Effects of microstructure on mixed-mode, high-cycle fatigue crack-growth thresholds in Ti-6

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

Effectsofmicrostructureonmixed-mode,high-cyclefatiguecrack-growththresholdsinTi-6Al-4Valloy

DepartmentofMaterialsScienceandEngineering,UniversityofCalifornia,Berkeley,California94720-1760,USA,2MetalsFabricationDivision,GeneralMotors,Troy,Michigan48084,USAReceivedinfinalform10January2002

R.K.NALLA1,J.P.CAMPBELL2andR.O.RITCHIE1

1

ABSTRACT

Effectofmicrostructureonmixed-mode(modeI II),high-cyclefatiguethresholdsinaTi-6Al-4Valloyisreportedoverarangeofcracksizesfromtensofmicrometerstoinexcessofseveralmillimeters.Specifically,twomicrostructuralconditionswereexam-inedÐafine-grainedequiaxedbimodalstructure(grainsize$20mm)andacoarserlamellarstructure(colonysize$500mm).Studieswereconductedoverarangeofmode-mixities,frompuremodeI(DKII/DKI 0)tonearlypuremodeII(DKII/DKI$7.1),atloadratios(minimumload/maximumload)between0.1and0.8,withthresholdscharacterizedintermsofthestrain-energyreleaserate(DG)incorporatingbothtensileandshear-loadingcomponents.Inthepresenceofthrough-thicknesscracksÐlarge(>4mm)comparedtomicrostructuraldimensionsÐsignificanteffectsofmode-mixityandloadratiowereobservedforbothmicrostructures,withthelamellaralloygenerallydisplayingthebetterresistance.However,theseeffectsweresubstantiallyreducedifallowancewasmadeforcrack-tipshielding.Additionally,whenthresholdsweremeasuredinthepresenceofcrackscomparabletomicrostructuraldimensions,specificallyshort($200mm)through-thicknesscracksandmicrostructurallysmall(<50mm)surfacecracks,wheretheinfluenceofcrack-tipshieldingwouldbeminimal,sucheffectsweresimilarlymarkedlyreduced.Moreover,small-crackDGTHthresholdsweresome50±90timessmallerthancorrespondinglargecrackvalues.SucheffectsarediscussedintermsofthedominantroleofmodeIbehaviourandtheeffectsofmicro-structure(inrelationtocracksize)inpromotingcrack-tipshieldingthatarisesfromsignificantchangesinthecrackpathinthetwostructures.

Keywordscrack-tipshielding;fatiguethresholds;high-cyclefatigue;loadratio;microstructure;mixedmode;shortcracks;Ti-6Al-4V;titanium.

INTRODUCTION

Thecontroloffailuresowingtohigh-cyclefatigue(HCF)inturbine-enginecomponentshasbeenidentifiedasoneofthemajorchallengesfacingthereadinessoftheUSAirForcefleettoday.1±3Inordertoaddressthisissue,aconsortiumofindustrial,governmentandaca-demicinstitutionshasbeenchargedwiththetaskofmodifyingtheexistingdesignmethodologiesforim-provingtheHCFreliabilityofthesecomponents.4Onecriticalissueinvolvestheeffectsofmixed-modecyclic

Correspondence:R.O.Ritchie,DepartmentofMaterialsScienceandEngin-eering,UniversityofCalifornia,Berkeley,California94720-1760,USA.E-mail:RORitchie@LBL.gov

loadsÐthatis,thepresenceofbothtensileandshearloadingÐonthecriticalstatesofdamageforsuchHCFfailures.Indeed,therearemanyfatigue-criticallocationswithintheturbineenginewheresuchmixed-modecon-ditionsexistÐe.g.inthepresenceoffrettingfatiguecracksintheblade±dovetailcontactsection.5Theeffect-ivecrack-drivingforceherecanbeconsideredtobeacombinationofthetensile(modeI)stress-intensityrange,DKI,thein-planeshear(modeII)stress-intensityrange,DKII,and/ortheantiplaneshear(modeIII)stress-intensityrange,DKIII.Fromtheperspectiveofprevent-ingHCFfailuresinturbineengines,itiscriticalthatfatiguecrack-growththresholdsarewell-characterizedforsuchloadingconditions,astheextremelyhighcyclicfrequencies($1±2kHz)involvedcanleadtoveryrapid

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606587

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

588R.K.NALLAetal.

failures,inwithoverthreemillioncyclesbeingaccumulatedmodelessmodeloadingthananconditionshour.Moreover,hasbeenthereportedpresenceofmixed-alloysTodate,Ifatiguestudiesthresholdstoreducetheon(e.g.Ref.[6]).

ofandTi-6Al-4VhavelargelyfocusedtheHCFonabimodalperformancemicrostructureofenginethecompressors,anina theballoytypicallyusedinfandiskspropagation,engine.Infront,low-temperaturestagesofiuminthecontextofmixed-modefatiguecrackthe(Ti)alloysinadditiontheliterature,toafew7±9earlierreportsontitan-Ti-6Al-4Vonlyresultsthesealloy.onInmixed-modeRefs[10±12]providethepresentwork,thresholdsweseekinatobimodalextendtureearlierobservationstoafullylamellarmicrostruc-ofSpecifically,theseinthetwosamemicrostructuresalloyandtocompareintherelativemeritsmodeofthicknesslargefatiguethe(>4thresholdsroleofcracksizemixed-modefatigue.mm)andisinvestigatedininfluencingmixed-short($200throughmastudysurfacepure(tensioncracks,cracks(Doverandmicrostructurallysmallm)(through-<50mm)Karangeofmode-mixities,fromII/DKImaximumDK 0)topredominantlyshearII/DKI$load),7.1),fromandloadR 0.1±0.8.

ratios(ratioofminimumtoBACKGROUND

ThewithselectionofasinglemicrostructureinTi-6Al-4Vtaskinoptimalfailures.viewresistanceofthenumeroustohigh-cyclefactorsfatigueisacomplexmanyfatigueTiForalloysexample,oftencoarseinfluencingHCFpossesslamellarmicrostructuresincrackstures;ascrack-growthcomparedtobehavioursuperiorinthepresencetoughnessoflargeandtigue-enduranceconversely,theythefinerequiaxedmicrostruc-growthstrengthscandisplayandlowerhigh-cyclefa-turalForthebehaviourpurposeof(e.g.thisRefsstudy,[13±15]).

inferiorsmall-cracktwocommontheconditionsofTi-6Al-4VareinvestigatedÐnamely,microstruc-bcoarse-grainedlamellarstructuresconsistingoflargealternatinggrains(diameterinaandbplates$1mm)(producedandalamellarmatrixofslowthebimodalcoolinghigh-temperaturebstructuresintotheb-phasefieldbyandheatsubsequenttreatment(produceda bphasebyfastfield)coolingandthefromfinerwidth-phasecharacterized$1field)mm).withindividualorientatedaplates(platetheabyWhilelargelamellaracoloniesstructures(apacketare,inofgeneral,aligned200±400platesofmwithminsamesize),crystallographicbimodalstructuresorientation,oftenconsistaboutaamatrixgrainslow-volume($20mfraction(typically$15±30%)ofprimary($20±40ofmalternatingminm).ForTi-6Al-4Vaandsize)bwithplatescolony-typeandotherwithinasmalllamellar bTiballoys,

grainsfatiguetures(e.g.generallyRef.iscrack-propagationwell-characterizedbehaviour[13±21]).Crackpropagationforpureinsuchmodemicrostruc-intheaIphaseloadingisperpendicularparalleltothetotheorientation(0001)basaloftheplane21alamellae.andhence22,23Thelarsuperiorcrack-growthresistanceexhibitedbynaturestructuresthresholdoftoregime.thehascracktrajectory,beenattributedtothiscrystallographiclamel-Asthecrackpathespeciallydiffersinfromthecolonynear-out-of-planecolony,significanttodeflectioncrack-pathandsecondarytortuositycracking,resultsfrommixed-modeAlthoughenhancedsimilarcrack-tipexplanationsshielding.

