FRACW06ThreePointXFEM.docx
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FRACW06ThreePointXFEM
Introduction
Inthisworkshopweconsidercrackgrowthinthethree-pointbendspecimenstudiedinearlierworkshopsusingtheextendedfiniteelementtechniqueorXFEM(seeFigureW6–1forgeometryandloaddetails).Enrichedfiniteelementsthatallowseparationandatraction-separationdamagecriterion,muchliketheoneusedforcohesiveelements,areusedtomodelthecrackgrowthbehavior.Linearelasticbehaviorisassumed(thecohesivetraction-separationlawisindirectlyrelatedtoLEFMinthattheareaunderneaththetraction-separationcurveisequaltothefracturetoughness,i.e.,thecriticalenergyreleaserate).
UnlikethecohesiveorVCCTmodels,thecrackpathisnotprescribedaprioriwiththeXFEMtechnique.Weneedonlyspecifythelocationandgeometryofacrack,bothofwhichcanbeindependentofthemesh.Thisadvantage,notavailableintheprevioustechniques,simplifiesmeshcreationconsiderablyaswewillseeshortly.
FigureW6–1Schematicofthethree-pointbendspecimen.
Insteadofapplyingmomentsasdonepreviously,wewillapplyprescribedrotationstoillustratethegeneraldifferencesbetweendisplacement-controlledandload-controlledcrackpropagation.
Preliminaries
1.Entertheworkingdirectoryforthisworkshop:
../fracture/bending
2.Openthemodeldatabasefilecreatedearlier(three-point-bend.cae).
Wewillslightlymodifythegeometryoftheplateandcreateaseparateparttospecifythecracklocation.Thenwewillstudythecrackgrowthinresponsetoanappliedrotation.TheloadatwhichthecrackbeginstogrowwillbecomparedwiththeonesobtainedfromthecohesiveandtheVCCTmodels.
Beforecontinuing,copythemodelnamedunfocusedtoonenamedxfem.IfyoudidnotcompletetheexerciseswiththeunfocusedmeshinWorkshop1,simplycopyanyofyourmodelsfromWorkshop1tothenewnamegivenabove.Inthenewmodel,followtheinstructionsgiveninWorkshop1fordeletingthecircularpartitionbeforeproceeding.
Theinstructionsthatfollowapplytothexfemmodel.
Editingthegeometry
Wewillfirstdeletethepartitiononthefacethatrepresentedthecrackintheoriginalmodel.IntheModelTree,expandthepartnamedplateforthemodelnamedxfem.IntheFeaturescontainer,clickMB3onthePartitionface-1featureandselectDeletefromthemenuthatappears.
Deletingobsoleteattributes
Thedeletionofthefacepartitioninthepreviousstepdeletedthemeshseamandthesharpcrackthatexistedintheoriginalmodel.Thus,anymodelattributesassociatedwiththesemustalsobedeleted.
3.IntheModelTree,expandtheEngineeringFeaturescontainerunderneaththeAssembly.ExpandtheCrackscontainerandclickMB3onCrack-1.Inthemenuthatappears,selectDelete.
4.IntheModelTree,expandtheHistoryOutputRequestscontainer.Deletetheoutputrequestsassociatedwiththesharpcrack(H-Output-2andH-Output-3).
CreatinganXFEMcrack
TospecifythelocationandgeometryofanXFEMcrackthatisindependentofthemesh,weneedageometricfeatureintheassemblythatcanbeselectedinAbaqus/CAE.Insteadofcreatingapartitionaswedidbefore,wewillnowcreateaseparatewirepartandinstanceitintheassembly.Thispartwillrepresentthecrack.
1.IntheModelTree,openthecontainercorrespondingtothemodelnamedxfemanddouble-clickPartstocreateadeformable2Dwire-basedpartnamedcrackwithanapproximatesizeof20.
2.UsingtheCreatelines:
Connectedtool
sketcha2mmlongverticallinestartingfromtheorigingoingupwards.ClickDonetoexitthesketcher.
3.OpentheAssemblycontainerintheModelTreeanddouble-clickInstancestocreateadependentinstanceofthepartnamedcrack.Theinstancewillappearsuperimposedontheplate’sleftverticaledge.
4.FromthemainmenubarintheintheAssemblymodule,selectInstance→Translate.SelectthecrackinstanceintheviewportandclickDone.
5.Enter(0.0,0.0)and(27.5,0.0)asthestartandtheendpointsforthetranslationvector,respectively.Thiswillmovetheparttothedesiredlocation.ConfirmthecurrentlocationbyclickingOKinthepromptarea.
WecannowproceedtocreateanXFEMcrackfeature.
1.SwitchtotheInteractionmodule.
2.Fromthemainmenubar,selectSpecial→Crack→Create.
3.Inthedialogboxthatappears,selectXFEMasthetypeasshowninFigureW6–2,andclickContinue.
FigureW6–2CreateCrackdialogbox.
4.SelecttheinstanceplateintheviewportastheCrackdomain.IntheEditCrackdialogboxthatappears,toggleonSpecifyintheCracklocationfield,andclickSelect(seeFigureW6–3).
5.SelectthepartinstancecrackasthecracklocationandclickDone.
6.ToggleonSpecifycontactpropertyandclickCreate.AcceptthedefaultnameandselectContactastheType.
FigureW6–3EditCrackdialogbox.
