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Lessoncontent:IntroductionDirectCyclicLow-cycleFatigueAnalysisLow-cycleFatigueCriterionWorkshop9:FatigueCrackGrowthinaDCBSpecimenLesson11:Low-cycleFatigue1hourIntroductionDelaminationgrowthincompositesduetosub-criticalcyclicloadingsisawidespreadconcernfortheaerospaceindustry.Thelow-cyclefatiguecriterionavailableinAbaqusmodelsprogressivedelaminationgrowthatinterfacesinlaminatedcompositessubjectedtosub-criticalcyclicloadings.Theinterfacealongwhichthedelamination(orcrack)propagatesmustbeindicatedinthemodel.TheonsetandgrowthoffatiguedelaminationattheinterfacesarecharacterizedbytherelativefractureenergyreleaserateThefractureenergyreleaseratesatthecracktipsintheinterfaceelementsarecalculatedbasedontheVCCTtechnique.DirectCyclicLow-cycleFatigueAnalysis(1/5)Low-cyclefatigueanalysisisaquasi-staticanalysisonastructuresubjectedtosub-criticalcyclicloading.Itmodelsprogressivedelaminationgrowthattheinterfaceinlaminatedcompositesandprogressivedamageandfailureinbulkmaterials*.TheonsetandgrowthofdelaminationarecharacterizedbytheParisLaw.Thedetailswillbediscussedlaterinsection“Low-cycleFatigueCriterion.”Itcanbeassociatedwiththermalaswellasmechanicalloading.*Progressivedamageandfailureinbulkmaterialswillnotbecoveredinthislecture.DirectCyclicLow-cycleFatigueAnalysis(2/5)Low-cyclefatigueanalysisusesthedirectcyclicproceduretodirectlyobtainthestabilizedcyclicresponseofthestructure.ThedirectcyclicprocedurecombinesaFourierseriesapproximationwithtimeintegrationofthenonlinearmaterialbehaviortoobtainthestabilizedcyclicsolutioniterativelyusingamodifiedNewtonmethod.YoucancontrolthenumberofFourierterms,thenumberofiterations,andtheincrementationduringthecyclictimeperiodtoimprovetheaccuracy.Withineachloadingcycle,itassumesgeometricallylinearbehaviorandfixedcontactconditions.GeometricnonlinearitycanbeincludedonlyinanygeneralsteppriortoadirectcyclicstepDirectCyclicLow-cycleFatigueAnalysis(3/5)Aside:ReviewofthedirectcyclicanalysisprocedureItiswellknownthatafteranumberofrepetitiveloadingcycles,theresponseofanelastic-plasticstructuremayleadtoastabilizedstateinwhichthestress-strainrelationshipineachsuccessivecycleisthesameasinthepreviousone.Toavoidtheconsiderablenumericalexpenseassociatedwithatransientanalysis,adirectcyclicanalysiscanbeusedtocalculatethecyclicresponseofthestructuredirectlyUsesacombinationofFourierseriesandtimeintegrationofthenonlinearmaterialbehaviorFormoredetails,pleasesee“Low-cyclefatigueanalysisusingthedirectcyclicapproach,”Section6.2.7oftheAbaqusAnalysisUser’sGuide.50-60cyclesDirectCyclicLow-cycleFatigueAnalysis(4/5)Defininglow-cyclefatigueanalysis

t0:initialtimeincrement T:

timeofasingleloadingcycle tmin:minimumtimeincrementallowed tmax:maximumtimeincrementallowed n0:initialnumberofterms

intheFourierseries nmax:

maximumnumberofterms

intheFourierseries n:incrementinnumberofterms

intheFourierseries imax:maximumnumberofiterations

allowedinastep*DIRECTCYCLIC,FATIGUE,[CETOL=tolerance,DELTMX=max]t0,

T,

tmin,

tmax,n0,

nmax,

n,

imax

Nmin,

Nmax,

N,

Dtolcontrolstheincrementationcontrols

theiterationcontrolstheFourierseriesrepresentationsDirectCyclicLow-cycleFatigueAnalysis(5/5)Defininglow-cyclefatigueanalysis(cont’d) N:totalnumberofcyclesallowedinastep Nmin:minimumincrementinNoverwhichthedamageisextrapolatedforward Nmax:maximumincrementinNoverwhichthedamageisextrapolatedforward Dtol:damageextrapolationtolerance*DIRECTCYCLIC,FATIGUE,[CETOL=tolerance,DELTMX=max]t0,

