Study of the hot forging of weld cladded work pieces using upsetting tests

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Jingcai WANG, Laurent LANGLOIS, Muhammad RAFIQ, Régis BIGOT, Hao LU - Study of the hot

forging of weld cladded work pieces using upsetting tests - Journal of Materials Processing

Technology - Vol. 214, n°2, p.365-379 - 2014

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tests

Jingcai

Wang

a,b

_,

_Laurent

_Langlois

a,∗

_,

_Muhammad

_Rafiq

a

_,

_Régis

_Bigot

a

_,

_Hao

_Lu

b

a_{LCFC,ParisTech,4rueAugustinFresnel,57070Metz,France}

b_{WeldingEngineeringInstituteofShanghaiJiaoTongUniversity,200240Shanghai,China}

Keywords: Multi-material Forgeability Stainlesssteel Weldcladding

a

b

s

t

r

a

c

t

Thispaperfocusesonthehotforgingofmulti-materialcladdedworkpiecesusingupsettingtests.The

casestudycorrespondstogasmetalarcweldingcladdingofaSS316Lonamildsteel(C15).Experimental

testsandsimulationsusingaslabmodelandthefiniteelementmethodwereperformedusingdifferent

temperaturesanddie/billettribologicalconditions.Asaresult,acrackmode,specifictocladbillets,was

observedexperimentallyandcanbepredictedbytheFEmethodusingaLathamandCockcroftcriterion.

ThematerialdistributionwaswellsimulatedbytheFEmethod;inparticular,theeffectsofthefriction

atdie/workpieceinterfaceonthecrackoccurrence,thematerialdistributionand,toalesserextent,

theforgingloadarewellpredicted.However,thelatterwasunderestimated,highlightingthefactthat

theeffectofthedilutionassociatedwiththecladdingprocessonthematerialbehaviorofthecladlayer

cannotbeneglected.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

The ability to achieve various mechanical and metallurgical propertiesisthemaindrivingforcesintheselectionofmany manu-facturingprocesses.Intheclassicalfabricationofcladdedproducts, hotforgingprocessisnormallyperformedbeforecladdingwhich inducesproblemsoflow efficiencyandbadqualitycontrol.Itis consideredthattheseproblemsmightbereducedbychangingthe orderofthetwoprocesses(seeFig.1)whereasimplepreformis claddedandthenforgedtoobtaina complexshape.Duetothe easeofautomationofthecladdingprocessforsimpleshapes,good controloncladdingqualitycanbeachieved.Thefinalmetallurgical structureofthecladlayeristhentheresultofhotworkinginstead ofsolidification.

Theobjectiveofthisstudyistoanalyzetheabilityofacladded workpieceunderhotforgingtoobtainadefect-freematerial dis-tributionandstructure.However,itmustbeconsideredthatthe forgeability of thebi-material claddedwork piece is heteroge-neous;theductilityof thecladdinglayeris unknownasit is a mixtureofthesubstratemetalandfillermaterialdependingon thedilutionrateandislikelyinfluencedbyconditionsthatexist duringhotforming.

Theinterfacebetweenthesubstrateandthecladlayerdepends onthecladdingprocess.Thecladdingconsideredinthisstudyisthe

∗ Correspondingauthor.Tel.:+33387375456. E-mailaddress:laurent.langlois@ensam.eu(L.Langlois).

gasmetalarcwelding(GMAW)claddingprocesswhich exhibits awavymorphology.Theinterfacedefectsand localgeometrical effectscanalsohaveagreatinfluenceontheductilityofthecladded workpiece.Besides,itcanbedifficulttocontrolthedistributionof materialsduringhotforming.

Due to the difference in rheological properties at different positionsofthecladdedworkpiece,acharacterizationofthe forge-abilityonthreelevelsisproposed(seeFig.2):

Level1:Theintrinsicforgeabilityofthematerialsconstituting thesubstrateandthecladlayer.Theintrinsicforgeabilityconcerns theflowstressdependingonthethermomechanicalparameters (temperature,plasticstrainandplasticstrainrate)andtheductility limit.Thislevelofforgeabilitydependsonthechemical composi-tionandmicrostructureofthematerial.

Level2:Thislevelofforgeabilityconcernstwoaspects:

◦theabilityoftheinterfacebetweenthesubstrateandthecladding to undergo thethermo mechanical loading generated during forming,

◦theinterfacecanexhibitawavymorphologyinthecaseofa step-by-stepcladdingprocesslikelaser cladding(Caoetal.,2008). Tothis morphologycancorrespondaheterogeneouscladding thicknesswithassociatedstressconcentrationleadingtostrain localizationandearlycracking.

Level3:Thislevel offorgeabilityconcerns thedifficultiesto achievetherequiredmaterialdistributionattheendofthe form-ingprocess.Thelocationofthecladdingontheinitialbillethasto

Preform manufacturing Cladding process Forging process Billet Filler material Cladded workpiece

Fig.1. Studiedmanufacturinglayoutconsistingofacladdingprocessanda subse-quentforgingprocess.

Substrate

Level 1 Level 2 Level3

Cladlayer

Fig.2.Characterizationapproachforbi-materialcladdedworkpiece.

bechosencarefullyinordertoobtainafterformingtherequisite materialdistributionwithinthefinalpart.Duetothedifference betweentheformingbehaviorofthesubstrateandthecladding,it canbedifficult,evenimpossible,tocontrolthematerialdistribution throughouttheformingprocess.

Theobjectiveofthepresentedworkistoevaluatethepotential ofhotupsettingintermsofcharacterizationofhotforgeabilityof claddedworkpiecesaccordingtothethreelevelsdefinedabove. Sofar,therehasbeenlittleactiveresearchontheforgeabilityof bi-materialcladdedworkpiecesgeneratedbyarc welding.This paperpresentsexperimental,analyticalandnumericalstudieson hotupsettingteststodeterminethehotforgeabilityofcladded workpieces.

Firstly,thearticlegivesabriefstateoftheartconcerningthe forgeabilityofcarbonsteelandstainlesssteel,depositingstainless steelonmildsteelandtheformingofmulti-material.Secondly,the experimentalsetupandresultsobtainedintheupsettingtestof claddedbilletsarepresented.Then,twomodelsofupsettingtests areintroducedwherethefirstisbasedontheslabmethodandthe secondonafiniteelementmodeling.Thelastpartisdevotedto studyingthesimulationpredictionsandcomparingthemwiththe experimentalresults.

