12024/10/27

Thestrengththeorywhichhavecrackinbody22024/10/27GOAL:recountconventionalstrengththeoryofnonindividualbody.Fundamentalassumptionofelasticandplastictheory.Basicapproachandequationtosolvethestress.Descriptionandanalysisofonepoint’sstressstate.APPLY：strengthdesignCalculateexternalforce；Countonepoint’sstressstate（theoryofelasticityandplasticity）；Verdictapoint’sstressiscriticalstate(yieldordestroy)ornotaccordingtothestrengthcondition.ATTENTION：Generallyusedforchecking.Briefsummaryoffirstfourchapters32024/10/27UncertaintiesduringstressanalysisIndeterminacyofexternalload.Indeterminacyduringstressanalysis.Indeterminacyofmaterialcharacteristics.Practicalapplication:Securitycoefficientwhichbiggerthanone.Design’sbasicideanonindividualbodyneverdamageProblemsandsolvesduringstrengthdesign

42024/10/27Realityofengineeringdamage52024/10/27Whoisresponsiblefortheaircrash?In1979,therewasalargestdisastereventinAmericanhistory,morethan270peopledied.Reason:Connectionwhichconnectenginesandwingshadfractured.ReviewofthehistoryRailway：England，

wheel、track、orbitalfractureBridge：Belgium，14accidentsin4yearsSteamship：WorldWarTwo，Americanfreighter、tanker，weldAirplane：British“comet”Missile：American“Polaris”Pressurevessel：Aerospaceplane、…Inthe1950s,

American“Polaris”solidfuelenginewasfracturedwhenlaunch.Thematerialwashigh-strengthsteel,yieldstrength

s=1400MPa，workingstress

900MPa。Accidentcase62024/10/27Whenitdamage,workingstressismuchlessthanmaterial’syieldlimit；Theprimarycauseofdamageisthatthereareallkindsofdefectsorcracksintheactualstructuralmaterials.Theexistenceofthesecrackssignificantlyreduceactualstrengthofstructuralmaterials.Theimportantreasonwhyitcausedamageisdefectsinthestructure.CommonfeaturesoftheaccidentsWheredocrackscomefrom？Materialdefect；Fatigueinitiation；Damagesinmachining、manufacture、assembleandsoon.72024/10/27After1950s,Crack-containingbodystrengththeorywasbeenresearchedanddeveloped

：FractureMechanicsHowtosolveit?Fissurecancauserupturefailure，howtoanalyseandcontrol?Ifyoudon’tknowhowtoanalyse，constructionalelementwillhavefissures,andthenuseless.82024/10/275.1Introduction5.2Thecrack-tip’sstress-strainfield5.3Stressintensityfactorandit’ssolution5.4Brittlerupture’sK-factors5.5Thepopularizationoflinearelasticfracturemechanicsinsmallscaleyielding5.6Elastic-plasticfracturemechanics5.7Fatiguecrackgrowthrate5.Crack-containingbodystrengththeory92024/10/275.1.1Developmentprocessoffracturemechanics5.1.2Researchcontentsoffracturemechanics5.1.3SeveralbasicconceptionoffracturemechanicsBrittleruptureandductilefractureTrans-granularfractureandinter-granularfractureThedivisionoflengthandbreakrelateddisciplines5.1.4FractureanalysisMacro-fractureanalysisMicro-fractureanalysis5.1

Introduction102024/10/2715century，Vinci：Ironwirebreakingloadandlengthareinreverseproportion.In1919，RussiaКолоcoB：Thestressconcentrationproblemwhentheinfinityplatecontainsanovalholestress.(stress)Conclusion：Elementswithcrackunableloadbearing.In1921，Griffithresearchbrittlematerial’sfractureproblem.(energy)AfterworldwarII，Irwin

andOrowansupplementedtheGriffiththeoryrespectivelyandindependently,sothatitcanbeapplicabletometallicmaterial.Linktheconceptofenergyreleaserateandstressintensityfactor.Laythefoundationsoflinearelasticfracturemechanics.5.1.1Developmentprocessoffracturemechanics112024/10/27In1958，Irwin,withamendmentstobroadenthescopeofapplicationoflinearelasticfracturemechanics；WellsproposeCOD;In1968，RiceandHutchinsonetal.work，providedatheoreticalbasisforj-integralmethod.