T,

tmin,

tmax,

n0,

nmax,

n,

imax

Nmin,

Nmax,

N,

Dtolcontrolsdamageextrapolationinbulkmaterials;notcoveredhereLow-cycleFatigueCriterion(1/14)TheonsetandfatiguedelaminationgrowthattheinterfacesarecharacterizedbyusingtheParisLaw,whichrelatescrackgrowthratesda/dNtotherelativefractureenergyreleaserateG,G=Gmax

–Gmin

whereGmaxandGmincorrespondtothestrainenergyreleaserateswhenthestructureisloadeduptoPmaxandPmin,respectively.TheParisregimeisboundedbyGthresh

andGpl.BelowGthresh,thereisnofatiguecrackinitiationorgrowth.AboveGpl,thefatiguecrackwillgrowatanacceleratedrate.a:

cracklengthN:numberofcyclesG:strainenergyreleaserateGthresh:strainenergyreleaseratethresholdGpl:strainenergyreleaserateupperlimitGequivC:criticalequivalentstrain

energyreleaserateLow-cycleFatigueCriterion(2/14)GequivCiscalculatedbasedonthe

user-specifiedmode-mixcriterion

andthebondstrengthoftheinterface.ThiswasdiscussedpreviouslyOnsetoffatiguedelaminationThefatiguecrackgrowthinitiationcriterionisdefinedas: wherec1andc2arematerialconstants.Theinterfaceelementsatthe

cracktipswillnotbereleasedunlesstheaboveequationissatisfiedandGmax

Gthresh.a:

cracklengthN:numberofcyclesG:strainenergyreleaserateGthresh:strainenergyreleaseratethresholdGpl:strainenergyreleaserateupperlimitGequivC:criticalequivalentstrain

energyreleaserateLow-cycleFatigueCriterion(3/14)FatiguedelaminationgrowthOncethedelaminationgrowthcriterionissatisfiedattheinterface,thecrackgrowthrateda/dNcanbecalculatedbasedonG.da/dNisgivenbytheParisLawifGthresh<Gmax<

Gpl,

wherec3andc4arematerialconstants.a:

cracklengthN:numberofcyclesG:strainenergyreleaserateGthresh:strainenergyreleaseratethresholdGpl:strainenergyreleaserateupperlimitGequivC:criticalequivalentstrain

energyreleaserateLow-cycleFatigueCriterion(4/14)FatiguecrackgrowthgovernedbytheParisLawRepeattheaboveprocessuntilthemaximumnumberofcyclesisreachedoruntiltheultimateloadcarryingcapabilityisreached.Calculatetherelativefractureenergyreleaserate,G,whenthestructureisloadedbetweenitsmaximumandminimumvalues.Crackinitiation:Crackevolution:Damageextrapolation:Calculatetheincrementalnumberofcycles,N,foreachcracktipandfindminimumcyclestofail,NminIfN+N>NoN+NRepeata:cracklengthN:numberofcyclesN:incrementalnumberofcyclesc1,c2,c3,c4:materialconstantsIf

Gthresh<Gmax<GplReleasethemostcriticalelementG=Gmax(Pmax)–Gmin(Pmin)231Low-cycleFatigueCriterion(5/14)Thesyntaxusedtodefinethelow-cyclefatiguecriterionandthecorrespondingoutputrequestsissimilartothoseusedfortheVCCTcriterionexceptthefollowing:Forthelow-cyclefatiguecriterion,setTYPE=FATIGUEonthe*FRACTURECRITERIONoption:Bydefault,Gthresh/GequivC=0.01

andGpl/GequivC=0.85.Note:Definingthelow-cyclecriterionisnotcurrentlysupportedinAbaqus/CAE.*FRACTURECRITERION,TYPE=FATIGUE,MIXEDMODEBEHAVIOR=[BK|REEDER]c1,

