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LibertyShipsinWWIIFactsonLibertyShipsTherewere2,751LibertyShipsmanufacturedbetween1941-1945.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,othersbyfractureAgivenmaterialmayfailbyyieldingorfracturestrengthdependingonitspropertiesandthestateofstressFailurecriterionforisotropicmaterialisexpressedastheprincipalnormalstresseshavereachedacriticalfailurestrength(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FracturestressforrealisticmaterialInglis(1913)analyzedfortheflatplatewithanellipticalholewithmajoraxis2aandminoraxis2b,subjectedtofarendstressThestressatthetipofthemajoraxis(pointA)isgivenby

Theratioisdefinedasthestressconcentrationfactor,Whena=b,itisacircularhole,thenWhenbisveryverysmall,Inglisdefineradiusofcurvatureas

Andthetipstressas

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’sEnergybalanceapproachFirstdocumentedpaperonfracture(1920)ConsideredasfatherofFractureMechanicsAAGriffithlaidthefoundationsofmodernfracturemechanicsbydesigningacriterionforfastfracture.Heassumedthatpre-existingflawspropagateundertheinfluenceofanappliedstressonlyifthetotalenergyofthesystemistherebyreduced.Thus,Griffith'stheoryisnotconcernedwithcracktipprocessesorthemicromechanismsbywhichacrackadvances.Griffith’sEnergybalanceapproach(Contd.)Griffithproposedthat‘Thereisasimpleenergybalanceconsistingofthedecreaseinpotentialenergywithinthestressedbodyduetocrackextensionandthisdecreaseisbalancedbyincreaseinsurfaceenergyduetoincreasedcracksurface’Griffiththeoryestablishestheoreticalstrengthofbrittlematerialandrelationshipbetweenfracturestrengthandflawsize‘a’

Griffith’sEnergybalanceapproach(Contd.)Theinitialstrainenergyfortheuncrackedplateperthicknessis(2.14)Oncreatingacrackofsize2a,thetensileforceonanelementdsonellipticholeisrelaxedfromtozero.Theelasticstrainenergyreleasedperunitwidthduetointroductionofacrackoflength2aisgivenby

(2.15)

Griffith’sEnergybalanceapproach(Contd.)Externalwork=(2.16)Thepotentialorinternalenergyofthebodyis

Duetocreationofnewsurfaceincreaseinsurfaceenergyis(2.17)Thetotalelasticenergyofthecrackedplateis

(2.18)

Griffith’sEnergybalanceapproach(Contd.)Thevariationofwithcrackextensionshouldbeminimum

Denotingasduringfracture(2.19)forplanestress(2.20)forplanestrainTheGriffiththeoryisobeyedbymaterialswhichfailinacompletelybrittleelasticmanner,e.g.glass,mica,diamondandrefractorymetals.Griffith’sEnergybalanceapproach(Contd.)GriffithextrapolatedsurfacetensionvaluesofsodalimeglassfromhightemperaturetoobtainthevalueatroomtemperatureasUsingvalueofE=62GPa,Thevalueofas0.15Fromtheexperimentalstudyonsphericalvesselshecalculatedas0.25–0.28However,itisimportanttonotethataccordingtotheGriffiththeory,itisimpossibletoinitiatebrittlefractureunlesspre-existingdefectsarepresent,sothatfractureisalwaysconsideredtobepropagation-(ratherthannucleation-)controlled;thisisaseriousshort-comingofthetheory.ModificationforDuctileMaterialsFormoreductilematerials(e.g.metalsandplastics)itisfoundthatthefunctionalformoftheGriffithrelationshipisstillobeyed,i.e..However,theproportionalityconstantcanbeusedtoevaluategs(providedEisknown)andifthisisdone,onefindsthevalueismanyordersofmagnitudehigherthanwhatisknowntobethetruevalueofthesurfaceenergy(whichcanbedeterminedbyothermeans).Forthesematerialsplasticdeformationaccompaniescrackpropagationeventhoughfractureismacroscopicallybrittle;Thereleasedstrainenergyisthenlargelydissipatedbyproducinglocalizedplasticflowatthecracktip.IrwinandOrowanmodifiedtheGriffiththeoryandcameoutwithanexpressionWheregprepresentsenergyexpendedinplasticwork.Typicallyforcleavageinmetallicmaterialsgp=104J/m2andgs=1J/m2.Sincegp>>gswehave

StrainEnergyReleaseRateThestrainenergyreleaserateusuallyreferredto

Notethatthestrainenergyreleaserateisrespecttocracklengthandmostdefinitelynottime.Fractureoccurswhenreachesacriticalvaluewhichisdeno