材料科学8chapter强度设计的一般方法

CHAPTER8:MECHANICALFAILURE断裂机理ISSUESTOHowdoflawsinamaterialinitiateHowisfracture fied;howdodifferentmaterialclassescompare?HowdoweestimatethestresstoHowdoloadingrate,loadinghistory,andtemperatureaffectthefailurestress?Computerchip-cyclicthermalloading.

Hipim nt-cyclicloadingfromwalking.1内内强？2研究含缺陷材料的强度--研究含缺陷材料的强度--3是总决定断面尺寸计算的名义断裂应力和断裂应变。4FractureSimplefracture:Separationofbodyintotwoormorepiecesinresponsetoanimposedstressthatisstatic(i.e.,constantorslowlychangingwithtime)andattemperaturesthatarelowrelativetothemeltingtemperature5DuctilevsBrittleFailure

AdaptedfromFig.%ARor Ductilefractureisthanbrittlefracture!

6Example:PipeFailuresDuctile--one--largeBrittle--many--smallFiguresfromV.J.ColangeloandF.A. ysisofMetallurgicalFailures(2nded.),Fig.4.1(a)and(b),p.66JohnWileyandSons,Inc.,1987.Usedwith7 YDUCTILEEvolutiontofailure:necking

voidnucleation

voidgrowthandlinkage

shearingatsurface

fracture50Resulting50(steel)particlesserveasvoidnucleation

FromV.J.ColangeloandF.A.ysisofMetallurgicalFailures(2nded.),Fig.11.28,p.294,JohnWileyandSons,Inc.,1987.(Orig.source:P.Thornton,J.Mater.Sci.,Vol.6,1971,pp.347-56.)

100100Fracturesurfaceoftirecordwireloadedintension.CourtesyofF.Roehrig,CC Dublin,OH.Used ModerayModerayDuctilevs.BrittleFailure AdaptedfromFig.8.3,Callister&Rethwisch9BrittleFailureArrowsArrowsindicatepointatwhichfailureAdaptedfromFig.8.5(a),Callister&RethwischBrittleFractureSurfaces(between 304S.Reprintedw/permission9thed,Fig.633,p.650.Copyright1985,ASMInternational,MaterialsPark,OH.(Micrographby4J.R.Keiserand4fromR.W.Hertzberg,"Defor-mationandFractureMechanicsofEngineeringMaterials",(4thed.)Fig.7.35(d),p.303,JohnWileyandSons,Inc.,1996.

(through316S.Reprintedw/permissionfrom"MetalsHandbook",9thed,Fig.650,p.357.Copyright1985,ASMInternational,MaterialsPark,OH.(MicrographD.R.Diercks,AlOxide3from"Failure ysisofBrittleMaterials",p.78.Copyright1990,TheAmericanCeramic(MicrographbyR.M.GruverandH.31(Orig.source:K.Friedrick,Fracture1977,13,ICF4,Waterloo,CA,1977,p.StressStress-strainbehavior(Room

perfectmat’l-noflawscarefullyproducedglassfiber

gineering<<TSperfect

typical typicalstrengthenedtypical Fracturestrengthofabrittlesolidisrelatedtothecohesive sbetweenatoms.thetheoreticalcohesivestrengthofabrittlematerialshouldbe~E/10. experimentalfracturestrengthisnormallyE/100-verysmall,microscopicflawsorcracksthatareinherenttothematerial.Theflawsactasstressconcentratorsorstressraisers,amplifyingthestressatagivenpoint.FlawsareStressThisdiscrepancyFlawsareStressThisdiscrepancyisinedbythepresence--thelongerthewire,thesmallertheloadforfailure.--flawscauseprematurefailure.--largersamplescontainlongerflaws!

