6013铝合金微裂纹分析

ContentslistsavailableatScienceDirect

JournalofMaterialsProcessingTechnology

journalhomepage:www.elsevier.com/locate/jmatprotec

Micro-scalemodelbasedstudyofsolidificationcrackingformationmechanisminAlfiberlaserwelds

XiaojieWanga,d,FengguiLua,b,∗,Hui-PingWangc,∗,ZhaoxiaQud,LiqianXiad

ShanghaiKeyLaboratoryofMaterialsLaserProcessingandModification,SchoolofMaterialsScienceandEngineering,ShanghaiJiaoTongUniversity,Shanghai200240,PRChinab

CollaborativeInnovationCenterforAdvancedShipandDeep-SeaExploration,Shanghai200240,PRChinac

ManufacturingSystemResearch,GMGlobalR&D,Warren,MI48090,USAd

WeldingandCorrosionProtectionTechnologyDepartmentResearchInstitute,BaoshanIron&SteelCo.Ltd.,Shanghai201900,PRChina

a

article

info

abstract

Articlehistory:

Received27September2015Receivedinrevisedform19November2015

Accepted11December2015

Availableonline15December2015

Keywords:

Micro-scalemodelSolidificationcrackingWeldingspeedPressuredropMicrostructure

Effectofweldingspeedonsolidificationcrackingsusceptibilityinfiberlaserweldingof6013aluminumalloywasinvestigatedbyconsideringbothmechanicalandmetallurgicalfactors.Afiniteelementmodelwasdevelopedatcolumnargrainscaletocalculatethestrainlocalizationinthemushyzone.BasedontheRappaz-Drezet-Gremaud(RDG)criterionandstudyfromthedevelopedmicro-scalemodel,thepressuredropintheinter-dendriticliquidfilmwasusedascrackingindextoinvestigatetheformationofsolidificationcracking.Coolingrate,solidfraction,localstrainrateandmicrostructurecharacteristicresultedfromdifferentweldingspeedswereexamined.Crackingsensitivitywasshowntodecreasewiththeincreaseofweldingspeedintherangebetween2.5m/minand3.5m/mininfiberlaserweldingof6013aluminumalloy.Numericalcalculationsshowedthatmechanicaltensilestraininthesolidgrainwasintheorderofmagnitudeof10−4whilethestrainintheliquidfilmisintheorderofmagnitudeof10−2.Thetotalpressuredropattherootofcolumnargrainswasmorethan150kPa,whichwasdeemedasthecriticalpressuredroptoformacrackinthisstudy.Thetransversesolidificationcrackingwaspronetoinitiateinthesecondhalfofmushyzonewherethesolidfractionwasbetween90%and94%.

©2015ElsevierB.V.Allrightsreserved.

1.Introduction

Aluminumalloyshavebeenwidelyemployedinbodycon-structionofautomobilesandaircraftduetotheiroutstandingmechanicalpropertiesandformability.Fusion-basedweldingpro-cessessuchasarcweldingandlaserweldingarecommonlyusedinjoiningtheAlmaterials.However,solidificationcrack,whichisharmfultostructuralintegrity,couldeasilyexistintheweldedAljoints(Kou2003).Thesolidificationcrackingoccursinthemushyzonewheninsufficientamountofliquidflowsbacktohealthetear-ingofinter-dendriticliquidfilmduringthematerial’ssolidificationprocesses(Hatamietal.,2008andSheikhietal.,2014).

Forhighmanufacturingproductivity,weldingspeedisusuallysettobeaslargeaspossibleinpracticalapplications.Itisgenerallyacceptedinweldingcommunitythatlargeweldingspeedwouldleadtohotcracking(Nieletal.,2013).Cicalaetal.(2005),Fabregue

∗Correspondingauthors.