leadinghavebeenproposedforTi-6Al-4Vmicrostructure,12therefatigueiscrack-propagationlittleinformationonbehaviourinmayinthesealloys,oronhowthecracksizeroleofworkisaffectmixed-modetoexaminethisrole.Theprimeobjectiveofthepresentsize,fatiguethethresholdseffectofmicrostructureasafunctionofonsuchlamellarspecificallymicrostructuresthroughinaTi-6Al-4Vstudyofbimodal.

andcrackfullyEXPERIMENTALPROCEDURES

Materials

The4VTalloy,materialwhichinvestigatedoriginatedwasasaturbine-engineTi-6Al-foreledynegram.theTitanium(Pittsburgh,barPA,stockproducedUSA)specificallybyTheThejointcompositiongovernment-industry-academia(inwt.%)isgiveninHCFpro-sectionedoriginalbarstock(63.5mmindiameter)Tablewas1.940plates.8Cforinto30minsegments400mmlong,preheatedto1h,fanTheseair-cooledplatesandforgedinto400Â150Â20mmandwerethensolution-treatedstabilizedat700at8925Cfor8C2forh.Bimodalmicrostructure

Thebimodalas-receivedtreatedconditionmicrostructure(sometimesreferredofthealloytoaswasintheof(Fig.equiaxedandoveraged,(standard1a).TheprimaryaSTOA),andlamellarandaconsisted b(transformedofsolution-coloniesb)of$20mm,deviationproportionslightly6.6%),elongatedwithofprimaryinantheaverageawas64.1%longitudinalgrainsize(L)

Table1ChemicalcompositionofTi-6Al-4Vbarstock(inwt.%)23BarlocationTiAlVFeONHTopBal.6.274.190.200.180.0120.0041Bottom

Bal.

6.32

4.15

0.18

0.19

0.014

0.0041

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

directionanalysis,990±1005theof8C.bthe-transusforging.24temperatureUsingdifferentialwasmeasuredthermaltobeLamellarmicrostructure

Forobtainedcomparison,À610±30mbarbyatsolutionafully10058treatinglamellarinamicrostructurevacuumof10Àwas510Àbyheliumaminrapid(dependingC(slightlyquench($on100theabovetheb-transus)for8Ccrosssection),followedachieve(He);bimodalasimilarthetransformedquenchratebwasminÀ1)inhigh-puritylathchosenspacinginasorderto700ambient8Cforstructure.temperature2hinvacuoThe.,beforealloyTheresultingslowlywasthenfurnacestabilizedintheWidmanstacoolingtoatÈtten

(a)

(b)

Fig.1Opticalmicrographsofthetwomicrostructuresof

Ti-6Al-4Vinvestigated:(a)bimodal(solution-treatedandoveraged,STOA)and(b)lamellar(b-annealed).Etchedinto$10secin5parts70%HNO3,10parts50%HF,85partsofH2O.

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

EFFECTSOFMICROSTRUCTUREONTI-6AI-4VALLOY589

microstructuregrainasizeof$1(Fig.mm,1b)ahadanaverageprior-b

lamellae-phasemellarlathlamellae)widthofof$$colony1±2500mmm,sizeand(parallelanaverageorientatedamicrostructure.

spacingofthetransformedm,similarbintothethebimodalinterla-Uniaxialtensileandtoughnessproperties

Uniaxialstructurestensile5tureÂ10À4sÀin1thetestsL-orientationwereconductedusingainstrainbothratemicro-ofstrength,wereandductilitytaken;additionalfromdataforthebimodalmicrostruc-andRef.toughness[23].Resultsintermsofthewhatshowahigherthatstrength,whereasthethearelistedinTable2,bimodallamellarstructurestructureexhibitshassome-overgrainfactoroffourhigherductility(owingtoitssmallerdespitesizehasoveritsthat50%lowerlimitstheeffectivesliplength).However,higherductility,plane-strainthelamellarfracturemicrostructuretoughness.Fatiguetesting

Largethrough-thicknesscracks

Largein(>4mm)fatigue-thresholdtestinginnerfour-pointbending,using6mmthicksampleswasperformedwithPurepointmodeandouterspansof12.7and25.4mm,ponentbending.ItestsasymmetricoftheForwereloadingmixed-modeconductedusingsymmetricfour-wasintroducedloading,theusingmodetheIIation25±28beshownvariedwherefour-pointusingthethemode-mixitybendingoffset,s,fromratio,(AFPB)theDloadKconfigur-II/Dline,KI,canasrange,inwereDKFig.2.ThevaluesofmodeIstress-intensityI,andmodeIIstress-intensityrange,DKII,tionsdeterminedHutchinson.forthis28

geometry,fromlinear-elasticrecentlydevelopedstress-intensitybyHesolu-andnear-identicalPrecrackingwasconductedinroomsamplesinordermannertoforavoidallanylarge-effectandtemperatureshort-cracktestairinaofprecracking

Table2UniaxialtensileandtoughnesspropertiesofTi-6Al-4V

UltimateFractureYieldtensiletoughnessstrengthstrengthReductionKMicrostructure(MPa)(MPa)inarea(%)(MPaIc

Hm)Bimodal9309784564Lamellar

975

1055

10

100

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

590R.K.NALLAetal.

Fig.2Theasymmetricfour-pointbendspecimen.Theoffset,s,fromtheloadlineisusedinordertocontrolthedegreeof

mode-mixity,DKKII/DKI,andtherebythephaseangle,b tanÀ1(DII/DKI).Thisgeometryisusedforthemixed-modelargeandshortcracktesting.

techniqueally,trodeposition-machinedfatigueoncrackssubsequentweregrownthresholdsfromobtained.a2mmdeepSpecific-elec-notchload(Thisratioinaofsymmetric(EDM)through-thickness0.1withfour-pointaconstantbendingloadingsamplefrequency.ataininroomalloylarthebimodalair,isspecificallyknowntoshowlittleeffectoffrequencystructure20overandtherangeof50±20000Hzcrack-lengthstructure22).Thesurfacesof50±1000allsamplesHzinthelamel-finish,bearingwhereasobservationthewerepolishedtorequireda0.05mformeffectpinofpinsfrictionwerebetweengroundsidestothetobeausedtocarrytheload-specimen600gritandfinish.theAsroller-thevalues,supports25contactfrictionalcansubstantiallyeffectswereaffectminimizedthestress-intensityatMoSpositionsthroughtheuseofahigh-pressurethepin-was2grease.The4.8bimodal+4.500.5+and0.256.8mmfinal+0.5atprecracklengthMPanear-thresholdHm,respectively,DthusKachievedIvaluesfortheofvariedForlargeandDfromcrack(lamellarDKD>microstructures.

K4mm)tests,mode-mixitieswereII/I 0(puremodeinKI)toDKII/ILoadphase$7.1angle,(nearlybpure tanmodeÀ1(DII),KrepresentingachangeII/DKI),from0to828.ingmixitycyclingratioswereprecrackedvariedspecimensfromR 0.1±0.8.Testsinvolv-growthwereperformedinthefollowingataspecifiedway:ifnomode-2$Â106wascycles,observed(usinganopticalmicroscope)crackafteringly0.25repeated.toMPaeitherDKIorDKIIwasincreasedbymaintainHm(withthethemode-mixity)otherbeingandincreasedaccord-boundingInextensionofdefiningthethisactualway,`growth'thresholda`growth/nogrowth'theprocedureconditionwaswastakenobtained.tobeofThetheordercrack$lamellar20themmcharacteristicforstructure,thebimodalmicrostructuralyieldingstructuredimensionÐthatis,thresholdand$growth500mmratesfortheof

notch

(a)

(b)

µm

precrack

Fig.3Theprocedureusedforremovingthecrackwakeofalargecrackinordertoproduceashortcrackisillustrated.

10À10À10À11forsamplingthelamellarmcycleÀ1structure.Thealsolargerserved`growth'toensureconditionadequatecomputingThemagnitudeoftherelativelyboththeeffectiveoftheheterogeneousmicrostructure.(near-tip)crack-tipcrack-drivingshieldingÐusedforceforindevelopedmodesIandIIÐwascharacterizedusingarecentlyopeninggaugesandcompliance-basedshear-typeloading,techniqueusingforbothtensileandmountednearthecracktiptotwomeasuredisplacementopeningRef.shearshielding[11],displacements.Asdescribed,indetail,inseparateinthecrack-tipload-displacementmodesdistinctionIandIIbetweenwasthecontributionstocurvesachievedusingbyexaminingclosure,gauges.ModeIshielding,intheformthesetwoforationthewasdeterminedfromthecomplianceofcrackcurveshielding,fromopeningasperityinlinearitydisplacementstheformonfromthefirstdevi-ofunloading,crack-surfacewhereasmodeIIanalogousrubbingandinterlock,wasdeterminedinterferenceinviaandisplacements.

fashionfromthecompliancecurveforshearShortthrough-thicknesscracks

Inmodeorderthrough-thicknessfatiguetoexaminethresholds,theinfluencethebehaviourofcracksizeoflargeon(mixed-shortcrackswascomparedwith>those4mm)of(($200mm)through-thicknesscracksandsmallof<50Appendixthesemm)typessurfaceofcracks.flawsThearedistinctiondiscussed,andindetail,relevanceinmeasuredMixed-modeA.

thresholdtestsontheshortcrackswereproceduresoncracks,identical6±12mmthickfour-pointbendbars,usingchinedexceptawaytothatwithinthetothosedescribedaboveforlarge$precrack200mmwakeofthewascracktipcarefullyusing

ma-a

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

EFFECTSOFMICROSTRUCTUREONTI-6AI-4VALLOY591

slow-speeddiamondsaw(Fig.3).Therationaleforthisprocedureofremovingmostofthecrackwakewastolimittheeffectofcrack-tipshieldingbyminimizingtheoccurrenceofanyprematurecontactofthecrackfacesduringunloading.However,astheshortcrackswerethrough-thickness,theystill`sampled'thecontinuummicrostructureÐthatis,typicallybetween30and300grains.Thresholdsweremeasuredinbothmicrostruc-turesatloadratiosofR 0.1±0.8formode-mixitiesofDKII/DKI 0toDKII/DKI$7.1(i.e.b 0±828).Smallsurfacecracks

Mixed-modethresholdsformicrostructurallysmallsurfacecrackswereperformedusinganinclined-cracktechnique.Widebendbars(16±25mmwidth,5mmthickness)weremachinedintheL±Torientation,withthesurfacesrequiredforobservationpolishedtoa0.05mmfinish,andthesidesusedtocarrytheload-bearingpinsgroundtoa600gritfinish.Astress-relieftreatmentof2hat6958Cinvacuowasusedinordertominimizeanyresidualstressesfrommachiningandspecimenpreparation.A`precrack'wasnaturallyiniti-atedatthestressofsmax 750MPaÐthatis,$80%ofyieldstrengthÐusingstandardthree-pointbending(withaloadratioof0.1andafrequencyof50Hz).Inordertoenablemeasurementofthesmall-crackthresholds,abendbarwascarefullymachinedoutfromtheoriginalprecrackedwidebarwiththecrackinclinedatthedesiredangle(Fig.4).Thissamplewassubsequentlysubjectedtofour-pointbendingbycyclingataloadratioof0.1.Ifnogrowth(definedasatotalcrackextensionoflessthan20mmper2Â106cyclesonbothendsofthesurfacecrack)wasobserved,themaximumload(andproportion-atelytheminimumload)wasincreasedby111Nandtheabove-mentionedprocedurewasrepeated.Thresholdswerethusagaindeterminedusinga`growth/nogrowth'criterion,butforthebimodalmicrostructureonly.Theinclined-cracktechniquecouldnotbeusefullyemployedforthelamellarmicrostructureasaresultofthehighlydeflectednatureoffatiguecrackinginthisstructure.Linear-elasticsolutionsforthestressintensitiesassoci-atedwiththesmall,semiellipticalsurfacecracksundermixed-modeloadingweretakenfromtwosources.On

(a) wide bend bar specimen (b) small ‘inclined crack’ specimen

Fig.4Schematicshowingtheproceduresutilizedforobtainingthesmall`inclinedcrack'specimen.(a)Thedottedlinesoutlinethesmall-cracktestsampletobemachinedatthedesiredangleofinclination,ffromtheoriginalwidebendbar.Thenominaldirectionofloadingforcrackinitiationisalsoshown.(b)Thefinal`inclinedcrack'specimenisillustrated.(c)Schematicoftheinclinedsemiellipticalsurfacecrack

configurationusedforthemicrostructurallysmall-cracktesting.Thetensileloadingcomponent,s22,inducesthemodeIcontribution,whereastheshear-loadingcomponent,s12,inducesthemodeIIandmodeIIIcomponents.

(c) mixed-mode small crack testing

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

592R.K.NALLAetal.

thesurface,basisthatthecrackplanewasnormaltothewassolution:computedthemodeIcomponentofthestressintensity,specimenKI,29fromthewell-knownNewman±Rajur KI st Hsb

paF a;ac ;;y 1

wherethemetricalremotestisuniformtheremoteouter-fibreuniformbendingtensionstress.stressTheandsgeo-biscrackdepth,factorsÐthickness,positiont;thea;specimentheH,crackhalf-length,QandFÐareevaluatedfrom:thehalf-width,b;cand;thethespecimenangularRef.alongthecrackfront,y,asdescribedindetailinfromThe[29].

modeellipticalthesurfacenewlyIIcomponent,derivedcracksunderHe±HutchinsonKII,conversely,wasmixed-modesolutioncomputed30loading:forKII ws12p

pa

2

whereswisanumericalfactordeterminedfromRef.[30];crackdepth.12isthesheardimensionalItcomponentshouldbeofnotedtheloadingherethatandaathree-isthethecornersingularityexistsinthesolutionatHowever,pointwherebecauseforthethepurposecrackintersectsofthisstudy,withthefreesurface.gible.theMoreover,errorscausedasonebysuchanassumptionthisisareignorednegli-decreasesinterior,themagnitudemovesofthealongmodetheIIcrackfrontcontributiontodeepestpenetrationwiththatofofmodethecrackisIIIincreasingtillthepointofwasThecomponents.resolvedappliedload/stresstrigonometricallyontheinclinedreached.

intotensilecrack(Fig.and4c)miningDDKThetensilecomponentwasusedfordeter-shearI,usingsmallKRef.[29]andtheshearcomponentforIIandwithsurfaceDKIIIcracks,usingandRef.the[30].variationAstheexactshapeofsuchonbehaviour,thecrackextensioncrack-drivingclearlycanhaveaninimportantthisaspecteffectratio31,32depth-to-surfacecrackshapesforceandhencethecrack-growthpostfracturelength(Fig.4)Ðintheformofthea/2c$0.45.

observations;ratio,thea/2ctypicalÐwereaspectdeterminedratiowasbycharacterizingTheuseoflinear-elasticjustifiedthedrivingforcesstress-intensityforthesmallsolutionscracksforincracksizesrelationontheto$ofcracksize.basisofthesmallcyclicplastic-zonesizesis$1mm,whereForexample,theDKforthesmallest(orderD1KMPamÀ1,plastic-zonesize(estimatedIthresholdsasrarey$1/2pI/sy)2wherescracksize,of100nm.Asyisthistheisyieldstrength)areonthesmall-scaleyieldingitisdeemedroughlyone-tenthoftheconditionsreasonableprevail.

toconcludethatRESULTS

Large-crackbehaviourEffectofloadratioandmode-mixity

LargemicrostructurescrackthresholdsFig.undermodeforIthe IIbimodalloadingandareshownlamellarwhere5inDthethemodeformofinIImixed-modethresholdthresholdenvelopes,modeKplottedasafunctionstress-intensityofthecorrespondingrange,II,TH,isthatwhicheachIthresholdthresholdstress-intensityisrepresentedrange,bytwoDKI,TH(noteTheloadphaseindicateanglestheinvestigated`growth'anddatapoints,were`nogrowth'conditions).offollowing0.8ratiosforofobservationsboth0.1andstructures.0.5,andcanbeBased0,26and0,26,62and828formade:

onthese628atresults,aloadratiothe.Akintobehaviourinmostmetallicalloys(e.g.Refs[8±9,33±35]),areductioninthefatiguethresholdvaluesisclearlyevidentforbothmicrostructureswithincreasingloadratio.TheslightincreaseinthemodeIthreshold,DKI,TH,withincreasingmode-mixityatlowphaseangles,observedinthepresentdataatphaseanglesbetween0and268,hasbeenattributedtotheeffectofmodeI/modeIIcrack-tipshielding.10±12