2. Stateofthearts

2.1. Forgeabilityandrelatedexperimentaltestofmildsteeland stainlesssteel

Onedefinitionof forgeabilityis that it is therelative ability ofamaterialtoflowundercompressiveloadingwithout crack-ing.Mostcarbonand low-alloysteelsareusuallyconsideredto havegoodforgeability,exceptforresulfurizedandrephosphorized gradesasreferredbyVanTyne(2005).Stainlesssteels,basedon forgingpressureandloadrequirements,areconsideredtobemore difficulttoforgethancarbonorlow-alloysteels,primarilybecause ofthegreaterstrengthatelevatedtemperaturesandlimitationson themaximumtemperatureatwhichtheycanbeforgedwithout incurringmicrostructural damageasshownbyMochnal(2005). Forgeabilityorworkabilityisevaluatedinseveralwaysthrough varioustypesoftestsreviewedbyDieter(2005).Thesetestsare commonlyappliedtomono-materialsamplestocharacterizethe flowstressofthematerialinrelationtothetemperature,the plas-tic strain and the plastic strain rate. Tensile tests or upsetting testsarealsoappliedtoassesstheductilitylimit. Theprinciple ofthesetestsconsistsinmeasuringthetestingloadasafunction ofthetesting displacement,measuringtheshapeofthesample andanalyzingtheoccurrenceofcracks.Thesefeaturesarelinked

tothematerialpropertiesthankstomodelsgenerallybased on theassumptionofhomogeneityofthematerial.Asthiscannotbe thecasewhenconsideringamulti-materialsample,therelation betweenthetestingloadanddisplacementandthelocal thermo-mechanicalparametersneedsmorecomplexmodelinglikefinite elementmodeltakingintoaccountthebehaviorofbothmaterials andtheinterface.

2.2. Weldcladdingofstainlesssteelonmildsteelsubstrate

Thetechniqueofweldcladdingrepresentsamethodthatcan beusedtoimpartdifferentsurfacepropertiestoasubstratethat arenotavailablefromthatbasemetal,ortoconserveexpensiveor difficult-to-obtainmaterialsbyusingonlyarelativelythinsurface layeronalessexpensiveorabundantbasematerialasreviewedby Davis(1993).Variousprocesseslikesubmergedarcwelding(SAW), gas tungsten arc welding (GTAW), plasma arc welding (PAW), gasmetalarcwelding(GMAW),universalgasmetalarcwelding (UGMAW),electroslag welding(ESW),stripcladding,explosive welding,frictionwelding,etc.havebeenusedforcladding oper-ationwithanaimtominimizingdilutionwithoutsacrificingthe jointintegrity.Govardhanetal.(2012)havecarriedoutresearchon thecharacterizationofausteniticstainlesssteeldepositedby fric-tionweldingonlowcarbonsteelsubstrates.Selectionofthemost appropriateweldingprocessislargelydependentonfactorssuchas thesizeofthecladarea,accesstotheareatobecladded,alloytype andspecifiedcladthickness,chemicalcompositionlimits, weld-ingpositionand NonDestructiveTestingacceptance standards. Forexample,Brown(2005)hasstudiedthepossibleapplication ofweldoverlaycladdinginthefieldofpumpstoresolvecorrosion problems.

Thestructureofthestainlesssteeldepositedoncarbonor low-alloysteelmayvary fromfull martensitictofullaustenitictoa mixtureofthetwowithferrite.Thisvariationinstructuredepends onlocalcompositionalgradientsanddiffusioneffects.Lippoldand Kotecki(2005)havefoundthatdissimilar metalweldsbetween carbonsteelandstainlesssteelcanexhibitanumberofcrack mech-anismslikesolidificationcrack,claddisbanding,reheatorPWHT (PostWeldHeatTreatment)crackandcreepfailureinHAZ(Heat AffectedZone).

2.3. Theforgeabilityofmulti-material

Insomeapplicationstheforgedpropertiesachievedfroma sin-glepieceofmonolithicbarstockcannotbetailoredtosatisfyallthe designrequirementsthatmayexistatdifferentlocationsinapart. Toresolvethisissue,bi-materialforging,whichhasasubstantial impactontheoperatingefficiencyoftheparts,isperformed.Use ofabi-materialpreformcouldalsominimizematerialcostwhile fulfillingthenecessarydesignrequirements.

Presently, littleworkhasbeencarried outonthe forgingof bi-metal.Thefeasibilityoftheweldedpreformconceptwas pre-viously usedby Domblesky et al. (2006).They studied thehot forgingbehaviorofdifferentmaterialssuchas:copper,aluminum, steeland304stainlesssteel.Sameanddissimilarmetalspreforms producedbyfrictionwelding,consistingoftwocylindrical spec-imensinwhichoneisplacedontopoftheother,areupsetand side-pressedtoassessworkabilityand theresultingmechanical properties(seeFig.3).AsshowninFig.3,inbi-metalpreforms, deformationoccurspreferentiallyinthelowerstrengthspecimen duringupsettingandtensiletestsofside-pressedpreforms. Frac-turewasfoundtobeductile and tooccuraway fromtheweld region.Theintrinsicforgeabilityofallthematerialsinvolvedisgood (forgeabilityofLevel1).Theweldingboundisstrongenoughto resistdeformation(forgeabilityofLevel2).Buttheflowstress dif-ferencesinvariousmaterialscouldleadtoabadglobalforgeability,

Fig.3.Dissimilarmetalpreformsafterhotcompressionto50%reductionshowingtheeffectof(a)smalldifference(Cu–Al),(b)intermediatedifference(stainlesssteel–steel), (c)largedifference(steel–cu)inflowstressbetweenthebasemetals(Dombleskyetal.,2006)

namelyaninabilitytocontrolthematerialdistribution(forgeability ofLevel3).

Thepreforms studiedabove areassemblagesof two dissim-ilar metals. Essa et al. (2012) have studied the cold upsetting ofbi-metallic ringbillets. Intheirstudy,preforms consistingof anouterringofnon-alloysteelC45E(EN1.1191)surroundinga solidcylinderofnon-alloysteelC15E(EN1.1141)arecompressed withflat platens of alloyed steel.As shown on Fig. 4, there is

nomechanical, welded or metallurgicalbond betweenthetwo materials.Theobjectiveisthentodeterminethescopeforcold forgingofbi-metalpreformswithnopre-processinterfacebond. The studyhasshown that undercertain conditions,bi-metallic ringsmaybeupsetwhilemaintainingagoodinterfacialcontact betweenthetwocomponentswithinarangeofgeometries.The increaseofinterfacefrictioneffectwillincreasethesurface con-tact.

Table1

Weldingparameters.

Parameters Nozzle-to-bar distance(mm)

Wirefeedspeed (mm/s)

Voltage(V) Weldingspeed (mm/s)

Protectiongas (%involume)

Generator Weldingmachine

Value 16 4.2 22 5.3 Ar96%,CO23%,

H21%

CY385MPR 6-Axes

polyarticularrobot (SCS)

Differentfromthemodelsabove,thespecimenstudiedinthis paperconsistsofaweldedbondbetweentheoutercladdingand innercylinder.Upsettingtestsareperformedtoevaluatethe defor-mationbehavioroftheinterfaceandtheforgingload.

3. Experimental

3.1. Experimentaldetails

Intheupsettingtest,acylindricalworkpieceisupsetbetween two flat dies to a pre-fixed ratio. The cladded specimens are obtainedbycuttingaweldcladdedbar.Amild steelbar(0.15% C,0.45%Mn,0.2%Si,0.023%Pand0.023%S)withadiameterof Ø27mm wascladdedusing astainless steel(0.02% C,1.8% Mn, 0.33%Si, 0.023%P, 0.013%S, 17.5% Cr, 2.55%Moand 12.2%Ni) wireofdiameter1.0mmbyGMAWprocessonrotatingwelding platforms.Thecladbaristhen cutinto45mm-long specimens. ThemainparametersoftheGMAWcladdingprocessareshown inTable1.

Themacrographofthemeridiancrosssectionofacladded bil-letisshowninFig.5.Thecladding/substrateinterfaceexhibitsa wavymorphology.Themeancladdingthicknessisabout3mm.For a45mmlongbillet,thereareabout10beads.Thecladdingis com-posedofjuxtaposedbeadrings(notacoil).Thebeginningofthe beadoverlapstheendofsamebead,whichisresponsibleforthe build-upofthecladlayerthatcouldbeobservedontheleftinFig.5. Theoveralldilutionratebetweenthefillermaterialandthe sub-strateisabout10%.ThisrelativelylowdilutionvalueforGMAW claddingisachievedthankstotheoverlapping.

ThesetupfortheexperimentalupsettingtestisshowninFig.6.A hydraulicpress“LoireACB”havingamaximumloadof6000kNwas used.Thespecimenswereheatedfor15minataconstant temper-atureinanelectricfurnace(seeFig.6(b)andTable2)undernormal atmosphere,whilethedieswerenotpreheated.

Twotypesof flatdies were used:striated and smooth dies. Upsettingtestswereperformedwithsmoothdies(lubricatedand dry)andstriateddies.Thelubricantconsistedofamixtureofoiland graphite(shellfenelloroilfluidF3802G)whichwasdepositedon thesmoothdiewithabrushbeforeeachtest.Regardingthestriated

Fig.5. Macrographofthemeridiancrosssectionofthecladbillet.

Table2

Variablesconsideredinperformedupsettingtests. Tool/temperature(◦_{C) Cladbillet}

750 900 1050

Striateddie Yes Yes Yes

Drysmoothdie Yes – Yes

Lubricatedsmoothdie Yes – Yes

dies,thestriationconsistedofmanyconcentriccirculargrooveson thesurfaceofthedie.Thedistancebetweentwosuccessivegrooves wasabout1mmwithadepthof1mm.Thespecimensweretaken outofthefurnaceandupsetimmediately.Theupsetvelocitywas constantabout30mm/s.Specimenswereupsettovarious upset-tingratioswiththehelpofstopblocksplaced betweenthedie holders.Dependingontheappearanceofthecrack,theupsetratio

Table3

Cracksoccurrenceintestsperformedusingstriateddie.

Temperature(◦C)/crackoccurrence/%upsetting 50% 60% 63% 65% 67% 70%

750 No No – Longitudinal Longitudinal –

900 – No No Longitudinal Longitudinal Longitudinal

1050 – No – – – Circumferential&longitudinal

Table4

Crackoccurrenceintestsperformedusingsmoothdie.

Die Temperature(◦_{C)/%upsetting 62% 63% 73% 74%}

Lubricatedsmoothdie 750 No – – Longitudinal

1050 – No – No

Smoothdie 750 Longitudinal – Longitudinal –

1050 – No – Longitudinal

ofthenexttrialwasincreasedordecreased.Theupsettingratio,ı, isdefinedasthepercentagereductioninlengthofthebillet(see Eq.(1))

ı=1− h h0

(1)

wherehandh0arerespectivelytheinstantaneousandtheinitial

lengthofthebillet.

Temperatureandfrictionatthedie/workpieceinterfacearethe twovariablesconsideredintheupsettingtests(seeTable2).Tests performedwithastriateddieareconsideredtohaveaveryhigh frictioncoefficientatthedie/workpieceinterface,approximating stickingcondition.Adrysmoothdierepresentsmediumfriction coefficient,whilealubricatedsmoothdierepresentsthelowest frictioncoefficientachievableexperimentally.Threetemperatures werechosen:750◦C,900◦Cand1050◦C.700◦Cisinthe tempera-turerangeofwarmforging.1050◦Cisinthetemperaturerangeof hotforgingofbothmaterials.900◦Cisinthetemperaturerangeof hotforgingofmildsteelbutrepresentsthelowerlimittemperature ofhotforgingforstainlesssteel(Mochnal,2005).

3.2. Experimentalresults

Theresultspresentedinthissectionconcernthreeparts:the ductility limit, theobtainedmaterial distribution and the forg-ingload.Theductilitylimitisdefinedbythemaximumupsetting ratioachievedwithoutcrackforming.Thematerialdistributionwas observedthankstomeridiancrosssectionoftheupsetbilletand

correspondedtosubstrateandcladdingmorphology.Theforging loadwasconsideredthroughouttheupsettingandwasprovided bythesensorofthehydraulicpress.

Forcladbillets,twotypesofcrackswereobservedinthe exper-imentaltests:longitudinalandcircumferentialcracks(seeFig.7). The (longitudinal and circumferential)crackswere observed to occuronlyinthecladlayerand neverpropagatedintothe sub-strate.Thecircumferentialcracksoccurredinthethinnerpartof thecladdingwithadirectionrelativetothebeads.Uptoa70% upsetratio,longitudinalcrackswereobservedtooccurinalltests performedwithasmoothdieorastriateddie,while circumfer-entialcracksoccurredonlyintestsperformedusingastriateddie at1050◦C.

The cracks are detected visually and by dye penetrant test performedafterthespecimenswerecompletelycooledtoroom temperature afterhot upsetting.The temperature,friction con-dition atdie/work pieceinterfaceand upsetting ratio aremain drivingforcesfor crackoccurrenceasshown inTables 3and4. Theductilityincreaseswithincreasingtemperature.Inupsetting testsperformedusingthesamefrictionconditions,cracksoccurred morefrequentlyatlowertemperatureandhigherupsettingratio. Furthermorethefrictionconditionatthedie/workpieceinterface mainlyaffectsthecracktype.