Sincethengraduallyestablishedasystemofmainparametersofelastic-plasticfracturemechanics;In1961，Parisproposedfamousformulathatistherelationshipbetweenstressintensityfactorandcrackgrowthrate;Studyonquantitativeanalysisofdynamicfractureisintheascendant……5.1.1Developmentprocessoffracturemechanics122024/10/27Researchthepowerandresistanceofmaterialorstructure’scrackgrowth(initiation).

Fracturecriterionanditsscopeofapplicationandapplicableconditions.Applytotheanalysisofmultiplestructure：Processofcrackfrominitiation,extendingtounstability.Estimationthelifeofstructurewithcracks：Fatigueproblems.Thegoaloffracturemechanicsisquantificationallyresearchontheconditionsoffracturewhichcausedbyhereasonthatthemaincrackinthesupportingbodyextend(includingstaticloadandtheexpansionunderfatigueload).5.1.2Researchcontentsoffracturemechanics132024/10/275.1.2ResearchcontentsoffracturemechanicsEngineeringapplicationUndertheactionofknownexternalload,howmuchisthecracklengthinthestructureallowing(i.e.criticalcracklength)?Whenstructureexist(orassumed)aninitialcracklength,howlongdoesitneedtoexpandtothecriticalcracklength(ornumberofloadcycles)?-----RemaininglifeWhatfunctionrelationsbetweenresidualstrengthsofstructureandcracklengths?142024/10/27IssuesrelatetomaterialselectWhatkindsofmaterialarenoteasygerminationcrack?Whatkindsofmaterialcanallowrelativelylongcrack’sexistbutnotbreak?Whatmaterialhavebetterperformanceinresistcrackgrowth?Howcanmelting,processingandtreatmentgetthebestresults?5.1.2Researchcontentsoffracturemechanics152024/10/27Fracturemechanicsinvolvemanyproblemsofmechanics,materialsscienceandengineeringapplication,itcanbeusedtoprocess：Whenstructurehasbeenset,crackingisknow,howaboutthisstructure’sbearingcapacity

(residualintensity)?Whenstructurehasbeenset,externalloadisknow,howmuchistheallowingmaximumcrack(Damagetolerance)?Knowingofdamagetoleranceandexternalloadofstructure,howtomakeeachcomponentofstructuremeetdimensionalrequirement(damagetolerancedesign)?Lifetimecalculation.（Fatiguecrackgrowth’slife）Selectingmaterial.5.1.2Researchcontentsoffracturemechanics162024/10/27BrittlefractureandductilefractureToughness：

Abilityofmaterialsabsorbenergyduringtheelastic-plasticdeformationwhichbeforematerialbreak.5.1.3Severalbasicconceptionoffracturemechanics172024/10/27Brittlefractureandductilefracture

Whenbreaking,thereisnotobviousplasticdeformation,itisasuddenbreakandwithoutwarningbeforebreaking;

Thefracturesurfaceisquitesmooth,anditisbasicallyperpendiculartotheaxial；

Thefractureisabreastandluminous,anditisperpendiculartothenormalstress.Onthefractureoftenfollowazig-zagorradiationpattern.

