Crack propagation and coalescence(5)

RFPA

C.A.Tang,S.Q.Kou/EngineeringFractureMechanics61(1998)311±324315

thestrengthparameterofthecorrespondingelement.Thebrighterthecoloris,thehigherwillbethevalueoftheelasticmodulusorthenormalizedshearstress.

3.Numericalresultsanddiscussions

ThesimulationresultsrelatedtothemodelinFig.1(a)foraxialcompressionwithoutcon®ningstressareshowninFig.2.Itisshownthat,underuniaxialcompression,thelarger¯awsnucleatedcracks®rst.AsshowninstagebinFig.2,wing-cracksinitiatedfromthetipofthe2nd¯aw,thenfrom3rd,6thand7th¯awsinstagec.Thesecracksgrewoutoftheirownplanesinastablemanner(staged),buttherateofgrowthincreaseddramaticallyafterasuitablelengthwasattained(stagee).Inthisstage,thecrackinteractionandcoalescenceoccurredbetweenthe3rdand4th¯awsandbetweenthe5th,6thandthe8th¯aws.Thecoalescencebetweenthe3rdand4th¯awsandbetween5thand6th¯awswascausedbythetensionfailure,whereasthecoalescencebetweenthe6thand8th¯awswascausedbyshearfailure.Thecrackpropagationandcoalescence®nallyledtoanunstablefailurebyaxialsplittingasshowninstageg-1tog-3,whilemanyofthesmall¯awsdidnotevennucleateanywing-cracks(stageg-1).Itisworthnotingthatthefractureprocessfromg-1tog-3inFig.2waswithinonestep,whichmeansthatnoextraexternalenergywasneededforthisprocess.Althoughtheoveralldirectionofthecrackpropagationtendedtobeparalleltotheloadingdirection,somedetailsofthecrackpropagationpathsareinterestingtonote.ItcanbeseenfromstageeinFig.2that,afterthecoalescenceofthe5thand6th¯aws,thewing-crackfromthetipof5th¯awcontinuedtopropagate,curvedtowardsanearbysmall¯aw(stagef)andwentthroughthe¯aw,stillbykeepingitsoriginalpropagationdirection(stageg-1tog-3).Asimilarprocesswasobservedforthecrackinitiatedfromthetipofthe4th¯aw.Itisfoundthatgenerallythecracksinitiatedfromthe¯awtipspropagatedina®naldirectionparalleltotheaxialload,butsometimesthepathsofsomecracksdeviatedduetoanearby¯aw(seethe1st,4thandthe5th¯awinstageg).Infact,thegrowthofthewing-crackbecameunboundedwhenweappliedasmalltensilestressnormaltotheaxialcompressiondirection.Whentheaxialloadreached8.1MPa,thecracksinitiatedatthetipsofthe3rd¯awsuddenlycoalescedwiththe1stand4th¯awsandpropagatedinanunstablemanner,joiningthesmall¯awsandleadingtoaxialsplitting(seestagee-1toe-5inFig.3).Theresultsrevealthattheaxialcompressionrequiredtoinduceunstablegrowthofcrackextensionsdecreasesdramaticallyasaslightlateraltensionisapplied.InuniaxialloadingconditionasshowninFig.2,thecorrespondingloadtoinitiateaxialsplittingfailureis16.3MPa,whichistwicetheloadinthecasewiththelateraltension(Fig.3).Theseresultsalsosupportmanyresearchers'explanationstotheexperimentallyobservedphenomenonofaxialsplittingundercompressionofrocksamplesthatisbelievedtobetheresultoftensioncracksdevelopedatthetipsofthepre-existing¯aws[24,25].Thesituationchangedcompletelywhenlateralcompressivestresswaspresent.Forthenumericalsamplewithexactlythesamegeometryofthepre-existing¯awsasinFigs.2and3,anaxialcompressionwithalateralpressureof6Mpawasapplied.AsshowninFig.4,atthebeginning,asinthecaseoftheuncon®nedsample,larger¯awsnucleatedwing-cracks(stagedinFig.4).However,thesecracksweresoonarrested,andsomeofthesmaller¯awsnucleated