.ThemodeIthreshold,DKI,TH,clearlydecreaseswithincreasingmode-mixity.However,ifamoreappropriatedrivingforceÐincorporatingbothmodeIandmodeIIcomponentsÐisusedinordertocharacterizethethresh-old,specificallytherangeinstrain-energyreleaserate,DG (D(KI2 DKII2)/E'whereE' E(EisYoung'smodulus)inplanestressandE/(1-n2)inplanestrain(nisPoisson'sratio),thenthereisaprogressiveincreaseinthemixed-modeDGTHfatiguethresholdwithincreasingmode-mixityinbothmicrostructuresforallloadratiosstudied(Fig.6).Thiscanalternativelyberepresentedintermsofanequivalentstress-intensityfactorrange,DKeq,TH (DGTHE')1/2,whichisalsoplottedinFig.6.Notethatinthisandallsubsequentfigures,thresholdvaluesarerepresentedbyasingledatapointshowingtheaveragevalueofthe`growth/nogrowth'conditions.Analternativemeansofcalculatingthemixed-modethresh-oldsisbrieflydescribedinAppendixB.

.Fromtheperspectiveofthresholdsforhigh-cyclefatigueinTi-6Al-4V,theresultsinFig.6stronglyimplythatdespitethepresenceofmixed-modeloading,themodeIthreshold,definedintermsofthestrain-energyreleaserate,DG,forcrackslargecomparedtomicrostructuraldimensions,representsaworst-caseconditionfortheonsetoffatiguecrackgrowthundermodeI IIloadingforbothmicrostructures.

.Thoughbothmicrostructuresshowedmixed-modeDGTHthresholdsthatincreasedsubstantiallywith

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

EFFECTSOFMICROSTRUCTUREONTI-6AI-4VALLOY593

KI,TH (ksiVin)

(a)

10

Mode II stress-intensity range at threshold

KII,TH (MPaVm)

8

6

8

6

4

4

2

2

(b)

10

Mode II stress-intensity range at threshold

8 KII,TH (ksiVin)

KII,TH (MPaVm)

8

6

6

4

4

2

2

Fig.5Mixed-modethresholdenvelopesfor

large(>4mm)through-thicknesscracksinthe(a)bimodaland(b)lamellar

microstructures.Notethatthelamellarstructureshowssuperiorresistancetocrackpropagation,particularlyatthelowerphaseangles.

0Mode I stress-intensity range at threshold

KI,TH (MPaVm)

increasingmode-mixity,ingeneralthelamellarstructurewasobservedtoexhibitthehigherthresholdvalues.However,thebetterfatigueresistanceofthelamellarstructurewasmarkedlyreducedathighmode-mixities,asisevidentfromthelarge-crackthresholdvalueslistedinTable3(thedifferencebetweenthethresholdsforthetwomicrostructuresisincludedinparenthesesforthepurposeofcomparison).Clearly,thesuperiorfatiguecrack-growthpropertiesofthelamellarstructureatlowmode-mixities(b 0and268)arenearlyeliminated,orinsomecasesreversed,whensignificantmodeIIloadingispresent(b 62and828).

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

KII,TH (ksiVin)

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

594R.K.NALLAetal.

(a)

11

Threshold strain-energy releaserate range, G TH ( J/m2)

Threshold equivalent strees-intesityThreshold equivalent strees-intesity

10

9

8

76

53

1020304050608011

Phase angle, b (8)

(b)

10

Threshold strain-energy releaserate range, G TH ( J/m2 )

987

range, K eq,TH (MPaVm )

range, K eq,TH (MPaVm )

653

Fig.6Thethresholdstrain-energyreleaserate,DGTH,isplottedasafunctionofphaseangle,b,forthe(a)bimodaland(b)lamellarmicrostructureforlargecrackssubjectedtomixed-modeloadingatR 0.1,0.5and0.8.Equivalentstress-intensityrangesatthreshold,DKeq,TH,forboth

microstructuresarealsoshown.The

lamellarmicrostructure,ingeneral,showssuperiorresistancetofatigue-crackpropagation,althoughthedifferenceisreducedathighmode-mixities.

Roleofcrack-tipshielding

AsdiscussedinRefs.[10,11]forthebimodalstructure,theincreaseinthelarge-crackmixed-modethresholdswithincreasingmode-mixitycanbedirectlyrelatedtoanincreasedroleofmodeIandmodeIIcrack-tipshielding,associatedwith,respectively,crackclosureandslidingcrackinterference(frictionandinterlockofcrack-surfaceasperities).Thiscanbeappreciatedbyquantifyingthemagnitudeofsuchshieldinginordertodetermineamixed-mode,effectivestrain-energyreleaserate,DGeff,andthen`correcting'thelarge-crackthresholddatainFig.6forsuchshieldingbycharacterizingintermsofDGeff.Theeffective(near-tip)strain-energyreleaserate,DGeff,canbedefinedas(DKI,eff2 DKII,eff2)/E',whereDKI,effistheeffectivestress-intensityrangeinmodeIandDKII,eff

isthecorrespondingeffectivestress-intensityrangeinmodeII.Inthepresentwork,DKI,effwasdeterminedintheusualfashionusedinordertomeasurecrackclosureÐthatis,intermsofKI,max±Kcl,whereKclistheclosurestressintensitydefinedatthefirstdeviationfromlinearityofthecrack-tipload-displacementcurveonunloading.Ontheotherhand,DKII,effwasmeasuredasthedifferencebetweenthenear-tipmaximumandmin-imummodeIIstressintensitiesinthefatiguecycle.Thenear-tipmodeIIstress-intensityrangediffersfromtheapplieddrivingforceasaresultofthepresenceofshear-inducedfracture-surfaceasperitycontactandinterlock.FurtherdetailsonthedeterminationofDKI,effandtheestimationofDKII,effusingcompliance-basedtechniquescanbefoundinRef.[11].

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

EFFECTSOFMICROSTRUCTUREONTI-6AI-4VALLOY595

(a)11

10

Threshold equivalent strees-intesityThreshold equivalent strees-intesity

range, K eq,TH (MPaVm )range, K eq,TH (MPaVm )

Threshold strain-energy releaserate range, G TH ( J/m2 )

9

87653

0Phase angle, b (8)

(b)

11

10

Threshold strain-energy releaserate range, G TH ( J/m2)

9

87

6

53

0Fig.7Thethresholdstrain-energyreleaserate,DGTH,isplottedasafunctionofphaseangle,b,forthe(a)bimodaland(b)lamellarmicrostructureforlargecrackssubjectedtomixed-modeloadingatR 0.1,0.5and0.8.ResultsfromFig.6arecomparedwiththeDGTH,effvalueswhichhavebeencorrectedforcrack-tipshielding.Notetherelativeabsenceofanyeffectofmode-mixityand/orloadratioontheshielding-correctedthresholds.

Phase angle, b (8)

BysocharacterizingthedrivingforceintermsofDGeffbysubtractingoutthecontributionsfromcrack-tipshielding(individualDKIandDKIIvaluesarelistedinTables4and5),theeffectofmode-mixityonthethresholdisfoundtobegreatlyreducedforbothmicrostructures.ThiscanbeseeninFig.7wherethe`shielding-corrected'DGeff,THthresholds(plottedashatchedregions)arecomparedwiththe`uncorrected'dataofFig.6.Severalpointsareworthyofnote:

.Theshielding-correctedDGeff,THthresholdvaluesaresubstantiallysmaller(byasmuchasafactoroffour)thantheuncorrectedDGTHvalues,especiallyathighphaseangles.

.Mixed-modethresholdvaluesareessentiallyindependentofbothloadratioandmode-mixity.WhileitisgenerallyappreciatedthattheeffectofloadratioonmodeIthresholdvaluesislargelyassociatedwithcrackclosure(e.g.Refs[19,20]),theseresultsconfirmearlierreportsforthebimodalstructure10,11thattheeffectofmode-mixityinincreasingtheDGTHthresholdinTi-6Al-4Vcanbeprincipallyattributedtoanincreaseincrack-tipshielding(mainlyfromenhancedcrack-surfaceinterference).