Therootofcutwhichbeforebreakingoccurplasticdeformation,andtheareaofsurplussectionwillreduce(i.e.necking)；

Fracturemaybejagged；

Withtheobservationofnakedeyeandlowtimemicroscope,thefractureisdarkgreyandfibrous.Brittlefracture：DuctilefractureNotice：Therelativityofconcept（Influencebytemperature,stressandenvironment）5.1.3Severalbasicconceptionoffracturemechanics182024/10/27Trans-granularfractureandinter-granularfractureCleavageforms(Simpleabruptionofatomicbinding)BrittlefractureSlipandemptyaggregationDuctilefractureFracturearousebytemperbrittlenessorcrystalboundaryhasbrittlephase,hydrogenembrittlementandanyotherreasons,italwaysbelongstothebrittlefracture.5.1.3Severalbasicconceptionoffracturemechanics192024/10/27Thedivisionoflengthdimensionandbreakrelateddiscipline(Subject)5.1.3Severalbasicconceptionoffracturemechanics202024/10/27Thedivisionoflengthdimensionandbreakrelateddiscipline(Fissure)Staticcracking(Stressanalysis)Subcriticalcrackgrowth(fracturecriterion)

UnstableextensionsCrackarrest5.1.3Severalbasicconceptionoffracturemechanics212024/10/275.1.4Fractureanalysis(concept)Metalfracture:Aftermetalcomponentsbreak,thegeneraltermsofdamagedpart’soutwardappearance.Recordingtheprocessofcrack’sgeneration,propagationandfracture.Fractureanalysis：Usingmethodsofmacroscopeandmicroscopetoanalyseandresearchtofracturemorphology.

Purpose：Analyzethematerialorganizationandthecharacteristicsandessenceofdefect,sothatitcanaccuratelydeterminesteelquanlity,improvementsmeltingandheattreatmenttechnology;Studingthemicro-mechanismofmetalfractureprocess,asthefoundationofexpositionfractureprocesselementarytheory;Explorationthecauseofaccident.Method:Macro-fractureanalysis,micro-fractureananlysis.222024/10/275.1.4Fractureanalysis(Macroscopic)Macro-fractureanalysisThroughmacroscopicfractureanalysis,wecandeterminethenatureofthemetalfracture(brittle,ductileor

fatigue);Cananalyzethecracksourcelocationandthedirectionofcrackpropagation；

Canjudgethequalityofthematerial.Distinguishbetweenthestaticloadfractureandfatiguefracture232024/10/275.1.4Fractureanalysis(Macroscopic)Staticloadfracture：threeelementsFiberareaRadiation

areaShearlipareaNon-gaptensilespecimenandimpacttestsamplefracturechart

242024/10/275.1.4Fractureanalysis(Macroscopic)RadiationareashapeCounterdirectional

cracksource252024/10/275.1.4Fractureanalysis(Macroscopic)Threeregionsofthefracturesurfaceexistornot,size,location,scaleandshape,etc.willhavegreatchangealongwiththedifferenceofmaterialintensitylevels,stressconditions,sizedimensions,geometricforms,insideandoutsideflawsandpositions,temperature,externalenvironmentandsoon.Thetoughnessofmaterialisgood,theareathattextilefiberareaoccupiesisbig,evenhasnotradiation

area,isfulloffiberareaandshearlip.Materialwithbigbrittleness,theradiationareaincreases,fiberareareduces,evenwillnothavefiberareaandshearlip,andthepatternofemissionareaisverytiny,becomeslessobviousandpresentsothercharacteristics.262024/10/275.1.4Fractureanalysis(Macroscopic)Fatiguefracture272024/10/275.1.4Fractureanalysis(Macroscopic)MacroscopicfractureanalysismethodObservingwhethertherehaveradiationpatternorherringbonepatternonfracturesurface,wecanfindthecracksourcepositionaccordingtothetrace;Meanwhile,accordingtotherelativescaleofradiation

areaandfiberareawecanroughlyestimatedfractureproperties.Thebiggertheproportionthattheradiationareaaccountsis,thenthebrittlenessisbigger.Observingwhetherthereisshellpatternonthefracturesurface,ifitis,itindicatesthatthecomponentisfatiguefracture,andwecanfindthefatigueinitiationaccordingtothetrace.