E-mailaddresses:Lfg119@sjtu.edu.cn(F.Lu),hui-ping.wang@gm.com(H.-P.Wang).

etal.(2008a)andTirandetal.(2013)independentlyinvestigatedtheeffectofweldingspeedonhotcrackingduringNd:YAGlaserweldingofAA6056aluminumalloywithweldingspeedintherangebetween3m/minand6m/min,4m/minand6m/min,and1.2m/minand3.5m/min,respectively.Theyallobservedthathighweldingspeedresultedinhighhotcrackingsusceptibility,whichwasexplainedbytheresultedhighweldpoolinstability,highcool-ingrateandhighsolidificationrate.El-BatahgyandKutsuna(2009)reportedthatthehotcrackingstartedtooccurinAA6061,AA5083andAA5052aluminumalloysduringCO2laserweldingwhentheweldingspeedincreasedfrom3m/minto6m/min.Haboudouetal.(2003)showedthatuseofasecondbeamtodecreasethecoolingrateofmoltenpoolwouldeffectivelypreventhotcracking.

However,positiveinfluenceofweldingspeedonhotcrackingofaluminumalloyswasalsoreported.Chihoski(1972)indicatedanimprovementinweldabilitywhenincreasingtheweldingspeedto0.8m/mininthegastungstenarc(GTA)weldingofAA2014alu-minumalloy.Thehighweldingspeedwouldinduceacompressiveloadingzoneatthetailofmoltenpoolthathelpedsuppress-inghotcracking.AbbaschianandLima(2003)studiedthehotcrackingsensitivityofAl–Cualloywithvariousweldingspeeds

http://dx.doi.org/10.1016/j.jmatprotec.2015.12.0060924-0136/©2015ElsevierB.V.Allrightsreserved.

X.Wangetal./JournalofMaterialsProcessingTechnology231(2016)18–26

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incontinuous-waveCO2laserwelding.Withincreasingweldingspeedfrom0.06m/minto3m/min,thecrackingsusceptibilityincreasedfirstandthendroppedduetotherefinementofporositiesandchangesofliquidfraction.

Asdiscussedabove,theinfluenceofweldingspeedonhotcrackingvariesfordifferentweldingprocessesandatdifferentweldingspeed.Thecoolingrate,solidificationrate,stressstateandmicrostructurecharacteristicallwouldinfluencethehotcrack-ingsusceptibility.EskinandKatgerman(2004)statedthatthehotcrackingwasaphysicalphenomenonaffectedjointlybythermal,mechanicalandmetallurgicalfeatures.Hence,acomprehensiveunderstandingofhotcrackingsensitivityatdifferentweldingspeedshouldtakeintoaccountallthefactorsmentionedabove.

Rappazetal.(1999)proposedahotcrackingmodel,namedasRDG(Rappaz-Drezet-Gremaud)model,whichconsideredtheeffectsofliquidfeeding,permeabilityofmicrostructure,solidfrac-tionanddeformationofthegrainsonthehotcrackinginitiation.Wangetal.(2004)analyzedtheeffectofgrainboundarymisorien-tationonhotcrackingtendencybasedontheRDGmodel.DrezetandAllehaux(2008)systematicallyanalyzedtheapplicationofRDGmodelinthepredictionofhotcrackingphenomenoninthewelds.Nieletal.(2013)extendedtheRDGmodelbyintroducingmicrostructurepredictionandinvestigatedtheeffectofweldingcurrentonhotcrackingintheGTAwelding.Sheikhietal.(2014)usedtheRDGmodeltocalculatethehotcrackingsensitivityinsuccessivelaserweldspotsconsideringpreheatingeffect.

Inthisstudy,theeffectofweldingspeedonsolidificationcrack-inginfiberlaserweldingof6013aluminumalloywasinvestigatedexperimentallyfirst.Next,amicro-scalefiniteelementmodelofacolumnargraininmushyzonewasdevelopedwhichmainlyinves-tigatedthestrainrateofgrainswiththeexistenceofliquidfilm.BasedontheRDGmodelandthecorrespondingpressuredrop,theeffectofweldingspeedonhotcrackingsensitivitywasanalyzed.Otherimportantstatevariablessuchascoolingrate,solidfraction,stressstateandmicrostructurecharacteristicwerealsoexamined.Also,thepossibleinitiationsiteofsolidificationcrackinginfiberlaserweldingofaluminumalloywaspredicted.