The longitudinal cracks are typical during the upsetting of mono-material.Theycorrespondtoductilecrackswhenthe mate-rial at the surface of the billet reaches its ductility limit. The circumferentialcracksarespecifictotheupsettingofcladbillets. Severalpotentialexplanationsforthecrackingphenomenonare

Fig.7. (a)Positionoflongitudinalandcircumferentialcracksinworkpiecesupsetusingstriateddie,(b)macrographoflongitudinalcracks,aquarteroftransversalsection, at900◦_{Cand(c)circumferentialcrack,halfofmeridiancrosssection,at1050}◦_C.

Fig.8. Macrographsofmeridiancrosssectionsofworkpieces70%hotupsetat1050◦_{Cindifferentfrictionconditions(a)striateddie,(b)drysmoothdieand(c)lubricated} smoothdie.

proposed.First,theremightbealocaleffectof thediestriation oncrackasitoccurredonlyintestsperformedwithstriateddies. Secondly,thefactthatthecrackoccurredatacertainlocationof thecladlayermightbeduetotheeffectofthebeadorientation relativetothethermalmechanicalloading.Indeed,thewavy mor-phologyoftheinterfacecangeneratestressconcentrationleading tothecircumferentialcracks.Finally,theareacoveredbytheclad layerismoreimportantinthecaseofstriateddiesthaninthecase ofsmoothdies.Thus,withastriateddie,thecladlayerismore stretchedthanintheothercases,whichleadstoearlycracking.

Thecracksneverpropagateintothesubstrate.Onepotential rea-sonforthisphenomenonmaybethattheductilityofmildsteelis betterthanthatofstainlesssteel.Anotherreasoncouldbethatdue tomaterialdiscontinuitythecladlayerismoreloadedthanthe sub-strate.Indeed,theremightbeadiscontinuityofthestressthrough thesubstrate/claddinginterface;theloadingtype(compressionor tensile)canbedifferentindifferentlocationsofthecladdedbillet, especiallyacrosstheinterface.Theinvestigationofthestressacross theinterfaceandtheeffectofweldbeadorientationareamongthe mainobjectivesofthefiniteelementsimulationstudy.

Thematerialdistributionofthecladdedbilletafterbeinghot forgedisobservedvisuallyinthemacrographsofmeridiancross sections.Theworkpieceiscut,polishedandchemicallyetchedfor afewsecondsbyNital2%whichcanetchC15butnotSS316L, allow-ingtodistinguishtheinterfacebetweenthetwomaterials.The macrographsofthemeridiancrosssectionofworkpiecesupsetin differentconditionsareshowninFig.8.Thematerialdistributionis theresultofacombinationofseveralfactors.Thedwelltime(about 5s)betweenplacingthebilletonthelowerdieandthebeginning oftheforging,frictionconditionatthedie/workpieceinterface,the wavymorphologyofsubstrate/claddinginterfaceandtheductility ofmaterialsconstitutingthesubstrateandthecladlayeraremain drivingforcesofmaterialdistributionduringthehotupsettingtest. AccordingtoFig.8,thesubstrateafterupsetiscomposedofa centraltrunksurroundedbyaring-likepart(seeFig.9).Theareaof theupper/lowersurfacecoveredbycladlayerdependsonthe diam-eterofthecentraltrunk.Thediameterofthecentraltrunkmainly dependsonthefrictionconditionatthedie/workpieceinterface.

Forspecimensupsetwithastriateddie,thediameterofthecentral trunkissmallerandthecladlayerismoreelongatedthanforthose upsetwithadryor alubricatedsmoothdie,becausethe mate-rialofthesubstratecanslidemoreeasilyonthem.Thematerial distributionislessinfluencedbytemperature.

Thematerialdistributionisasymmetricbetweentheupperand lowersurface of theupsetbillet. Thisphenomenon isprobably causedbythedwelltimebeforeupsettingduringwhichthe bil-letischilledbythelowerdie.Therefore,thematerialinthelower partofthebilletiscolder,causinggreaterflowstress.This phe-nomenonemphasizestheimportanteffectof heatexchange on thematerial distribution of hot-upsetclad billets.In tests per-formedwithastriateddie,thematerialispreventedfromsliding onthediesurface.Theupperandlowersurfacesofthesubstrate remainnearlyunchanged duringthetest, hencethesymmetric distribution.

Theforgingloadanddisplacementweredirectlyprovidedbythe sensorsinthehydraulicpress.Theforgingloadiscalculatedfrom thepressureinthemaincylinderofthemachine.Fig.10showsthe curvesoftheforgingloadasafunctionoftheupsettingratioofhot upsettingtestsperformedindifferentconditions.

Table5

Parametersofthehydraulicpress.

Parameters Initialheightofupperdie(mm) Finalheightofupperdie(mm) Direction Speed(mm/s) Initialwaitingtime(s)

Value 46 13.5 −Z 30 5

(a)

(b)

0 400 800 1200 70 60 50 40 30 20 10 0 Forging load (kN) % Upsetting 750°C, striated die 900°C, striated die 1050°C, striated die 0 400 800 1200 70 60 50 40 30 20 10 0 Forging load (kN) % Upsetting 1050°C, lubricated 1050°C, non lubricated 1050°C, striated

Fig.10.Hotupsettingtestsofcladbilletsperformedindifferentconditions(a)at differenttemperaturesand(b)indifferentfrictionconditions.

Theforgingloadincreaseswiththeupsettingratio,temperature andfrictionatthedie/workpieceinterface.Thetemperatureaffects thewholecurve,whilethefrictionismoresensitivetothelatter partoftheupsettingtest.Theseeffectsarethesameashot upset-tingofbothmono-materialbilletasshownbyLin(1995)andclad billet.

4. Modelingandsimulations

Theupsettingtestwasalsostudiedanalyticallyandnumerically andthispartisdevotedtothemodelingandsimulationofthe bi-materialupsettingtest.Itaimstoconstructamodeltoexplainthe crackphenomenoninthecladdedbillet,toestimatematerial dis-tributionandforgingload,andtostudytheeffectoftheprocess parameters.

4.1. Modeling

In theanalytical analysis,theslab methodwasapplied.The parametersofthemodelareshowninFig.11.Valuesofthe param-etersaregiveninTable5.