Observingtotheroughdegree,glossandcoloroffracture.Thefractureisrougher,thecolorisgloomier,indicatedthatinthefracturegrowthprocesstheplasticdeformationisbigger,thedegreeofductilefractureisbigger;Otherwise,fractureisthinandflat,multi-gloss,itmeansthattheproportionofbrittlefractureissignificant.282024/10/275.1.4Fractureanalysis(Microscopic)Micro-fractureanalysisInadditiontobeingabletounderstandthecauseofthefracture,butcanalsostudymechanismsoffractureoccurred.

Method：transmissionelectronmicroscope（TEM）andscanningelectronmicroscopeMicrofracturemorphology：CleavagefractureToughnessnestfractureFatiguefracture292024/10/275.1.4Fractureanalysis(Microscopic)Cleavagefractureisakindoftransgranularfracture,onaspecificcrystalsurface,occurduetothesimplebreakdownofatomickeyfracture.Withinagrain,cleavagecrackhasrelativelyflat.Itmustchangedirectionatthegrainboundary,socleavagefractureiscomposedofmanysmallsmoothplaneswhichorientationisslightlydifferent,eachgroupofsmallplanerepresentsagrain;Themostimportantcharacterofcleavagefractureis"riverspattern"。Cleavagefracture:Akindofthecrispestfractureformwhichoccursinthecrystallizationmaterial.302024/10/275.1.4Fractureanalysis(Microscopic)Toughnessnestfracture：Toughnessnestfractureisamaintypeofductilefracture,italsobelongstotransgranularfracture;Thechieffeatureofthefracturesurfaceoftoughnessnestfractureistohavedimple;

Accordingtothedifferentforce,itwillformdifferentshapesofdimple,thereareisometrictoughnessnest,parabolictoughnessnestandelongationtoughnessnestandsoon.Fracturesurfacepresentsroughandirregularshape.312024/10/275.1.4Fractureanalysis(Microscopic)IsometrictoughnessnestParabolictoughnessnestElongationtoughnessnest322024/10/275.1.4Fractureanalysis(Microscopic)Fatiguefracture

Thechieffeatureoffatiguefractureisthereisshellpattern(ornamesbeachpattern,tree-ringpattern)inthefatiguezones(fracturegrowtharea).Sometimesitisunclearwiththeobservationofmacroscopicmethod,andpresentsclearwiththemicroapproach.Shellpattern’sstripesarebasicparallel,butslightlycurved,presentwave-shaped;Stripelineisperpendiculartothecrackdehiscencedirection;Eachstriperepresentsaloadprocess,stripetotalnumberisthenumberofvaryingload;Thetraceoftopandbottomfracturecorrespondcompletely.

332024/10/275.2Thecrack-tip’sstressanddisplacementfieldCrackBasictypesofcrackThestressfieldanddisplacementfieldnearbycrack-tip342024/10/275.2Thecrack-tip’sstressanddisplacementfieldCrackTheactualcomponentdefects：Entrappedslagandblowholegenerateinsmeltingproduce;Toolmarksandnotchgroovecauseduringmachining;Crack,notpenetration,blowhole,undercut,overburningandinclusionproduceduringwelding;Theshrinkholeandlooseincasting;Thecorrosioncrackandfatiguecrackproducewhenstructureareusedindifferentenvironment.352024/10/275.2.1Basictypesofcrack

Accordingtothelocationofcrack：Through-wallcrackSurfacecrackHiddencrackAccordingtocrackstresssituation：openingmode(I)Slidingmode(Ⅱ)Tearingmode(Ⅲ)5.2.1Basictypesofcrack

ModeI(openingmode):Bearwithcracksurfaceverticalnormalstress

,cracksurfacedisplacementalongtheYdirection,crackopening.

，裂紋張開。ModeII(slidingmode):Bearwithshearingstrength

ofplaneXY,cracksurfacedisplacementalongtheXdirection,andcracksurfaceslidesinXdirection.ModeIII(tearingmode):Bearwithshearingstrength

ofplaneYZ,,cracksurfacedisplacementalongtheZdirection,andcracksurfacetearsinZdirection.372024/10/275.2.2Thestressfieldanddisplacementfieldnearbycrack-tip

Analyticalmethod:Accordingtoelastictheory;Analysingtheboundaryconditions;Solvethestressfieldanddisplacementfield382024/10/27Stressanddisplacementnearbyopeningmode’scrack-tip.5.2.2Thestressfieldanddisplacementfieldnearbycrack-tip

ThemostcommonandharmfulcrackinengineeringismodeIcrack.