2.Weldsolidificationcrackingmodel

2.1.RDGcriterion

Duetolargetemperaturegradientexistingnearfusionlineofthemoltenpoolinlaserwelding,columnardendritestructurewouldappearnearthefusionlinewhileequiaxedgrainsexistinthecenteroffusionzonewheretemperaturegradientdecreases(Nieletal.,2013).AccordingtothestudyofFabregueetal.(2008b),solid-ificationcrackinginitiatesnearthefusionlinewherecolumnargrainsexist.Toinvestigatetheformationofsolidificationcrack-ingincolumnardendritestructure,Rappazetal.(1999)proposedtheRDGmodelanddeemedcrackasaresultbetweenflowrateandthedeformationandshrinkageofcolumnargrains,asshowninEq.(1):

󰀃

L

flvl,x=−(1+ˇ)

fsεdx˙−vTˇfl

(1)0

vT=Vcos˛

(2)

whereflistheliquidfraction,vl,xisthevelocityofthefluidalong

thex-axiswhichisparalleltocolumnargraingrowthdirection,ˇistheshrinkagefactor,Listhemushyzonelengthalongx-axis,fsis

thesolidfraction,ε

˙isthedeformationrateofgrainboundaryper-pendiculartothegraingrowthdirection,andvTisthesolidificationrate.Thefirsttermontheright-handsideofEq.(1)istheflowratecausedbythetensiledeformationofmushyzone,andthesecondtermontheright-handsideofEq.(1)istheflowrateassociated

withthesolidificationshrinkageofmushyzone.Raietal.(2008)providedtherelationshipbetweenthesolidificationrateandtheweldingspeedinEq.(2),whereVistheweldingspeedand␣istheanglebetweenthenormalofsolid-liquidinterfaceandthedirectionofweldingvelocity.

Thepermeabilityofmicrostructurereflectsthedegreeofmicrostructureinbeingfilledbackbyliquidflow.Nieletal.(2013)definedthepermeabilityofmushyzoneinAlweldsasfollows:

K=

󰀅2

3

2(1−fs)180f(3)

s2

where󰀅2isthesecondarydendritearmspacing.Theflowrateisrelatedtothepressuregradientintheliquid,thepermeabil-ityofthemushyzoneandviscosityoftheliquid(󰀆)byf−(K/󰀆)(dp/dx),lvl,x=whichcitedfromthestudyofKuboandPehlke(1985).SubstitutingthisflowratecalculationintoEq.(1),thepres-suredropintheinterdendriticliquidcouldbecalculatedasfollows(Rappazetal.,1999):

󰀃

L

󰀁P=

180fs2󰀅2(1+ˇ)󰀆

E(x)

20

(1−fs3

dx+

1802vTˇ󰀆

)

󰀅2

󰀃L×

󰀁fs

󰀂2

dx

(4)

0

1−fs

IntheRDGmodel,theinterdendriticliquidpressuredropbetweenthetipandrootofthedentriteisrequiredtoensurethatadequateliquidfeedingbackoccurstocompensatethedeforma-tionandshrinkageofmushyzone.Ifthepressuredropreachesthecriticalpressuredropthatacavityforms,hotcrackinginitiates.Eq.(4)tellsusthatthesolidificationrateatcolumnargraintip,solidfraction,deformationrateofthecolumnargrain,lengthofmushyzoneandsecondarydendritearmspacingallwouldaffectthepres-suredrop,hencethesusceptibilityofsolidificationcracking.

BasedontheworkofRappazetal.(1999),shrinkagefactorandviscosityweretakenas0.06and0.001PasforAlwelds,respec-tively.Thesecondarydendritearmspacing󰀅2couldbeobtainedbyexperimentalobservation.Theothers,suchasmushyzonelength,solidfraction,solidificationrateandstrainrate,aretakenfromcalculatedresults.

