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复合材料的疲劳损伤模型---英文

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Afatiguedamagemodelofcompositematerials

FuqiangWu*,WeiXingYaoKeyLaboratoryofFundamentalScienceforNationalDefense-AdvancedDesignTechnologyofFlightVehicle,NanjingUniversityofAeronauticsandAstronautics,Nanjing210016,China

articleinfoArticlehistory:Availableonline20February2009Keywords:CompositeFatigueAccumulativedamagePredictedlifeabstractThemechanicalpropertiesofcompositematerialsdegradeprogressivelywiththeincreasingofthenum-berofcyclicloadings.Basedonthestiffnessdegradationruleofcomposites,aphenomenologicalfatiguedamagemodelispresentedinthispaper,whichcontainstwomaterialparameters.Theyareproportionaltothefatiguelifeofmaterialsandinverselyproportionaltothefatigueloadinglevel.Thirteensetsofexperimentaldataofcompositestiffnessdegradationwereemployedtoverifythepresentedmodel,andthestatisticalresultsshowedthatthismodeliscapableofdescribingthedamageevolutionofcom-positematerials.Thecharacteristicsofdamagedevelopmentandaccumulationofcompositematerialssubjectedtovariableloadingwerestudiedinthispaper.Foursetsoftwo-levelloadingexperimentaldatawerecitedtoverifythedamagemodel,andtheresultsshowedthatthepredictedlifeisingoodagree-mentwiththeexperimentalones.Ó2009ElsevierLtd.Allrightsreserved.

1.IntroductionThedamageevolutionmechanismisoneoftheimportantfo-cusesoffatiguebehaviorinvestigationofcompositematerialsandalsoisthefoundationtopredictfatiguelifeofcompositestruc-turesforengineeringapplications.Asknown,thefatiguedamageandfailuremechanismofcompositesismorecomplexthanthatofmetalsandfourbasicfailuretypeswilloccurrincompositesun-dercyclicloading,whicharematrixcracking,interfacialdebond-ing,delaminationandfiberbreakage.Basedonagreatdealofexperimentalinvestigations,manydamagemodels[1–8],whichhavebeen,respectively,definedbystrengthdegradation,stiffnessdegradationandenergydissipationofcomposites,havebeenem-ployedtodescribethedamagedevelopmentofmaterialsinthere-centdecades.Thecognitiontodamageevolutionmechanismhadbeendevelopedfromlinearmodeltononlinearmodel.However,mostmodelsarejustsuitedtoaspecialcompositeandarenotcapableoffittingothers.Toobtaintheparametersofthemodels,amassoffatigueexperimentaldataisnecessary.Thefatiguedam-agemechanismofcompositeshasnotyetbeenrecognizedwholly.Inthispaper,thefactorsrelatedtofatiguedamagedevelopmentofcompositeswereanalyzedandaphenomenologicalfatiguedamagemodeldefinedbymaterialstiffnessdegradationisde-scribed.Thirteensetsofexperimentaldatawereemployedtover-ifythemodel,andtheresultsshowthatthemodelcandescribethedamageevolutionofcompositelaminatesunderthedifferentfati-gueloadings.Anditisalsoverifiedthatthemodelcanpredictresidualfatiguelifeofcompositelaminatesquitewellbyfoursetsoftwo-levelexperimentaldata.2.DamagemodelUndercyclicstressorstrain,thenon-inversestructuralchangewilloccurinmicrolocalfieldincompositematerialsandthesechangesleadtofatiguedamageofcomposites.Withanincreaseinthenumberofloadingcycles,thequantityofthischangewillin-creaseandthedamagewillcumulatesynchronously.Theaccumu-lationofdamageleadstoachangeinthemacroscopicmechanicalpropertiesofthecomposites,suchasthedegradationofstrengthorstiffnessofthematerial.Basedontheexperimentalinvestigation,Reifsnider[1]concludedthatfatiguedamageevolutionisnonlin-earincompositematerials.Duringtheinitialperiodoffatiguelife,manynon-interactivecracksoccurinthematrix.Whenthematrixcrackdensityreachessaturation,thefiberfailure,interfacialdeb-ondinganddelaminationoccurinthecomposites.Damagewillrapidlydevelopandthematerialcauses‘‘suddendeath”intheendperiodoffatiguelife,asshowninFig.1.TotestthechangeinYoung’smodulusofmaterials,thedamagedevelopmentofcompositematerialscanbedescribedbystiffnessdegradationofmaterialsinfatiguebehaviorinvestigation.Basedonthistechniquethatspendslessexperimentaltimeandcost,manynonlineardamageevolutionmodels[8]werepresented.Andthemodelsdefinedbystiffnessdegradationofcompositelam-inatesarewidelyinvestigatedtheoreticallyandexperimentallyandtheyfairlydescribedthedamageprogressintheinitialor/andmiddleperiodofthefatiguelife.However,theyarenotcapableoffittingthedamageprogressinthewholeperiod,asshownin0142-1123/$-seefrontmatterÓ2009ElsevierLtd.Allrightsreserved.

doi:10.1016/j.ijfatigue.2009.02.027*Correspondingauthor.Tel.:+862584892576.E-mailaddress:stonefuq@hotmail.com(F.