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

596R.K.NALLAetal.

Table3FatiguethresholdvaluesforlargefatiguecracksinTi-6Al-4V

DGTH(JmÀ2)

Mode-mixity

R 0.1

Bimodalmicrostructure:08200268280628410828850LamellarmicrostructureÃ:08320( 60%)268395( 41%)628450( 10%)828815(À4%)

Ã

DKeq,TH(MPaHm)

R 0.5

R 0.8

R 0.1

R 0.5

R 0.8

80

150375575

170( 113%)255( 70%)345(À8%)660( 15%)

80100320±

110( 38%)165( 65%)305(À5%)±

4.95.87.010.16.26.97.49.9

3.14.36.78.34.55.56.58.9

3.13.56.2±3.64.56.1±

ThenumbersinparenthesesindicatethedifferencebetweenthemagnitudesoftheDGTHthresholdofthelamellarstructureascomparedtothebimodalthreshold.

Table4Comparisonoftheappliedandshielding-correctedmodeIstress-intensityranges

DKI,THDKI,TH,effReductionin

LoadratioMode-mixity(MPaHm)(MPaHm)DKI(MPaHm)ÃBimodalmicrostructure:0.108

628828

0.508

628828

0.808

628Lamellarmicrostructure:0.108

628828

0.508

628828

0.808

628

Ã

Table5Comparisonoftheappliedandshielding-correctedmodeIIstress-intensityranges

DKII,THDKII,TH,effReductionin

LoadratioMode-mixity(MPaHm)(MPaHm)DKII(MPaHm)ÃBimodalmicrostructure:0.1628

828

0.5628

828

0.8628

5.0

3.61.53.33.31.23.23.16.53.61.44.63.11.33.92.9

4.72.80.63.31.70.03.22.34.62.20.84.32.80.53.72.5

0.30.80.90.01.61.20.00.81.91.40.60.30.30.80.20.4

(6%)(22%)(60%)(0%)(48%)(100%)(0%)(26%)(29%)(39%)(43%)(7%)(10%)(62%)(5%)(14%)

6.510.46.08.65.63.94.84.65.35.05.26.63.86.22.9

2.6(40%)5.6(54%)1.4(23%)3.3(38%)0.6(11%)1.5(22%)3.5(35%)2.0(35%)2.9(32%)2.6(47%)

Lamellarmicrostructure:0.16286.7

82810.1

0.56285.8

8289.1

0.86285.5

Ã

ThenumbersinparenthesesindicatethepercentagereductioninDKIIowingtocorrectionforcrack-tipshielding.

ThenumbersinparenthesesindicatethepercentagereductioninDKIowingtocorrectionforcrack-tipshielding.

Crackpathandfractography

Akintofatiguecrack-growthbehaviourinpuremodeIinthepresenceoflargecracks,22thelamellarmicrostruc-turedisplayssuperiorcrack-growthresistanceundermixed-modeloadingcomparedtothebimodalstructure.Thiscanbeattributedtothelargedegreeofcrack-pathdeflection,bifurcationandsecondarycrackformationassociatedwithcrackgrowthinthelamellarstructure.TypicalcrackpathsareillustratedinFig.8forbothmicrostructures,andshowthepuremodeIprecrack(grownatR 0.1)andsubsequentcrackgrowthunder

.Thesuperiormixed-modefatiguethresholdpropertiesofthelamellarmicrostructurearesubstantiallyreducedwhenresultsareplottedintermsofDGeff,suggestingthatthisisalsoassociatedwithhigherlevelsofcrack-tipshielding.Thisisconsistentwiththesignificantlymoretortuouscrackpathsobservedinthelamellarstructure,whichwouldpromotecrack-surfaceinterference,asdis-cussedinthefollowingsection.

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

EFFECTSOFMICROSTRUCTUREONTI-6AI-4VALLOY597

400µm

qMTS =39.7

qexp ~39

Mode I

b applied = 26

(a)

200µm

qMTS =60.8

Fig.8Typicalfatiguecrackprofilesarecomparedforthe(a)bimodal(R 0.8,b 268,DGTH 100JmÀ2)and(b)lamellar(R 0.1,b 628,

DGTH 450JmÀ2)microstructures.

OpticalmicrographsshowboththemodeIfatigueprecrackandtheregionofdeflectedcrackgrowthfollowingtheapplicationofcyclicmixed-modeloading.Measuredcrackdeflectionangles,yexp,arecomparedwiththosepredictedbythepathofmaximumtangentialstress,yMTS(seeRef.[12]).

qexp ~37

(b)

Mode I

b applied = 62

mixed-modeloading(atR 0.8withDKII/DKI 0.5forthebimodalstructureandatR 0.1withDKII/DKI 1.9forthelamellarstructure).Thereisclearlyasubstantialdifferencebetweenthetrajectoriesofcracksinthetwostructures.Thisisevident(i)inthecrackpathespeciallyduringmodeIcrackgrowth,wherethelamel-larstructureshowssubstantiallyhighertortuosityowingtointeractionofthecrackwiththemuchcoarserlamellarmicrostructureÐwithcharacteristiclengthscalesof$500mmÐand(ii)inthecrackdirectionattheonsetofmixed-modeloading,asdiscussedbelow.

Thecrack-pathdirectionisdeterminedthroughacom-petitionbetweenthemaximumcrack-drivingforceandtheweakestmicrostructuralpath.Infine-scale,homoge-neousmicrostructures,suchasthebimodalmicrostruc-ture(wherecharacteristiclengthscalesare$20mm),thecrack-drivingforcebecomesthedominantfactor.Fornominallyelasticconditions,thepathofagrowingfatiguecrackwillchangeinresponsetoachangeintheappliedphaseangle,sothatapuremodeInear-tipconditionismaintainedÐthatis,thecracktipfollowsapathdictatedbyeitherazeromodeIIstressintensity(KII 0),maximumtangentialstress(MTS),ormax-imumstrain-energyreleaserate,Gmax36,37Ðallcriteriathatyieldessentiallythesamecrack-pathpredictions(exceptatveryhighphaseangles).Accordingly,cracksinthebimodalstructuredeflectundermixed-modeloadingtofollowamodeIpath,asillustratedinFig.8awherethecrackdeviatesalmostexactlyalongthepathofmaximumtangentialstress.Forthecoarselamellarstruc-ture,conversely,Fig.8bshowsthatthecrackdoesnotdeflectalongthemaximumtangentialstressdirectionattheonsetofthemixed-modeloading;here,thecharac-teristicmicrostructuraldimensionsarefarlarger,sothatthecrackpathonthisscaleofobservationcannotbede-scribedbycontinuumnotionsandismarkedlyinfluencedbymicrostructure.SimilardeviationsfrompredictedmodeIcrackpathsundermixed-modeloadinghave

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

598R.K.NALLAetal.

CRACK - PROPAGATION DIRECTION

Fig.9Typicalfractographyformixed-modefatiguecrackgrowthinthe(a)bimodal(DGTH 410JmÀ2)and(b)lamellar

microstructures(DGTH 450JmÀ2).Bothspecimensweretestedatloadratio,R 0.1,andphaseangle,b 628.Themuchcoarserlengthscalesinvolvedforthelamellarstructureareevident.

beenturesobservedforcoarse-grainedcracksinacantitaniumfollowaluminidelamellarmicrostruc-aintermetallics,wherefatiguesurfacesAllsinglepreferentialinterlamellarpathwithintheselargewith(Fig.factorscolony.38

9)inresulttheinlamellarsubstantiallymicrostructure,rougherfracturewhichthroughlargeloading,prematurecrackspromotescrack-surfacebothasperitymodeIcontactcrackclosure,enhancedandslidingasperitymodeIIonun-rubbingcrack-surfaceandinterference,throughsuchandsignificant5,closurecrackfaces.Measurementsinterlockingofthemagnitudewithintheofprovideandexperimentalsurfaceinterference,confirmationlistedinTables4lamellarthismicrostructurestructure;roleofthiscrack-tipshieldinginofthethecoarsermoredisplaysprovidessuperiortheresistancemainreasonto(large

whycrack)fatiguefatiguemixed-modethresholdcrackloadingvaluespropagation,conditions.underbothwithpurehighermodemeasuredIandShort-crackbehaviour