Tomakecrackgrowth,must

>0.

NamelyonlythetensilestresscancausecracksopenextensionsDiscussingtothesituationthatainfiniteplatewhichhavea2a-longpenetratingcrack,anditstwoendssubjecttotensilestress

thatisperpendiculartothecrack.392024/10/27

Whatwediscussistheplaneproblem,so

yz=

zx=0；

Forplanarstressstate,

z=0。

Ifitisplanestrainstate,then

z=

(

x+

y)。ssxy2adxdyrqsysxtxyssqyar=+221cos[qq232sinsin]tsqqqxyar=22232sincoscosssqxar=-221cos[qq232sinsin]Attheplacethatisapartfromcrack-tipr,withtheXaxisanglefor

,pickupamicro-surfacewhosesizeisdx、dy；Usingmethodsofelasticmechanics,wecanobtainanypoint’s(r,

)normalstress

x

yandshearstress

xynearbythecrack-tip,thatis:5.2.2Thestressfieldanddisplacementfieldnearbycrack-tip

(5-1)402024/10/27Whatfracturemechanicscareforisthestressfieldnearbycrack-tip.Theaboveequationisthedominanttermofcrack-tip’sstressfield,alsohaver0steptermetc.

0,stress

ijtendtobeinfinityatr-1/2step,existingsingularity;Andthenr0stepbecomesubordinate,itcanbeignored.(5-1)theaboveequationmaywriteas：spfqijijKr=12()Ka1=sp式中：r

，

ijapproachtozero;Butobviously,when

=0,ontheXaxis,farawayfromthecrack,itmaybe

y=

，anddoesn’tinfluencebyr.Thereforethistimeweshouldtaketheafterr0stepasthedominantterm.ssxy2adxdyrqsysxtxy5.2.2Thestressfieldanddisplacementfieldnearbycrack-tip

412024/10/27Kreflectthestrengthofcrack-tipstressfield;Thesubscript1meansitismold1.If

ijisbigger,thenKisbigger;Cracksizeaisbigger,thenKisbigger.TheKdimensionis[stress][lengh]1/2，incommonuseMPamCrack-tip’sstressintensityfactorK1：

f(a,W,...)isgeometriccorrectionfunction,itcanbecheckedthroughhandbook.Particularly,whena<<wora/w

0,i.e.

Fortheinfinitewidth

centercrackedplatewhichbearingstretch，f=1；

Fortheinfinitewidthunilateralcrackplate,f=1.12.5.2.2Thestressfieldanddisplacementfieldnearbycrack-tip

Formula(5-1)isthesolutionofcenterthroughcrackinfiniteplane.

FracturemechanicsresearchindicatethatK1canmoregenerallywriteas:KafaW1=sp(,,...)422024/10/275.2.2Thestressfieldanddisplacementfieldnearbycrack-tip

Thestressanddisplacementnearthecrack-tipofslidingmodecrack.432024/10/275.2.2Thestressfieldanddisplacementfieldnearbycrack-tip

Thestressanddisplacementnearthecrack-tipoftearingmodecrack442024/10/275.3Stressintensityfactorandit’ssolutionThegeneralformulaofcrack-tip’sstressfieldanddisplacementfield:Analysisofstressfield：Thestressdistributionofcrack-tipnearbyregionisthefunctionofpositiondata,hasnothingtodowiththestresssizeandcracklengthofinfinitedistantplace;Thestresspresentssingularpointinthecrack-trip;

Atthecrack-tip,stressintensityfactorisafinitequantity;