2.2.Thermal-mechanicalsimulationofweldingprocess

Wenowknowthathotcrackingsusceptibilityisaffectedbymanyfactorsandthesefactorsaredeterminedbythethermalfieldandmechanicaldeformationintheprocess.Inordertoobtaintemperatureandstrain/stressdistributionintheweld,athermal-mechanicalsimulationofthelaserweldingprocessisperformed.Theheatconductionandthethermal-elastic-plasticdeformationareconsideredinthesimulationtocalculatethetem-peratureandstrain/stress.Toincreasecalculationprecisiont,athreedimension’s(3D)thermal-mechanicalmodelisdevelopedwiththemodelsizeof60mm×35mm×2.5mm.Inaddition,themodelconsiderstemperature-dependentmaterialphysicalparam-eters,avolumetricheatsourcemodel,strain/stressrelaxationintheweldmoltenpoolandsolidificationshrinkageoftheweldmetal.Thetemperature-dependentmaterialphysicalparametersof6013aluminumalloyusedinthemodelaregiveninFig.1.

ThefiberlaserheatinputwasmodeledbyacylindricalGaussiandistributionheatmodel,whichwasproposedbyKongetal.(2011).ItisdescribedbyFeng(1994)torepresentthestress/strainrelax-ationofliquidmetalinweldpoolandtheelementrebirthmethodwasadopted.Elementswhosetemperaturesareovertheliquiduspointwouldbekilled(zerostress)inthemodel,andre-birthedagainastheirtemperaturesdroptobelowerthantheliquidus

20

X.Wangetal./JournalofMaterialsProcessingTechnology231(2016)18–26

Fig.1.Temperature-dependentmaterialphysicalparametersof6013aluminumalloy:(a)physicalparametersand(b)mechanicalproperties.

point.Thesolidificationshrinkageofweldmetalwasconsideredinthemodelbysettingthereferencetemperatureofsolidifiedmetaltoliquiduspointandaddingthevolumeshrinkageofsolidifiedmetaltothermalexpansion.

2.3.Micro-scalemodelforlocalstraininthemushyzone

Accordingtothesolidificationtheory,DavidandVitek(1989)indicatedthatthecolumnartoequiaxedtransition(CET)meantthattherapidgrowthofequiaxedgrainsinthecenteroffusionzoneinhibitedthecolumnargraingrowth.Forweldmicrostruc-ture,thepossiblelocationofcrackinitiation,whichissurroundedbyliquidusline(TL),solidusline(Tcoalescence)andCETline,wouldbesubdividedintotworegions,asshowninFig.2.RegionAisdefinedaslocationwherecolumnargraintipconnectswithmoltenpoolwhileRegionBisdefinedaslocationwherecolumnargraingrowthispreventedbyequiaxedgrain.MicrostructureinRegionAhasasimilarcolumnarmorphologyasonediscussedinRDGmodel.How-ever,thesolidificationrateatthecolumnargraintipiszeroduetothecolumnartoequiaxedtransitioninRegionB,andtherequiredflowrateinPartBisonlytocompensatethedeformationofmushyzoneifnocrackforms.

Predictionofthecrackingsusceptibilityandpossibleinitiationlocationrequiresknowledgeofmicrostructurecharacteristicandlocalstrainrateperpendiculartocolumnargrain.Themicrostruc-turecharacteristic,whichincludesthecolumnargrainlength,primarydendritearmspacingofcolumnargrainandorientationofthegrainboundaryinthemacroscopicframe,canbeobtainedby

Fig.2.Theschematicofweldmicrostructure.

Fig.3.SizeandboundaryconditionoftheFEMmodeloncolumnargrains.

experimentalobservations.ThelocalstrainrateoncolumnargrainiscalculatedbyaFEMmodeloncolumnargrainsinthisstudy.AsshowninFig.3,thedimensionsofFEMmodeloncolumnargrainsaredeterminedbymushyzonelength(L),primaryden-dritearmspacing(󰀅)andthicknessofliquidfilm(d).Basedonthetemperaturedistributionobtainedfromthethermal-mechanicalweldingprocesssimulation,themushyzonelengthistakenasdis-tancebetweenliquiduspointline(921K)andfusionlineinRegionA,andthecolumnargrainlengthisdeemedasmushyzonelengthinRegionB.Thicknessofliquidfilmbetweencolumnargrainsiscal-culatedbyEq.(5)where󰀅isprimarydendritearmspacingandfsisthesolidfraction,whichiscalculatedwiththehelpofThermo-Calcsoftware.

