FRACW06ThreePointXFEM.docx

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