Conclusion:Thestressisnotsuitableasestablishingthephysicalparameterofstrengthcondition.452024/10/275.3Stressintensityfactorandit’ssolutionThecharacterofSIF：TheSIFismeasurementofcrack-tipstress-strainfieldintensity;TheSIFismeasurementofcrack-tipstress-strainfieldwhohassingularity;ThemarginalvalueofSIFismaterial'sinherentattribute.Conclusion:EstablishesfailureconditiontobesuitablebyusingtheSIF.462024/10/275.3Stressintensityfactorandit’ssolutionGeneralformulaofSIFCalculationmethodofSIFMethodofcalculationMethodoflook-uptableMethodofsuperposition472024/10/275.3Stressintensityfactorandit’ssolutionThesuperpositionprincipleofsoughtofSIFThedecompositionandsuperpositionofstressStructureandforcedecompositionandsuperpositionatthesametimeInviewofdifferentkindsofcrack,consideringcomplexcriteria.482024/10/275.3Stressintensityfactorandit’ssolutionThesuperpositionofSIF492024/10/275.4TheKcriterionofbrittlefracture5.4.1StrainenergyreleaserateandGcriterion5.4.2TherelationshipbetweenSIFandstrainenergyreleaserate.5.4.3TheKcriterionofbrittlefracture5.4.4TheengineeringapplicationofKcriterion5.4.5Mixedmodefracturecriterion

502024/10/275.4.1StrainenergyreleaserateandGcriterionAnalysisprinciple：EnergymethodStrainenergyreleaserateEnergyratethatfracturegrowthneedstoabsorbExpandStabilizeCriticalCrackcriticalcondition：Gcriterion512024/10/275.4.1StrainenergyreleaserateandGcriterionExampleofinfiniteplatesubjectedtotensileinstanceCriticalconditionCriticalstressCriticalcracklength522024/10/275.4.1StrainenergyreleaserateandGcriterionDiscussionGicismaterialconstant,representtheabilityofmaterialresistofcrackgrowth,itwillbedeterminedbyexperiment.

Theaboveexampleofengineeringapplicationisapplicabletobrittlematerial.FortheGcriterionofmetalmaterialwhohassomeplasticity:Strainenergyreleaserate=Energythatformanewsurfaceneeds+Plasticdeformationenergythatcrackgrowthneeds532024/10/275.4.2TherelationshipbetweenSIFandstrainenergyreleaserateWhendiscussinglinearelasticfractureproblems,applyingGandKastheparameterisequal.542024/10/275.4.3TheKcriterionofbrittlefractureK

criterion:ThephysicalsignificanceofKiandKIcKI

：SIF，ObtainingthroughcalculationKIc

：Fracturetoughness：Abilityofmaterialresistbrittlefracture.TheexperimentobtainofKIcFracturetoughnessofplanestrain552024/10/275.4.4TheengineeringapplicationofKcriterionK

criterion:CriticalstressCriticalcracklength562024/10/275.4.4TheengineeringapplicationofKcriterionApplyingsituation：Knownstress,soughtthecriticalcracklength;Knowncracklength,soughtcriticalstress(residualintensity).Applicationsteps：Throughnon-destructivetesting,determinethelengthandpositionofcracka;Ananalysisofthedefects,calculateofchecktabletoobtaintheexpressionofSIFK;Throughexperimentorchecktable,determinematerialplanestrainfracturetoughnessKic;AccordingtoKcriterion,analysisoffracturemechanics,determinethecriticalcracklengthacorcriticalstress(residualstrength).572024/10/27Solution：1）Donotconsiderthedefects,consideronitstraditionalstrengthdesign.

Whenchoosethetwomaterials,thesafetycoefficientis:

Material1：n

1=

ys1/

=1800/1000=1.8Material2：n

2=

ys2/

=1400/1000=1.4excellentqualified5.4.4TheengineeringapplicationofKcriterion2）Consideringthedefects,accordingtocrackdesignconsideration.Because“a”isverysmall,forunilateralthroughcrack,itwillbeCase1：Somecomponenthasaunilateralthroughcrack,itslonga=1mm,sufferfromtensilestress

=1000MPa.Trytochoosematerial.

