金属材料失效在abaqus中的应用

18.2.8DYNAMICFAILUREMODELS

Product:Abaqus/ExplicitReferences

••••••••

“Equationofstate,”Section17.9.1

“Classicalmetalplasticity,”Section18.2.1“Rate-dependentyield,”Section18.2.3“Johnson-Cookplasticity,”Section18.2.7“Materiallibrary:overview,”Section16.1.1“Inelasticbehavior,”Section18.1.1*SHEARFAILURE*TENSILEFAILURE

Overview

Theprogressivedamageandfailuremodelsdescribedin“Damageandfailureforductilemetals:overview,”Section19.2.1,aretherecommendedmethodformodelingmaterialdamageandfailureinAbaqus;thesemodelsaresuitableforbothquasi-staticanddynamicsituations.Abaqus/Explicitofferstwoadditionalelementfailuremodelssuitableonlyforhigh-strain-ratedynamicproblems.Theshearfailuremodelisdrivenbyplasticyielding.Thetensilefailuremodelisdrivenbytensileloading.Thesefailuremodelscanbeusedtolimitsubsequentload-carryingcapacityofanelement(uptothepointofremovingtheelement)onceastresslimitisreached.Bothmodelscanbeusedforthesamematerial.

Theshearfailuremodel:

••••••••••

isdesignedforhigh-strain-ratedeformationofmanymaterials,includingmostmetals;usestheequivalentplasticstrainasafailuremeasure;

offerstwochoicesforwhatoccursuponfailure,includingtheremovalofelementsfromthemesh;canbeusedinconjunctionwitheithertheMisesortheJohnson-Cookplasticitymodels;andcanbeusedinconjunctionwiththetensilefailuremodel.

isdesignedforhigh-strain-ratedeformationofmanymaterials,includingmostmetals;

usesthehydrostaticpressurestressasafailuremeasuretomodeldynamicspallorapressurecutoff;offersanumberofchoicesforwhatoccursuponfailure,includingtheremovalofelementsfromthemesh;

canbeusedinconjunctionwitheithertheMisesortheJohnson-Cookplasticitymodelsortheequationofstatematerialmodel;and

canbeusedinconjunctionwiththeshearfailuremodel.

Thetensilefailuremodel:

18.2.8–1

DYNAMICFAILUREMODELS

Shearfailuremodel

TheshearfailuremodelcanbeusedinconjunctionwiththeMisesortheJohnson-CookplasticitymodelsinAbaqus/Explicittodefineshearfailureofthematerial.Shearfailurecriterion

Theshearfailuremodelisbasedonthevalueoftheequivalentplasticstrainatelementintegrationpoints;failureisassumedtooccurwhenthedamageparameterexceeds1.Thedamageparameter,,isdefinedas

whereisanyinitialvalueoftheequivalentplasticstrain,isanincrementoftheequivalentplastic

isthestrainatfailure,andthesummationisperformedoverallincrementsintheanalysis.strain,

Thestrainatfailure,,isassumedtodependontheplasticstrainrate,;adimensionlesspressure-deviatoricstressratio,(wherepisthepressurestressandqistheMisesstress);temperature;andpredefinedfieldvariables.Therearetwowaystodefinethestrainatfailure,.Oneistousedirecttabulardata,wherethedependenciesaregiveninatabularform.Alternatively,theanalyticalformproposedbyJohnsonandCookcanbeinvoked(see“Johnson-Cookplasticity,”Section18.2.7,formoredetails).

Whendirecttabulardataareusedtodefinetheshearfailuremodel,thestrainatfailure,,mustbegivenasatabularfunctionoftheequivalentplasticstrainrate,thepressure-deviatoricstressratio,temperature,andpredefinedfieldvariables.ThismethodrequirestheuseoftheMisesplasticitymodel.

FortheJohnson-Cookshearfailuremodel,youmustspecifythefailureparameters,–(see“Johnson-Cookplasticity,”Section18.2.7,formoredetailsontheseparameters).Theshearfailuredatamustbecalibratedatorbelowthetransitiontemperature,,definedin“Johnson-Cookplasticity,”Section18.2.7.ThismethodrequirestheuseoftheJohnson-Cookplasticitymodel.