d=󰀅(1−fs)

(5)

TheFEMmodeloncolumnargrainsconsistsofsolidandliq-uidphasesatthesametime,andacontinuum-levelmodelingisemployedtocalculatethelocalstrainrateperpendiculartocolum-nargrainbyspecialtreatmentofliquidphysicalparameters.ThesolidandliquidphysicalparametersusedinthemodelaregiveninFig.1(b)andFig.4,respectively.Themechanicalpropertiesofliquidphaseweretreatedasone-twentiethofthesolidbyatrial-and-erroriterativeprocessbasedonthereportedfindingsbyConiglioandCross(2009)andBordreuilandNiel(2014).Theirworkshowedthatthelocalstraininliquidwasabout102-103timesoflocalstraininsolid.Theboundaryconditionoftemperatureanddisplacementwereobtainedfromprocesssimulationandlinearlyinterpolatedfromtheprocessdomaintothecolumnargraindomain.Temper-aturealongthecolumnargrainisusedtocalculatesolidfraction,

X.Wangetal./JournalofMaterialsProcessingTechnology231(2016)18–26

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Fig.4.Temperature-dependentmaterialphysicalparametersusedintheFEMmodeloncolumnargrains.

andthecalculatedlocalstrainrateofthesolid-liquidinterfaceisadoptedasthedeformationrateofsolidsinEq.(4).

TheRDGcriterionsimplifiesthefeedingbackofliquidflowsonlyalongthegrowthdirectionofcolumnargrain.Therefore,onlystrainongrainboundaryperpendiculartothegrowthdirectionofgrainisrequired.Consideringtheorientationofcolumnargrainboundaryinmacroscopicframe,BordreuilandNiel(2014)proposedthefor-mulationforthestrainperpendiculartocolumnargrainasfollows:

referringtothetestofPloshikhinetal.(2007)thatthemechanicalclampingwasappliedononesideoftheweldlinewhiletheothersideisfree.Inthisstudy,thedistancebetweenweldcenterlineandclosestfreeedgewas7.5mm,andthedistancefromtheweldcen-terlinetotheclampingedgewas20mm.Bead-on-plateweldwasadoptedintheexperimenttoavoidtheinfluenceofgapbetweentwooverlapsheetsonthecrackingsusceptibility.TheAlspecimensurfaceswerecleanedpriortoweldingtesttoremoveanyoilsandcontaminations.

Theweldingtestshowedthattransversecrackappearedwhentheweldingspeedswere2.5m/min,2.7m/minand3.0m/min.Thatis,thetransversesolidificationcrackingispronetoinitiatewhentheweldingspeedisrelativelylowforfiberlaserweldingof6013aluminumalloy.Fig.5givespicturesoftheweld’stopsurface.Fig.5(a)showstheweldsurfaceforV=2.7m/minwhileFig.5(b)givestheweldsurfaceforV=3.3m/min.AtthelowweldingspeedofV=2.7m/min,theweldbeamiswideandthetransversesolidificationcrackingwasobservedtoinitiatenearthefusionline,asshowninFig.5(a).Whentheweldingspeedincreasedto3.3m/min,thetransversesolidificationcrackingdisappeared.Therefore,theexperimentalresultsindicatedthatthelowweldingspeedincreasedsolidificationcrackingsusceptibilityinthefiberlaserweldingof6013aluminumalloys.

4.Resultsanddiscussion

4.1.Metallographicanalysis

ε=εxsinÂ+εycos2Â+2󰀇xysinÂcosÂ

2

(6)

whereεxismechanicalstraininhorizontaldirection,εyismechan-icalstraininverticaldirectionandÂistheanglebetweenthecolumnargraindirectionandtheweldingvelocity.Oncethestrainwasobtained,thestrainratecanbeeasilycalculatedanditvariesfromlocationtolocationinthemushyzone.

