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1、journalofMaterialsProcessingTechnologyELSEVIERJournalofMaterialsProcessingTechnology60(1996)649--656IntrinsiccriterionofplasticinstabilityH.Moritoki,E.OkuyamaDepartmentofMechanicalEngineering,MiningCollege,AkitaUniversity1-1Gakuen-cho,Tegata,AkitaOIOJAPANAbstractH
2、ithertotheapproachesonplasticinstabilityhavebeencarriedoutmainlyinevaluatingsheetformability.Theneckinginpressformingisaphenomenonrelatingtoplasticinstability.Itisclassifiedintodiffuseandlocalizedneckings.Swift[1]proposedthecriterionofdiffusenecking,andforlocalize
3、dneckingStOrenandRice[3]presentedthemodifiedcriterionofHill's[2]inordertomakeitpossibletopredicttheformabilityinbiaxialstretching.Sincethereissomeimperfectionsinthesecriteriaandtheydonotprovidesufficientconditionsfortheemergenceofneckingphenomena,theymustbeimprove
4、d.Thispaperpresentscomprehensivecriteriabasedonthemultiplicityofsolution.Keywords:PlasticInstability,DiffuseNecking,LocalizedNecking,ModeofNeckingPlane,MultipleSolutions1.IntroductionsubstantiallythesameasHill'sone.Furthermore,itleadstoimaginarysolutionwhenitisapp
5、liedtobiaxialstretching.InThecriterionofthediffuseneckingisproposedbySwiftconsideringthecriterionoflocalizednecking,the[1],anditisrepresentedassimultaneousstationarityofthestationarityofappliedloadsoughttobealsorequiredasinloadsactingalongasheetplane.However,thest
6、ateobtaineddiffusenecking.fromthecriterionisstrangelyenoughnottosatisfyitsThispaperpresentstheintrinsiccriteriaofplasticcondition.Ontheotherhand,itisproventhatthemultipleinstabilitysatisfyinganecessaryandsufficientconditionforsolutionscannotberealizedunlesstheload
7、ratesvanish,thattheemergenceofthenecking.Thenecessaryconditionisis,theloadstationarityholdstrue.Thesefactscontradicteachintroducedfromtheconditionsadmittingthemultiplicityofotherforestablishingthecriterionofthenecking.Then,wesolutionunderthespecifiedsurfacetractio
8、nrateandvelocity.lookfortheconditionunderwhichthesimultaneousNext,itssufficientconditionwillbediscussedusingthestationarityofloadsisledtoandtheexistence