InputFileUsage:

UsebothofthefollowingoptionsfortheMisesplasticitymodel:*PLASTIC,HARDENING=ISOTROPIC*SHEARFAILURE,TYPE=TABULAR

UsebothofthefollowingoptionsfortheJohnson-Cookplasticitymodel:*PLASTIC,HARDENING=JOHNSONCOOK*SHEARFAILURE,TYPE=JOHNSONCOOK

Elementremoval

Whentheshearfailurecriterionismetatanintegrationpoint,allthestresscomponentswillbesettozeroandthatmaterialpointfails.Bydefault,ifallofthematerialpointsatanyonesectionofanelementfail,theelementisremovedfromthemesh;itisnotnecessaryforallmaterialpointsintheelementtofail.Forexample,inafirst-orderreduced-integrationsolidelementremovaloftheelementtakesplaceassoonas

18.2.8–2

DYNAMICFAILUREMODELS

itsonlyintegrationpointfails.However,inashellelementallthrough-the-thicknessintegrationpointsmustfailbeforetheelementisremovedfromthemesh.Inthecaseofsecond-orderreduced-integrationbeamelements,failureofallintegrationpointsthroughthesectionateitherofthetwoelementintegrationlocationsalongthebeamaxisleads,bydefault,toelementremoval.Similarly,inthemodifiedtriangularandtetrahedralsolidelementsfailureatanyoneintegrationpointleads,bydefault,toelementremoval.Elementdeletionisthedefaultfailurechoice.

Analternativefailurechoice,wheretheelementisnotdeleted,istospecifythatwhentheshearfailurecriterionismetatamaterialpoint,thedeviatoricstresscomponentswillbesettozeroforthatpointandwillremainzerofortherestofthecalculation.Thepressurestressisthenrequiredtoremaincompressive;thatis,ifanegativepressurestressiscomputedinafailedmaterialpointinanincrement,itisresettozero.Thisfailurechoiceisnotallowedwhenusingplanestress,shell,membrane,beam,andtrusselementsbecausethestructuralconstraintsmaybeviolated.

InputFileUsage:

Usethefollowingoptiontoallowelementdeletionwhenthefailurecriterionismet(thedefault):

*SHEARFAILURE,ELEMENTDELETION=YES

Usethefollowingoptiontoallowtheelementtotakehydrostaticcompressivestressonlywhenthefailurecriterionismet:*SHEARFAILURE,ELEMENTDELETION=NO

Determiningwhentousetheshearfailuremodel

TheshearfailuremodelinAbaqus/Explicitissuitableforhigh-strain-ratedynamicproblemswhereinertiaisimportant.Improperuseoftheshearfailuremodelmayresultinanincorrectsimulation.

Forquasi-staticproblemsthatmayrequireelementremoval,theprogressivedamageandfailuremodels(Chapter19,“ProgressiveDamageandFailure”)ortheGursonporousmetalplasticitymodel(“Porousmetalplasticity,”Section18.2.9)arerecommended.Tensilefailuremodel

ThetensilefailuremodelcanbeusedinconjunctionwitheithertheMisesortheJohnson-CookplasticitymodelsortheequationofstatematerialmodelinAbaqus/Explicittodefinetensilefailureofthematerial.Tensilefailurecriterion

TheAbaqus/Explicittensilefailuremodelusesthehydrostaticpressurestressasafailuremeasuretomodeldynamicspallorapressurecutoff.Thetensilefailurecriterionassumesthatfailureoccurswhenthepressurestress,p,becomesmoretensilethantheuser-specifiedhydrostaticcutoffstress,.Thehydrostaticcutoffstressmaybeafunctionoftemperatureandpredefinedfieldvariables.Thereisnodefaultvalueforthisstress.

ThetensilefailuremodelcanbeusedwitheithertheMisesortheJohnson-Cookplasticitymodelsortheequationofstatematerialmodel.

InputFileUsage:

UsebothofthefollowingoptionsfortheMisesorJohnson-Cookplasticitymodels:

18.2.8–3

DYNAMICFAILUREMODELS

*PLASTIC

*TENSILEFAILURE

Usebothofthefollowingoptionsfortheequationofstatematerialmodel:*EOS

*TENSILEFAILURE

Failurechoices

Whenthetensilefailurecriterionismetatanelementintegrationpoint,thematerialpointfails.Fivefailurechoicesareofferedforthefailedmaterialpoints:thedefaultchoice,whichincludeselementremoval,andfourdifferentspallmodels.Thesefailurechoicesaredescribedbelow.Elementremoval

Whenthetensilefailurecriterionismetatanintegrationpoint,allthestresscomponentswillbesettozeroandthatmaterialpointfails.Bydefault,ifallofthematerialpointsatanyonesectionofanelementfail,theelementisremovedfromthemesh;itisnotnecessaryforallmaterialpointsintheelementtofail.Forexample,inafirst-orderreduced-integrationsolidelementremovaloftheelementtakesplaceassoonasitsonlyintegrationpointfails.However,inashellelementallthrough-the-thicknessintegrationpointsmustfailbeforetheelementisremovedfromthemesh.Inthecaseofsecond-orderreduced-integrationbeamelements,failureofallintegrationpointsthroughthesectionateitherofthetwoelementintegrationlocationsalongthebeamaxisleads,bydefault,toelementremoval.Similarly,inthemodifiedtriangularandtetrahedralsolidelementsfailureatanyoneintegrationpointleads,bydefault,toelementremoval.