Thecylindricalsymmetryoftheproblemrequiresavelocityfield inthebarinthefollowingform:



v

(r,z)=

v

r(r,z)−→er+

v

z(r,z)−→ez (2)

Thecladbilletisassumedtoremaincylindricallysymmetricand itsbulgingisneglected.Thetemperatureofthebilletisassumedto beconstantanduniformduringtheupsetting.Thermalexchange withthediesandenergydissipationareneglected.Accordingto theseassumptions,andconsideringtheprincipleofmass conser-vation,thevelocityfieldisobtainedasbelow:



v

(r,z)=−₂r.˙h h−→er+z

˙h

h−→ez (3)

Theplasticstrainεp_{andtheplasticstrainrate ˙ε}p_areuniformin

thecladbilletandgivenbyEqs.(4)and(5).

εp=

⎛

⎜

⎜

⎜

⎝

−1 2 0 0 0 −1₂ 0 0 0 1

⎞

⎟

⎟

⎟

⎠

ln



h h0

(4) ˙εp₌

⎛

⎜

⎜

⎜

⎝

−1 2 0 0 0 −1₂ 0 0 0 1

⎞

⎟

⎟

⎟

⎠

˙h h



(5)

withhand h0 theinstantaneousand initiallengthofthebillet

respectivelyand ˙htheupsettingvelocity.

VonMisesplasticitycriterionisadopted.Inthatcase,the devia-torystressisparalleltostrainrateandtheequivalentstressisequal totheflowstressofthematerial.Theexpressionofthestresstensor andthedeviatoricstresstensorsaregivenbyEqs.(6)and(7)in thecylindricalcoordinatereference(seeFig.11):

=

⎛

⎜

⎝

rr r rz r  z rz z zz

⎞

⎟

⎠

(6) s=

⎛

⎜

⎜

⎜

⎝

2 3rr− 1 3(+zz) r rz r 2 3− 1 3(rr+zz) z rz z 2 3zz− 1 3(rr+)

⎞

⎟

⎟

⎟

⎠

(7)

Theplasticitycriterion,assumingthatsisproportionaltothe plasticstrainratetensor ˙εp_,gives:

r=rz=z=0 (8)

and

rr= (9)

ThestresstensorcanbesimplifiedasEq.(9):

=

⎛

⎜

⎝

rr 0 0 0 rr 0 0 0 zz

⎞

⎟

⎠

(10)

Accordingtotheplasticitycriterion,theequivalentstressshould beequaltotheflowstressofthematerial0.Thus,thestresstensor

becomes: =

⎛

⎜

⎝

rr 0 0 0 rr 0 0 0 rr−0

⎞

⎟

⎠

(11)

where0istheflowstressofthematerialandrristhenormal

stressinthedirection −→er.Thisrelationisobtainedby

consider-ingthatthefreelateralsurfaceofthebilletisfree(rr=0)andthe

normalstresszzinthedirection −→ezisnegative.

Thefundamentalprincipleofappliedstaticsisappliedtothe slabboundedby:

r∈[r; r+dr], (12) ∈



−d₂; +d₂

, (13) z∈[0,h] (14)

Consideringtheequilibriuminthedirection −→er,onecanget:

(rr+drr)(r+dr)·h·d−rr·r·h·d−2rrh·dr·sind₂

−2·r·dr·d=0 (15)

whereisthetangentialstressatthetool/workpieceinterface cor-respondingtofriction. isnegativeand opposesthemotionof materialonthedie.Developingtherelationshipoforder2onecan get:

drr=−2

hdr (16)

Coulombfrictionisassumed.Inthiscase,thefrictionalshear stressisrelatedtothenormalpressureofcontactbythefollowing relation:

=−n (17)

withthefrictionfactorandnthenormalpressureonthe

die-materialcontact.

Intheslabmethod,thestressfieldisassumedtobeuniform throughouttheslab.Thestresszzistheoppositeofthecontact

pressure.Onecangetthefollowingrelationforthecomponentsof thestresszzwhichisapplicabletobothsubstrateandcladding:

dzz

zz =−

2

h dr (18)

ThesolutionofEq.(18)isgivenbyEqs.(19)and(20):

r∈[0,R] zz=s·exp



−2s h r

(19) r∈[R,R+e]zz=s·exp



−2r h r

(20)

whereeisthecladlayerthicknessandRtheradiusofthesubstrate cylinder.InEqs.(19)and(20),sandrarethetool/substrateand

tool/cladlayerfrictioncoefficientrespectively.sandraretwo

integrationconstantstocalculate.

The boundary conditions at the external surface and sub-strate/cladlayerinterfacearegivenbyEqs.(21)and(22):

rr(R+e)=0 (21)

rrr=R=0 (22)

whererrr=Risthediscontinuityfunctionofrrthroughthe

sub-strate/cladlayerinterface.

ConsideringEq.(19)toEq.(22),onegets:

r=−0rexp



_2 r(R+e) h

(23) s=



0r



1−exp



_2 re h

−0s

exp



_2 sR h

(24)

where0rand0sarerespectivelytheflowstressinthecladlayer

andinthesubstrate.

Theforgingload,F,canbecalculatedastheintegralofthecontact pressureoverthebillet/diecontactarea:

F=2



R+ 0 −zzrdr=2



R 0 −s·exp



−2s h r

rdr +2



R+ R −r·exp



−2r h r

rdr (25)

Fig.12.Finiteelementmodeling(a)withcylindricalinterfaceand(b)withwavyinterfacebillet.

Assumingthatthefrictioncoefficientssandrareequalto,

theforgingloadisgivenbyEq.(26):

F= h 22



hs+exp



−2R h

(r+s)(h+2R) −exp



−2R+e h

r(h+2(R+e))



(26)

Randearefunctionsoftheinitialgeometry(h0,e0,R0)ofthe

billetandtheupsettinglength,h.Accordingtotheprincipleofmass conservation: R=R0



h0 h (27) e=e0



h0 h (28)

Duetothefactthatthetemperature,strainandstrainrateare assumedtobeuniformoverthebillet,thesolutionofthe differ-entialEq.(18)isindependentoftheconstitutivelawofthetwo materials.Theintegrationconstantsdefinedbyrelations(23)and (24)canbecalculatedfromtheexpressionofflowstressdefined byasimplifiedHansel–Spittellawthatiswellsuitedtorepresent thehotformingbehaviorofmetals:

0=A·exp(m1T)·εm2· ˙εm3·exp



_m 4 ε

(29)

whereεand ˙ε aretheequivalentplasticstrainandequivalent plas-ticstrainraterespectively.

TheSpittellawwithassociatedcoefficientsisonlyvalidfora givenrangeoftemperatures,strainandstrainratedataforeach material.

Theforgingload,calculatedbytheslabmethod,dependsonly on:

-Theinitialgeometryofthecladbillet(h0,e0,R0).

-Thefrictionfactorbetweenthesubstrate/cladlayeranddie. -Theflowstressofthetwomaterials.

