationtemperatur

TemperaFRONTDAQ20 differentwith an acqduring laseof 200Hz. Tpotential di(1V to1

The accuracy of temperature measurements for K-type thermo-couple (180 C to +1300 C) using the Frontdaq system is 1.2 C.The results of TC measurements are presented for comparison with

ical simulation results in Section 4.2.

fra-r

infrtem,ringlaneithi

uracye waas usmert it c. In oof p

d surwn ele wo measmavityyed f4.1

hedisedkle p

emed in

thiet al

C (9rvedwerFig. 2. Micrographs of FZ and HAZ Case 01.

ature measurements by thermocouples

ork, Beck [23] suggests that K-type thermocouplessed for measuring temperatures up to 850 C. Addition-dings show that, due to reasons of increasing thermalincreasing wire diameter, TC wires with the smallestmeter should be used. Furthermore, if a temperaturees not exist upon the workpiece surface, the two wires

numer

2.3. In

Theing sysmeasufocal-psitive wby accstoraglens wThe caso thalengthvaluespainteof knoing tabused ttionwemissiemploSection

Polis Oxid Spec

Thereportused inKanianat 660is obsetures loay be welded separately; which implies that for awith signicant thermal gradient, TC wires should bed at a single point.e temperatures to be measured in the HAZ of laserplates/T-joints remainwell below850 C, the test cases

in this work made use of K-type (ChromelAlumel)les with wire diameters of 79m. The accuracy in

e measurement for these TCs is 1.1 C and the sensi-V/C. In order to avoid the effect of thermal gradiente to directional heating duringwelding, all the TCswered at a single point at specied locations (Table 3). Thed region and unsheathed wires were protected fromradiation by applying a drop of nail polish. During

e solvent ethyl acetate contained innail polish vaporisesature of 77.1 C, thereby leaving behind a thin exibleticizers, which not only protects the TCs from radia-o serves as an adhesive agent. It was ensured that theand the later vaporisation of solvent did not affect thee measured by the TCs by testing a separate specimen.ture acquisition during welding was made using a: FD20 acquisition system, which is capable of treatingial inputs from two to fourwire sensors simultaneouslyuisition rate of 7680Hz. The temperature acquisition

r beam welding experiments was made at a frequencyhe system is capable of using two different ranges offferences; range 1 (from 15mV to 1V) and range 20V),withanachievableprecisionof10Vto100V.

higher, evauid aluminreactions bawaybybuhave also b(1900K) inin vacuum.of 20 l/minassume tha

The evoFig. 3 for Cathermograpthese resulthree of theall the specical evolutioin all the cstart and enpeaks are th3.5mmfromweld centretemperaturthe vicinityadhesive agthe start ansure of the kthe remained camera observations

a-red camera used was a FLIR ThermaCam S40 imag-capable of storing images at a frequency of 60Hz and

the temperatures up to 1700 C. It has a 240320pixels-array uncooledmicrobolometer detector,which is sen-n a wavelength range of 812m and is characterizedin temperature measurement of 2 C. Imaging and

s made at a frequency of 50Hz. An 80mm close-uped, which could allow a spatial resolution of 100m.a was mounted along with the laser welding headould capture images of the FZ over the entire weldrder to calibrate the camera for different emissivityolished aluminium, oxidised aluminium and specklefaces, one of the test plates was coated with a paintmissivity. This test plate was then positioned on a heat-hose temperature was controlled and the camera wasasure the temperature of the painted surface. Calibra-de over a temperature range of 0500 C. The followingvalues were measured for various surfaces and wereor numerical simulation of heat transfer analysis, see.

aluminium surface, =0.08;aluminium surface, =0.22;ainted surface, =0.71.

issivity value of 0.090.01 for liquid aluminium isthe literature [24,25] at 1277 C (1550K) and has beens work for the weld pool surface temperature. Sarou-. [24] reports that formation of liquid aluminiumoccurs33K). During heating of an aluminium drop, aluminasystematically on the surface of the liquid at tempera-than 1327 C (1600K).When the temperature becomesporation of the drop becomes more important and liq-a disappears from the Al surface because of chemicaletween Al and Al2O3 to form Al2O(gas) which is takenoyancydrivengasow(Ar +10%H2). Theseobservationseen reported by Krishnan and Nordine [25] at 1627 Cpure He and by Laurent et al. [26] at 727 C (1000K)Since, in this work, 99.9% pure argon with a ow ratewas used for laser welding experiments; it is safe tot Al2O(gas) escapes from the weld pool surface.lution of weld pool surface temperature is presented inse 03 where maximum temperature, as observed fromhs, is shown as a function of time. Reproducibility of