Reprintedw/"DeformationandFractureMechanicsofEngineeringMaterials",(4thed.)Fig.7.4.JohnWileyandSons,Inc.,1996.FLAWSARESTRESSEllipticalholein •Stressdistrib.infrontofahole:te:

maxo

Stressconc.factor:

Ktmax/o LargeKtpromotesfailure:BAD

Kt=3

BAD! ENGINEERINGFRACTUREAvoidsharpcorners!StressConc.Factor,Kt=w

maxr,filletradius

h

increasingw/hAdaptedfromFig.8.2W(c),Callister6e.(Fig.8.2W(c)isfromG.H.Neugebauer,Prod.Eng.(NY),Vol.14,pp.82-871943.)

0

1.0sharperfilletradius

r/hCrackPropagationCrackshavingsharptipspropagateeasierthancrackshavingblunttips sticmaterialdeformsatacracktip,which“blunts”thecrack.EnergybalanceontheElasticstrain

energystoredinmaterialasitiselasticallythisenergyisreleasedwhenthecrackcreationofnewsurfacesrequiresCriterionforCrackPropagationElasticstrainenergyisreleasedbythepropagationofacrackinalarge,stressedcomponent.Thickness=ModulusThickness=Modulus=ElasticbycrackSurfaceenergyperunitarea= e2ESurfaceUs4at2newCriterionforCrackPropagationThetotalenergyofthesystemisafunctionofcrackCriticalCrackLength

ElasticStrain 2a2teEUs4atStrain

CrackLength,U=Us-

Atthecriticalcrack0sECriterionforCrackPropagationCrackpropagatesifcrack-tipstress(m)exceedsacriticalstress(c)

m>E=modulusof

c

as=specificsurfacea=onehalflengthofinternalForductilematerials=> ceswiths+wherep sticdeformationWHENDOESACRACKConditionforcrackpropagation:KKcStressIntensityFactor:--Dependsonload&geometry.

Fracture--Dependsonthematerial,temperature,environment,&rateofloading.ValuesofKforsomestandardloads&geometries:unitsofKmmor K K Yieldoccurs:y,yYieldoccurs:y,yFractureoccurs:KKcKcJustlikeKc:fracturetoughness断裂韧性Ameasureofamaterial’s tobrittlefracturewhenacrackispresentKcdependsonthethicknessofthesample.Asthicknessincreases,Kcdecreasestoaconstantvalue.The straintoughness,K1c,isthelowestvalue.Itisaconservativemeasureofthetoughness.KK1c:平面应变断裂韧性Afundamentalmaterialproperty! SicarbideAlSinitrideSicrystalGlass-Al/Al Aloxid/SiC(w)3SiAloxid/ZrO2(p)4C-C(||TiAlalloysMgalloysKIcKIc(MPa765432

fibers

FractureBasedondatainTableKmetalscKKmetalscKcerKpolyccincreasing1DESIGNAGAINSTCRACKCrackgrowthcondition: KKc Failure！ Largest,moststressedcracksgrowfirst!--Result1:Maxflawsizedictatesdesignstress.

--Result2:Designstressdictatesmax.flawsize. 2YY

amax

Y fracturenofracture fracturenofracture

designfracturenofracture

DESIGNEX:AIRCRAFTMaterialhasKc=26MPa-Twodesignstoconsider...Design--largestflawis9mm--failurestress=112

Design--usesamematerial--largestflawis4mm--failurestress=Y YKeypoint:YandKcarethesameinbothdesigns.--Result:112

9 4 amaxAReducingflawsizepaysoff!

Answer: LOADINGIncreasedloadingrate...--increasesyand--decreasesWhy?Anincreasedrategiveslesstimefordisl.tomovepastobstacles.

larger

smallerImpactloading:--severetesting--morebrittle

case

sample--smallertoughnessImpacttoughnessfinalheight

initialheightCharpyImpactData:EnergyvsTemperatureDuctile-to-brittletransitiontemperature(DBTT)...ImpactImpactEnergy

BCCmetals(e.g.,ironatT<polymersMoreDuctileHighstrengthmaterialsDuctile-to-

Temperaturetransitiontemperatureoc6nDesignStrategy:StayAboveTheDBTT!Pre-WWII:The •WWII:LibertyReprintedw/permissionfromR.W.Hertzberg,"DeformationandFractureMechanicsofEngineeringMaterials",(4thed.)Fig.7.1(a),p.262,JohnWileyandSons,Inc.,1996.(Orig.source:Dr.RobertD.Ballard,TheDiscoveryoftheTitanic.)