4.2. Finiteelementsimulations

The simulation analysis was carried out using Forge2011©. Consideringthesymmetryoftheproblem,a2-Daxisymmetrichot forgingmodulewasadopted.

ThefiniteelementsimulationmodelisshowninFig.12. Consid-eringtheeffectofthesubstrate/claddinginterface,specialattention waspaidtotheinterfacegeometry,there-meshoftheinterface zoneinthesimulationmodelandthecontinuityconditionthrough theinterface.

Twotypesofsubstrate/claddinginterfaceareadoptedand com-pared in the study, a cylindrical one and a sinusoid one. The latterisimplementedinordertoestimatetheeffectofthewavy morphologyof thesubstrate/cladlayerinterface.The geometri-calparametersofthesinusoidinterface(seeFig.13)arecalculated fromthemacrographofFig.5.

Sincethecladlayerisobtainedbywelding,thevelocityand tem-peraturefieldsareassumedtobecontinuousthroughtheinterface, imposingthefollowingboundaryconditions:



v





= 0 (30)



_T



₌0 (31)

Fig.13.Geometricalparametersofthewavysubstrate/claddinginterfacein simu-lation.

0 100 200 300 400 500 600 70 60 50 40 30 20 10 0 Forging load (kN) % Upsetting 1050°C,µ=0.3,e=3mm Zone-I Zone-II Zone-III

Fig.14.Evolutionofforgingloadin70%upsettingtestat1050◦_Cbasedonslab methodformulation.

where





v



and



T



arerespectivelythediscontinuityvectorof thevelocityandthediscontinuityofthetemperaturethroughthe substratecladlayerinterface.

Inthis study,thesubstrate andthecladlayeraretwo sepa-ratemeshedobjects.Inordertoapproachtheboundaryconditions ofEqs.(30)and (31),a bilateralstickingconditionisappliedat thesubstrate/cladlayerinterface.Ahighheatexchangecoefficient (2×104_Wm−2_K−1_{)isappliedinordertoreducethetemperature}

discontinuityattheinterfaceregardlessoftheheatflux.Themesh sizeofthecladlayerissmallerthanthatofthesubstrate.Zones closetotheinterfacehavebeenre-meshed(seeFig.12)toimprove thecontinuityofthesubstrate/cladlayerinterface.

Atthedie/billetinterface,heatexchangeisdrivenbyaconstant coefficientwhilefrictionismodeledbyaCoulomblaw.Thedies areconsideredtoberigid.ThepressishydraulicasshowninFig.6. Theforgingoperationiscomposedofadwelltime,duringwhich theworkpieceisplacedonthelowerdie,followedbysubsequent upsetoperation.

Comparedwithananalyticalanalysis,thefiniteelement sim-ulationanalysisconsidersthethermalconductionofmaterials.As fortheslabmethod,theflowstressofthematerialisassumedtobe governedbyHansel–Spittel.Thethermalbehaviorofthematerialis definedbyaconductionfactor,aheatcapacityandthedensityofthe materials.Atthedie/billetinterface,therepartitionoftheenergy producedbythefrictionisgovernedbyaclassicallawincluding thermaldiffusivityofthematerials.Finally,aconstantconvection factorisconsideredattheexternalsurfaceofthecladbillettotake intoaccounttheheatexchangewiththeenvironment.

5. Results

5.1. Slabmethod

Theupsettingtestsofcladbilletsarefirststudiedanalytically withtheslabmethod.Fig.14showstheforgingloadduringthe upsetting test of a mild steel billet(Ø27mm×45mm)cladded withstainless steel(thicknesse=3mm)at 1050◦Cusinga fric-tioncoefficientof=0.3 atthedie/billetinterface.Thevalueof thecoefficientsin Hansel–Spittel law(takenfromFORGE2011®

database)isgiveninTable6.Inthisstudy,theeffectofthe dilu-tionontheflowstressofthecladlayerisnottakenintoaccount. Theflowstressofthecladlayerisassumedtobeclosetothatof pureSS316L.Inthedevelopedslabmethod,thestickingcondition

(a)

(b)

(c)

0 250 500 750 1000 0 10 20 30 40 50 60 70 Forging load (kN) % Upsetting µ=0.1 µ=0.3 µ=0.5 0 200 400 600 800 0 10 20 30 40 50 60 70 Forging load (kN) % Upsetting m3=0.1 m3=0.2 m3=0.5 0 400 800 1200 1600 0 10 20 30 40 50 60 70 Forging load (kN) % Upsetting 750°C 900°C 1050°C

(d)

0

200

400

600

800

0

10

20

30

40

50

60

70

Forging load (kN)

% Upsetting

e=1.5mm

e=3mm

e=4.5mm

Fig.15. Effectofdifferentparametersonforgingload.

couldnotbetakenintoaccount.Therefore,testsperformedwitha striateddiearenotincludedinthispart.

ThecurveofforgingloadversusupsettingratioinFig.14,similar tothatoftheexperimentaltest,couldbedividedintothreezones

Table6

ValuesofcoefficientsoftheHansel–Spittellaw.

Material CoefficientsofsimplifiedHansel–Spittellaw

A(MPa) m1 m2 m3 m4

Mildsteel 890.4543 −0.00234 −0.12626 0.13938 −0.0477

Stainlesssteel 8905.34 −0.00383 0.01246 0.09912 −0.02413

ingeneral.InZone-I,theforgingloadincreasessharplyduetoa hardeningphenomenon.Zone-IIisatransitionbetweenZone-Iand Zone-III.TheinflexionofZone-IIisthesmallest.In Zone-III,the forgingloadincreasesrapidlyagainwiththeincreaseofupsetting duetoacombinationofthreemainfactors:

-Increaseoftheupperandlowersurfaceofthebillet.

-Increaseofstrainratewiththeincreaseofupsettingratio,the upsettingvelocitybeingconstant.

-An accumulation of tangential friction forces leading to an increaseofhydrostaticpressurewithinthebillet.

Variationsinfrictioncoefficient,temperature,cladding thick-nessandcoefficientsofHansel–SpittelLaw(especiallym3)have

agreateffectontheforgingload(seeFig.15).Variationsinthe friction coefficient and m3 (viscosity coefficient) mainly affect

Zone-IIIoftheforgingload/upsetting ratiocurve(seeFig.15(a) and (b)); the effect of m3 is much weaker than that of

fric-tion. Generally, the value of m3 for steels is less than 0.2.

Temperature and cladding thickness impact the whole curve, theireffectbeinggreateronZone-IIand Zone-III(seeFig.15(c) and(d)).

5.2. Finiteelementmodel

WiththeparametersgiveninTable6,simulationswere con-ductedfortheupsettingtestofacladbilletat1050◦Cwithsticking frictionatthedie/billetinterface.

