A Review of Dynamic Experimental Techniques and Me

REVIEWPAPERAReviewofDynamicExperimentalTechniquesandMechanicalBehaviourofRockMaterialsQ.B.Zhang•J.ZhaoReceived:10March2013/Accepted:22July2013/Publishedonline:13September2013Springer-VerlagWien2013AbstractThepurposeofthisreviewistodiscussthedevelopmentandthestateoftheartindynamictestingtechniquesanddynamicmechanicalbehaviourofrockmaterials.Thereviewbeginsbybrieflyintroducingthehistoryofrockdynamicsandexplainingthesignificanceofstudyingtheseissues.Loadingtechniquescommonlyusedforbothintermediateandhighstrainratetestsandmea-surementtechniquesfordynamicstressanddeformationarecriticallyassessedinSects.2and3.InSect.4,methodsofdynamictestingandestimationtoobtainstress–straincurvesathighstrainratearesummarized,followedbyanin-depthdescriptionofvariousdynamicmechanicalprop-erties(e.g.uniaxialandtriaxialcompressivestrength,tensilestrength,shearstrengthandfracturetoughness)andcorrespondingfracturebehaviour.Someinfluencingrockstructuralfeatures(i.e.microstructure,sizeandshape)andtestingconditions(i.e.confiningpressure,temperatureandwatersaturation)areconsidered,endingwithsomepopularsemi-empiricalrate-dependentequationsfortheenhance-mentofdynamicmechanicalproperties.Section5dis-cussesphysicalmechanismsofstrainrateeffects.Section6describesphenomenologicalandmechanicallybasedrate-dependentconstitutivemodelsestablishedfromtheknowledgeofthestress–strainbehaviourandphysicalmechanisms.Section7presentsdynamicfracturecriteriaforquasi-brittlematerials.Finally,abriefsummaryandsomeaspectsofprospectiveresearcharepresented.KeywordsRockmaterialStrainrateExperimentaltechniquesMechanicalbehaviourDynamicloadingRockdynamicsDynamicfractureListofSymbolsaCracklengthAB,As,AshearCross-sectionalareaofthebarandthespecimen,andshearareaofthespecimenA(v)UniversalfunctionBs,BwsThicknessofthespecimenandwallthicknessofthetubespecimenCB,CsLongitudinalwavespeedsofthebarandthespecimenCL,CS,CRLongitudinalwavespeed,shearwavespeedandRayleighwavespeeddGrainsizeofthespecimenDB,DsDiameterofthebarandthespecimenEB,EsYoung’smodulusofthebarandthespecimenE,EdQuasi-staticanddynamicYoung’smodulusEmax,Emin,EavgMaximum,minimumandaverageYoung’smodulusofthespecimenfFrequencyfactorf(a/R),f(a/W),f(S/2R)GeometriccorrectionfunctionFReturnforceQ.B.ZhangJ.ZhaoE´colePolytechniqueFe´de´raledeLausanne(EPFL),SchoolofArchitecture,CivilandEnvironmentalEngineering,LaboratoryofRockMechanics(LMR),BaˆtimentGCD0-407,Station18,1015Lausanne,Switzerlande-mail:qianbing.zhang@epfl.ch;[e-mail](&)DepartmentofCivilEngineering,MonashUniversity,Building72,Clayton,Melbourne,VIC3800,Australiae-mail:[e-mail]123RockMechRockEng(2014)47:1411–1478DOI10.1007/s00603-013-0463-yGdCDynamicfractureenergyhInitialdistancebetweentwoplates_hVelocityoftwoplatesintheStefaneffectequationHLoadinghistoryKKineticenergyofthefragmentKIC,KIICModeIandIIfracturetoughnessKId,KIDDynamiccrackinitiationandpropagationtoughnessKdynIðtÞDynamicstressintensityfactor_KdynILoadingrateoffracturetoughnessLs,LstrLengthofthespecimenandthestrikerbarnNumberofreflectionsP(t)ApplieddynamicloadP1,P2Forcesatbar–specimeninterfacesPcConfiningpressureQActivationenergyRAirconstantinArrheniusequationRRadiusofthespecimenR(t)RatioofstressdifferenceSSpanofbendingt0TransittimetotravelthroughthespecimenoncetequilTimetoreachstressequilibriumtfTimetofracturetIn.DurationoftheincidentpulsetriseRisetimeofthestresshistoryTTemperatureTdDynamictorque_u1,_u2Velocitiesattheincidentbar–specimenandspecimen–transmittedbarinterfacesv,vlim,vmaxCrackpropagationvelocity,limitofvelocityandmaximumvelocityv1,v2VelocitiesoffragmentsVVolumeofliquidVejectEjectionvelocityoffragmentVpParticlevelocityDVpb‘Pull-back’velocityVstrVelocityofthestrikerWWidthofthespecimenWFDFractureanddamageenergyWIn.,WRe.,WTr.Strainenergiesoftheincident,reflectedandtransmittedstresswavesWsEnergyabsorbedbythespecimenxfDistancefromfreeendtofracturepositionGreekSymbolsaAngleofthewedgecShearstrain_cðtÞShearstrainratee1AxialstrainefStraintofailureeIn:,eRe:,eTr:Incident,reflectedandtransmittedstrainsmeasuredbystraingaugesonthebars_e,_elim,_ecri,_emaxStrainrate,limitofstrainrate,criticalstrainrateandmaximumstrainrategViscosityofliquid_h1ðtÞ,_h2ðtÞAngularvelocitiesofthespecimenendslFrictioncoefficientbetweenthewedgeandthebarmPoisson’sratioqsDensityofthespecimenrdðtÞDynamicstresshistoryrd,rsDynamicstrengthandquasi-staticstrengthrspallSpallingstrengthrt,rtdQuasi-staticanddynamictensilestrengthrtc,rtcdQuasi-staticanddynamictriaxialcompressivestrengthruc,rucdQuasi-staticanddynamicuniaxialcompressivestrengthrRe:t;maxMaximumreflectedtensilestressrucd=rucNormalizeddynamicuniaxialcompressivestrengthr1r3Differentialstress_rStressratesðtÞShearstresss,sdQuasi-staticanddynamicshearstrengthxAngularvelocityoffragmentAbbreviationsASTMAmericanSocietyforTestingandMaterialsBDBraziliandiscCBChevronbendCCNBDCrackedchevronnotchedBDCCNSCBCrackedchevronNSCBCDMContinuumdamagemechanicsCEBComite´Euro-InternationalduBe´tonCODCrackopeningdisplacementCPGCrackpropagationgaugeCRDCommissiononRockDynamicsCSRConstants