Analytical approach to the strain rate effect on the dynamic tensile strength of brittle materials

InternationalJournalofImpactEngineering37(2010)942e945

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Analytical approach to the strain rate effect on the dynamic tensile strength of brittle materials

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ShortCommunication

Analyticalapproachtothestrainrateeffectonthedynamictensilestrengthofbrittlematerials

Zhuo-ChengOu*,Zhuo-PingDuan,Feng-LeiHuang

StateKeyLaboratoryofExplosionScienceandTechnology,SchoolofMechatronics,BeijingInstituteofTechnology,Beijing100081,PRChina

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Articlehistory:

Received8March2009Receivedinrevisedform31December2009

Accepted23February2010Availableonline3March2010Keywords:StraineffectBrittlematerialsFailurecriteriaDynamicloadings

abstract

Anexplicitmathematicalexpressionforthedynamicload-carryingcapacityofbrittlematerialsunderdynamictensileloadsisderivedbasedonakindofstructural-temporalfailurecriterion[1]andtheone-dimensionallongitudinalplanewavepropagationmodel.Itisshownthatthedependenceofthedynamicload-carryingcapacityonthestrainratecanbedeterminedonlybythestaticmaterialparameterssuchastensilestrength,density,incubationtime,criticalfailurelengthandconstitutiveconstants,whichveri esthatthewellknownstrainrateeffectonmaterialstrengthcanbeconsideredasanstructuralratherthanmaterialbehavior,aspointedoutbyCotsovosandPavlovi c[2]recently.Moreover,itisfoundthat,underconstantstrainrate,thedynamicload-carryingcapacitydependsalsoontheamplitudesofimposedboundaryloads,whichexplains,toasigni cantextent,thescatterthatcharacterizestheavailableexperimentaldata.Furthermore,thederivedexpressioncanalsobeusedasafoundationoftheoreticalanalysesonotherproblemsinvolvingthestrainrateeffectsuchasdynamicsizeeffect,dynamicfailureofquasi-brittlematerialsandcomposites.

Ó2010ElsevierLtd.Allrightsreserved.

1.Introduction

Asiswellknown,mostofmaterialscanbearhigherdynamicloadingswithoutfailurethanquasi-staticones,whichisusuallyknownasthestrainrateeffectuponstrengthofmaterial.Thestrainrateeffectiscrucialwhendealingwithproblemsinvolvingdynamicloadingssuchasinthe eldsofpenetrationmechanics,explosionmechanicsandhighvelocitycollision.Overthepastdecades,anumberofresearchpapers,seeforexamplesreferences[3e8],havebeenpublishedonboththetheoreticalandtheexperimentalstudiesofthestrainrateeffectforvariousmaterials,andsomedynamicfailurecriterionsareestablished.However,uptonow,thestrainrateeffectsarestillfarfromtobewellunder-stood.Ontheonehand,mostofthedynamicfailurecriterionsareobtainedbythecurve ttingofexperimentaldata,whichmaynotgiveresultsthatareapplicableinallsituations.Ontheotherhand,fromthetheoreticalpointofview,thephysicalmechanismaswellasthemathematicalexpressionofthestrainrateeffectsisstillunclear.Amongthosepreviousstudiesonthestrainrateeffect,twocommonlyacceptedviewpointsemerged.Onewastosaythatmaterialfailureoccursinstantaneouslywhenthelocalstressreachesacriticalstress(thedynamicfailurestrengthofmaterials);thedynamicfailurestrengthisassumedtobedependenttothe

*Correspondingauthor.Tel.:þ8601068915921;fax:þ8601068461702.E-mailaddress:zcou@http://www.51wendang.com(Z.-C.

Analytical approach to the strain rate effect on the dynamic tensile strength of brittle materials

Ou).0734-743X/$eseefrontmatterÓ2010ElsevierLtd.Allrightsreserved.doi:10.1016/j.ijimpeng.2010.02.003

localstrainrate,andtherelationbetweenthedynamicfailurestrengthandthestrainratewastakenasanintrinsicpropertyofmaterials,whichcanbederivedexperimentally.Thisviewpointleadstotheso-calledcriticaldynamicstrengthcriterion,whichisanaturalextensionoftheclassicalmaximumstresscriterionunderquasi-staticloadingsandhasbeenusedwidelyinmanyengi-neeringapplications.However,itshouldbestressedthat,ontheonehand,thedynamicfailurestrengthcriteriondoesnotre ectdirectlytimeeffectsonthedynamicresponseofmaterials,andtime-dependentphenomenasuchasinertialandwaveeffectsareusuallycrucialintheproblemsofdynamicmechanics.Ontheotherhand,thefactitiousassumptionthatthedynamicfailurestrengthisdependentonthestrainratemaylackthenecessaryphysicalbasis,whichcanbepartlyveri edtobeproblematicbythescatterthatcharacterizestheavailableexperimentaldata.Theotherpointofviewwastosaythatthedynamicfailurestrengthisnotanintrinsicpropertyofmaterials(and,insteadofthedynamicfailurestrength,anewnomenclatureissuggestedinthispapertermedthedynamicload-carryingcapacitytoavoidambiguity),butjustacomputablecharacteristic,whichcanbedeterminedde nitelybystaticmate-rialparameters,imposedboundaryloadingsandstructuralgeom-etry.CotsovosandPavlovi c[2]investigatedthedynamicfailureofconcretebythenumerical niteelementmethodusingaquasi-staticconstitutivemodelaswellasstaticmaterialstrength,andclaimedthatthenumericalresultswereconsistentwiththepublishedexperimentaldata.Thissecondviewpointattributesthe

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