ts was ensured by measuring several specimens; whilem, numbered T13, are shown. It is to be noted that formens, temperature values followmoreor less an identi-n pattern. Four distinct temperature peaks are observedases where the rst (a) and last (e) peaks show thed of welding, respectively. The second (b) and third (d)e ones noted in the immediate vicinity of TC1 (installedtheweld centre line) andTC4 (installed4mmfromtheline), respectively. Fig. 3 also presents the contours of

e distribution in and near the FZ. The peaks observed inof TC1 and TC4 are due to the burning/vaporisation ofent applied upon them. However, the ones observed atd stop ends of welding are due to the formation and clo-eyhole, respectively. Excluding the temperature peaks,

ing parts of the curves show uniform evolution of tem-

M. Zain-ul-abdein et al. / Materials Science and Engineering A 527 (2010) 30253039 3029

perat

perature ththat the weinstant of tiof heat ener

2.4. Displac

A total owired to staenvironmenwelding explacementsinterface seLVDTs are 0post-travelward positiand from thposition forthe FRONTDmeasuremeulation resu

2.5. Digital

DIC offedimensionacorrelation(nal state)are taken bBefore carrythese cameusing 20 imknown spablack dots edirections,18.02mm.using commdened in t

re x a

l lengra.: devtionsa 1:a, Bect to

ive py, and

m.

ing pons oFig. 3. Evolution of weld pool surface tem

roughout the welding process; which, in turn, impliesld pool dimensions remain almost constant at everyme. Moreover, the specimens absorb a regular amountgy.

ement measurements from LVDT sensors

f 4 Solartron analogue spring type AX/1/S LVDTs pre-ndard BICM in-line conditioning transducers for harshts with an output signal of 10V were used for the

periments. These LVDTs are capable of measuring dis-up to 1mm with an accuracy of 0.5% and electricalnsitivity of 200mV/V/mm. The pre- and post-travel of.15mm and 0.35mm, respectively. The terms pre- andrefer to the mechanical movements from the fully out-

Centera.

Focacame

Skewdirec

Kapp Alph

resperelat

Tx, T1 in m

Havdeviation to the start of the measurement range for the formere end of the measurement range to the fully inwardthe latter. The displacement acquisitionwasmadewithAQ: FD20 system at a frequency of 200Hz. The LVDTnts are presented for comparison with numerical sim-lts in Section 5.2.

image correlation (DIC) technique

rs contact-less and full eld measurement of three-l displacements of an object surface. The imagetechnique requires digital images of a deformed objectand a reference image of the object (initial state),whichy means of two charge-coupled device (CCD) cameras.ing out image correlation of the object, calibration of

ras is necessary. The calibration of cameras is performedages of a translated and rotated planar dot pattern of

cing. The target used in this work contained 12 and 9qually spaced on a white background in the x- and y-respectively. The grid spacing between the dots wasThe calibration of the stereo-system was performedercial software Vic-3D 2007. The calibration results areerms of following parameters:

pixels for thtion residucorrelation

Table 4Components a

CamerasCameras resLenses

Lighting

ObjectSoftwareCalibration t

Standard defor all view

Subset size (Step size (piInterpolatioCorrelation

Points analyPixel sizeErrorure Case 03.

nd centre y: image plane centre in pixels for each cam-

th x and focal length y: focal length in pixels for each

iation fromorthogonality between the rowandcolumnin the sensor plane.

radial distortion coefcient.ta and Gamma: relative orientation of camera 2 withcamera 1 (), where alpha is the relative tilt, beta is the

an angle and gamma is the swing angle.Tz: position of pinhole in camera 2 relative to camera

erformed the calibration, Vic-3D 2007 yields standardf residuals for all views, which was found to be 0.0199

e cases under investigation. A higher value of calibra-

als leads to a higher value of error in the measure ofaccuracy for the image correlation of an object surface.

nd settings of image correlation technique.

