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NumericalsimulationofdynamicfractureofconcretethroughuniaxialtensionandL-specimenJoškoOzˇbolta,AkanshuSharmaa,b,⇑aInstituteforConstructionMaterials,UniversityofStuttgart,Stuttgart70569,GermanybReactorSafetyDivision,BhabhaAtomicResearchCentre,Mumbai400085,IndiaarticleinfoArticlehistory:Received26September2011Receivedinrevisedform9February2012Accepted19February2012Keywords:DynamicfractureConcreteUniaxialtensionCrackbranchingCrackpropagationabstractDynamicfractureofconcreteisnumericallyevaluatedusinguniaxialtensionandL-speci-men.Previousworkbyauthorsdemonstratedinterestingaspectssuchascrackbranchingbeyondthresholdcrackspeed.Uniaxialtensilebehaviourofconcreteunderdynamicloadsisdifficulttostudyevennumericallyduetolocalproblemsnearloadingpoints.Aspecimenisdesignedtonumericallyassessthedynamictensilebehaviourthatseemstobepracticalenoughforcarryingoutexperimentalstudiesaswell.Theresultsdemonstratevariousphe-nomenasuchascrackbranching,interceptingandre-branching.DynamicbehaviourofL-specimenshowsthatthedirectionofcrackpropagationstronglydependsondisplacementrate.2012ElsevierLtd.Allrightsreserved.1.IntroductionUniaxialtensilebehaviourofconcreteinvariablydominatesthebehaviourofconcretespecimensaswellasstructuralele-ments.Therefore,inordertounderstandthedynamicfractureofconcrete,itisessentialtounderstandthedynamicfractureofconcreteunderuniaxialtension.However,toexperimentallystudytheuniaxialtensilebehaviourofconcreteisdifficultevenunderstaticloads,andthereforeindirectmethodssuchasBraziliantestsandcompacttensiontestsareoftenemployed.Evennumerically,itisdifficulttoevaluatethedirectdynamicuniaxialtensilebehaviourofconcretesince,athighloadingrates,thefailurealwaysoccurslocally,neartheloadingpoints.Therefore,underdynamicloads,theproblemisstudiedthroughindirecttestssuchassplitHopkinsonbartests[2–11],withtheunderlyingconceptoftheexperimentinvolvedinacompressionwavefromtheimpactthattravelsalongthespecimenandgetsreflectedattheendofthespecimenasatensionwave.However,sofarthetestshavebeenmostlyorientedtostudycertainparameterssuchastensilestrengthasafunctionofloadingrateinsteadofstudyingthecompletefracturebehaviour.Fig.1showstheresultsobtainedbyvariousresearchersontheeffectofloadingrateontensilestrengthofconcreteassummarizedbyMalvarandRoss[12].L-specimenposesaveryinterestingproblemfromthepointofviewofcrackpropagationandfractureofconcreteandisoftenusedtodemonstratethecapabilitiesofmaterialmodelsaswellasthephenomenonofmeshsensitivity[13,14].Thisisarelativelysimpletestsetupbuttotheknowledgeofauthors,therehasbeennoexperimentalornumericalstudytoassessthedynamicbehaviourofthespecimen.Inthiswork,numericalinvestigationsarecarriedoutonauniaxialtensionspecimenandanL-specimenastested,forquasi-staticloadingconditions,byWinkleretal.[13]subjectedtohighrateloading.Theanalysisiscarriedoutusingthe3DFEcodeMASAbasedonthemicroplanemodelwithrelaxedkinematicconstraint[15],developedatInstitutefor0013-7944/$-seefrontmatter2012ElsevierLtd.Allrightsreserved.doi:10.1016/j.engfracmech.2012.02.013⇑Correspondingauthorat:ReactorSafetyDivision,BhabhaAtomicResearchCentre,Mumbai400085,India.E-mailaddresses:akanshu@barc.gov.in,akanshusharma@yahoo.co.in(A.Sharma).EngineeringFractureMechanics85(2012)88–102ContentslistsavailableatSciVerseScienceDirectEngineeringFractureMechanicsjournalhomepage:[1,16,18–20]thattheratesensitiveNomenclaturec0,c2materialrateconstants,calibratedbyfittingtestdataC1,C2constantsdeterminedfromexperimentsCRconstantdependingonpoisson’sratioDfractureenergyEeffectiveYoung’smodulusofbulkmaterialE0initialenergyattimet0fccylindercompressivestrengthofconcretefddynamicstrengthfsstaticstrengthundermonotonicloadftuniaxialtensilestrengthofconcreteGcshearmodulusGFfractureenergykiandmidirectionsofshearmicroplanecomponentsninormalvectorcomponentsSsurfaceoftheunitradiusspherescrspacingoftheparallelcracksTkineticenergyVdeformationenergyvRRayleighwavespeedWexternalwork_wcrackopeningratioaparameterdependentonloadandtypeofmaterialandthewayofloadingdijKroneckerdeltaeaveragemacroscopicstrainnormaltothedirectionofparallelcracks_estrainrateeijmacroscopicstraintensor_eijcomponentsofthemacroscopicstrainratetensor(indicialnotation)qcspecificweightofthematerialrstressatdynamicloadr0stressatstaticload_rstressrateunderdynamicload_r0stressrateunderstaticloadrD,eDdeviatoricstress,straincomponentsofthenormalstressonmicroplanerK,rM,eK,eMtwoshearstress–straincomponentsonmicroplanerN,eNnormalstress,straincomponentsonmicroplanerV,eVvolumetricstress,straincomponentsofthenormalstressonmicroplaneFig.1.Strain-ratedependenceforconcreteintension,basedonMalvarandRoss.J.Ozˇbolt,A.Sharma/EngineeringFractureMechanics85(2012)88–10289microplanemodelalongwiththedynamicfiniteelementanalysiscanpredictthedynamicbehaviourofconcretespecimensaswellasstructuralelementsincludingtheirresistance
本文标题:Numerical simulation of dynamic fracture of concre
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