7.FromtheMechanicalmenuselectNormalBehaviorasshowninFigureW6–4.AcceptthedefaultchoicesandclickOK.
FigureW6–4EditContactPropertydialogbox.
8.ClickOKintheEditCrackdialogbox.ThiscompletesthedefinitionoftheXFEMcrack.
Thismethodofspecifyingthecracklocationandgeometryisveryusefulincaseswherethecrackgeometryiscomplex.Onecaneasilycreateaseparatepartandinstanceitintheassemblywithouthavingtocreatenumerouspartitionsintheexistingpart,whichwouldintroducedifficultiesincreatingthemesh.
EditMaterialProperties
Wemustincludedamageinitiationanddamageevolutioncriteriatomodelfailure.
1.IntheModelTree,double-clicksteelintheMaterialscontainertoeditthematerialproperties.
2.DefinedamageinitiationusingtheMaxpscriterion(Mechanical→DamageforTractionSeparationLaws→MaxpsDamage).Enter100inthedatafield.
Note:
Weused175fortheQuadscriterioninthecohesivemodels.Onecanarriveatthisvaluebasedonasimplecalibrationstudy.Usually,weknowKIcorJcfromexperiments.Foragivengeometry,astudyinvolvingafocusedmeshwithelementsthatcapturethesingularityatthecrack-tipwillgiveustheloadordisplacementrequiredtoreachthesecriticalvalues.Then,bytrialanderror,wecalibratethecohesiveparameterssuchasthemaximumstressandpenaltystiffness,sothattheelementsfailattheappropriatevalueofappliedloadordisplacement.SinceXFEMandcohesivezonemethodsemploydifferentformulations,thedamageparametersdifferbetweenthem.Itisalsoimportanttobecautiousaboutthefracturecriterionitselfbeforeusingdamageparametersfromoneformulationinanother,becausenotallthefractureformulationssupportallthefracturecriteria.
3.Definedamageevolutionusingtheenergycriterion(selectDamageEvolutionfromthelistofSuboptionsinthematerialeditor).Inthesuboptioneditor,selectEnergyasthetype,BKasthemixedmodebehavior,andsetthepowerto2.284.Enter0.1ineachofthedatafields.
Stepdefinitionandoutput
Thestepdefinitionwillbeeditedtoadjustthetimeincrementationparametersandincludenonlineareffectstoaidconvergence.Theappliedrotationandresultingreactionmomentatoneofthereferencepointswillbewrittenashistorydatatotheoutputdatabasefiletoevaluatethemoment-rotationresponseanddetecttheonsetofcrackgrowth.
1.IntheModelTree,expandtheStepscontaineranddouble-clickStep-1.
2.IntheBasictabbedpageofthestepeditor,toggleonNlgeom.
3.Toaidconvergenceifthespecimenweretobreakinhalf,useautomaticstabilizationwithaconstantdampingfactorequalto0.0001.Toggleoffadaptivestabilization.
4.Setthemaximumnumberofincrementsto250,theinitialtimeincrementsizeto0.01,theminimumtimeincrementsizeto1.e-8,andthemaximumtimeincrementsizeto0.01.
5.WritehistoryoutputofthevariablesUR3,CM3andRM3forthesetright-refPttotheoutputdatabasefile.
6.EditthedefaultfieldoutputrequesttoincludePHISLM(levelsetvaluephi)fromtheFracture/Failuresubsection,andSTATUSXFEM(statusofthexfemelement)fromtheState/Field/User/TimesubsectionasshowninFigureW6–5.Thiswillallowyoutoeasilyevaluatewhentheenrichedelementsfailduringpostprocessing.
FigureW6–5STATUSXFEMfieldoutputrequest
7.Editthegeneralsolutioncontrolstoallowupto10attemptsperincrement:
a.FromthemainmenubaroftheStepmodule,selectOther→GeneralSolutionControls→Edit→Step-1.
b.Inthedialogboxthatappears,selectSpecifytomodifythedefaultsettings.
c.IntheTimeIncrementationtabbedpage,setIAequalto10.
BoundaryConditions
Wewillapplyrotationstoboththereferencepointsinsteadofmomentsasdonepreviously.Displacement-controlledloadingallowsthecracktogrowinastablefashion,whichisnotpossibleunderloadcontrol.First,webeginbysuppressingthetwoloads.
1.IntheModelTree,clickMB3ontheloadnamedleftandselectsuppressfromthemenuthatappears.Repeattheprocedurefortheloadnamedright.
2.Double-clicktheBCscontainertocreateanewboundaryconditionnamedleft-rotationtobeappliedduringStep-1.ChooseDisplacement/RotationasthetypeandclickContinue.
3.Choosethesetleft-refPTasthelocation,andsetUR3to-0.003.
4.Usingthesameprocedure,createanotherboundaryconditionnamedright-rotationappliedtothesetright-refPT,andspecifyUR3tobe0.003.
5.Leavethepreviouslydefinedboundaryconditionnamedrightunchanged.
6.ClickMB3ontheboundaryconditionnamedleftandclickEdit.UncheckthelabelforU1toremovetheconstraintintheX-direction,whichwasusedearliertopreventrigidbodymotion.Wewillpreventitthroughaconstraintequationinthismodelasdiscussedbelow.
Constraints
Theconstraintsdefinedintheprevious