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1、Int.J.Mech.Sci.Vol.32,No.5,pp.375389,19900020-7403/90$3.00+.00PrintedinGreatBritain.©1990PergamonPresspieAQUASI-THREE-DIMENSIONALANALYSIS,OFTHEDEFORMATIONPROCESSINGOFSHEETSWITHAPPLICATIONSM.E.KARABINandR.E.SMELSERAlcoaLaboratories,AlcoaCenter,PA15069,U.S.A.
2、(Received15November1988;andinrevisedform17October1989)Abstract--Inanefforttodescribethree-dimensional,non-uniformeffectsinsteady-staterollingordrawingprocesses,anEulerianfiniteelementmodelispresented.Themodelemploysanumberofsimplifyingkinematicassumptionswh
3、ichpreservetheessentialphysicsoftheproblem.Thevariationofstrainrateinthelongitudinalandlateraldirectionsisretained,butauniformstrainrateinthethicknessdirectionisassumedgivingcomputationalefficiency.InterfacemodelswhichrecovertheclassicalCoulombmodelandthefr
4、ictionfactormodelareimplemented,andtwoconstitutivemodelsareincorporated.Theeffectoffrictiononlateralflowisexamined,andthetrendsarequalitativelycomparedtorecentpublisheddata.Resultsarealsopresentedfortworolling-typedeformationprocessesusingdifferentplatensha
5、pesandshowavariationinlateralflow.NOTATIONAconstitutiveconstantsastreamlinestraininterpolationconstantsBpenaltyconstantforincompressibilityBcpenaltyconstantforshapedtoolsurfacebstreamlinevelocityinterpolationconstantsEssecantmoduluseiunitvectorsinthecoordin
6、atedirectionsFfunctiondescribingtoolsurfacefappappliedforcehstripheightkshearflowstressLcontactlengthlfrictionexponentonqJMnumberoffrictioniterationsmfrictionexponentonpNshapefunctionrlconstitutiveequationexponentPstrip-toolinterfacepressureqderivativeoffun
7、ctional~withrespecttovelocitySsurfaceareaSstreamlinevariableTtemperaturettimeU,V,Wx,y,zvelocitycomponentsVvolumev,toolvelocitywcfunctionaltoenforcetangencyofstripvelocitytotoolsurfaceWstripwidth(orhalfwidthwhereappropriate)x,y,zlongitudinal,through-thicknes
8、sandtransversecoordinatesZconstitutiveparameterO:modificationfactortodampanincrementinsolutionvariableweightingfactorforstreamlineintegrationA~factorlimitingrelativevelocityinfrictionmodel'£strain~,~no
