外文翻译--基于三维有限元方法的AZ31镁合金等通道弯角挤压的模具结构设计 英文版.pdf

angularChinaReceived5September2008Accepted17January2009AvailableonlinexxxxKeywords:AZ31magnesiumalloyEqualchannelangularextrusionFiniteelementmethodfinegrainedmicrostructuresinmagnesiumalloys.Itiscrucialtounderstandtheeffectofdiedesignontoobtainthesematerialswithhighstrengthandtoughness.InECAE,aworkpieceispressedthroughadiethatcontainstwochan-nelswithequalcross-sectionmeetingatanangle.Becausethecross-sectionoftheworkpieceremainsthesameduringextrusion,theprocesscanberepeateduntiltheaccumulateddeformationreachesadesiredlevel.Highstraincanbeachieved.FiniteelementmethodisoneoftheimportantapproachestounderstandtheofbackpressurebySonetal.,theoptimumdiedesignforhomoge-neousplasticdeformationbyYoonSCetal.7.However,thesestudiesassumedtwo-dimensional(2D)approximationofplanestrainconditionanddonotdiscusstheinhomogeneityofstressandstrain.Resultsobtainedby2Danalysisgivelimitedinforma-tion,inadditiontotheinherent2Dapproximationerrors.Someresearchers810haveexploredtheECAEprocessusingthree-dimensions(3D)plasticitytheoreticandsimulationsoft-ware.LuisPérezandLuri11usedupperboundmethodtoanalyzeinthree-dimensionsECAEdiesforrectangularorsquarecross-sec-*Correspondingauthor.Fax:+862368851783.MaterialsandDesignxxx(2009)xxxxxxContentslistsavailableandARTICLEINPRESSE-mailaddress:hhjcqit.edu.cn(H.-J.Hu).1.IntroductionUltra-finegrainedmaterialshavebeenwidelyinvestigatedduetotheirimprovedmechanicalpropertiessuchashighstrengthandductility.Varioustechniqueshavebeendevelopedtoobtainultra-finegrainedmaterials.Severeplasticdeformation(SPD)tech-niques,likeequalchannelangularextrusion(ECAE),highpressuretorsion(HPT),cyclingchanneldiecompression(CCDC)andaccu-mulativerollbonding(ARB)aremostcommonlyforproducingsubmicrongrainstructuresinmetallicmaterialsatarelativelylowcost.Amongthem,theequalchannelangularextrusion(ECAE),originallydevelopedbySegal,isoneofthemosteffectivemethodsdeformationoccurringintheECAEprocess.ManyFEM-basedanal-yseshavebeenperformedtodeterminethedeformationbehaviorofmaterialsandtoestimatethedevelopedstrainintheECAPpro-cess.TheseresearchworkincludetheeffectofchannelangleandoutercornerforfrictionlessconditionbyRaghavanS1,theeffectofchannelangleandoutercornerbyKimetal.,theeffectofoutercorneroninhomogeneitybySuhJ-Yetal.2,thecornergapfor-mationanditseffectbyKimandKim3,theeffectofchannelan-gleandcornerangleonmaterialflowbyLangandShyong4,theextensiveworkondifferentmaterialmodels,outercornerangleandcoefficientoffrictionbyLeeSCetal.5,theworkonoriginofinhomogeneousbehaviorofmetalbyWeietal.6,theeffectOutercornerangleDeformationinhomogeneity0261-3069/$-seefrontmatterC2112009Publishedbydoi:10.1016/j.matdes.2009.01.022Pleasecitethisarticleinpressas:HuH-J(2009),doi:10.1016/j.matdes.2009.01.022thedeformationbehavior,straindistributionandloadrequirement.Inthepapernewthree-dimensional(3D)geometricmodelswithdifferentcornerangles(90C176,120C176)andwithorwithoutinnerroundfilletsinthebottomdieweredesigned.SomeimportantprocessparameterswereregardedastheinitialandboundaryconditionsusedinDEFORMTM-3Dsoftwaresuchastemperaturesofthedieandbillet,thefric-tioncoefficient,etc.Toensuretheconvergenceofthesimulation,thegeometricalanddisplacementcon-ditionsandreasonableconvergenceerrorlimits,etc.havebeenconsidered.ThedeformationheterogeneityofECAEwasanalyzedfromthesimulationandexperimentalresults.Thedeformationhomogeneitycausedbyfilletsatoutercornerwasimprovedcomparingwiththediewithoutfillets.ThecumulatemaximumstrainsdecreasedwiththefilletsofoutercornermanufacturedinECAEdieandtheinnercorneranglesincreasing.TherequirementextrusionforcedecreasedwiththefilletsmadeatoutercornerangleinECAEdie.TheanalysesshowedthatbetterstructuresofECAEdieincludedappro-priateoutercornerfilletsandtheinnercornerangle90C176.Itwasdemonstratedthatthepredictedresultswereingoodagreementwithexperimentsandthetheoreticalcalculationandtheresearchconclusionsfromotherliteratures.C2112009PublishedbyElsevierLtd.Articlehistory:Equalchannelangularextrusion(ECAE)iswidelyinvestigatedbecauseofitspotentialtoproduceultra-Thediestructuredesignofequalchannelmagnesiumalloybasedonthree-dimensionalHuHong-Juna,*,ZhangDingFeia,b,YangMingBocaNationalEngineeringResearchCenterforMagnesiumAlloys,ChongqingUniversity,ChongqingbCollegeofMaterialsScienceandEngineering,ChongqingUniversity,Chongqing400045,cCollegeofMaterialsScienceandEngineering,ChongqingInstituteofTechnology,ChongqingarticleinfoabstractMaterialsjournalhomepage:www.elseElsevierLtd.etal.ThediestructuredesignextrusionforAZ31finiteelementmethod400044,China400050,ChinaatScienceDirectDesignvier.com/locate/matdesofequalchannelangularextrusionforAZ31.JMaterDesigntionwherebothinternalandexternalradiiweretakenintoac-countandtheintersectionanglewasmade.The3DsimulationanalysisofECAPwasperformedbyChungetal.12usingacom-mercialfinitevolumemethod(FVM)codetoanalyzetheeffectivestrainandstressforonepassoftheprocess.3DFEMwasappliedtoanalyzethecommercialpureTi(CP-Ti)billetsubjectedtofour-passNomenclatureUtheinnercornerangle(C176)estrain(mm/mm)eccriticalstrain(mm/mm)Wtheoutercornerangle(C176)2H.-J.Huetal./MaterialsandDesignARTICLEINPRESSECAEprocessat400C176CwithBcrouteinRef.13.Buttherewerefewresearchersadopted3DsimulationtechnologiestoinvestigatethedeformationbehaviorsofmagnesiumAZ31especiallytheinfluencesofdiestructuresonstraindistributionsandextrusionquality.ManyoftheearlystudiesofECAPwerelimitedtothepro-cessingofsoftpuremetalsorsolidsolutionalloys.Morerecently,significantattentionhasbeendevotedtothepressingofmorecomplexalloysandsomemetalswithlimitednumbersofslipsys-temsespeciallyformagnesiumalloys.Forthesedifficult-to-workmaterials,threedifferentstrategieshavebeenadoptedwiththeoverallobjectiveofachievingsuccessfulprocessingbyECAE.Cur-rentresearchinterestisintheprocessingtoobtainfine-grainedbulkmagnesiumalloyspecimensfromECAE1420.AsketchofsuchanECAEdieisshowninFig.1.Thebottomdieconsistsoftwointersectingchannelsofthesamecross-sectionmeetingataninnercornerangleU(seeFig.1).Inthisfigure,thean-gleWdefinestheoutercurvatureoftheintersectionbetweenthetwochannels.Inthiscontext,theuseoftheextremeprinciples,forinstance,theupperboundmethodhasgainedalotofattentiontoestimatethepressureneededfortheplungeraswellastheaccu-mulatedeffectivestrainresultingfromtheECAEmethod.Thenumericalsimulationwiththehelpofthefiniteelementmethod(FEM)hasbeenextensivelyusedtobetterunderstatingtheECAEmethod2125.TheplasticdeformationbehaviorduringECAEisgovernedmainlybythediegeometry,thematerialitselfandtheprocessingconditions.ExperimentaldataandfiniteelementstudyofdiesgeometryinfluenceonECAEprocesshimselfarepresented.ItisnecessarytotheoreticallymodeltheECAEprocessinordertostudyvariouscomplicatedeffectsforbetterprocesscontrol.Thisstudyistonumericallyanalyzethedeformationbehaviorsinequalchannelangularextrusions(ECAE)ofmagnesiumalloyAZ31andpredictthestrainsandextrusionforcesofECAEtoformnanostructureprocessbasedonvariousdiestructures.Fig.1.SchematicdiagramofanECAPdieshowinginnercornerangle(U)andoutercornerangle(w).Pleasecitethisarticleinpressas:HuH-Jetal.Thediestructuredesign(2009),doi:10.1016/j.matdes.2009.01.022Inthepresentwork,aquasi-staticsolutiontotheECAEmethodbytheFEMsimulationwascarriedoutusingdieswithintersectinganglesU=90C176and120C176byonlyonepassofextrusion.ThefourECAEmodelshavebeenerectedinUGsoftwareandmeshedandsimulatedinDEFORMTM-3Dcode.Numericalsimulationproceduresandmodelingofthediesandbillet,boundaryconditions,conver-genceerrorlimitsfordeformationsimulationsandelementformu-lationshavebeenintroduced.TheeffectsofdifferentdiegeometriesonthedeformationinhomogeneityduringECAPwereinvestigated.ExperimentsfortwoECAEdieswithorwithoutfilletshavebeendoneinlaboratorytovalidatethesimulationresults.Be-causetheevolutionofthemicrostructuresandmechanicalproper-tiesofdeformedmaterialaredirectlyrelatedtotheamountofplasticdeformation,theunderstandingofthephenomenonassoci-atedwiththestraindevelopmentisveryimportantinECAE.Distri-butionsofeffectivestressandstrain,influencesofchannelangleonthedeformationindifferentzonesanddeformationhomogeneity,maximumstrainhavebeendiscussedindetail.2.MaterialmodelsandsimulationdetailsThecommercialFEMcode,DEFORM3DVersion5.0,wasusedtocarryoutthesimulationofone-passECAEprocess.2.1.AssumptionsandnumericalsimulationproceduresAwroughtmagnesiumalloyAZ31with3%aluminum,1%zincwasusedasthebilletmaterialbothincomputersimulationandexperimentalverification.Thenumericalsimulationswereper-formedquasi-staticallyusingacommercialfiniteelementcode(DEFORMTM-3D).DEFORMTM-3Dwasacommercialpackagedevel-opedbySFTC(ScientificFormingTechnologyCorporation).Itwasafiniteelementmethod(FEM)basedprocesssimulationsystemdesignedtoanalyze3Dflowofvariousmetal-formingprocesses.Itprovidedvitalinformationaboutmaterialandthermalflowdur-ingformingprocesses.Thebilletwasassumedtobeelasticplasticmaterial.Thefollowingassumptionswasadoptedinpresentanal-ysis:(1)boththecontainerandthediearerigidbodies；(2)theextrusionbilletwasarigid-plasticmaterial；and(3)thefrictionfactorsbetweentheextrusionbilletandtheram,container,anddiewereconstant.Thesimulationprocedureswereasfollows:(1)the3Dgeome-tries(billets,ramsanddies)achievedbyconstructing3DCADmodelsweredefinedinUnigraphicssoftware.Geometriescanbedefinedas3DIGESorSTLfiles.(2)Stoppingstrokewasset,theRradiusoftheinnercorner(mm)_eeffectivestrainrate(sC01)xxx(2009)xxxxxxnumberofstepsdefinedandsimulationmodeandEnglishorSIunitswereselected.(3)Theobjects(billetsanddies)weremeshed.Theobjectswerepositioned,withtheworkpieceasthereferenceobject；bothtoolsandramincontactwiththeworkpiece.Thematerialspropertiesweredefined.(4)Thermalboundarycondi-tionsweredefined.(5)Objectstemperatureswereinitialized.(6)Contactboundaryconditionsweregeneratedandfrictioncoeffi-cientsbetweenbilletsanddies,billetsandramsweredefined.(7)Rammovementparameters(directionandspeed)wereas-signed.(8)Thedatabasewascheckedandgeneratedandcalcu-lated,FEAtosimulatethehotextrusionprocesswasperformed.(9)Thesimulationresultswerereadfromthepostprocessor.ofequalchannelangularextrusionforAZ31.JMaterDesign2.2.ModelingofthediesandramsThediegeometriesusedinthesimulationsareshowninFig.2.Thebilletcoordinateaxis(xyz)employedinthepresentstudyisshowninFig.2.Thex-,y-andz-directionswereparalleltoextru-siondirection(ED),verticaldirection(ND)andtransversedirection(TD),respectively.ThechannelanglesU=90C176andU=120C176areconsideredandillustratedrespectivelyinFig.2aandbandthecor-nerangle(W)ofthediesareassumedtoequalto0.ThemodifiedgeometricmodelswithinnerroundfilletsattheoutercornerareshowninFig.2candd.ThegeometricalparametersofthefourECAEdiesforFig.2arelistedinTable2.Thechannelanglecornerradiusattheintersectionofthetwochannelswas2mmandoutercornerangleradiuswas18mm.Thelengthofinletchannelwas50mmandoutletchannellengthwas25mm.Boththeinletandoutletchannelshadthesamedimensionsofsquarecross-section(£16mm).Table3givesthedimensions,extrusionspeedandtemperatureusedincomputersimulation,etc.,whichareidenticaltothoseap-pliedinextrusionexperiments.Thespeedofram(moveddownalongtheinletchannel)was10mmsC01asinthesimulationsandexperiments.Thestrokeoframwas50mm.Forthesakeofsimplicity,thediesandpressingramwereas-sumedtoberigidbodiesthatundergonopermanentdeformation,whichmechanicalpropertiesemployedanH13toolsteelwiththeYoungmodulusandthermalconductiondependentonthetemper-atureshowninFig.3aandb.Poissonsratio(m)was0.3.Fourdis-tinctgeometricmodelshavebeenanalyzedby(finiteelementTable2ThegeometricalparametersoftheECAEdie.U(C176)W(C176)RrFig.3a90000Fig.3b99182Fig.3c120000Fig.3d12060182Table3Simulationandexperimentalparameters.Billetlength(mm)50Billetdiameter(mm)16insiderdiameterofECAEdie(mm)16outsidediameterofdie(mm)50Initialbillettemperature(C176C)300Initialtoolingtemperature(C176C)275Strainraterangeforflowstressmeasurement(sC01)0.0110Temperaturerangeforflowstressmeasurement(C176C)250450Ramspeed(mm/s)10Frictionfactorofthecontainerbilletinterface0.25Frictionfactorbetweenthebilletanddie0.25H.-J.Huetal./MaterialsandDesignxxx(2009)xxxxxx3ARTICLEINPRESSFig.2.Schematicdiagramsofthethree-dimensionalECAPdieFEMmodelingshowing:(a)channelangleequalto90C176；(b)channelangleequalto120C176；(c)channelangle90C176withoutercornerangle；(d)channelangle120C176withoutercornerangle,whererdenotestheradiusofthechannelangle,Rtheradiusoftheoutercornerangle.Table1PhysicalpropertiesoftheAZ31workpiece.PropertyAZ31Poissonsratio0.35Coefficientoflinearexpansion26.8EC06Density1780kg/m3Poissonsratio0.35Youngsmodulus45,000MPaEmissivity0.12Pleasecitethisarticleinpressas:HuH-Jetal.Thediestructuredesign(2009),doi:10.1016/j.matdes.2009.01.022Fig.3.ThematerialpropertiesforH13.ofequalchannelangularextrusionforAZ31.JMaterDesignanalysis)FEAtorevealthedeformationbehaviorsandtheirrela-tionshipwiththedesignconfiguration.2.3.ModelingofthebilletThemagnesiumbilletusedinthecalculationswasaroundcross-section(diameter16mm)andalengthof50mm(£16mmC250mm).TheAZ31wasconsideredasanisotropicelasticplasticmaterial.Thetensilestressstraincurveat300C176CofAZ31billet(annealedat400C176Cfor12h),asshowninFig.4,theflowstress/straindataobtainedfromtheuniaxialcompressiontestswereintroducedintoFEAusingcommercialsoftwarepack-agesDEFORMTM-3D.TheelasticpropertieswereYoungsmodulusE=45GPaandPoissonsratiom=0.3.Materialpropertyparame-tersoftheAZ31workpiecearelistedinTable1.2.4.MeshingmethodInallsimulations,anautomaticremeshingschemewasusedto4H.-J.Huetal./MaterialsandDesignARTICLEINPRESSaccommodatelargestrainsandtotakeintoaccounttheoccurrenceofflowlocalization,whichpreventedfurthercalculationduringthesimulation.Theelementswereautomaticallyremeshediftheybe-cametoodistortedduringECAEsimulationprocess.Alltheextrusiontoolingincludedinthesimulationwasmeshedwithtetrahedralelementsanditsheatexchangewiththework-pieceincorporatedintosimulation.ThesimulationparametersusedarelistedinTable3.Toenhancetheefficiencyofsimulationandobtainspecificresolutionsintheareasofparticularinterest,anumberofwindowswithanincreasedelementdensitywereap-pliedtogeneratelocalfinerelements,especiallyaroundthechan-nelcornerfordie.Toensuresimulationaccuracyandstability,theabsolutemeshdensitywasusedtokeeptheelementsizeatanypositionnearlyconstantduringthesimulation,becauseitwasthisdensitythatdefinedthenumberofelementsperunitlengthonthesurfaceoftheworkpiece.Theminimumsizeoftheelementwas0.250.35mm.Thebilletwasdividedinto20,000four-nodetetra-hedralelements.Totalnumberofelementsoframanddiewere8000and20,000,respectively.Thenumbersofelementswerefoundtobesufficienttoexpresslocaldeformationofthestrainrateinsensitiveworkpiecesthroughcalculationswithvaryingthenum-berofelements.Tolimitthesizesofsimulationdatabasefilesandenhancesimulationspeed,theroundextrudatewascutoffatthelengthof50mmwhenitslengthexceeded50mm.Asmallrelativeinterferencedepthof0.3wasdefinedtotriggertheremeshingpro-Fig.4.Truestress/truestraincurvesofAZ31obtainedfromcompressiontestsat300C176Cunderdifferentstrainrateandcorrectedfordeformationheatingduringthetesting.Pleasecitethisarticleinpressas:HuH-Jetal.Thediestructuredesign(2009),doi:10.1016/j.matdes.2009.01.022cedurewhenanyelementattheedgeoftheworkpiecehadbeenpenetratedintoandthepenetrationdepthexceeded30%oftheori-ginallengthofthesurfaceedgethathadacontactnodeateachend.2.5.Boundaryconditions2.5.1.ContactandfrictionboundaryconditionsContactboundaryconditionswereappliedtonodesofbillet,andspecifycontactbetweenthosenodesandthesurfaceofram.InordertoassurethequadraticconvergenceoftheNewtonRaph-sonmethodusedinthecode,thecompressivedisplacementsim-posedonthebillettopregionintheverticaldirectionwerefixedinincrementsof0.10mmuptoatotaldisplacementof50mm.TheNewtonRaphsonmethodwasrecommendedformostprob-lemsbecauseitgenerallyconvergedinlessiterationthantheotheravailablemethods.However,solutionsweremorelikelytofailtoconvergewiththismethodthanwithothermethods.Torepresentthefrictionbehaviorasaconsequenceoftheshearstressandthecontactpressure,thegeneralizedCoulombslawwasused.Thefrictionattheworkpiecetoolinginterfaceswasconsid-eredtobeofshear-type.Itwaswellknownthatthislawstatedproportionalitybetweenshearyieldstressandthecontactpres-sureduetothepresenceofthefriction.SpecificallyintheDEFORMcode,thisrelationwasverifiedbymeansofvonMisesyieldcrite-rioncorrectedtothesimpleshearconditionandwasgivenbyEq.(1):s¼lr3p；ð1Þwheresisthefrictionalshearstressandristheeffectiveflowstressoftheworkpiece.l(06l61)thefrictionfactor.Inthepres-entsimulations,africtionfactorof0.25atthediebilletinterfacewaschosen.Thesamefrictionfactorwasassumedattheinterfacebetweenthebilletandram.2.5.2.TemperatureboundaryconditionRegardlessoftheheattransferbetweenthedieandtheambi-ence,theheattransferbetweenthebilletandthediewasconsid-ered.NewtoncoolingprinciplewasusedandexpressedasEq.(2):kTxini¼C0hðTC0TwÞ；ð2Þwherehisthecoefficientoftheheattransferbetweenthematerialanddie,Twisthetemperatureofthedie.niisthenormalini-direction.Inthispaper,theambienttemperaturewasconsideredas25C176C,andtemperatureoftheECAEdie275C176C.Theinitialbillettemper-aturewaschosentobeatarelativelyhighlevel300C176Cwithoutrunningtheriskofreachingthepressforcelimitduringexperi-mentsathighramspeeds.Heattransfercoefficientbetweentool-ingandbilletwas11N/C176Csmm2,andthevalueHeattransfercoefficientsbetweentooling/billetandairare0.02N/C176Csmm2.EmissivitycoefficientsoftheAZ31andH13toolsteelwere0.12and0.7,respectively.2.6.ConvergencestudiesinsimulationsConvergenceoftheinvestigatedvariabletoaconstantvaluebychangingvariousnumericalparametersisanessentialprocedureinfiniteelementsimulation26.Theparametersthatmustbecontrolledaremeshsizeandtopology(theminimumsizeoftheelementwas0.250.35mminthispaper),contactparameters,xxx(2009)xxxxxxremeshingparameters,incrementsize(timestepwas0.01s),con-vergencelimits,solverparameters(thedisplacementincrementwas0.1mm),frictionmodelparameters(Coulombslawused),ofequalchannelangularextrusionforAZ31.JMaterDesign