Using-the-Brittle-Cracking-Material-Model-in-Abaqu

CopyrightDassaultSystèmes|(*TENSILEFAILURE),whichisalsoapplicabletobrittlematerials.Inaddition,thebrittlecrackingmodelallowsmoredetailedmodelingofpost-crackingresponsethanthesimpletensilefailuremodel.CapabilitysummaryThebrittlecrackingmodelinAbaqus/Explicit:•Isapplicabletobrittlematerialswhosecompressiveandpre-crackingtensilebehaviorcanberepresentedthroughlinearelasticity•Doesnottrackindividualmacro-cracks,butcapturestheeffectofcrackinganddamageonstressesandstiffnessthroughconstitutivecalculations•Accountsforcrack-inducedanisotropy•IsconceptuallycompatiblewiththeideasoftheAbaqusprogressivedamageframework(i.e.“damageinitiation”and“damageevolution”),eventhoughtheuserinterfaceisdifferent•CanbeviewedascomplementarytotheductiledamagecapabilityinAbaqus/Explicit•Accomplishesthesameend-resulteffectastheAbaqus/StandardXFEMapproach(i.e.throughjumpsindisplacements)thoughthetwomodelingapproachesarequitedifferentCrackinitiation•AsimpleRankinecriterionused:•Crackinitiateswhenthemaximumprincipalstressexceedsthematerialtensilestrength•Multiplecracks(asmanyasthenumberofdirectstresscomponents)caninitiateatapoint,inorthogonaldirections•Thecrackorientationsaregovernedbytheprincipalstressdirections•Post-crackingtensile(ModeI)andshear(ModeII)behaviorcanbeindependentlycontrolled•Conceptuallysimilarto“damageinitiation&evolution”(i.e.materialstiffnessdegradationisspecifiedwithapost-initiation“damageevolution”behavior)Post-crackingbehavior•ModeI(i.e.normal,tensile)responsespecifiedbymaximumstrain,maximumdisplacementorModeIfractureenergy•Strain-baseddefinitioncanintroducemeshsensitivity(duetothesameargumentsasforductiledamage)•Notrecommendedexceptforreinforcedconcrete•Displacement-orenergy-basedspecificationofpost-crackingModeIresponseisrecommended(onecanbederivedfromtheother)CopyrightDassaultSystèmes|•Elementcharacteristiclengthmaybeusedtoconvertstrain-typedatatodisplacement(orenergy-based)definition(again,thisissimilartoductiledamagemodeling)•ModeII(shear)responseisspecifiedbyprovidingshearstiffnessasafunctionofopeningstrainacrossthecrack•Directtabularentries(fractionofinitialstiffnessvs.crackopeningstrain)oranalyticalform(powerlaw)canbeusedElementdeletionoption•Elementsmayberemovedfromthemodeloncethefailurestrain(ordisplacement)isreached•Allowsspecificationofnumberofcracksatamaterialpointthatshouldfailbeforecompletefailureofthematerialoccurs•Usefulinovercomingpossibleexcessiveelementdistortionissueswhenthematerialpointfailsintension•Exercisecautionwhenusingelementremovaloption,sinceitprecludesavailabilityoftheelementtoresistcompressionandhencemaynotberealisticforallbrittledamageapplications!RequiredinputparametersFigure1showsaschematicofthematerialparametersandpropertiesthatareapplicablewhenusingthebrittlecrackingmodel:Figure1:RequiredinputparametersfortheAbaqus/ExplicitbrittlecrackingmodelCopyrightDassaultSystèmes|(Release6.9);there,itissolvedinAbaqus/StandardusingXFEM.Thehalf-symmetricmodelisshowninFigure2.Equalandoppositedisplacementsareprescribedatthetwoendsoftheplate.Fractureparametersused:-Maxprincipalstress:22.0E6Pa-Fracturetoughness(ModesI&II):2.87E3N/m(BK-typemode-dependenceisusedfordamageevolutionintheXFEMversionofthemodel)-Linearshearstiffnessdegradationoveracrackopeningstrainof0.001usedinthebrittlecrackingmodel,alongwithelementdeletion(using“brittlefailure”option)Figure2:Half-symmetrymodelofaplatewithaholeCopyrightDassaultSystèmes|–agoodagreementisobserved.Figure3:Comparisonofload-displacementresponsesfrombrittlecrackingandXFEMapproachesThefollowingpointsshouldbenoted:•CPE4RelementswithenhancedhourglasscontrolwereusedintheExplicitanalysis(XFEMmodelusedfullyintegratedelement)-Defaulthourglasscontrolpredictslowerpeakload,withasomewhatlargerdeviationfromtheXFEMresult•Nosignificantsensitivitytoloadamplitudetype(smoothstepvs.rampvs.constantvelocity)observedinthequasi-static,Explicitresult(allresultsnotshownhere)•Lackofcrackorientationoutputandcrackstatusoutputtotheoutputdatabase(ODB)preventsadirectcomparisonofbrittlecrackingresultwiththeanalyticalappliedstressvs.variationofcracklength•Roughcomparisonusingelementstatuscanstillbemade(notpresentedhere)CopyrightDassaultSystèmes|–BrazilianFractureTestIntheso-calledBraziliantestforbrittlefracture,acylinderiscompressedbetweentworigidplatens(Figure4).Figure4:CylindercompressedbetweentworigidplatensThepeakloadisgivenbythetheoreticalexpression:Fmax=πRfto