InputFileUsage:

*TENSILEFAILURE,ELEMENTDELETION=YES(default)

Spallmodels

Analternativefailurechoicethatisbasedonspall(thecrumblingofamaterial),ratherthanelementremoval,isalsoavailable.Fourfailurecombinationsareavailableinthiscategory.Whenthetensilefailurecriterionismetatamaterialpoint,thedeviatoricstresscomponentsmaybeunaffectedormayberequiredtobezero,andthepressurestressmaybelimitedbythehydrostaticcutoffstressormayberequiredtobecompressive.Therefore,therearefourpossiblefailurecombinations(seeFigure18.2.8–1,where“O”isthestressthatwouldexistifthetensilefailuremodelwerenotused).Thesefailurecombinationsareasfollows:

•

Ductileshearandductilepressure:thischoicecorrespondstopoint1inFigure18.2.8–1andmodelsthecaseinwhichthedeviatoricstresscomponentsareunaffectedandthepressurestressislimitedbythehydrostaticcutoffstress;i.e.,.

InputFileUsage:

*TENSILEFAILURE,ELEMENTDELETION=NO,

SHEAR=DUCTILE,PRESSURE=DUCTILE

•

Brittleshearandductilepressure:thischoicecorrespondstopoint2inFigure18.2.8–1andmodelsthecaseinwhichthedeviatoricstresscomponentsaresettozeroandremainzerofor

18.2.8–4

DYNAMICFAILUREMODELS

qO142−σcutoff

Figure18.2.8–1

3p

Tensilefailurechoices.

therestofthecalculation,andthepressurestressislimitedbythehydrostaticcutoffstress;i.e.,

.

InputFileUsage:

*TENSILEFAILURE,ELEMENTDELETION=NO,SHEAR=BRITTLE,PRESSURE=DUCTILE

•

Brittleshearandbrittlepressure:thischoicecorrespondstopoint3inFigure18.2.8–1andmodelsthecaseinwhichthedeviatoricstresscomponentsaresettozeroandremainzerofortherestofthecalculation,andthepressurestressisrequiredtobecompressive;i.e.,.

InputFileUsage:

*TENSILEFAILURE,ELEMENTDELETION=NO,

SHEAR=BRITTLE,PRESSURE=BRITTLE

•

Ductileshearandbrittlepressure:thischoicecorrespondstopoint4inFigure18.2.8–1andmodelsthecaseinwhichthedeviatoricstresscomponentsareunaffectedandthepressurestressisrequiredtobecompressive;i.e.,.

InputFileUsage:

*TENSILEFAILURE,ELEMENTDELETION=NO,

SHEAR=DUCTILE,PRESSURE=BRITTLE

Thereisnodefaultfailurecombinationforthespallmodels.Ifyouchoosenottousetheelementdeletionmodel,youmustspecifythefailurecombinationexplicitly.Ifthematerial’sdeviatoricbehaviorisnotdefined(forexample,theequationofstatemodelwithoutdeviatoricbehaviorisused),thedeviatoricpartofthecombinationismeaninglessandwillbeignored.Thespallmodelsarenotallowedwhenusingplanestress,shell,membrane,beam,andtrusselements.Determiningwhentousethetensilefailuremodel

ThetensilefailuremodelinAbaqus/Explicitissuitableforhigh-strain-ratedynamicproblemsinwhichinertiaeffectsareimportant.Improperuseofthetensilefailuremodelmayresultinanincorrectsimulation.

18.2.8–5

DYNAMICFAILUREMODELS

Usingthefailuremodelswithrebar

Itispossibletousetheshearfailureand/orthetensilefailuremodelsinelementsforwhichrebarsarealsodefined.Whensuchelementsfailaccordingtothefailurecriterion,thebasematerialcontributiontotheelementstress-carryingcapacityisremovedoradjusteddependingonthetypeoffailurechosen,buttherebarcontributiontotheelementstress-carryingcapacityisnotremoved.However,ifyoualsoincludefailureintherebarmaterialdefinition,therebarcontributiontotheelementstress-carryingcapacitywillalsoberemovedoradjustedifthefailurecriterionspecifiedfortherebarismet.Elements

TheshearandtensilefailuremodelswithelementdeletioncanbeusedwithanyelementsinAbaqus/Explicitthatincludemechanicalbehavior(elementsthathavedisplacementdegreesoffreedom).Theshearandtensilefailuremodelswithoutelementdeletioncanbeusedonlywithplanestrain,axisymmetric,andthree-dimensionalsolid(continuum)elementsinAbaqus/Explicit.Output

InadditiontothestandardoutputidentifiersavailableinAbaqus/Explicit(“Abaqus/Explicitoutputvariableidentifiers,”Section4.2.2),thefollowingvariablehasspecialmeaningfortheshearandtensilefailuremodels:STATUS

Statusofelement(thestatusofanelementis1.0iftheelementisactive,0.0iftheelementisnot).