5.2.1. Materialdistribution

The material distribution varies with variations in param-eters of the upsetting test. Besides, the configuration of the substrate/claddinginterfacealsoaffectsmaterialdistribution,as shown in Fig. 16. The result of simulation with a wavy sub-strate/claddinginterfaceisclosetothatofexperimentaltesting.The deformationofthecladlayerduringtheupsettingtestisnot uni-form.Thefirsttwoorthreecladbeadsclosetotheupperandlower surfaceofthebilletarestretched,thewavyaspectoftheinterface mitigating.Thosein-betweenarecompressedandbended, curva-turesincreasing.Theedgeareasoftheupperandlowersurfaces exhibit thethinnestcladlayer.Thecladlayeris notsymmetric betweenupperandlowersurface.Asmentionedinthepart dedi-catedtotheexperimentalresults,thisphenomenonisattributedto theinitialdwelltime(seeTable5)duringwhichthebilletischilled bythelowerdie.

Fig.16.Materialdistributionobtainedbysimulationsandexperimentsat1050◦_{Cusingdifferentfrictionconditions(a)and(b)stickingfriction,(c)weakfriction,(d)strong} friction,(e)testperformedusingstriateddie,(f)testperformedusinglubricatedsmoothdieand(g)testperformedusingdrysmoothdie.

Fig.17.LathamandCockcroftcriterionobtainedforsimulationofexperiment per-formedusingstriateddieat1050◦_{C(a)macrographofhalfmeridiancrosssection,} (b)simulationwithcylindricalsubstrate/claddinginterfaceand(c)simulationwith wavysubstrate/claddinginterface.

The configuration of substrate/cladding interface affects the materialdistribution(seeFig.16(a)and(b)).However,theoverall materialdistributioncouldbeobtainedevenwithoutconsidering thewavymorphologyoftheinterface.

5.2.2. Hotductilitycriterion

InForge2011©,itispossibletoestimatetheprobabilityofthe damageofaworkpiecebycalculatingtheLathamandCockcroft coefficientLa.Thisindicatorwasalsousedtopredicttheoccurrence ofcrack.ItsexpressionisgivenbyEq.(32).

La=



ε 0

max

eq dε (32)

wheremaxisthemaximumprincipaltensilestress,otherwiseitis

equaltozero,andeqisthevonMisesequivalentstress.

Withthiscriterion,onecanobservethattheperipheralzoneof theworkpieceissusceptibletorupture(seeZoneAinFig.17(b) and(c)).Thisisclassicalforductilecracksduringupsettingtest.In thecaseofstriateddies,anotherzone(seeZoneBinFig.17(b)and (c))withhighvalueofLaappears.Thiszonecorrespondstothe circumferentialcrackobservedinexperimentsperformedwitha striateddie(seeTable3).Regardlessofthecladding/substrate inter-faceconfiguration,ZoneBappearsinallsimulationswithsticking friction.

ItwasexperimentallyobservedthatthecracksinZoneAandB occurredonlyinthecladdingandneverpropagatedintothe sub-strate.Thiscouldbecausedbytheweakductilityofthecladding materialathightemperature,butinFig.17(b)and(c)onecansee thattheLafactorisnegativeorclosetozerointhesubstrate.The

Fig.18. Distributionofradialstress(rr)obtainedbysimulationperformedat 1050◦Cinstickingfrictioncondition,(a)cylindricalinterfaceand(b)wavyinterface.

distributionoftheradialstressofthesimulationwithawavy sub-strate/claddinginterface(70%upset)isstudied(seeFig.18).Inthe biggrayregion,rr islessthan−200MPa,rr beingtheleading

stressforcracksoccurringinZoneB.rrispositiveinZoneB,but

negativeintheareaofthesubstrateinthevicinityofZoneB.The onlyoccurrenceofcrackinthecladlayerisdueinlargepartto thestressdiscontinuitythroughtheinterfaceasaresultofaglobal bimaterialstructureeffect.Indeed,duringtheupsettingtheclad layerisstretchedandtheinnersubstrateiscompressed.

Theevolution oftheindicatorLa(seeFig.19)helpstobetter understandtheinitiationanddevelopmentofcracksoccurringin ZoneAandB.At1050◦C,inthetestperformedwithastriateddie, thereisarapidincreaseinLainZoneBattheendofupsetting whereasthisphenomenondoesnotexistintestsperformedwith adrysmoothdie(=0.3)oralubricatedsmoothdie(=0.15). Duringupsettingperformedusingsmoothdies,thevalueofLain zoneAisalwaysgreaterthanthatofZoneB.

AccordingtotheLathamandCockcroftcriterion,crackingoccurs whenLagivenbyEq.(32)ishigherthanacriticalvaluedepending onthetemperature.Theupsettingtemperaturehasaslighteffect onthevalueofLaasshowninFig.20.AccordingtoTable3, lon-gitudinalcrackswereobservedonabilletupsetat900◦Cusinga striateddieforanupsetratioofabout65%.Thisvaluecorresponds toavalueofLaof0.55inZoneAand0.4inzoneB(seeFig.20).At 1050◦Cusingastriateddie,longitudinalandcircumferentialcracks wereexperimentallyobservedforanupsetratioof70%.The cor-respondingsimulationspredictedthesimultaneousoccurrenceof bothtypesofcrackforanupsetratioofabout68%withacritical Lavalueof0.6.Thefiniteelementsimulation,usingaLathamand Cockcroftcriterion,isabletopredictthelocationofthecracksand, byinverseanalysis,itispossibletoestimatethecriticalvalueofLa forthetestingtemperatures.

5.2.3. Forgingload/upsettingratio

Similartothatoftheexperimentaltestandtheslabmethod,the forgingload/upsettingratiocurvecouldbedividedintothreezones ingeneral.Besidesthereasonsreferredtoabove,anotherreasonfor therapidincreaseinZone-IIIisthecoolingofthebilletduringupset whichincreasestheflowstressofthematerials.

(a)

(b)

(c)

0 0.2 0.4 0.6 0.8 1 70 60 50 40 30 20 10 0 La % Upsetting 1050°C,sticking,wavy,Zone A 1050°C,sticking,wavy,Zone B 1050°C,sticking,cylindrical,Zone A 1050°C,sticking,cylindrical,Zone B 0 0.2 0.4 0.6 0.8 1 70 60 50 40 30 20 10 0 La % Upsetting 1050°C,μ=0.3,Zone A 1050°C,μ=0.3, Zone B 0 0.2 0.4 0.6 0.8 1 70 60 50 40 30 20 10 0 La % Upsetting 1050°C,μ=0.15,Zone A 1050°C,μ=0.15,Zone B

Fig.19. Evolutionof the indicator La (a)stickingfriction anddifferent sub-strate/claddinginterface,(b)strongfrictionandwavysubstrate/claddinginterface and(c)weakfrictionandwavysubstrate/calddinginterface.