c2,

c3,

c4,

Gthresh/GequivC,

Gpl/GequivC,

GIC,

GIICGIIIC,

,

,

fv*FRACTURECRITERION,TYPE=FATIGUE,MIXEDMODEBEHAVIOR=POWERc1,

c2,

c3,

c4,

Gthresh/GequivC,

Gpl/GequivC,

GIC,

GIICGIIIC,

am,

an,

ao,

,

fvLow-cycleFatigueCriterion(6/14)Example:Low-cyclefatiguepredictionfortheDCBmodelThiscaseconsistsofthefollowingsteps:Step1:VCCTanalysisThisstepcanbeusedtocheckwhetherthepeakloadingleadstostaticcrackpropagation.Step2:Low-cyclefatigueanalysisThisstepassessesthefatiguelifeoftheDCBmodelsubjectedtosub-criticalcyclicloading.displacementloadinginonecycle010.50=0.001u2tBotSurfTopSurfbondu2u2Low-cycleFatigueCriterion(7/14)Partialinput:Step1:VCCTanalysis*STEP,INC=5000*DIRECTCYCLIC,FATIGUE0.25,1,,,25,25,,5,,1000*DEBOND,SLAVE=TopSurf,MASTER=BotSurf*FRACTURECRITERION,TYPE=FATIGUE,MIXEDMODEBEHAVIOR=BK0.5,-0.1,4.8768E-6,1.15,,,280,280280,2.284*OUTPUT,FIELD*CONTACTOUTPUTBDSTAT,

DBT,DBS,OPENBC,CRSTS,ENRRT...*ENDSTEP...*CONTACTPAIR,SMALLSLIDINGTopSurf,BotSurf*INITIALCONDITIONS,TYPE=CONTACTTopSurf,BotSurf,bond*STEP,NLGEOM*STATIC...*DEBOND,SLAVE=TopSurf,MASTER=BotSurf*FRACTURECRITERION,TYPE=VCCT,

MIXEDMODEBEHAVIOR=BK280,280,280,2.284*OUTPUT,FIELD*CONTACTOUTPUT,SLAVE=TopSurf,MASTER=BotSurfBDSTAT,DBT,DBS,OPENBC,CRSTS,ENRRT*ENDSTEPStep2:FatigueanalysisModeldataBotSurfTopSurfbondLow-cycleFatigueCriterion(8/14)TheproceduretocompletetheDCBmodelthroughthefirststep(theVCCTanalysis)isexactlythesameasthatdiscussedpreviously.DefinecontactpairsforpotentialcracksurfacesDefineinitiallybondedcracksurfacesActivatethecrackpropagationcapabilityinthefirststepSpecifytheVCCTcriterioninthefirststep(astatic,generalstep)Thedetailsofdefiningthelow-cyclefatigueanalysis(thesecondstep)willbediscussednext....*CONTACTPAIR,SMALLSLIDINGTopSurf,BotSurf*INITIALCONDITIONS,TYPE=CONTACTTopSurf,BotSurf,bond*STEP,NLGEOM*STATIC...*DEBOND,SLAVE=TopSurf,MASTER=BotSurf*FRACTURECRITERION,TYPE=VCCT,

MIXEDMODEBEHAVIOR=BK280,280,280,2.284*OUTPUT,FIELD*CONTACTOUTPUTBDSTAT,DBT,DBS,OPENBC,CRSTS,ENRRT...*ENDSTEPStep1:VCCTanalysismodeldataBotSurfTopSurfbond4321Low-cycleFatigueCriterion(9/14)Definethelow-cyclefatigueanalysisThefollowingdataareusedtodefinethislow-cyclefatigueanalysis:Initialtimeincrement:0.25

secTimeofasingleloadingcycle:1

secInitialnumberoftermsintheFourierseries:25MaximumnumberoftermsintheFourierseries:25Maximumnumberofiterations

allowedinthestep:5Totalnumberofcyclesallowedin

thestep:1000Defaultvaluesareusedforallotherentries....*STEP,INC=5000

Low-cycleFatigueAnalysis*DIRECTCYCLIC,FATIGUE0.25,1,,,25,25,,5,,1000BotSurfTopSurfbond5Low-cycleFatigueCriterion(10/14)ActivatethecrackpropagationcapabilitySimilartotheVCCTanalysis,the*DEBONDoptionisusedtoactivatethecrackpropagationinthelow-cyclefatigueanalysisstep.TheSLAVEandMASTERparametersidentifythesurfacestobedebonded....*STEP,INC=5000

Low-cycleFatigueAnalysis*DIRECTCYCLIC,FATIGUE0.25,1,,,25,25,,5,,1000*DEBOND,SLAVE=TopSurf,MASTER=BotSurfBotSurfTopSurfbond6Low-cycleFatigueCriterion(11/14)Specifythelow-cyclefatiguecriterionInthismodel,thematerialconstantsareassumedtobethefollowing:c1=0.5,c2=–0.1c3=4.8768E–6c4=1.15Note:Theva