18.2.8–6

POROUSMETALPLASTICITY

18.2.9POROUSMETALPLASTICITY

Products:Abaqus/StandardReferences

Abaqus/ExplicitAbaqus/CAE

••••••

“Materiallibrary:overview,”Section16.1.1“Inelasticbehavior,”Section18.1.1*POROUSMETALPLASTICITY*POROUSFAILURECRITERIA*VOIDNUCLEATION

“Definingporousmetalplasticity”in“Definingplasticity,”Section12.8.2oftheAbaqus/CAEUser’sManual,intheonlineHTMLversionofthismanual

Overview

Theporousmetalplasticitymodel:

•••

isusedtomodelmaterialswithadiluteconcentrationofvoidsinwhichtherelativedensityisgreaterthan0.9;

isbasedonGurson’sporousmetalplasticitytheory(Gurson,1977)withvoidnucleationand,inAbaqus/Explicit,afailuredefinition;and

definestheinelasticflowoftheporousmetalonthebasisofapotentialfunctionthatcharacterizestheporosityintermsofasinglestatevariable,therelativedensity.

Elasticandplasticbehavior

Youspecifytheelasticpartoftheresponseseparately;onlylinearisotropicelasticitycanbespecified(see“Linearelasticbehavior,”Section17.2.1).

Youspecifythehardeningbehaviorofthefullydensematrixmaterialbydefiningametalplasticitymodel(see“Classicalmetalplasticity,”Section18.2.1).Onlyisotropichardeningcanbespecified.Thehardeningcurvemustdescribetheyieldstressofthematrixmaterialasafunctionofplasticstraininthematrixmaterial.Indefiningthisdependenceatfinitestrains,“true”(Cauchy)stressandlogstrainvaluesshouldbegiven.Ratedependencyeffectsforthematrixmaterialcanbemodeled(see“Rate-dependentyield,”Section18.2.3).Yieldcondition

Therelativedensityofamaterial,r,isdefinedastheratioofthevolumeofsolidmaterialtothetotalvolumeofthematerial.Therelationshipsdefiningthemodelareexpressedintermsofthevoidvolumefraction,f,whichisdefinedastheratioofthevolumeofvoidstothetotalvolumeofthematerial.ItfollowsthatForametalcontainingadiluteconcentrationofvoids,Gurson(1977)proposed

18.2.9–1

POROUSMETALPLASTICITY

ayieldconditionasafunctionofthevoidvolumefraction.ThisyieldconditionwaslatermodifiedbyTvergaard(1981)totheform

where

isthedeviatoricpartoftheCauchystresstensoristheeffectiveMisesstress;

isthehydrostaticpressure;

istheyieldstressofthefullydensematrixmaterialasafunctionofequivalentplasticstraininthematrix;andarematerialparameters.

,the

;

,,

TheCauchystressisdefinedastheforceper“currentunitarea,”comprisedofvoidsandthesolid(matrix)material.

f=0(r=1)impliesthatthematerialisfullydense,andtheGursonyieldconditionreducestotheMisesyieldcondition.f=1(r=0)impliesthatthematerialiscompletelyvoidedandhasnostresscarryingcapacity.Themodelgenerallygivesphysicallyreasonableresultsonlyfor0.1(0.9).

Themodelisdescribedindetailin“Porousmetalplasticity,”Section4.3.6oftheAbaqusTheoryManual,alongwithadiscussionofitsnumericalimplementation.

Iftheporousmetalplasticitymodelisusedduringaporepressureanalysis(see“Coupledporefluiddiffusionandstressanalysis,”Section6.7.1),therelativedensity,r,istrackedindependentlyofthevoidratio.

Specifyingq1,q2,andq3

Youspecifytheparameters,,anddirectlyfortheporousmetalplasticitymodel.Fortypicalmetalstherangesoftheparametersreportedintheliteratureare=1.0to1.5,=1.0,and==1.0to2.25(see“Neckingofaroundtensilebar,”Section1.1.9oftheAbaqusBenchmarksManual).TheoriginalGursonmodelisrecoveredwhen===1.0.Youcandefinetheseparametersastabularfunctionsoftemperatureand/orfieldvariables.

InputFileUsage:Abaqus/CAEUsage:

*POROUSMETALPLASTICITY

Propertymodule:materialeditor:Mechanical→Plasticity→PorousMetalPlasticity

FailurecriteriainAbaqus/Explicit

TheporousmetalplasticitymodelinAbaqus/Explicitallowsforfailure.Inthiscasetheyieldconditioniswrittenas

18.2.9–2