第1讲断裂力学导论.

断裂力学第一讲导论：什么是断裂力学？断裂力学研究什么？断裂力学和材料力学有什么联系和区别？从强度理论到断裂理论断裂力学和破坏力学（failure)之间的关系断裂力学•从材料力学、弹性力学发展起来•固体力学中最活跃的研究领域–实用性：大量的工程应用要求研究材料破坏；–跨学科：力学、材料、物理、环境、分析计算方法、测试技术；–科学、工程结合形形色色的断裂现象疲劳断裂脆性断裂断裂的扳手韧性试件的断裂LibertyShipsinWWIIFactsonLibertyShips•Therewere2,751LibertyShipsmanufacturedbetween1941-1945.Crackspropagatedin400oftheseshipsincluding145catastrophicfailures;only2existtodaywhicharesea-worthy.•ThehullsofLibertyShipsfracturedwithoutwarning,mainlyintheNorthAtlantic.•Thesearethefirstshipsmassproducedwithwelds.•ThelowtemperaturesoftheNorthAtlanticcausedthesteeltobebrittle.•Fracturesoccurredmainlyinthevicinityofstressraisers.•Theproblemmaybepreventedbyemployinghigherqualitysteelsandimprovementofthedesignoftheship.TheAlohaBoeing737AccidentOnApril28,1988,partofthefuselageofaBoeing737failedafter19yearsofservice.Thefailurewascausedbyfatigue(multi-sitedamage).TheAlohaBoeing737Accident一个不断发展的学科：强度问题、裂纹问题、断裂问题、疲劳、损伤、分析和规范、结构完整性问题，等等损伤分布与裂纹共生的结构工程问题:•结构承载能力(Structuralsafetyandintegrity).•结构承载时间(Durability).•结构可信度(Reliability).•安全性评估(Confidencelevel).经济问题:•建造成本和获取手段(capitaloracquisitioncost);•运行代价(operationalcost)，废弃代价(disposal/recyclingcost)•成本优化和使用寿命优化(Optimizecapitalcostsandlifecyclecost)结构完整性和寿命评估系统从强度理论到裂纹力学应力状态和主应力参数强度函数•SomeCriteriapredictmaterialsfailurebyyielding,othersbyfracture•Agivenmaterialmayfailbyyieldingorfracturestrengthdependingonitspropertiesandthestateofstress•Failurecriterionforisotropicmaterialisexpressedastheprincipalnormalstresseshavereachedacriticalfailurestrength(c)f(1,2,3)=c常用的强度准则•最大主应力准则；•最大剪切应力准则；•最大主应变准则；•最大总应变能准则；•最大畸变应变能准则；•最大VonMises应力准则；•Etc.孔洞导致应力集中-Inglis理论2a2bAArFracturestressforrealisticmaterialInglis(1913)analyzedfortheflatplatewithanellipticalholewithmajoraxis2aandminoraxis2b,subjectedtofarendstressThestressatthetipofthemajoraxis(pointA)isgivenbyTheratioisdefinedasthestressconcentrationfactor,Whena=b,itisacircularhole,thenWhenbisveryverysmall,InglisdefineradiusofcurvatureasAndthetipstressasm2a1bmtktk3.2barma12rInglis理论推广到裂纹玻璃纤维的断裂强度（示意图）Griffith关于裂纹扩展的概念Griffith’sEnergybalanceapproach•Firstdocumentedpaperonfracture(1920)•ConsideredasfatherofFractureMechanicsAAGriffithlaidthefoundationsofmodernfracturemechanicsbydesigningacriterionforfastfracture.Heassumedthatpre-existingflawspropagateundertheinfluenceofanappliedstressonlyifthetotalenergyofthesystemistherebyreduced.Thus,Griffith'stheoryisnotconcernedwithcracktipprocessesorthemicromechanismsbywhichacrackadvances.Griffith’sEnergybalanceapproach(Contd.)2aXYBGriffithproposedthat‘Thereisasimpleenergybalanceconsistingofthedecreaseinpotentialenergywithinthestressedbodyduetocrackextensionandthisdecreaseisbalancedbyincreaseinsurfaceenergyduetoincreasedcracksurface’Griffiththeoryestablishestheoreticalstrengthofbrittlematerialandrelationshipbetweenfracturestrengthandflawsize‘a’f2aXYBGriffith’sEnergybalanceapproach(Contd.)Theinitialstrainenergyfortheuncrackedplateperthicknessis(2.14)Oncreatingacrackofsize2a,thetensileforceonanelementdsonellipticholeisrelaxedfromtozero.Theelasticstrainenergyreleasedperunitwidthduetointroductionofacrackoflength2aisgivenby(2.15)2iAUdA2Ea1a20U4dxvdxwheredisplacementvasinEusingxacos22aaUEGriffith’sEnergybalanceapproach(Contd.)2aXYBExternalwork=(2.16)ThepotentialorinternalenergyofthebodyisDuetocreationofnewsurfaceincreaseinsurfaceenergyis(2.17)Thetotalelasticenergyofthecrackedplateis(2.18)wUFdy,whereF=resultantforce=area=totalrelativedisplacementpiawU=U+U-UsU=4a222tsAaUdAFdy4a2EEP1P2(a)(a+da)Load,PDisplacement,vCrackbeginstogrowfromlength(a)Crackislongerbyanincrement(da)22aaUEvGriffith’sEnergybalanceapproach(Contd.)Energy,UCracklength,aSurfaceEnergyU=4as22aaUEElasticStrainenergyreleasedTotalenergyRates,G,sPotentialenergyreleaserateG=Syrfaceenergy/unitextension=Ua¶¶Cracklength,aacUnstableStable(a)(b)(a)VariationofEnergywithCracklength(b)VariationofenergyrateswithcracklengthThevariationofwithcrackextensionshouldbeminimumDenotingasduringfracture(2.19)forplanestress(2.20)forplanestraintU2tsdU2a040daEf1/2sf2Ea1/2sf22Ea(1)TheGriffiththeoryisobeyedbymaterialswhichfailinacompletelybrittleelasticmanner,e.g.glass,mica,diamondandrefractorymetals.Griffith’sEnergybalanceapproach(Contd.)GriffithextrapolatedsurfacetensionvaluesofsodalimeglassfromhightemperaturetoobtainthevalueatroomtemperatureasUsingvalueofE=62GPa,Thevalueofas0.15Fromtheexperimentalstudyonsphericalvesselshecalculatedas0.25–0.28However,itisimportanttonotethataccordingtotheGriffiththeory,itisimpossibletoinitiatebrittlefractureunlesspre-existingdefectsarepresent,sothatfractureisalwaysconsideredtobepropagation-(ratherthannucleation-)controlled;thisisaseriousshort-comingofthetheory.2s0.54J/m.1/2s2EMPam.1/2sc2EaMPam.ModificationforDuctileMaterialsFormoreductilematerials(e.g.metalsandplastics)itisfoundthatthefunctionalformoftheGriffithrelationshipisstillobeyed,i.e..However,theproportionalityconstantcanbeusedtoevaluates(prov