3.Weldingexperiment

AA6013aluminumalloyspecimenswiththedimensionof150mm×125mm×2.5mmwereusedintheweldingtest.ThechemicalcompositionofAA6013is0.95Mg,0.62Si,0.95Cu,0.22Fe,0.37Mn(wt.%),balancedbyAl.YLS-10000fiberlasersystemwastakenasheatingsourcewithspotdiameterbeing0.8mm.ToinvestigatetheeffectofweldingspeedonsolidificationcrackinginfiberlaserweldingofAA6013aluminumalloy,wetestedwiththeweldingvelocitybeing2.5m/min,2.7m/min,3.0m/min,3.3m/minand3.5m/min.Thelaserpowerwas3.3kW,andargonshieldinggasflowratewas15L/min.Experimentaltestsystemwassetup

Grainstructurecharacteristicplaysasignificantroleinsolidificationcrackingbehavior.ThemetallographicpicturesofmicrostructurefortwodifferentweldingspeedsaregiveninFig.6(a–d).Thepicturesshowthatthecolumnardendritegrainsgrowneartwosidesoffusionzoneandtheequiaxeddendritegrainsappearinthemiddleoffusionzoneforbothcases.Sincetheweld-ingspeeddeterminesthetemperaturegradientandsolidificationrate,theresultantmicrostructureinFig.6(a,b)exhibitobviousdis-tinction.Thecolumnartoequiaxedtransitionwasadvancedwhentheweldingspeedincreasedfrom2.7m/minto3.3m/min.Thelengthofcolumnargrainwasabout500␮mwithweldingspeedof2.7m/minand300␮mwithweldingspeedof3.3m/min.Fig.6(c)and(d)showsthelocalamplificationofcolumnargrainsfortwocases.Thecolumnargrainboundariesareplottedbyblackdottedlines.Asasimpleestimation,theprimarydendritearmspacingisabout51␮mforthespeedof2.7m/minand60␮mforthespeedof3.3m/min.BasedonthestudyofKimuraetal.(2009)thatafinergrainsizeledtolowersusceptibilitytocracking,grainmorphol-ogyinducedbythelowerweldingspeedinthisstudyhadlessequiaxedgrainsandmorecolumnargrains,henceahighersolidifi-cationcrackingsusceptibility.Fromthemetallurgicalpointofview,

Fig.5.Thetopsurfacesofweldgeneratedwithweldingspeedof:(a)V=2.7m/minand(b)V=3.3m/min.

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X.Wangetal./JournalofMaterialsProcessingTechnology231(2016)18–26

Fig.6.Themicrostructurecharacteristicsofweldfordifferentweldingspeeds:(a)V=2.7m/min;(b)V=3.3m/min;(c)and(d)arelocalamplificationofcolumnargrains.

Fig.7.Calculatedtemperatureevolutionversustheweldingtimeatapointoftheweldcenterline.

Fig.8.Thecalculatedlongitudinalmechanicalstraindistributionontopsurfaceoftestplatesfortwocases:(a)V=2.7m/minand(b)V=3.3m/min.

X.Wangetal./JournalofMaterialsProcessingTechnology231(2016)18–26

23

Fig.9.Thelocalmechanicalstrainperpendiculartocolumnargrainsontopsurface:(a)V=2.7m/minand(b)V=3.3m/min.

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X.Wangetal./JournalofMaterialsProcessingTechnology231(2016)18–26

thelongmushyzoneincreasesthedifficultyofliquidmetaltoflowback,andsmallprimarydendritearmspacingincreasesthedegreeofstressconcentration.

4.2.Thermal-mechanicalfieldduringweldingprocess

Fig.7illustratesthetemperatureevolutionversustheweldingtimeatapointoftheweldcenterline.Thecoolingratebetweentheliquidusandsoliduspointsisinvestigated.Duetothefastweldingspeedinlaserwelding,thecoolingratesforbothcasesareveryhighwith3380K/sfor2.7m/minand4770K/sfor3.3m/min.Thehighertheweldingspeed,thehigherthecoolingrate.