Theconfigurationofthesubstrate/claddinginterfacehaslittle effectonforgingloadasshowninFig.21,andthesimulationof upsettingfora cladbilletwitha wavysubstrate/cladding inter-face takes more time. If only theprediction of forging load is required,thereisnoneedtoconsidertheconfigurationofthe sub-strate/claddinginterface.

Similarlytotheslabmethod,othereffectiveparameterssuch ascladdingthickness,frictioncoefficientandtemperaturehavea greateffectonforgingload.Besides,theheatexchangecoefficient alsoimpactsforgingload,affectingmainlyZone-III,althoughthe effectisquiteslight.

Fig.22presentsacomparisonbetweenexperimentaland sim-ulatedcurvesobtainedbythefiniteelementmethodandtheslab

(a)

(b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0

10

20

30

40

50

60

70

La

% Upsetting

1050°C,sticking,ZoneA

900°C

,sticki

ng,Z

one

A

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

10

20

30

40

50

60

70

La

% Upsetting

1050°C,sticking,Zone B

900°C

,sticki

ng,Z

one

B

Fig.20.EffectoftemperatureonLa(a)ZoneAand(b)ZoneB.

methodusingdifferentfrictionconditionsandtemperatures.One cannotethattheexperimentalloadinZone-II(SeeFig.14)ishigher thanthatofthesimulationobtainedbythefiniteelementmethod ortheslabmethod.Thisfeatureisnotableforeachexperimental test,thedifferenceappearingmoreimportantatlower tempera-ture.

0

200

400

600

0

10

20

30

40

50

60

70

Forging Load (kN)

% Upsetting

1050°C, wavy interface,sticking

1050°C, cylindrical interface, sticking

Fig.21.Simulatedforgingloadobtainedwithdifferentconfigurationsofthe sub-strate/claddinginterfaceat1050◦_{C,stickingfrictionatdie/billetinterface.}

Fig.22.Forgingloadversusupsettingratioobtainedexperimentally,byfinite ele-mentsimulationandbyslabmethod(a)smoothdrydie(m=0.5),1050◦C,(b)smooth lubricateddie(m=0.3),1050◦Cand(c)striateddie(sticking),900◦C.

Thisdifferencecannotbeduetotheimplementationofatoolow frictioncoefficientbecausetheeffectoffrictionisnoticeableatthe endoftheupsetting(Zone-IIIofthecurve).However,theSpittellaw parametersforthebehaviorofthecladlayerinthefiniteelement modelortheslabmethodisthatofSS316LintheFORGE2011®

database.Thechemicalcompositionofthecladlayerisdifferent fromthatoffillermaterialbecauseofthedilutionofthesubstrate

occurringduringfusionweldcladding.Thechemicalcomposition andtheinitialmetallurgicalstructureofthecladbilletaredifferent fromthatofarolledbarofSS316Lbecauseofdilutionandduetothe factthatthecladlayerisobtainedbysolidification.Furthermore, duringthetransferofthebilletfromthefurnacetothedies, ther-malexchangebetweenthecladbilletanditsenvironmentcanlead tothecoolingofthecladlayer.AsshownonFig.15,theeffectof temperatureandflowstressofthecladdedmaterialisnoticeablein Zone-IIoftheformingcurve.Thiscoolingcanbetakenintoaccount inthefiniteelementmodelbyintroducingatthebeginningofthe simulationastageduringwhichthereisthermalexchangewiththe environmentbutnocontactbetweenthedieandthebillet.

6. Conclusion

Theresearchproposestoevaluatethecharacterizationofthe forgeabilityofweldcladbilletbyupsettingtest.Theexperiments, thefiniteelementsimulationandtheslabmethodweredeveloped andcomparedintermsofductilitylimit,materialdistributionand forgingload.

Theexperimentalupsettingtestshighlightaspecificcracktype thatlimitstheglobalductilityofthebi-materialcladbillet.Thiskind ofcrackistheresultoftheglobalmechanicalinteractionbetween thesubstrateandthecladlayer.Thesubstratedoesnotpresentfree surfaceduringtheforgingprocess;itiscladdedandisincontact withthediesatitstopandbottomsurfaces.Eveniftheflowstress ofthesubstrateislowerthanthatofthecladlayer,theincreasein hydrostaticpressurewithinthesubstrateisabletogeneratestress inthecladlayerleadingtoelongationandductilecrackingofthe cladlayer.Theoccurrenceandthelocationofthisspecificcrack canbepredictedbythefiniteelementmethodusinga conven-tionalLathamandCockcroftcriterion.Itisnotnecessarytotakeinto accountthewavymorphologyoftheinterfacebetweentheclad layerandthesubstratetopredictthisphenomenonnumerically.

Thematerialdistributionduringupsettingcanbesimulatedby thefinite element method.In thecase ofupsetting tests, even whenusinganapproximatebehaviorlawforthecladmaterial,the obtainedmaterialdistributioncorrespondswellwiththatof exper-iments.Amongothers,theeffectoffrictioniswellreproduced.Even ifthefiniteelementmethodisabletosimulatetheforgingofclad billetwithmorerealisticinterfacegeometry,thewavymorphology seemstohavealimitedeffectontheglobalmaterialdistribution.It canbeneglectedinordertoreducethedurationofthecalculation. Thematerialofthecladlayerisamixtureofthefillermaterial andthesubstrate.Thedilutionphenomenoncanleadtoa consti-tutivematerialofthecladlayerwithahotformingbehaviorvery differentfromthatofthepurefillermaterial.Thisphenomenoncan beresponsibleforthelackofcorrespondencebetween experimen-talandsimulatedresultsconcerningtheevolutionoftheforging load.It canbeexpectedtohavealsogreateffects onthe mate-rialdistributioninthecaseofforgingusingasubstratewithfree surfaces.Thedifferenceofthehotformingbehaviorbetweenthe substrateandthecladlayercannotbeobserveddirectlyviathe upsettingtestofacladbillet.Inversecalculationmethodshaveto beappliedinordertoestimatethecoefficientofthebehaviorlawof thecladlayer.Inordertoimprovetheperformanceofthismethod, afirstcalculationcanbeperformedusingtheslabmethodfollowed byamorepreciseoptimizationusingthefiniteelementmethod.

Acknowledgements

Theauthorswould liketothankRegionLorraineandHECof Pakistanfortheirfinancialsupport.

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