Reprintedw/permissionfromR.W.Hertzberg,"DeformationandFractureMechanicsofEngineeringMaterials",(4thed.)Fig.7.1(b),p.262,JohnWileyandSons,Inc.,1996.(Orig.source:EarlR.Parker,"BehaviorofEngineeringStructures",Nat.Acad.Sci.,Nat.Res.Council,JohnWileyandSons,Inc.,NY,Problem:SteelswereusedhavingDBTT’sjustbelowroomtemperature.Fatigueisaformoffailurethatoccursinstructuressubjectedtodynamicstressesoveranextendedperiod.UndertheseconditionsitispossibletofailatstresslevelsconsiderablylowerthantensileoryieldstrengthforastaticSinglelargestcauseoffailureinmetals;alsoaffectspolymersandceramics.Commonfailureinbridges,aircraftand 才发生破坏，即破坏有一个过程。 FatigueFailure.AlohaAirlinesFlight243–April28th1988

19yearsAllrequiredsafetycheckshadbeenTheProblem“..at24,000ft,bothpilotsheardaload”clap”or“whooshing”sound,followedbyawindnoisebehindthem……Thecaptainobservedthat…therewas skywherethefirstclassceilinghadBasicFatigueTerminologyStressvarieswithtime.--keyparametersareSand

r=maxmeanmaxmin S=amplitudemaxmintimeR=min/N=numberoffatigueNf=numberofcyclestoAimtopredictfatiguelife umumcyclicloadsforinfiniteTypesofFatigueBehaviorFatiguelimit,--nofatigueifS<

S=stress S=stressN=Cyclesto

caseforsteel(typ.)AdaptedfromFig.Forsomematerials,thereisnofatigue

S=stress S=stressN=Cyclesto

caseforAlAdaptedfromFig.FATIGUECrackgrowsincrementallyrangeofstressintensityatroot

crack,calculatedfrommaxstressminusminimumstresscrackoriginincreaseincracklengthperloadingcrackoriginFailedrotatingshaft--crackgreweventhoughKmax<Kc--crackgrowsfasterifincreasescrackgetslongerloadingfreq.increases.C.;;ImprovingFatigueLifeImposecompressivesurfacestresses(tosuppresssurface

AdaptedS=stressFig.8.24,S=stressnearzeroorcompressivemoderatetensileLargertensileN=Cyclesto--Method1:shot

--Method2:C-richRemovestress

Fig.8.25,Callister&Rethwisch8e.Creep:Time-dependentandpermanentdeformationconstantstressesbelowOccursatelevatedtemperature,T>0.4Deformationchangeswithtime.

strain,

INCREASING TT<0.4elastic0

secondary

tertiary

timeCreepcurvePrimarycreepDecreasingcreepratestrainhardensMicrostructurechangeSteady-statecreepWithoutmicrostructurechangeconstantslopeLinearorpower-lawrelationshipwithstressFlowofatomormotiondislocationTertiarycreepAccelerationofratevoidformation/neckingRupture(failurebelowtheyieldstress)

SECONDARYMostofcomponentlifespenthere.StrainrateisconstantatagivenT,--strainhardeningisbalancedbyrecovery

ssexpoQssexpoQc

nent(materialparameter)activationenergyforcreepstrainratematerialconst.

RT (materialparameter)appliedstressStrainrateincreasesforlargerT,

4020

Stress

2 1 Steadystatecreeprates CreepFailureFailure:alonggraing.b.FromV.J.ColangeloandF.A.Heiser, ysisofMetallurgicalFailures(2nded.),Fig.4.32,p.87,JohnWileyandSo