Crack propagation and coalescence(12)

RFPA

322C.A.Tang,S.Q.Kou/EngineeringFractureMechanics61(1998)311±324

Fig.7.Stress±strainrelationforbrittlerockcontaininginhomogeneitiesunderuniaxialcompression(simulatedwithRFPA2D).

process.Thefailuremodeseemstoindicatethatthefailureinaxialcompressionofbrittlematerialsisthe®nalmanifestationofearliertensilecrackgrowthinducedunderoverallcompression.

4.Conclusions

Twoparticularcasesconcerningcrackpropagationandcoalescenceinbrittlematerialsaremodeledbyusingarockfailureprocessanalysiscode,RFPA2D.Numericalsimulationsreproducedqualitativelythegeneralobservationsmadeinlaboratoryexperiments.Themostsigni®cantresultthatemergedfromthenumericalsimulationisthee ectoflateralstressonthefailuremechanisms.Thenumericalsimulationsofsampleswithsuitablyoriented,pre-existing¯awsunderaxialcompressionshowthatmicrocracksmaynucleateattipsofthe¯awsandgrowinthedirectionoftheaxialload.However,thepresenceofslightlateraltensionresultsinout-of-plane,curvedcrackgrowthinanunstablemannerwhenasuitablecriticallengthwasattained.Inthatcase,thecracksgrowalmostspontaneouslyandwithoutanincreaseintheaxialcompression,leadingtothecollapseofthesampleinthemannerofaxialsplitting.Ontheotherhand,nounstablegrowthoccursifalateralcon®ningpressureisappliedtothesample.Asamatteroffact,thecracksinitiatedfromthe¯awtipsstoppropagationafterreachinga®nitelength.Itiscon®rmedthat,underaxialcompression,thenucleation,growth,interactionandcoalescenceofmicrocracksarethedominantcontrollingsourcesthatleadstomacroscopicfailureofrocks.However,thecoalescenceofthewing-cracksmaybeineithertensilemodeorshearmode,oracombinationofbothmodes.Thenumericalresultsshowqualitativelyareasonablygoodagreementwithreportedexperimentalobservationsforthesampleswithsimilar¯awarrangements,andsupporttheexperimentallyinferredconclusionthatbothsplittingandshearfailuresoftenobservedinexperimentsinaxialcompressionofrocksandotherbrittlematerialsarethe®nalmanifestationofearliertensilecrackgrowthinducedunderoverallcompression.TheuseofRFPA2Dtosimulateamorerealisticmaterialcontaininginhomogeneitiesongrainscaleshowsthatthefailuremodestronglydependsonthemechanicalandgeometricpropertiesofthegrainsandinclusions.Theresultagainshowsthatthefailureof

brittle