Corresponding(mixed-modeDGTHlamellar$200mm)plottedstructuresthrough-thickness(atb 0±82cracksthresholds8andinRtheforshort bimodal0.1±0.8)andareasafunctionofthephaseangleinFig.10;areuncorrectedcomparedfromandwithshielding-corrected)thecorrespondingthresholdsresultsforlarge(bothshieldingFig.7.Asnotedabove,theeffectofcrack-tipcracksthefrictionpresenceintheofcrackwakshearloadingeisparticularlysignificantinowingatedDGwithtoandtheinterlockingofasperities.owing39±41toConsequently,crack-surfacethresholdscracksminimalofwere:

limitedroleofwake,crack-tipmeasuredshieldingshortassoci-crackTH.substantiallylowerthanthecorrespondinglarge-crackvalues(similartoresultsformodeIthresholds22),

.essentiallyinsensitivetothedegreeofmode-mixity,inmarkedcontrasttothelargecrackthresholds,and

.relativelyinsensitivetotheloadratio,againincontrasttolargecrackresults.

listedMoreover,theshort-crackthresholdvalues,whicharebandingforinTable6,wereobservedtoliewithinthescatter-conditions,that,shielding-correctedsimilartoobservationslargecracks,underagainpureindicat-isresponsiblethelimitedeffectofshieldingforshortmodecracksItionWithrespectfortotheirtherolelowerofmicrostructure,thresholdvalues.

insubstantiallytermsbetweenofthethebimodalandlamellarmicrostructuresthedistinc-forreducedmixed-modeforshortcrack-growthcrackscomparedresistancetothatiseffectlargeoldsofmicrostructurecracks.Thisagainonimpliesthattheprimarycrack-tipinTi-6Al-4Varisesthroughmixed-modethefatiguemechanismthresh-ofrestricted,shielding.wake,asintheWherecasetheroleofsuchshieldingismodaldifferencesinfatigueofresistanceshortcracksbetweenwithlimitedthecant.loadingAnalogousandlamellarbehaviourstructurescanbecomemuchlesssignifi-bi-tieswherethesuperiorfatiguebecrack-growthseenundermodeproper-Iwhereoftheoncethelamellarstructurearelostathighloadratios,throughagain,effectmechanismstheofprimarycrackclosureofcrack-tiproleofbecomesshielding.microstructureinsignificant;22occursSmall-crackbehaviour

AmonlymoreencounteredrealisticflawÐininrealtermsstructuresÐisofwhatisthatmostofcom-the

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

EFFECTSOFMICROSTRUCTUREONTI-6AI-4VALLOY599

(a)

Threshold equivalent strees-intesity

Threshold strain-energy releaserate range, G TH ( J/m2 )

(b)

Threshold equivalent strees-intesity

Threshold strain-energy releaserate range, G TH ( J/m2 )

range, K eq,TH (MPaVm )

Fig.10Variationinmixed-mode

thresholds,DGTH,asafunctionofphaseangle,b,in(a)bimodaland(b)lamellarstructures.Shownareresultsatthreeloadratiosforlarge(>4mm)cracks,beforeandafter`correcting'forcrack-tipshielding,andforshort($200mm)through-thicknesscracks.Thelamellarmicrostructureshowssomewhatsuperiorresistancetocrackpropagationintheshortcrackregime.

Phase angle, b (8)

small,semiellipticalsurfacecrack,whichissmallinalldimensions.Likeshortcracks,suchcracksexperienceaminimaleffectofcrack-tipshieldingowingtotheirlimitedwake.InthepresentstudyonTi-6Al-4V,modeIDGTHthresholdsforsuchmicrostructurallysmall(<50mm)cracksinboththebimodalandlamellarstruc-turesarecomparedwithcorrespondingmixed-modelarge-crackdatainFig.11.Thresholdvaluesforthesmallcracksareclearlymuchsmallerthanthecorres-pondingvaluesforlargecracks.Indeed,smallcracksareobservedtopropagateatthresholdlevelsaboveDGTH 8.3JmÀ2(DKI,TH$1MPaHm),whereastheworst-caseDGthresholdforlargecracks,namelyDGTH 29.9JmÀ2(DKI,TH$1.9MPaHm),isafactorofthreelarger.

Microstructurally,againitisclearthatwhereasthelamellarstructurehassuperiorlarge-crackthresholdproperties,thisisnotapparentinthepresenceofsmallcrackswherethemodeIthresholdsarealmostidentical.Eventhesubsequentsmall-crackgrowthrates,shownasafunctionofDKIinFig.12fromaparallelstudyontheeffectsofforeign-objectdamageonhigh-cyclefatigueinTi-6Al-4V42revealfewdifferencesinthebehaviourofthebimodalandlamellarmicrostructuresÐobservations

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

range, K q,TH (MPaVm )

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

600R.K.NALLAetal.

whichcanberelatedtotheminimalroleofcrack-tipshieldingwithcracksoflimitedwake.

However,thebehaviourofthesmallsurfacecrackisdifferentfromthatoftheshort(andlarge)through-thicknesscrackinthemannerinwhichitstatistically`samples'themicrostructure.Inthepresentexperimentswherethesmall-crackdimensionswerecomparablewithcharacteristicmicrostructuralsize-scales,theircrackfrontscannotsamplethe`continuum'microstructure.Forexample,whereastheaverageshortcrackinthebimodalmicrostructurewould`sample'some300grains,

Table6ThresholdsobtainedforshortfatiguecracksinTi-6Al-4V

DGTH(J/m2)

DKeq,TH(MPaHm)

Mode-mixityR 0.1R 0.5R 0.8R 0.1R 0.5R 0.8Bimodalmicrostructure:0872662681251056287264828148140Lamellarmicrostructure:08159110268176131628180142828210145

thesmallcrackmerely`samples'oneortwograins.Data

onthebehaviourofsuchcracksundermixed-modeloadingareextremelylimitedalthoughpresentresultsforthebimodalstructure,atR 0.1only,areshowninFig.13andarecomparedwiththecorrespondinglarge-andshort-crackmixed-modethresholdvalues.Clearly,theadditionaleffectofmicrostructuralsamplingisevi-dentintheseresultsinwhichthesmall-crackthresholdscanbeseentobelowerthanthecorrespondingvaluesforshortcracksandshielding-correctedlargecracks.Whilethemarkedeffectofcracksizeonthemixed-modethresholdsuptonowhasbeenattributedtoadifferenceinthemagnitudeofthecrack-tipshielding,theevenlowermixed-modethresholdsformicrostructurallysmallcracksreflectthisadditionalfactorofthebiasedsamplingofthe`weaklinks'inthemicrostructurebythesmallflaw.Indeed,quantitatively,large-crackmixed-modeDGTHthresholdsinthebimodalstructureathighmode-mixitiesDKII/DKI 7.1canbesome$50±90timeslargerthansuchmeasuredsmall-crackthresholds.

DISCUSSION

59855213096119121125

2.93.92.94.24.44.64.75.0

2.83.62.84.13.64.04.14.2

2.73.22.54.03.43.83.83.9

Inthepresentstudy,wehaveexaminedhowvaryingthemicrostructurecanaffectthemixed-modefatiguecrackgrowththresholdsinaTi-6Al-4Valloyasafunctionofloadratioandmode-mixity.Whathasbeenfoundisthatmicrostructure,mode-mixityandloadratioallcanhaveamajorinfluenceonthevalueofthemixed-modethresh-old,butonlyinthepresenceofcrackslargecomparedwith

Threshold strain-energy release rate range, GTH (J/m2 )

Mode I

10

20

30

40

50

60

70

80

90Phase angle, b ( )

Fig.11Mixed-modethresholdsforlarge(>4mm)through-thicknessfatiguecracksinbimodalandlamellarTi-6Al-4VarecomparedwithpuremodeIthresholdsformicrostructurallysmallcracks.Thesuperiorresistanceofthelamellarstructureobservedinthelargecrackregimeiseliminatedforsmallcracks,wheretheroleofmicrostructuralsamplingbecomesimportant.