Solidificationcrackingoccursinmushyzonewhereliquidandsolidphasescoexist.Inthisstudy,thetemperaturerangebetweenliquiduspointandcoalescencepointisdefinedasmushyzone.Thelongitudinalmechanicalstrain,whichisrelatedtotransversesolidificationcracking,isshowninFig.8.Thetensilelongitudi-nalstrainappearsinlaterpartofmushyzoneforbothcases,whichpromotescracking.Themaximumlongitudinalmechanicalstraininmushyzoneis1.4%for2.7m/minand0.9%for3.3m/min,respectively.Basedontheresultsofweldingprocesssimulation,relativelysmallcoolingrateandlargedeformationareinducedatlowweldingspeed.Inordertodeterminethecrackingsensitivity,westillneedtoknowlocalstrainrateinadditiontothecoolingrateanddeformationofthemushyzonewehavecalculatedfromthethermal-mechanicalanalysis.

4.3.Distributionoflocalstrainrate

Fig.9givesthecontouroflocalmechanicalstrainperpendic-ulartocolumnargrainsatdifferentpositionsinmushyzone.Theliquidfilmsitsinthemiddleofcolumnargrains.Thedifferencesofcolumnargrainsarethethicknessofliquidfilm,whichpresentsthedifferentsolid-liquidfractionduringthesolidificationprocess.

Forpositionsaandb,whichsitsintheearlypartofmushyzone,thecompressivemechanicalstrainoccurs.Frompositionctopositione,thetensilemechanicalstraindistributesinthewholecolumnargrain.Itisnotedthatthelocalmechanicalstraininsolidcolumnargrainismuchsmallerthanmechanicalstraininliquidfilm,andtheextentofdifferenceincreaseswiththedecreasingofliquidfilmthickness.Forthecasewithweldingspeedof2.7m/min,themagnitudeorderoflocalmechanicalstrainisabout10−4insolidgrainandtheorderoflocalmechanicalstraininliquidfilmis10−2,whichisabout102–103timesthanthemechanicalstraininsolid.Thesamecharacteristicisalsofoundincasewithweldingspeedof3.3m/min.Inaddition,thelocalmechanicalstrainofsolid–liquidinterfaceisrelativelylargeinthecaseoflowweldingspeed.

Forthetestcasewithweldingspeedbeing2.7m/min,therateofmechanicalstrainperpendiculartothesolid-liquidinterfacealongcolumnargrainisshowninFig.10.Theblackdottedlinerepresentsinitiationofthecolumnargrainandthex-coordinaterepresentsthelocationalongthelengthofgrain.Intheearlypartofmushyzonesuchaspositionsa,bandc,themechanicalstrainrateonthesolid-liquidinterfaceislowerthanthemechanicalstrainrateinthelatterpartofmushyzonesuchaspositionsdande.Themaximumlocalmechanicalstrainrateoccursinthelatterpartofmushyzonewiththemagnitudeorderof10−1underthetestcondition.

4.4.Analysisofsolidificationcrackingsusceptibility

Thefeedingbackofliquidflowplaysasignificantroleinthesolidificationcrackingbehavior.Fig.11showstherequiredflowratetocompensatedeformationandshrinkageofcolumnargrainsinthemushyzone.Therequiredflowrateissameatpositionaandpositionbsincethesolidificationshrinkageisthedominanteffectinthisregion,whereasthecontributionofstrainrateisvery

Fig.10.Theperpendicularstrainratesonthesolid-liquidinterfacealongcolumnargrain.

Fig.11.Therequiredflowratetocompensatedeformationandshrinkageofcolum-nargraininmushyzone.

little.Atpositionc,theeffectofsolidificationshrinkagedisappearsbecausethecolumnargrainsstopgrowthalreadyandtheeffectofstrainrateisstillsmallatthismoment.Hence,therequiredflowratereachesthesmallestvaluesatpositionc.Withtheincreaseofsolidfraction,thestrainrategrowssignificantly,asshowninFig.10.Asaresult,therequiredflowrateishighatpositiond.Thecolumnargrainlengthdecreasesfrompositiondtopositionewhilethestrainratedoesnotincreasetoomuch,andthecompetingresultsisthattherequiredflowratedecreasesagainfrompositiondtopositione.Comparingtwodifferentweldingspeeds,wenotethatthelowweldingspeedneedsrelativelyhighflowratetocompensategraindeformationandshrinkage,whichismainlyinducedbythehighstrainrateandlargecolumnargrainlengthatlowweldingspeed.

