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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

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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

angularChinaReceived5September2008Accepted17January2009AvailableonlinexxxxKeywordsAZ31magnesiumalloyEqualchannelangularextrusionFiniteelementmethodfinegrainedmicrostructuresinmagnesiumalloys.Itiscrucialtounderstandtheeffectofdiedesignontoobtainthesematerialswithhighstrengthandtoughness.InECAE,aworkpieceispressedthroughadiethatcontainstwochannelswithequalcrosssectionmeetingatanangle.Becausethecrosssectionoftheworkpieceremainsthesameduringextrusion,theprocesscanberepeateduntiltheaccumulateddeformationreachesadesiredlevel.Highstraincanbeachieved.FiniteelementmethodisoneoftheimportantapproachestounderstandtheofbackpressurebySonetal.,theoptimumdiedesignforhomogeneousplasticdeformationbyYoonSCetal.7.However,thesestudiesassumedtwodimensional2Dapproximationofplanestrainconditionanddonotdiscusstheinhomogeneityofstressandstrain.Resultsobtainedby2Danalysisgivelimitedinformation,inadditiontotheinherent2Dapproximationerrors.Someresearchers8–10haveexploredtheECAEprocessusingthreedimensions3Dplasticitytheoreticandsimulationsoftware.LuisPérezandLuri11usedupperboundmethodtoanalyzeinthreedimensionsECAEdiesforrectangularorsquarecrosssecCorrespondingauthor.Fax862368851783.MaterialsandDesignxxx2009xxx–xxxContentslistsavailableandARTICLEINPRESSEmailaddresshhjcqit.edu.cnH.J.Hu.1.IntroductionUltrafinegrainedmaterialshavebeenwidelyinvestigatedduetotheirimprovedmechanicalpropertiessuchashighstrengthandductility.Varioustechniqueshavebeendevelopedtoobtainultrafinegrainedmaterials.SevereplasticdeformationSPDtechniques,likeequalchannelangularextrusionECAE,highpressuretorsionHPT,cyclingchanneldiecompressionCCDCandaccumulativerollbondingARBaremostcommonlyforproducingsubmicrongrainstructuresinmetallicmaterialsatarelativelylowcost.Amongthem,theequalchannelangularextrusionECAE,originallydevelopedbySegal,isoneofthemosteffectivemethodsdeformationoccurringintheECAEprocess.ManyFEMbasedanalyseshavebeenperformedtodeterminethedeformationbehaviorofmaterialsandtoestimatethedevelopedstrainintheECAPprocess.TheseresearchworkincludetheeffectofchannelangleandoutercornerforfrictionlessconditionbyRaghavanS1,theeffectofchannelangleandoutercornerbyKimetal.,theeffectofoutercorneroninhomogeneitybySuhJYetal.2,thecornergapformationanditseffectbyKimandKim3,theeffectofchannelangleandcornerangleonmaterialflowbyLangandShyong4,theextensiveworkondifferentmaterialmodels,outercornerangleandcoefficientoffrictionbyLeeSCetal.5,theworkonoriginofinhomogeneousbehaviorofmetalbyWeietal.6,theeffectOutercornerangleDeformationinhomogeneity02613069/seefrontmatterC2112009Publishedbydoi10.1016/j.matdes.2009.01.022PleasecitethisarticleinpressasHuHJ2009,doi10.1016/j.matdes.2009.01.022thedeformationbehavior,straindistributionandloadrequirement.Inthepapernewthreedimensional3Dgeometricmodelswithdifferentcornerangles90C176,120C176andwithorwithoutinnerroundfilletsinthebottomdieweredesigned.SomeimportantprocessparameterswereregardedastheinitialandboundaryconditionsusedinDEFORMTM3Dsoftwaresuchastemperaturesofthedieandbillet,thefrictioncoefficient,etc.Toensuretheconvergenceofthesimulation,thegeometricalanddisplacementconditionsandreasonableconvergenceerrorlimits,etc.havebeenconsidered.ThedeformationheterogeneityofECAEwasanalyzedfromthesimulationandexperimentalresults.Thedeformationhomogeneitycausedbyfilletsatoutercornerwasimprovedcomparingwiththediewithoutfillets.ThecumulatemaximumstrainsdecreasedwiththefilletsofoutercornermanufacturedinECAEdieandtheinnercorneranglesincreasing.TherequirementextrusionforcedecreasedwiththefilletsmadeatoutercornerangleinECAEdie.TheanalysesshowedthatbetterstructuresofECAEdieincludedappropriateoutercornerfilletsandtheinnercornerangle90C176.Itwasdemonstratedthatthepredictedresultswereingoodagreementwithexperimentsandthetheoreticalcalculationandtheresearchconclusionsfromotherliteratures.C2112009PublishedbyElsevierLtd.ArticlehistoryEqualchannelangularextrusionECAEiswidelyinvestigatedbecauseofitspotentialtoproduceultraThediestructuredesignofequalchannelmagnesiumalloybasedonthreedimensionalHuHongJuna,,ZhangDingFeia,b,YangMingBocaNationalEngineeringResearchCenterforMagnesiumAlloys,ChongqingUniversity,ChongqingbCollegeofMaterialsScienceandEngineering,ChongqingUniversity,Chongqing400045,cCollegeofMaterialsScienceandEngineering,ChongqingInstituteofTechnology,ChongqingarticleinfoabstractMaterialsjournalhomepagewww.elseElsevierLtd.etal.ThediestructuredesignextrusionforAZ31finiteelementmethod400044,China400050,ChinaatScienceDirectDesignvier.com/locate/matdesofequalchannelangularextrusionforAZ31...JMaterDesigntionwherebothinternalandexternalradiiweretakenintoaccountandtheintersectionanglewasmade.The3DsimulationanalysisofECAPwasperformedbyChungetal.12usingacommercialfinitevolumemethodFVMcodetoanalyzetheeffectivestrainandstressforonepassoftheprocess.3DFEMwasappliedtoanalyzethecommercialpureTiCPTibilletsubjectedtofourpassNomenclatureUtheinnercornerangleC176estrainmm/mmeccriticalstrainmm/mmWtheoutercornerangleC1762H.J.Huetal./MaterialsandDesignARTICLEINPRESSECAEprocessat400C176CwithBcrouteinRef.13.Buttherewerefewresearchersadopted3DsimulationtechnologiestoinvestigatethedeformationbehaviorsofmagnesiumAZ31especiallytheinfluencesofdiestructuresonstraindistributionsandextrusionquality.ManyoftheearlystudiesofECAPwerelimitedtotheprocessingofsoftpuremetalsorsolidsolutionalloys.Morerecently,significantattentionhasbeendevotedtothepressingofmorecomplexalloysandsomemetalswithlimitednumbersofslipsystemsespeciallyformagnesiumalloys.Forthesedifficulttoworkmaterials,threedifferentstrategieshavebeenadoptedwiththeoverallobjectiveofachievingsuccessfulprocessingbyECAE.CurrentresearchinterestisintheprocessingtoobtainfinegrainedbulkmagnesiumalloyspecimensfromECAE14–20.AsketchofsuchanECAEdieisshowninFig.1.ThebottomdieconsistsoftwointersectingchannelsofthesamecrosssectionmeetingataninnercornerangleUseeFig.1.Inthisfigure,theangleWdefinestheoutercurvatureoftheintersectionbetweenthetwochannels.Inthiscontext,theuseoftheextremeprinciples,forinstance,theupperboundmethodhasgainedalotofattentiontoestimatethepressureneededfortheplungeraswellastheaccumulatedeffectivestrainresultingfromtheECAEmethod.ThenumericalsimulationwiththehelpofthefiniteelementmethodFEMhasbeenextensivelyusedtobetterunderstatingtheECAEmethod21–25.TheplasticdeformationbehaviorduringECAEisgovernedmainlybythediegeometry,thematerialitselfandtheprocessingconditions.ExperimentaldataandfiniteelementstudyofdiesgeometryinfluenceonECAEprocesshimselfarepresented.ItisnecessarytotheoreticallymodeltheECAEprocessinordertostudyvariouscomplicatedeffectsforbetterprocesscontrol.ThisstudyistonumericallyanalyzethedeformationbehaviorsinequalchannelangularextrusionsECAEofmagnesiumalloyAZ31andpredictthestrainsandextrusionforcesofECAEtoformnanostructureprocessbasedonvariousdiestructures.Fig.1.SchematicdiagramofanECAPdieshowinginnercornerangleUandoutercorneranglew.PleasecitethisarticleinpressasHuHJetal.Thediestructuredesign2009,doi10.1016/j.matdes.2009.01.022Inthepresentwork,aquasistaticsolutiontotheECAEmethodbytheFEMsimulationwascarriedoutusingdieswithintersectinganglesU90C176and120C176byonlyonepassofextrusion.ThefourECAEmodelshavebeenerectedinUGsoftwareandmeshedandsimulatedinDEFORMTM3Dcode.Numericalsimulationproceduresandmodelingofthediesandbillet,boundaryconditions,convergenceerrorlimitsfordeformationsimulationsandelementformulationshavebeenintroduced.TheeffectsofdifferentdiegeometriesonthedeformationinhomogeneityduringECAPwereinvestigated.ExperimentsfortwoECAEdieswithorwithoutfilletshavebeendoneinlaboratorytovalidatethesimulationresults.Becausetheevolutionofthemicrostructuresandmechanicalpropertiesofdeformedmaterialaredirectlyrelatedtotheamountofplasticdeformation,theunderstandingofthephenomenonassociatedwiththestraindevelopmentisveryimportantinECAE.Distributionsofeffectivestressandstrain,influencesofchannelangleonthedeformationindifferentzonesanddeformationhomogeneity,maximumstrainhavebeendiscussedindetail.2.MaterialmodelsandsimulationdetailsThecommercialFEMcode,DEFORM3DVersion5.0,wasusedtocarryoutthesimulationofonepassECAEprocess.2.1.AssumptionsandnumericalsimulationproceduresAwroughtmagnesiumalloyAZ31with3aluminum,1zincwasusedasthebilletmaterialbothincomputersimulationandexperimentalverification.ThenumericalsimulationswereperformedquasistaticallyusingacommercialfiniteelementcodeDEFORMTM3D.DEFORMTM3DwasacommercialpackagedevelopedbySFTCScientificFormingTechnologyCorporation.ItwasafiniteelementmethodFEMbasedprocesssimulationsystemdesignedtoanalyze3Dflowofvariousmetalformingprocesses.Itprovidedvitalinformationaboutmaterialandthermalflowduringformingprocesses.Thebilletwasassumedtobeelastic–plasticmaterial.Thefollowingassumptionswasadoptedinpresentanalysis1boththecontainerandthediearerigidbodies2theextrusionbilletwasarigidplasticmaterialand3thefrictionfactorsbetweentheextrusionbilletandtheram,container,anddiewereconstant.Thesimulationprocedureswereasfollows1the3Dgeometriesbillets,ramsanddiesachievedbyconstructing3DCADmodelsweredefinedinUnigraphicssoftware.Geometriescanbedefinedas3DIGESorSTLfiles.2Stoppingstrokewasset,theRradiusoftheinnercornermm_eeffectivestrainratesC01xxx2009xxx–xxxnumberofstepsdefinedandsimulationmodeandEnglishorSIunitswereselected.3Theobjectsbilletsanddiesweremeshed.Theobjectswerepositioned,withtheworkpieceasthereferenceobjectbothtoolsandramincontactwiththeworkpiece.Thematerialspropertiesweredefined.4Thermalboundaryconditionsweredefined.5Objectstemperatureswereinitialized.6Contactboundaryconditionsweregeneratedandfrictioncoefficientsbetweenbilletsanddies,billetsandramsweredefined.7Rammovementparametersdirectionandspeedwereassigned.8Thedatabasewascheckedandgeneratedandcalculated,FEAtosimulatethehotextrusionprocesswasperformed.9Thesimulationresultswerereadfromthepostprocessor.ofequalchannelangularextrusionforAZ31...JMaterDesign2.2.ModelingofthediesandramsThediegeometriesusedinthesimulationsareshowninFig.2.ThebilletcoordinateaxisxyzemployedinthepresentstudyisshowninFig.2.Thex,yandzdirectionswereparalleltoextrusiondirectionED,verticaldirectionNDandtransversedirectionTD,respectively.ThechannelanglesU90C176andU120C176areconsideredandillustratedrespectivelyinFig.2aandbandthecornerangleWofthediesareassumedtoequalto0.ThemodifiedgeometricmodelswithinnerroundfilletsattheoutercornerareshowninFig.2candd.ThegeometricalparametersofthefourECAEdiesforFig.2arelistedinTable2.Thechannelanglecornerradiusattheintersectionofthetwochannelswas2mmandoutercornerangleradiuswas18mm.Thelengthofinletchannelwas50mmandoutletchannellengthwas25mm.Boththeinletandoutletchannelshadthesamedimensionsofsquarecrosssection£16mm.Table3givesthedimensions,extrusionspeedandtemperatureusedincomputersimulation,etc.,whichareidenticaltothoseappliedinextrusionexperiments.Thespeedoframmoveddownalongtheinletchannelwas10mmsC01asinthesimulationsandexperiments.Thestrokeoframwas50mm.Forthesakeofsimplicity,thediesandpressingramwereassumedtoberigidbodiesthatundergonopermanentdeformation,whichmechanicalpropertiesemployedanH13toolsteelwiththeYoungmodulusandthermalconductiondependentonthetemperatureshowninFig.3aandb.Poissonsratiomwas0.3.FourdistinctgeometricmodelshavebeenanalyzedbyfiniteelementTable2ThegeometricalparametersoftheECAEdie.UC176WC176RrFig.3a90000Fig.3b99182Fig.3c120000Fig.3d12060182Table3Simulationandexperimentalparameters.Billetlengthmm50Billetdiametermm16insiderdiameterofECAEdiemm16outsidediameterofdiemm50InitialbillettemperatureC176C300InitialtoolingtemperatureC176C275StrainraterangeforflowstressmeasurementsC010.01–10TemperaturerangeforflowstressmeasurementC176C250–450Ramspeedmm/s10Frictionfactorofthecontainer–billetinterface0.25Frictionfactorbetweenthebilletanddie0.25H.J.Huetal./MaterialsandDesignxxx2009xxx–xxx3ARTICLEINPRESSFig.2.SchematicdiagramsofthethreedimensionalECAPdieFEMmodelingshowingachannelangleequalto90C176bchannelangleequalto120C176cchannelangle90C176withoutercornerangledchannelangle120C176withoutercornerangle,whererdenotestheradiusofthechannelangle,Rtheradiusoftheoutercornerangle.Table1PhysicalpropertiesoftheAZ31workpiece.PropertyAZ31Poissonsratio0.35Coefficientoflinearexpansion26.8EC06Density1780kg/m3Poissonsratio0.35Youngsmodulus45,000MPaEmissivity0.12PleasecitethisarticleinpressasHuHJetal.Thediestructuredesign2009,doi10.1016/j.matdes.2009.01.022Fig.3.ThematerialpropertiesforH13.ofequalchannelangularextrusionforAZ31...JMaterDesignanalysisFEAtorevealthedeformationbehaviorsandtheirrelationshipwiththedesignconfiguration.2.3.ModelingofthebilletThemagnesiumbilletusedinthecalculationswasaroundcrosssectiondiameter16mmandalengthof50mm£16mmC250mm.TheAZ31wasconsideredasanisotropicelastic–plasticmaterial.Thetensilestress–straincurveat300C176CofAZ31billetannealedat400C176Cfor12h,asshowninFig.4,theflowstress/straindataobtainedfromtheuniaxialcompressiontestswereintroducedintoFEAusingcommercialsoftwarepackagesDEFORMTM3D.TheelasticpropertieswereYoungsmodulusE45GPaandPoissonsratiom0.3.MaterialpropertyparametersoftheAZ31workpiecearelistedinTable1.2.4.MeshingmethodInallsimulations,anautomaticremeshingschemewasusedto4H.J.Huetal./MaterialsandDesignARTICLEINPRESSaccommodatelargestrainsandtotakeintoaccounttheoccurrenceofflowlocalization,whichpreventedfurthercalculationduringthesimulation.TheelementswereautomaticallyremeshediftheybecametoodistortedduringECAEsimulationprocess.Alltheextrusiontoolingincludedinthesimulationwasmeshedwithtetrahedralelementsanditsheatexchangewiththeworkpieceincorporatedintosimulation.ThesimulationparametersusedarelistedinTable3.Toenhancetheefficiencyofsimulationandobtainspecificresolutionsintheareasofparticularinterest,anumberofwindowswithanincreasedelementdensitywereappliedtogeneratelocalfinerelements,especiallyaroundthechannelcornerfordie.Toensuresimulationaccuracyandstability,theabsolutemeshdensitywasusedtokeeptheelementsizeatanypositionnearlyconstantduringthesimulation,becauseitwasthisdensitythatdefinedthenumberofelementsperunitlengthonthesurfaceoftheworkpiece.Theminimumsizeoftheelementwas0.25–0.35mm.Thebilletwasdividedinto20,000fournodetetrahedralelements.Totalnumberofelementsoframanddiewere8000and20,000,respectively.Thenumbersofelementswerefoundtobesufficienttoexpresslocaldeformationofthestrainrateinsensitiveworkpiecesthroughcalculationswithvaryingthenumberofelements.Tolimitthesizesofsimulationdatabasefilesandenhancesimulationspeed,theroundextrudatewascutoffatthelengthof50mmwhenitslengthexceeded50mm.Asmallrelativeinterferencedepthof0.3wasdefinedtotriggertheremeshingproFig.4.Truestress/truestraincurvesofAZ31obtainedfromcompressiontestsat300C176Cunderdifferentstrainrateandcorrectedfordeformationheatingduringthetesting.PleasecitethisarticleinpressasHuHJetal.Thediestructuredesign2009,doi10.1016/j.matdes.2009.01.022cedurewhenanyelementattheedgeoftheworkpiecehadbeenpenetratedintoandthepenetrationdepthexceeded30oftheoriginallengthofthesurfaceedgethathadacontactnodeateachend.2.5.Boundaryconditions2.5.1.ContactandfrictionboundaryconditionsContactboundaryconditionswereappliedtonodesofbillet,andspecifycontactbetweenthosenodesandthesurfaceofram.InordertoassurethequadraticconvergenceoftheNewton–Raphsonmethodusedinthecode,thecompressivedisplacementsimposedonthebillettopregionintheverticaldirectionwerefixedinincrementsof0.10mmuptoatotaldisplacementof50mm.TheNewton–Raphsonmethodwasrecommendedformostproblemsbecauseitgenerallyconvergedinlessiterationthantheotheravailablemethods.However,solutionsweremorelikelytofailtoconvergewiththismethodthanwithothermethods.Torepresentthefrictionbehaviorasaconsequenceoftheshearstressandthecontactpressure,thegeneralizedCoulombslawwasused.Thefrictionattheworkpiece–toolinginterfaceswasconsideredtobeofsheartype.Itwaswellknownthatthislawstatedproportionalitybetweenshearyieldstressandthecontactpressureduetothepresenceofthefriction.SpecificallyintheDEFORMcode,thisrelationwasverifiedbymeansofvonMisesyieldcriterioncorrectedtothesimpleshearconditionandwasgivenbyEq.1s¼lrffiffiffi3pð1Þwheresisthefrictionalshearstressandristheeffectiveflowstressoftheworkpiece.l06l61thefrictionfactor.Inthepresentsimulations,africtionfactorof0.25atthedie–billetinterfacewaschosen.Thesamefrictionfactorwasassumedattheinterfacebetweenthebilletandram.2.5.2.TemperatureboundaryconditionRegardlessoftheheattransferbetweenthedieandtheambience,theheattransferbetweenthebilletandthediewasconsidered.NewtoncoolingprinciplewasusedandexpressedasEq.2kTxini¼C0hðTC0TwÞð2Þwherehisthecoefficientoftheheattransferbetweenthematerialanddie,Twisthetemperatureofthedie.niisthenormalinidirection.Inthispaper,theambienttemperaturewasconsideredas25C176C,andtemperatureoftheECAEdie275C176C.Theinitialbillettemperaturewaschosentobeatarelativelyhighlevel300C176Cwithoutrunningtheriskofreachingthepressforcelimitduringexperimentsathighramspeeds.Heattransfercoefficientbetweentoolingandbilletwas11N/C176Csmm2,andthevalueHeattransfercoefficientsbetweentooling/billetandairare0.02N/C176Csmm2.EmissivitycoefficientsoftheAZ31andH13toolsteelwere0.12and0.7,respectively.2.6.ConvergencestudiesinsimulationsConvergenceoftheinvestigatedvariabletoaconstantvaluebychangingvariousnumericalparametersisanessentialprocedureinfiniteelementsimulation26.Theparametersthatmustbecontrolledaremeshsizeandtopologytheminimumsizeoftheelementwas0.25–0.35mminthispaper,contactparameters,xxx2009xxx–xxxremeshingparameters,incrementsizetimestepwas0.01s,convergencelimits,solverparametersthedisplacementincrementwas0.1mm,frictionmodelparametersCoulombslawused,ofequalchannelangularextrusionforAZ31...JMaterDesign

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