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

EFFECTSOFMICROSTRUCTUREONTI-6AI-4VALLOY

Surface crack length 2 c (µm)

10 5

601

10 6

Crack-growth rate, da/dN (m/cycle)

10 7

10 8

10 9

10 10

Fig.12Fatiguecrackgrowthratesasafunctionofappliedstress-intensityrangeatR 0.1formicrostructurallysmall

($2±50mm)rge-crackgrowthdataatR 0.1wereobtainedfromconstantload-ratiotests,whereas

correspondingdataatR 0.91±0.95wereobtainedusingconstant-Kmax/increasing-Kmintesting(afterRef.[42]).

10 11

0.612468102040

Stress-intensity range, K (MPaV

m)

4

3

5

Fig.13Variationinmixed-mode

thresholds,DGTH,asafunctionofphaseangle,b,formicrostructurallysmall(<50mm)surfacecracksinthebimodalmicrostructure.Shownforcomparisonareresultsforshort($200mm)through-thicknesscracksandforlarge(>4mm)through-thicknesscracksunderworst-case,highRconditions.

21

1020304050607080Phase angle, b(8)

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

Threshold equivalent strees-intensityrange, Keq,TH (MPaVm )

6

Threshold strain-energy releaserate range, GTH ( J/m 2 )

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

602R.K.NALLAetal.

microstructuralmode-mixitycantthrough-thicknesseffectonanddimensions.Thefactthatmicrostructure,fatigueloadthresholdsratioallhaveinthearelativelypresenceinsignifi-surfacecrack-tipcracksshieldingstronglycracksdictatedimpliesandmicrostructurallyofshortbycrackapath.

dominantrolesmalloflarge-crackThesuperiorcrack-growthresistance,andhencehigherappearstakentoDbeGTHaconsequencethresholds,inofthelamellarstructurehigherbystructures,levelsthepropagatingthepreferentialpathofcrack,whichinturnpromotesbasaltheacrack-tipphaseisorientatedshielding.perpendicularInalignedlamellartotheplaneplane;21crackpropagationparalleltothebasallartoorientationtheorientationisthusofgenerallythealaths.observed22perpendicu-layercantlyofbphasethatsurroundsthealathsBecausecannotthethinoccursalterthecrackpath,crackpropagationinvariablysignifi-entirecrystallographiccolonywithalmostofsimilarlynochangeorientatedindirectionlaths.Thisthroughanevidenttion,inthesignificantinfluenceamountontheoffatigueout-of-planecrackpathstronglyischaracteristicsecondarycomparedofcrackingthecoarserandlamellarcrack-pathtortuositydeflec-thatisbimodalstructurestothealmost(Fig.8).

planarcrackpathsmicrostructures,inthefinerasoneSuchlamellarintrinsicmicrostructuralandonefactorsextrinsic.canInleadthetotwoeffectsÐloading,differentthestructure,crackattemptsatthetoonsetdeviateofthecoarser-grainedalongmixed-modetated(MTS)byfromdrivingcriteria.theGthatofthepreferredpathÐthatadirectionis,dic-maxAlthough,KII 0thisormaximumtensilestressdebatableforce,structuraleffectpath.becauseitseffectontheclearlymeasuredrequiresthresholdahigherisMoretheimportantcrackisfollowingthoughaisweaktheerextrinsicmicro-higherinence,consequencesaslevelswhichshown,ofthecrackclosureroughercrackpathsgiverisetotherespectively,andincrackTables-surface4andinterfer-5.Theactoninthecrackwakofthise,arethethatprimebecausethesemechanismsthetheexpectedprecrack.mixed-modeThus,thresholdariseseffectfromofthemicrostructurepresenceoflessthattheseasmicrostructurehasbeenobserved,effectswillitistobeshortapparentcracks.

iftheDGbefarTHthresholdsaremeasuredformicrostructureAfurtherpointfrontcasesamplesacanofnotelargeonlyisenoughbethatdevelopedsuchbeneficialeffectsofnumberofwheregrains,theasincrackthestudy.ofstructurallyIndeed,thelargethesmallwhereandshortcracksexaminedinthepresentcracksÐthisthisisnotmaythecaseÐe.g.leadtoareversalformicro-theThepresentrelativebasisresultsrankingforthisdoofnotthetwostructures21althoughofreversalshowinvolvesthistooclearlythedensity(Fig.11).of

microstructuralForriersÐrgeandshortbarrierscracks,rlytoorientatedgraincolonies,boundaries,numberofsuchbar-etc.Ðareinterfacesbetweendissimi-tortuosityfrequentture.characteristicHowever,andchangeshigherinpath,andencountered,henceincreasedleadingforsmallthresholdscracks,comparableforthelamellarinsizestruc-tomaytheresultinglamellarencountermicrostructuralstructureasfewasbeonecontainedorsize-scales,twograins,thecrackfrontthewithinorainthecaseofoftheirbarriersinthetocrackfrontsamplingamuchlowersingledensitygrain,canthanshowsuperiorcrackpropagation.poorerlarge-crackproperties,Consequently,despiteresistancetolamellarstructureseffectFinally,bimodaloldsofmode-mixityitisstructuresapparentinthesmall-crackregime.fatiguecrackpropagation21

onthatthethelarge-cracknear-eliminationDGoftheTHmeasurementwhencrack-tipimpliesorbyremovalshieldingisaccountedfor(eitherthresh-byunderthatthethresholdbehaviourofthecrackwakoffatiguee),stronglycracksphenomenon.mixed-modeshearTheloadingprincipalisinfluencepredominantlyoftheamodeIdeflection,loadingtureinconjunctionappearstobewithindictatingthecrack-pathappliedsethencebyinthethecoarsermicrostructures;theoncenear-tipthecrackpathmicrostruc-iseffectivethephasemixed-modeangle,thethresholdinitialcrackextensionaredictatedbyandentmixed-modeofmode-mixity.crack-drivingTheforce,implicationswhichislargelyindepend-theidenticaltionstomodefatiguethresholdbehaviourforthisisareessentiallythattheatothecrack-tipIbehaviourshieldingifthattheareadditionalinducedcontribu-over,deflectedureditfurthercrackpathimpliesarecarefullyaccountedfor.owingMore-toalowerunderbound.

puremodeIthatloading,theDcanGTHbethreshold,consideredmeas-tobeCONCLUSIONS

Basedfatigueonaninvestigationofthemixed-modehigh-cycle(grainturesizebehaviour$20mm)ofandthethefinebimodalmicrostructureengine(colonyalloy,thesizefollowing$500mm)coarserconclusionsinalamellarTi-6Al-4Vmicrostruc-canbemade:

turbine-1Bothmicrostructuresdisplayedamarkedeffectofmode-mixityandloadratioonthemeasuredmixed-modefa-tiguethresholdsforthrough-thicknesslarge(>4mm)cracks.Bycharacterizingthecrack-drivingforceintermsofthestrain-energyreleaserate,DG,themodeIthresholdwasfoundtorepresenttheworst-casecondition.

2Thecoarse-grainedlamellarmicrostructurewasgener-allyobservedtohavehigherthresholds,andhencesuper-iormixed-mode,near-thresholdfatiguecrack-growth

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

resistance,comparedtothebimodalstructure,inthepresenceoflargethrough-thicknessfatiguecracks.How-ever,thisdifferencewassignificantlyreducedathighphaseangles.

3

Themarkedeffectofloadratioandmode-mixitywassubstantiallyreducedwhenthelarge-crackDGTHthresh-oldswere`corrected'forcrack-tipshieldingowingtomodeIcrackclosureandmodeIIcrack-surfaceinterfer-ence.Assuchshieldingwaspromotedinthecoarserlamellarmicrostructurebyahigherdegreeofcrack-pathtortuosityandfracture-surfaceroughness,thesuperiorlarge-crackpropertiesofthisstructureweresignificantlyreducedbysuchcorrections.

4

Mixed-modeDGTHthresholdsforthrough-thicknessshortcracks($200mm)weresubstantiallylowerthancorrespondinglarge-crackthresholdsinbothmicrostruc-tures;moreover,short-crackthresholdvalueswereessen-tiallyinsensitivetoloadratioandmode-mixity.

