斷裂力學

第一講導論：什么是斷裂力學？斷裂力學研究什么？斷裂力學和材料力學有什么聯(lián)系和區(qū)別？從強度理論到斷裂理論斷裂力學和破壞力學（failure)之間的關系斷裂力學從材料力學、彈性力學發(fā)展起來固體力學中最活躍的研究領域實用性：大量的工程應用要求研究材料破壞；跨學科：力學、材料、物理、環(huán)境、分析計算方法、測試技術；科學、工程結合形形色色的斷裂現(xiàn)象疲勞斷裂脆性斷裂斷裂的扳手韌性試件的斷裂LibertyShipsinWWIIFactsonLibertyShipsTherewere2,751LibertyShipsmanufacturedbetween1941-1945.Crackspropagatedin400oftheseshipsincluding145catastrophicfailures;only2existtodaywhicharesea-worthy.ThehullsofLibertyShipsfracturedwithoutwarning,mainlyintheNorthAtlantic.Thesearethefirstshipsmassproducedwithwelds.ThelowtemperaturesoftheNorthAtlanticcausedthesteeltobebrittle.Fracturesoccurredmainlyinthevicinityofstressraisers.Theproblemmaybepreventedbyemployinghigherqualitysteelsandimprovementofthedesignoftheship.TheAlohaBoeing737AccidentOnApril28,1988,partofthefuselageofaBoeing737failedafter19yearsofservice.Thefailurewascausedbyfatigue(multi-sitedamage).TheAlohaBoeing737Accident一個不斷發(fā)展的學科：

強度問題、裂紋問題、斷裂問題、疲勞、損傷、分析和規(guī)范、結構完整性問題，等等損傷分布與裂紋共生的結構工程問題:結構承載能力(Structuralsafetyandintegrity).結構承載時間(Durability).結構可信度(Reliability).安全性評估(Confidencelevel).經濟問題:建造成本和獲取手段(capitaloracquisitioncost);運行代價(operationalcost)，廢棄代價(disposal/recyclingcost)成本優(yōu)化和使用壽命優(yōu)化(Optimizecapitalcostsandlifecyclecost)結構完整性和壽命評估系統(tǒng)從強度理論到裂紋力學應力狀態(tài)和主應力參數(shù)強度函數(shù)SomeCriteriapredictmaterialsfailurebyyielding,othersbyfractureAgivenmaterialmayfailbyyieldingorfracturestrengthdependingonitspropertiesandthestateofstressFailurecriterionforisotropicmaterialisexpressedastheprincipalnormalstresseshavereachedacriticalfailurestrength(c)

f(1,2,3)=c常用的強度準則最大主應力準則；最大剪切應力準則；最大主應變準則；最大總應變能準則；最大畸變應變能準則；最大VonMises應力準則；Etc.孔洞導致應力集中-Inglis理論FracturestressforrealisticmaterialInglis(1913)analyzedfortheflatplatewithanellipticalholewithmajoraxis2aandminoraxis2b,subjectedtofarendstressThestressatthetipofthemajoraxis(pointA)isgivenby

Theratioisdefinedasthestressconcentrationfactor,Whena=b,itisacircularhole,thenWhenbisveryverysmall,Inglisdefineradiusofcurvatureas

Andthetipstressas

Inglis理論推廣到裂紋玻璃纖維的斷裂強度（示意圖）Griffith關于裂紋擴展的概念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