2 LIMESS 12 bit grey scale CCD 1.34 in.olution 20482048pixels

2 Nikon Micro-NIKKOR (f=55mm,1:2.8D)2 compact uorescent lamps, OsramDelux EL 30W/840AA 6056-T4 platesVic-3D 2007

arget 129 black dots on white background;spacing: 18.02mm

viation of residualss

0.0199133pixels

pixels) 2121xels) 5n function Quintic B-splinecriterion Zero-normalized sum of squared

differencessed Over 46,497

1pixel = 0.16mm0.0116198pixel = 1.859168m

3030 M. Zain-ul-abdein et al. / Materials Science and Engineering A 527 (2010) 30253039

Table 5Calibration results for DIC system.

Parameter Camera 1 Camera 2 Camera 12 transformationCentre x (pixel) 984.65 1045.2 Alpha () 0.1683Centre y (pixel) 1014.48 1002.33 Beta () 13.301Focal length x (pixel) 7887.49 7868.11 Gamma () +0.00743732Focal length y (pixel) 7888.03 7867.1 Tx (mm) +270.68Skew 0.8123 0.1236 Ty (mm) 1.5706Kappa 1 0.0276 0.0325 Tz (mm) +31.871

Baseline (mm) 272.55

The components and settings of the image correlation are shownin Table 4. The calibration results of the DIC system are shown inTable 5.

A random grey speckle pattern is generally required on theobject surface, which is created with the help of white and blackpaints. A subset window (or correlation window) is subsequentlydened in the reference image as a neighbourhood of mm pixelsthat forms a unique stamp of the centre point of this neigh-bourhood. The speckle pattern of this neighbourhood should holdenough contrast and directional information to track the localdeformation to the rst order of approximation (afne transfor-mation) by using a cross-correlation algorithm. In the correlationalgorithm the centres of the neighbouring subset windows areshifted by a step size of n pixels, where n must be smaller thanthe subset size to enable overlapping of the subsets. Once these set-tings are dened, the displacement eld is calculated as an updateddisplacement for every subset centre.

For cases 02 and 03, over 46,497 points were analysed on a sur-face area ofound to bevalue accouof Cases 02(Section 5.2

3. Finite el

A sequeformed, whanalysis. Th

Table 6Mesh details.

Case Nodes Elements Smallest element dimensions

02 (test plate) 63,287 53,808 0.5mm0.31mm0.25mm03 (T-joint) 76,788 63,600 0.5mm0.38mm0.24mm

analysis were used as a predened eld for mechanical analysis inorder to determine the distortions and residual stress state inducedby welding. It is safe to assume that the mechanical response of thetest specimensdependsupon the thermal loading;while there is noinverse dependency. This is because the amount of heat generateddue to the mechanical dissipation is negligibly small as comparedto the heat energy supplied by the heat source.

Finite element (FE) simulation was performed using the com-mercial code Abaqus/Standard. Owing to the symmetry of the testplates and T-joints along the weld centre line, symmetric modelswere assumed; where the base plate, ller wire and stiffener (incaseofT-joi

mody deyed cmes) com; whirelatwhice mereseetaif 300mm170mm. The error for displacements was0.0116pixels. For a pixel size of 0.16mm, this error

nts for 1.86m (

M. Zain-ul-abdein et al. / Materials Science and Engineering A 527 (2010) 30253039 3031

ft); so

High temsimulation,formation u

4. Heat tra

In orderfer analysisproperties.(x, y, z) wastion:

x

(k(T)

T

x

Here, k(T) isin Wm1 Kkgm3, Cp(J kg1 K1 a

The commakes it exoccurringwalways requofmoltenm

4.1. Heat so

The heacise applicarequired weselection ofconcern ansions, geomthe FZ, thewmodels in tGaussian diin accordansource comple, Lundbawith a doubprocess witof heat uxthe keyholeGilles et al.distributionmodel used

e 02ong wd.e 03,the Fan dias a

e hever, tted rottourceerpeas:

0exp

, Qv isalueesianr therma

ze

zi

her

9(1

+ (reFig. 5. Schematic representation of heat source model (le

perature material properties were used for numericalwhich were likely to capture the effect of precipitatepon mechanical properties.

nsfer analysis

to compute the temperature histories, the heat trans-was performed using temperature dependent thermalThe transient temperature eld (T) in time (t) and spaceobtained by solving the following heat transfer equa-

)+

y

(k(T)

T

y

)+

z

(k(T)

T

z

)