Material1：

ys1=1800MPa，K1C1=50MPam1/2

；Material2：

ys2=1400MPa，K1C2=75MPam1/2.582024/10/27Selectingmaterial1，low-stressbrittlefracturewillhappen;Selectingmaterial2，meetthestrengthconditionsandtherequestofanti-break.Selectingmaterial1：

1c=50/[1.12(3.14

0.001)1/2]=796MPa<

Selectingmaterial2：

2c=75/[1.12(3.14

0.001)1/2]=1195MPa>

rupturesafeAttention,a0issmaller，K1Cbecomesbigger,criticalrupturestress

cisbigger.So,enhanceK1C,managea0,canhelppreventlow-stressfracture.5.4.4TheengineeringapplicationofKcriterionMaterialrupturestressisMaterialrupturestressis:592024/10/275.4.4TheengineeringapplicationofKcriterion(Case1)

Whenamissileengineshellhavingthehydrostatictest,ithasaexplosion.KnowntheshellmaterialisD6GChigh-strengthsteel,～，traditionalexaminationisqualified,whencontinuethehydrostatictest,ithasaexplosion,thebreakdownstressis

.Thematerialfracturetoughnessis～,trytoanalysisthereasonsoflow-stressbrittlefracture.

602024/10/275.4.4EngineeringapplicationofK（Example1）stressanalysiscircumferentialstressandaxialstress612024/10/275.4.4EngineeringapplicationofK（Example1）ConventionalintensityanalysisIfitdoesn'texceedthepermissiblestress,thestrengthisqualified.fractureanalysisWhenthecriticalcracklengthis0.36mm，missingdetectioniseasy.improvementmeasuresChoosingthematerialthatKrcishighcanimprovethecriticalcracklengthtoensurethedetectionrate.622024/10/275.4.4EngineeringapplicationofK（Example2）Baosteel'sreductionboxfractographicanalysisstressanalysisbasicassumptionfractureanalysislifecalculation632024/10/27lowstressfracture：fractureundertheconditionsofenoughstaticstrengthresidualintensity:reducedstrengthundertheinfluenceofcrackmodeI(openingmode)isthemostcommonandharmfulintheengineering.normalstressσx，σyandshearstressτxyofanarbitrarypoint（r，θ）nearthecracktipcanbeobtainedbyelasticmechanicsmethod：spfqijijKr=12()Ka1=spsummaryThestressintensityfactorKreflectsthestrengthofstressfieldatcracktip；ThedimensionofKis[stress][length]1/2，alwaysMPa

642024/10/27Duringthestructurefacturedesign,threekeyfactorsmustbetakenintoaccount:workstress、defectsizeandfracturetoughness.

Fracturemechanicsshowthemathematicalrelationshipbetweenthesequantities.Onlyknowtwootherscanwecalculatethethirdquantity.summaryFracturedesignshouldbebasedontheavailabledata,suchasmaterialproperties,

workingenvironmentandstructuralload.IfK1Cisavailableanddesignstressislow,linearelasticfracturemechanicsisappropriate.652024/10/27Thestressintensityfactorofcracktipcanbemoregenerallywrittenas：KafaW1=sp(,,...)infinitelywidecenter-crackedplateunderstretching，f=1；infinitelywidesingle-edge-crackedplate，f=1.12

crack

lengthandshapeworkstressfracturetoughnessK1C

threeelementsoffractureorK

K1CKfaWa=(,)Lsp￡Kc1fracturecriterion：resistanceactingsummary662024/10/27Question：MWMTMWMTI、I+III裂紋表面裂紋前緣IIIIII+III+II+III5.4.5Mixed-modefracturecriterionlargerotatingcomponent（suchasgeneratorshaft,etc），modeIcrackandmodeIIcrackcoexist.672024/10/27裂紋表面裂紋前緣IIIII5.4.5Mixed-modefracturecriterionThebackgroundofmixedmodecrack'sformationofplanebendingstructure.Themaindifferenc