Crack propagation and coalescence(2)

RFPA

312C.A.Tang,S.Q.Kou/EngineeringFractureMechanics61(1998)311±324

1.Introduction

Numerousexperimental[1±8]andtheoretical[3,6,9±11]e ortshavebeendevotedtotheunderstandingofthecrackinitiation,propagation,andcoalescenceofpre-existing¯awsinbrittlematerials.Uniaxialcompressionexperimentswitharock-likemodelmaterialcontainingdouble¯awsconductedbyReyesandEinstein[6]showedthatpre-existingnon-persistent¯awscoalesceintwodi erentmodes:(1)ifthepre-existing¯awsoverlap,thecoalescenceoccursthroughinterconnectionofthedevelopingwingcracks;(2)ifthepre-existing¯awsdonotoverlap,coalescenceoccursthroughsecondarycracks.FurtherexperimentalworkonthistopichasbeencarriedoutbyBobetandEinstein[7],andShenetal.[8].Experimentswithsamplescontainingmultiplepre-existing¯awswerecarriedoutbyNemat-NasserandHorii[3].Itwasshownthatforacertainoverallorientationofthe¯awsthegrowthoftheout-of-planecracksmaybecomeunstable,leadingtopossiblemacroscopicfaulting.Althoughfracturemechanicsprovidesafundamentalbasisinunderstandingcrackbehavior,theuseoffracturemechanicstodescribethepropagationandcoalescenceofmultiplecracksingeomaterialsisarduous.Asamatteroffact,muchofthetheoreticalstudyoffractureisfocusedonanindividualcrack.Althoughthisapproachismostsuccessfulwhenfractureoccursbythepropagationofasinglecrack,forrockmechanicsorcivilengineeringandgeophysicalproblems,theanalysisofmaterialfailuremodescharacterizedbymultiplecrackingeventscanbetreatedthroughdi erentapproaches.Severalnumericalmodelshaveemergedasusefultoolstosimulatefailurebymultiplecrackingeventsandtostudythegeneralbehaviorsofbrittlefractures[3,6,9±18].Forexample,bycombiningasmearedcrack/damagemechanicsapproachwithastrain-basedfailurecriterion,coalescencethroughsecondarycrackswasanalyzedbyReyesandEinstein[6].SimilarworkwasperformedbyShenandStephansson[10]byusingtheDDM(discontinuousdeformationmethod)modelwithamodi®edG-criterion.IntheworkofNemat-NasserandHorri[3],aclosedformsolutionwasobtainedforaregularsetof¯aws,assumingthatthepre-existingstraight¯terontheyimprovedtheirmodeltoconsiderthepossiblecurvedbranchingpath[4].ZaitsevandWittmann[16]havepublishedapaperoncrackpropagationinthespecimenwithacompressiveloadbutwithoutconsiderationoftheinteractionamongthedistributedcracks.WithintheframeworkofBEMandDDM,crackpropagation,interactionandcoalescence,andthesizee ectsonstrengthforbrittlespecimenhavebeenstudiedbyCarpinterietal.[17].AdamagemechanicsmodelhasbeenusedbyHanandSwoboda[18]tosimulateasetof¯awsdistributedregularlywiththesameorientation.Inthepresentpaper,twoparticularcasesconcerningcrackpropagation,interactionandcoalescenceinbrittlematerialsarestudiedwithanumericaltoolcalledtherockfailureprocessanalysiscode,RFPA2D,developedrecentlybyTang[19].Thepurposeofthisapproachistoaccentuatethefundamentallydi erentmechanismswhichmaybeinvolvedinfailureeitherintensionorshearmode,dependingonthecon®nementconditions.MotivatedbytheobservationsofthemodelexperimentsconductedbyHoriiandNemat-Nasser[4],numericalmodelsamplescontainingpre-existingmultiple¯awssimilartothesetupintheirexperimentshavebeenadopted.The¯awsmaybepre-existingcracks,orsomeirregularinhomogeneitiessuchasweakinclusions.Fromthemathematicalpointofview,thisrepresentsaratherdi cultprobleminnumericalmodeling,whichhasnotbeendealtwithbefore.Thesecondsimulated