+ Qv = (T)Cp(T)(

T

t

)(1)

the thermal conductivity as a function of temperature1, (T) is the density as a function of temperature inT) is the specic heat as a function of temperature innd Qv is the volumetric heat ux in Wm3.plex nature of weld pool formation due to the keyholetremely difcult to model each and every phenomenonithin theweldpool. Some simplications are, therefore,ired. The phenomena like formation of ions, circulationetal, and ejection ofmaterialwere ignored in thiswork.

urce model and boundary conditions

t source model plays a vital role in achieving the pre-tion of the heat ux, which, in turn, helps to predict theld pool dimensions and desired thermal histories. Thean appropriate model is, therefore, a matter of great

d depends largely upon factors like weld pool dimen-

for Castion aldene

Casetry ofGaussiFortranthat thMoreodeposiat the bheat soplane pwritten

Qv = Q

wheremumvof Carteter fothe the

P =

From w

Qv =

with,

rc = rietry of the weld-joint, temperature elds in and neareldingprocess being simulated, etc. There exist various

he literature ranging from surface heat sources with astribution to double-ellipsoidal volumetric heat sourcece with Goldak et al. [27]; while sometimes a heatposed of two different models is also used. For exam-ck and Runnemalm [28] used Goldaks double ellipsoidle elliptic cone to simulate the electron beam weldingh a keyhole. Ferro et al. [29] used a conical distributionwith an upper and lower hollow sphere to describephenomenon during electron beam welding. Similarly,[30] used a prismatic surface heat source with linearto model the TIG welding process. The heat source

by Zain-ul-abdein et al. [22]was employed in thiswork

Here, P iprocess. Ththe cone rez-coordinatshown in Fanalysis witers re, ri, zegeometry. Afusion betw644 C, resp

Since waluminiumof heat enerinterface ofurce implementation (right).

; where a conical heat source with Gaussian distribu-ith an upper hollow sphere with linear distribution is

being different from Case 02 with respect to the geom-Z,made use of a 3D volumetric conical heat sourcewithstribution. The heat source model was programmed insubroutine called DFLUX. The term volumetric implies

at ux was distributed along the work-piece thickness.he volumetric heat ux assumed that the heat intensityegionwasamaximumat the top surface andaminimummsurface of the cone. A schematic representation of themodel and its implementation is shown in Fig. 5. At anyndicular to the z-axis, the heat ux distribution may be

(3r

2

r2c

)(2)

the total volumetric heat ux inWm3,Q0 is themaxi-ofheatux inWm3, r is the current radius as a functioncoordinates x and y, rc is the ux distribution param-cone as a function of depth (z). Q0 is determined froml energy conservation rule.

2

0

rc0

Q0exp

(3r

2

r2c

)r dr d dh (3)

e,

P

e3)1

(ze zi)(r2e + reri + r2i )exp

(3r

2

r2c

)(4)

ri)z zize zis the laser beampower inWand is the efciency of thee parameters re and ri are the larger and smaller radii ofspectively. Likewise, ze and zi are the upper and loweres of the cone respectively. These parameters are alsoig. 5. An efciency () of 80% was used for the thermalth a beam power (P) of 2500W. The remaining parame-and zi were adjusted to obtain the required weld poolvalue of 4105 J kg1 was used as the latent heat of

een the solidus and liquidus temperatures of 587 C andectively.elding was performed by placing the specimens on ansuction table, it is believed that a considerable amountgy was lost due to the thermal contact resistance at thethe plate and support (qcond). The remaining surfaces

3032 M. Zain-ul-abdein et al. / Materials Science and Engineering A 527 (2010) 30253039

Fig. 6. Ca

of the specheat loss inheat loss thEqs. (5) andduring the s

qconv+rad =qcond = hconHere, T, T0,ent temperrespectivelyradiation co

Convectiv Emissivit Emissivit Stefan-Bo Heat tran

support, h

The emipattern weIn order to

(hconv), fusion welding of test plate (Case 01) was rst performedin air (i.e. without using aluminium support); where the test platewas held in position from the edges with 25mm wide insulatedclamps. The calibration of hconv was then performed through aseparate simulation run, where experimental results at several TCpositions (TC1, TC3, TC4 and TC6) were compared with simulatedresults (Fig. 6). It was found that a value of 15WK1 m2 yieldedtemperature histories comparable to experimental results. Simi-larly, the heat transfer coefcient at the interface of the test plateand support was calibrated through the comparison of simulatedand experimental results at TCs (TC7TC9) of Case 02 (Fig. 8(b)).

