损伤初始及扩展

DamageinitiationcriterionanddamageevolutionresponseAbaqus/StandardandAbaqus/Explicitofferageneralcapabilityforpredictingtheonsetoffailureandacapabilityformodelingprogressivedamageandfailureofductilemetals.Inthemostgeneralcasethisrequiresthespecificationofthefollowing:theundamagedelastic-plasticresponseofthematerial(“Classicalmetalplasticity,”Section20.2.1);adamageinitiationcriterion(“Damageinitiationforductilemetals,”Section21.2.2);andadamageevolutionresponse,includingachoiceofelementremoval(“Damageevolutionandelementremovalforductilemetals,”Section21.2.3).DamageinitiationcriterionDamageinitiationcriteriaforthefractureofmetals,includingductileandshearcriteria.Damageinitiationcriteriafortheneckinginstabilityofsheetmetal.Theseincludeforminglimitdiagrams(FLD,FLSD,andMSFLD)intendedtoassesstheformabilityofsheetmetalandtheMarciniak-Kuczynski(M-K)criterion(availableonlyinAbaqus/Explicit)tonumericallypredictneckinginstabilityinsheetmetaltakingintoaccountthedeformationhistory.Morethanonedamageinitiationcriterioncanbespecifiedforagivenmaterial.Ifmultipledamageinitiationcriteriaarespecifiedforthesamematerial,theyaretreatedindependently.DamageevolutionThedamageevolutionlawdescribestherateofdegradationofthematerialstiffnessoncethecorrespondinginitiationcriterionhasbeenreached.FordamageinductilemetalsAbaqusassumesthatthedegradationofthestiffnessassociatedwitheachactivefailuremechanismcanbemodeledusingascalardamagevariable,(),whererepresentsthesetofactivemechanisms.AtanygiventimeduringtheanalysisthestresstensorinthematerialisgivenbythescalardamageequationwhereDistheoveralldamagevariableandistheeffective(orundamaged)stresstensorcomputedinthecurrentincrement.arethestressesthatwouldexistinthematerialintheabsenceofdamage.Thematerialhaslostitsload-carryingcapacitywhen.Bydefault,anelementisremovedfromthemeshifallofthesectionpointsatanyoneintegrationlocationhavelosttheirload-carryingcapacity.InputFileUsage:Usethefollowingoptionimmediatelyafterthecorresponding*DAMAGEINITIATIONoptiontospecifythedamageevolutionbehavior:*DAMAGEEVOLUTIONAbaqus/CAEUsage:Propertymodule:materialeditor:MechanicalDamageforDuctileMetalscriterion:SuboptionsDamageEvolution1.DuctilecriterionTheductilecriterionisaphenomenologicalmodelforpredictingtheonsetofdamageduetonucleation,growth,andcoalescenceofvoids.Themodelassumesthattheequivalentplasticstrainattheonsetofdamage,,isafunctionofstresstriaxialityandstrainrate:whereisthestresstriaxiality,pisthepressurestress,qistheMisesequivalentstress,andistheequivalentplasticstrainrate.Thecriterionfordamageinitiationismetwhenthefollowingconditionissatisfied:whereisastatevariablethatincreasesmonotonicallywithplasticdeformation.Ateachincrementduringtheanalysistheincrementalincreaseiniscomputedas2.Johnson-CookcriterionTheJohnson-Cookcriterion(availableonlyinAbaqus/Explicit)isaspecialcaseoftheductilecriterioninwhichtheequivalentplasticstrainattheonsetofdamage,,isassumedtobeoftheformwhere–arefailureparametersandisthereferencestrainrate.ThisexpressiondiffersfromtheoriginalformulapublishedbyJohnsonandCook(1985)inthesignoftheparameter.Thisdifferenceismotivatedbythefactthatmostmaterialsexperienceadecreaseinwithincreasingstresstriaxiality;therefore,intheaboveexpressionwillusuallytakepositivevalues.isthenondimensionaltemperaturedefinedas3.ShearcriterionTheshearcriterionisaphenomenologicalmodelforpredictingtheonsetofdamageduetoshearbandlocalization.Themodelassumesthattheequivalentplasticstrainattheonsetofdamage,,isafunctionoftheshearstressratioandstrainrate:Hereistheshearstressratio,isthemaximumshearstress,andisamaterialparameter.Atypicalvalueofforaluminumis=0.3(Hooputraetal.,2004).Thecriterionfordamageinitiationismetwhenthefollowingconditionissatisfied:4.Forminglimitdiagram(FLD)criterionTheforminglimitdiagram(FLD)isausefulconceptintroducedbyKeelerandBackofen(1964)todeterminetheamountofdeformationthatamaterialcanwithstandpriortotheonsetofneckinginstability.Themaximumstrainsthatasheetmaterialcansustainpriortotheonsetofneckingarereferredtoastheforminglimitstrains.AFLDisaplotoftheforminglimitstrainsinthespaceofprincipal(in-plane)logarithmicstrains.Inthediscussionthatfollowsmajorandminorlimitstrainsrefertothemaximumandminimumvaluesofthein-planeprincipallimitstrains,respectively.Themajorlimitstrainisusuallyrepresentedontheverticalaxisandtheminorstrainonthehorizontalaxis,asillustratedinFigure21.2.2–1.Thelineconnectingthestatesatwhichdeformationbecomesunstableisreferredtoastheforminglimitcurve(FLC).TheFLCgivesasenseoftheformabilityofasheetofmaterial.StrainscomputednumericallybyAbaquscanbecomparedtoaFLCtodeterminethefeasibilityoftheformingprocessunderanalysis.Figure21.2.2–1Forminglimitdiagram(FLD).TheFLDdamageinitiationcriterionrequiresthespecificationoftheFLCintabularformbygivingthemajorprincipalstrainatdamageinitiationasatabularfunctionoftheminorprincipalstrainand,optionally,temperatureandpredefinedfieldvariables,.ThedamageinitiationcriterionfortheFLDisgivenbythecondition,wherethevariableisafunctionofthecurrentdeformationstateandisdef