Fig.12showstheshrinkageanddeformationcontributionstothepressuredropintheinterdendriticliquid.Undertheconditionofthistest,themagnitudeofpressuredropinducedbydeforma-tionisobviouslyhigherthanpressuredropinducedbyshrinkage,whichindicatesthatthestrainrateismoresignificantthansolid-ificationrateincontrollingthesolidificationcrackinginitiationinthistest.Fig.13showsthesolidificationcrackingsusceptibilityfordifferentweldingspeedsbasedonthepressuredropattherootofcolumnargrains.Drezetetal.(2008)used150kPaasthecriti-calpressuredropforcrackinginitiationinAlweldsandthisvalueisalsoadoptedinthisstudy.Thecalculatedresultindicatesthatthetestcasewithweldingspeedbeing2.7m/minissusceptibleto

X.Wangetal./JournalofMaterialsProcessingTechnology231(2016)18–26

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Fig.12.(a)Mechanicalcontributiontothepressuredropand(b)shrinkagecontributiontothepressuredropattherootofcolumnargrains.

whichisalmost102–103timesofthelocalmechanicalstraininsolid.

3.Pressuredropexceedingthecriticalvalueforcrackformationmainlyoccursinthesecondhalfofmushyzonewherethesolidfractionisbetween90%and94%.Thesolidfractionof90%couldbedeemedasthecriticalsolidfractionatwhichcrackinitiates.4.Themodeldevelopedinthisstudydeemsthecrackasaresultofthefracturebyliquidfilmamongcolumnargrains.So,thepro-posedmicroscalemodelcouldbeextendedtootherAl-basedalloyswhensolidificationcrackinginitiationrelateswiththeliquidfilm.

Acknowledgments

Fig.13.Thetotalpressuredropattherootofcolumnargrainsandthepotentiallocationofsolidificationcrackinginmushyzone.

solidificationcracking,whichagreeswellwiththeexperimentaltests.ThesusceptiblelocationofcrackinginitiationisalsorevealedinFig.13wherethefirsthalfofmushyzonewasnotsensitivetocrackingandtheriskyregionofcrackinginitiationmainlycon-centratedonthesecondhalfofmushyzonenearpositiond.Inthisstudy,thedifferentpositionscouldbedeemedasdifferentsolidfractionsduringsolidificationprocess.Basedonthecalculatedresults,solidfractionof90%couldbedeemedasthecriticalsolidfractionatwhichpressuredropexceedsthecriticalvalueforcrackformation.

Thisworkwascarriedoutintheframeworkoftheproject“Investigationonlaserweldingofaluminumalloysthroughpro-cesssimulation”sponsoredbyGeneralMotorsGlobalResearch&Development.Theauthorsalsogratefullyacknowledgethefinan-cialsupportbytheNationalNaturalScienceFoundationofChina(GrantNo.51204109).

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Inthisstudy,effectofweldingspeedonsolidificationcrackingsusceptibilityduringfiberlaserweldingof6013aluminumalloywasinvestigatedconsideringboththemechanicalandmetallurgi-calfactors.First,afiniteelementmodelwasdevelopedatcolumnargrainscaletocalculatethestrainlocalizationinthemushyzone.TheRDGcriterionwasusedforthestudyofeffectofweldingparametersoncrackingsusceptibility.Themainconclusionsareasfollows:

1.Duringthefiberlaserweldingof6013aluminumalloy,increas-ingweldingspeedfrom2.5m/minto3.5m/minwouldincreasethesusceptibilityoftransversesolidificationcracking.

2.Overtherangeofexperimentsconsidered,theorderofmag-nitudeoflocaltensilemechanicalstrainisabout10−4insolidgrainwhiletheorderofmagnitudeofstraininliquidfilmis10−2,

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