4.2. Thermal simulation results

The results of thermal simulations are presented together withexperimental results. Fig. 7 compares the experimental and simu-lated weld pool dimensions for Cases 02 and 03. Fig. 8 shows thecomparisonof timetemperature curves forCase02at various ther-mocouple positions. Good agreement is found for the TCs at thebottom surface of the specimen. However, at the top surface, sim-

under-predicts cooling at TC1TC3, while it over-predictsandnsta[10,ientn simratur9 p

3. Inmentoolurcetedtabliver,ctoryew dperimed duithinrmocre go

chanlibration of convective heat transfer coefcient in air Case 01.

imens, being exposed to the atmosphere, experiencedair due to free convection and radiation (qconv+rad). Therough the plane of symmetry was assumed to be zero.(6) present the thermal boundary conditions integratedimulation.

hconv(T T0) + ((T Tabs)4 (T0 Tabs)4) (5)

d(Ts T) (6)Tabs and Ts are the temperature of the T-joint, ambi-ature, absolute zero and temperature of the support,. The values used for the heat transfer coefcients andnstants are as follows:

e heat transfer coefcient of air, hconv = 15WK1 m2.y of aluminium surface, =0.08.y of speckle pattern, =0.71.ltzmann constant, =5.68108 J K4 m2 s1.sfer coefcient at the interface of the test plate and

ulationat TC4of a cosurveycoefcment itempe

Fig.Case 0experiweld pheat sosimulaalso esMoreosatisfa

A fand exassumtionwof theelds a

5. Me

cond =284WK1 m2.

ssivity factors of the aluminium surface and specklere measured with the infra-red camera (Section 2.3).compute the convective heat transfer coefcient of air

A structand stress strially emplnodal temp

Fig. 7. Comparison of weld pool dimensions: Case 02 (TC5. The probable reason for this difference is the usent heat transfer coefcient in air (hconv). A literature31,32] shows that the natural convective heat transferis a function of temperature in some cases. Improve-ulation results may, therefore, be expected by using ae dependent heat transfer coefcient.resents a comparison of time-temperature curves forthis case, there exists a good agreement between theal and simulation results at all the TCs. The simulateddimensions verify the correct implementation of themodel. The conformance of the heating rate and the

peak temperatures with those of experimental onesshes the precise distribution of volumetric heat ux.the cooling parts of the simulated curves indicate thedescription of thermal boundary conditions.iscrepancies, however, observed between simulationental results may be attributed to the simplicationsring simulation, imprecision in the heat ux distribu-the FEmodel andminute inaccuracies in thepositioningouples. Nevertheless, the overall simulated thermalod enough toproceed furtherwithmechanical analysis.

ical analysis

ural analysis was performed to calculate the distortiontate induced during welding while taking care of indus-oyed mechanical loading and boundary conditions. Theerature values calculated during heat transfer analysis

left); Case 03 (right).

M. Zain-ul-abdein et al. / Materials Science and Engineering A 527 (2010) 30253039 3033

Fig. 8.

were integrto follow an(von Misesbased uponerature [12,Eq. (7).

= e + p

where, isth is the tstrain tensotensor () winverse of thby the twoPoissons ra

e = C1(T)The thermathermal diltemperatur

th = (T)(TThe plasticito the startdomain (deExperimental vs simulated temperature histories Case 02.

ated as a predened eld. The material was assumedelasto-plastic law with isotropic hardening behaviour

plasticity model). The choice of isotropic behaviour wasthe hardening models used for FE simulation in the lit-15,16]. The strain tensor decomposition is presented in

+ th (7)the total strain tensor, e is the elastic strain tensor,

hermal strain tensor and p is the plastic or inelasticr. The elastic strain tensor (e) is related to the stressith the help of compliance tensor, C1(T), which is thee 4th order stiffness tensor, C(T), and is further denedelastic coefcients namely Youngs modulus, E(T), andtio, (T), for an isotropic material.

: (8)

l strain tensor (th) is dened in Eq. (9) in terms of theatation coefcient, (T), temperature (T) and referencee (T0).

T0)I (9)ty criterion species the 3D stress state with respectof plastic ow and determines, therefore, the elastic

ned in space in terms of stress, temperature and hard-

Fig. 9.

ening variabdomain and

f (, T, R)