Wu).InternationalJournalofFatigue32(2010)134–138

ContentslistsavailableatScienceDirectInternationalJournalofFatigue

journalhomepage:www.elsevier.com/locate/ijfatigu

eFig.1.Accordingtothefatiguemechanismsofcomposites,aversa-tilenewfatiguedamagemodelispresentedtodescribethestiff-nessdegradationruleofcompositematerialsintheloadingdirection.TheproposedmodelofthedamageisthatDðnÞ¼E0ÀEðnÞE0ÀEf¼1À1ÀnN󰀂󰀃B󰀄󰀅Að1ÞwhereE0isinitialYoung’smodulus,EfisthefailureYoung’smodu-lus,E(n)isYoung’smodulusofthematerialsubjectedtothenthcy-clingloading,nisthecycle,Nisthefatiguelife,AandBaremodelparameters,D(n)isthefatiguedamage,whichequals0whenn=0andequals1whenn=N.3.StatisticalanalysisAccordingtothestiffnessdegradationexperimentaldataofcompositematerials,thematerialfatiguedamagevaluesaregottenunderdifferentcycles.Then,thecurveofEq.(1)canbegottenbytheleastsquaresfitting.ThecomprehensivedatapublishedinRefs.[3,9,10]wereusedtovalidatetheproposeddamagemodel.ThevaluesofAandBinEq.(1)andthecorrelativecoefficientR2arelistedoutinTable1andareshowninFig.2.Eq.(1)iscapableofdescribingthenonlineardamageevolutionmacro-mechanicallyinallperiodsofthefatiguelifeofcompositematerialssubjectedtodifferentfatigueloadings,asshowninFig.2.Duringtheinitialperiodofthefatiguelife,themaindamagetypeismatrixcrackinginthecomposite.ThebiggertheappliedloadingisorthelesstheratioRofstressorstrain(R=rmin/rmaxorR=emin/emax)is,thefasterthedamagedevelopmentis.Whenthecrackdensityissaturatedinthematrix,therateofdamagedevelopmentofthematerialissteadyandslow.Duringthefinalperiodoffatiguelife,fiberbreakingcontrolsthecompositefailure.Thefasterthefracturedrateofthefiberis,theshorterthefatiguelifeis.Withtheincreaseinthenumbersoffracturedfibers,therateofdamagedevelopmentofmaterialincreasesquicklyandagain.Therefore,thechangeruleofthedamagedevelopmentrateincom-positesisfromquicktoslowandtoquickagaininthewholeperiodofthefatiguelife.InEq.(1),thenormalizationfatiguelifen/Nisrewrittenasx=n/N.Then,therateofdamagedevelopmentoflaminateisdDdx¼ABxBÀ1ð1ÀxBÞAÀ1ð2ÞAccordingtothevaluesofparametersAandBinTable1,thedam-agedevelopmentratesofthelaminatescanbegotten,asshowninFig.3.Basedonthecharacteristicsofdamageevolutionofcompositematerials,theratesofdamagedevelopmentbetweentheinitialperiodandthefinalperiodoffatiguelifearesame,asshowninFig.3.Then,anassumptionisproposed,whichisthattheratesatanynormalizationlifex1andx2(0

ItcanbeverifiedmathematicallythattherelationbetweenAandBinEq.(3)approximatesthelinearrelation,whenx1andx2arediscretionarilygiven.Therefore,Eq.(3)canbeapproximatelyex-pressedasA¼pBþqð4Þwherepandqareconstants.TofitthevaluesofparametersAandB,asshowninTable1,aquantitativerelationshipbetweentheparam-etersisproposedA¼0:67Bþ0:44ð5ÞWhenthelaminatesaresubjectedtothefatigueloading,thelesstheultimatestrength,theratioRofstressorstrain,thefatiguelifeundergivenloadingisorthebiggertheloadingis,thebiggerthefatiguedamageintheinitialperiodofthefatiguelifeis.InEq.(1),theparameterBdescribesthecharacteristicsoflaminatedamageintheinitialperiodofthefatiguelife.ThelessBis,thebig-gerthelaminatedamageis.Therefore,theparameterBispropor-tionaltothefatiguelifeNandisinverselyproportionaltotheloadinglevelrmax=rult.B¼klgNð1ÀRÞðrmax=rultÞð6Þwherermaxisthemaximumstress,rultistheultimatestrength,andkisaproportional

constant.Fig.1.Fatiguedamageevolutionincompositelaminates[1].

Table1Thevaluesoftheparametersofthepresentedmodel.MaterialsLoading/sequenceABR2Glass/HC9106-3[0/903]S[3]75%rult0.3140.0250.94980%rult0.4190.0550.9805T300/QY8911[9][45/90/À45/02/À45/90/45]S509.7MPa0.6150.2960.9997441.7MPa0.7030.4450.9991424.7MPa0.7420.5110.9995[À45/0/45/902/45/0/À45]S462.1MPa0.6640.2920.9527431.3MPa0.7530.4010.9809400.5MPa0.8420.5140.9888[02/45/02/À45/0/90]S946.2MPa0.5030.0250.8855917.5MPa0.5710.0570.8668888.8MPa0.5810.1090.9804AS4/PR500[0/90W2]S[10]Unagedspecimen0.7150.4750.9842Agedspecimen0.6790.3840.9992F.Wu,W.Yao/InternationalJournalofFatigue32(2010)134–138135