ABAQUS應(yīng)變塑性模型

Ramberg-OsgoodrelationshipFromWikipedia,thefreeencyclopediaJumpto:navigation,searchTheRamberg-Osgoodequationwascreatedtodescribethenonlinearrelationshipbetweenstressandstrain—thatis,thestress-straincurve—inmaterialsneartheiryieldpoints.Itisespeciallyusefulformetalsthathardenwithplasticdeformation(seestrainhardening),showingasmoothelastic-plastictransition.Initsoriginalform,itsays￡isstrain,gisstress,EisYoung'smodulusandKandnareconstantsthatdependonthematerialbeingconsidered.Thefirsttermontherightside,"'-,isequaltotheelasticpartofthestrain,whilethesecondterm, ，accountsfortheplasticpart,theparametersKandndescribingthehardeningbehaviorofthematerial.Introducingtheyieldstrengthofthematerial,aanddefininganewparameter,a,relatedtoKas'1=Kg/E)",itisconvenienttorewritethetermontheextremerightsideasfollows:Replacinginthefirstexpression,theRamberg-Osgoodequationcanbewrittenas

[edit]HardeningbehaviorandYieldoffsetInthelastformoftheRamberg-Osgoodmodel,thehardeningbehaviorofthematerialdependsonthematerialconstantsand.■?.Duetothepower-lawrelationshipbetweenstressandplasticstrain,theRamberg-Osgoodmodelimpliesthatplasticstrainispresentevenforverylowlevelsofstress.Nevertheless,forlowappliedstressesandforthecommonlyusedvaluesofthematerialconstantsaandn,theplasticstrainremainsnegligiblecomparedtotheelasticstrain.Ontheotherhand,forstresslevelshigherthanaplasticstrainbecomesprogressivelylargerthanelasticstrain.d— .ThevalueEcanbeseenasayieldoffsetasshowninfigure1.Thiscomesfromthefactthat1 1■-'ri",when門門...Accordingly(seeFigure1):elasticstrainatyield=plasticstrainatyield=plasticstrainatyield=W「=yieldoffsetCommonlyusedvaluesforare~5orgreater,althoughmoreprecisevaluesareusuallyobtainedbyfittingoftensile(orcompressive)experimentaldata.Valuesfonicanalsobefoundbymeansoffittingtoexperimentaldata,althoughforsomematerials,itcanbefixedinordertohavetheyieldoffsetequaltotheacceptedvalueofstrainof0.2%,whichmeans:□罕=0?002

Figure1:GenericrepresentationoftheStress-StraincurvebymeansoftheRamberg-Osgoodequation.Straincorrespondingtotheyieldpointisthesumoftheelasticandplasticcomponents.[edit]Sources仁Ramberg,W.,&Osgood,W.R.(1943).Descriptionofstress-straincurvesbythreeparameters.TechnicalNoteNo.,9NationalAdvisoryCommitteeForAeronautics,WashingtonDC,[1]11.2.13DeformationplasticityProducts:ABAQUS/StandardABAQUS/CAEReferences.“Materiallibrary:overview,”Section9.1.1.“Inelasticbehavior,”Section11.1.1?^DEFORMATIONPLASTICITYOverviewThedeformationtheoryRamberg-Osgoodplasticitymodel:isprimarilyintendedforuseindevelopingfullyplasticsolutionsforfracturemechanicsapplicationsinductilemetals;andcannotappearwithanyothermechanicalresponsematerialmodelssinceitcompletelydescribesthemechanicalresponseofthematerial.One-dimensionalmodelInonedimensionthemodeliswherecristhestress;isthestrain;EisYoung'smodulus(definedastheslopeofthestress-straincurveatzerostress);qisthe“yield”offset;istheyieldstress,inthesensethat,when-—,",I,「? ■';andisthehardeningexponentforthe“plastic”(nonlinear)term:，IThematerialbehaviordescribedbythismodelisnonlinearatallstresslevels,butforcommonlyusedvaluesofthehardeningexponent(.?. ormore)thenonlinearitybecomessignificantonlyatstressmagnitudesapproachingorexceeding.GeneralizationtomultiaxialstressstatesTheone-dimensionalmodelisgeneralizedtomultiaxialstressstatesusingHooke'slawforthelineartermandtheMisesstresspotentialandassociatedflowlawforthenonlinearterm:whereisthestraintensor,isthestresstensor,istheequivalenthydrostaticstress,istheMisesequivalentstress,isthestressdeviator,andisthePoissonsratio.Thelinearpartofthebehaviorcanbecompressibleorincompressible,dependingonthevalueofthePoisson'sratio,butthenonlinearpartofthebehaviorisincompressible(becausetheflowisnormaltotheMisesstresspotential).Themodelisdescribedindetailin“Deformationplasticity,”Section4.3.9oftheABAQUSTheoryManua..Youspecifytheparameters,?,一n,and「directly.Theycanbedefinedasatabularfunctionoftemperature.InputFileUsage: *DEFORMATIONPLASTICITYABAQUS/CAEUsage:Propertymodule:materialeditor:Mechanical—:，DeformationPlasticityTypicalapplicationsThedeformationplasticitymodelismostcommonlyappliedinstaticloadingwithsmall-displacementanalysis,wherethefullyplasticsolutionmustbedevelopedinapartofthemodel.Generally,theloadisrampedonuntilallpointsintheregionbeingmonitoredsatisfytheconditionthatthe“plasticstrain”dominatesand,hence,exhibitfullyplasticbehavior,whichisdefinedasorYoucanspecifythenameofaparticularelementsettobemonitoredinastaticanalysisstepforfullyplasticbehavior.Thestepwillendwhenthesolutionsatallconstitutivecalculationpointsintheelementsetarefullyplastic,whenthemaximumnumberofincrementsspecifiedforthestepisreached,orwhenthetimeperiodspecifiedforthestaticstepisexceeded,whichevercomesfirst.InputFileUsage: *STATIC,FULLYPLASTIC=ElsetNameABAQUS/CAEUsage:Stepmodule:CreateStep:General:Static,General:Other:Stopwhenregionregionisfullyplastic.ElementsDeformationplasticitycanbeusedwithanystress/displacementelementinABAQUS/Standard.Sinceitwillgenerallybeusedforcaseswhenthedeformationisdominatedbyplasticflow,theuseof“hybrid”(mixedformulation)orreduced-integrationelementsisrecommendedwitht