5

Comparedtolarge-crackthresholdbehaviour,theinflu-enceofmicrostructureonsuchshort-crackmixed-modeDGTHthresholdswassubstantiallyreduced.Thiswasattributedtotheabsenceofcrack-tipshieldingeffectswithcracksoflimitedwake.

6

Resultsfornaturallyinitiatedmicrostructurallysmall(<50mm)semiellipticalsurfacecracksinthebimodalmicrostructureindicatethatmixed-modeDGTHthresholdsforsuchcracksaresubstantiallylowerthanthoseforlargecracks;indeed,large-crackthresholdsathighmode-mixities(DKII/DKI$7.1)canbesome50±90timeslargerthansuchmeasuredsmall-crackthresholds.Thesubstantiallylowersmall-crackthresholdswereassociatedwithalimitedroleofcrack-tipshieldingandadditionallywithbiasedmicrostruc-turalsamplingbycracksofadimensioncomparablewiththecharacteristicmicrostructuralsize-scales.

7

Theprimesourceoftheinfluenceofmixed-modeloadingindictatingthevalueofthemixed-modeDGTHthresholdisconsideredtoariseprimarilyfromthetrajectoryoftheprecrack.Becausemicrostructurecaninfluencethistra-jectory,ingeneralmicrostructuraleffectsonmixed-modethresholdsresultmainlyfromtheroleofcrack-tipshieldingthatarisesfromsuchcrackpaths.Wherecracksizesaresmallenoughsothatsuchshieldingcannotfullydevelop,theinfluenceofmicrostructureonmixed-modethresholdsbecomesminimal.

Acknowledgements

ThisScientificworkwassupportedbytheUSAirForceOfficeunderResearchtheResearchauspicesunderoftheGrantNo.F49620-96-1-0478ofsityDrsofInitiativeonHigh-CycleMultidisciplinaryFatiguetotheUniversityUniver-ThompsonB.CaliforniaL.Boyce,atBerkeley.SpecialthanksareduetoforhelpfulI.Altenberger,discussions.

J.O.PetersandA.W.ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

EFFECTSOFMICROSTRUCTUREONTI-6AI-4VALLOY603

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APPENDIXA

Distinctionbetweenlarge,shortandsmallcracksAlargepointA1a),shortofnoteandsmallinthiscracks.workisLargethedistinctionfatiguecracksbetween(paredaredefineddirections.totheasscalehavingofthedimensionsmicrostructurethatarelargevelopedmicrostructurecrack-tipTherefore,shieldingtheyzonegenerallyandhavecanafullyinbothde-Withdescribedrespectasbeingtoinlargeastatisticalcomparablecracks,small(continuum)`sample'manner.the43insizecracksto:44

aregenerally.microstructuraldimensions,wherebiasedstatisticalsam-plingofthemicrostructurecanleadtoacceleratedcrackadvancealong`weak'paths;thatis,microstructuralfeaturesorientatedforeasycrackgrowth(acontinuumlimitation),.theextentoflocalinelasticityaheadofthecracktip,wheretheassumptionofsmall-scaleyieldingimplicitintheuseofthestressintensity,K,isnotstrictlyvalid(alinear-elasticfracturemechanicslimitation),

.theextentofcrack-tipshielding(e.g.crackclosure)behindthecracktip,wherethereducedroleofshieldingleadsto

ß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

Large Crack

a >> IsW >> r

ahigherlocaldrivingforcethanthecorrespondinglargecrackatthesameappliedKlevel(asimilitudelimitation).

(a)

sShort crack

a < IsW >> r

(b)

Small cracka < Isa ~ r

(c)

Fig.A1Schematicillustrationshighlightingthekeydistinctionsbetweenlarge,rgecracks(a)havelength,a,andwidth,W,whicharelargebothwithrespecttotheequilibriumshielding-zonelength,ls(indicatedhereasaregionofdebrisinthecrackwakewhichproducescrackclosure),andthecharacteristicmicrostructuralsizescale,r,e.g.thegrainsize.Incontrasttothis,shortfatiguecracks(b)arecharacterizedbya<ls,butW)r.Thereducedcrack-wakelengthresultsinalowerlevelofcrack-tipshielding.Forsmallcracks(c),thefracturesurfaceisreducedinbothdimensions,witha(andW)beingsmallwithrespecttobothlsandr.Thefactthata$rimpliesthatthecrackfrontsamplesonlyafewmicrostructuralentities,leadingtoabiasedsamplingofthemicrostructure.

However,afurtherimportantdistinctioncanbemade,namelythatofashortvs.smallcrack.Thisdistinctionalludesnotsimplytophysicalsizebuttheextenttowhichafatiguecrackissubjectedtothefirstandthirdfactorslistedabove.Shortfatiguecracks(Fig.A1b)arephysic-allyshortinonlyonedimension,aconditionthatisoftenrealizedexperimentallybymachiningawaythewakeofalargecrack.Thistypeoffatigueflawexperienceslimitedcrack-tipshieldingowingtoitsreducedlength,45yetsamplesthemicrostructureasacontinuumbecauseofitsextensivecrackfront.Bycontrast,smallfatiguecracks(Fig.A1c)aresmallandcomparabletothemicrostruc-turalsize-scaleinalldimensions,astypifiedbythesmall,semiellipticalsurfaceflaw(e.g.Refs[44,46]).Withsuchcracks,crack-tipshieldingissignificantlyreduced(e.g.Ref.[43]),andsincethecrackfrontsamplesonlyafewmicrostructuralentities,thisallowsforabiasedsamplingofmicrostructurallyweakpaths.Becauseofthisrestric-tioninshieldingandthebiasedmicrostructuralsam-pling,fatiguecrackgrowthresistanceinthepresenceofsmallcracksoftentendstobelowest.AppendixB

Calculationofthemixed-modethreshold

Inthiswork,asinpriorstudies(e.g.Refs[7±12,33,34])onmixed-modefatiguethresholds,thethresholdvaluesofthemodeIandmodeIIstressintensitiesrequiredtoinitiatecracking,DKI,THandDKII,TH,arecalculatedbasedonthemodeIprecrack(whichisgeneratedinnear-identicalfashionforeachtest);thecorrespondingmixed-modethreshold,DGTH,orequivalentstressinten-sity,DKeq,TH,arethencomputed

from:

b << a

a

ABSTRACT Effect of microstructure on mixed-mode (mode I ? II), high-cycle fatigue thresholds in a Ti-6Al-4V alloy is reported over a range of cracksizes from tens of micrometers to in excess of several millimeters. Specifically, two microstructural conditi

606R.K.NALLAetal.

ÁGTH À

ÁKI;TH2 ÁKII;TH

2

Á=EH1 ÀÁKeq;TH2Á

=EH A1

whereE'isalongHowever,criterionadifferentsincetheappropriateoncepaththe(correspondingcrackstartselasticmodulus.

totogrow,alocalitdeflectsKII alternativemodifiedtheAssumingpresencecalculationbytheeffectofthemicrostructure),an0ofaninfinitesimalofthethresholdcanbebasedontheanglecracklength)forsimplicityrepresentsthatthekinkankinkalongin-plane(oflengththisdirection.tiltthroughb<<a,modeadeflectedIandtothecracktipmodeprecrackplaneIIwillstressbeintensities,(Fig.A2),givenby:47,48Dkthenthe,atlocal1andDk2theÁk1 a c11ÁKI c12ÁKIIÁk2 a c21ÁKI c22ÁKII

A2

where(pre)crack,DKIandtionandtheDKIIcoefficientsarethestresscintensitiesforamainthresholds,ofa,areij,whichareasolefunc-from:

DGgiven'inRefs[47,48].Themixed-modeTHandDK'TH,canthenbecomputedÁGHÀÁEH TH Ák1;TH2 Ák2;TH2=ÁKTH

H2

=EH A3

theAsdiscussedelsewhere,49theuseofEqn.A3tocalculate

putedmixed-modemuchvaluesofDthresholdKcaninfactreducethecom-eq,TH,atspecificphaseanglesbythisvaluestranslatesas40%.Forbytypicallyintothe1±2abimodalMPareductionandHm.

inlamellarthresholdTi-6Al-4VasDK,eq,THß2002BlackwellScienceLtd.FatigueFractEngngMaterStruct25,587±606

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