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V.FAILUREOFFIBERCOMPOSITELAMINATES–PROGRESSIVEDAMAGEANDPOLYNOMIALINVARIANTSFibercompositesaretypicallyusedinflat,laminatedformsorvariationsthereof,oftenalsoinvolvingwovenorbraidedconstructions.Thetreatmentgivenherewillbefortheflatlaminatedformwherethealignedfibersinthevariouslaminatakedifferentdirectionswithinthelaminate.Failureatthelaminateleveliscomplexandnotanobviousmatterintermsofdeducingthetheoreticalbasisfortherelatedfailurecriteria.Twoverydifferentbutmainlinemethodswillbegivenhere,althoughtherearemanyotherapproaches.Thebestplacetostartiswithanunderstandingofthedefectstatesthatcananddoexistincommercialfibercompositeproducts.Thesedefectshaveaprofoundinfluenceuponthestrengthperformanceoftheresultingmaterials.Therearebrokenfibers,fiberslacks,fibermisalignments,debonds,resinrichpockets,cracks,porosity,andonandon.Effectivemodulidonotdependmuchonthedefects,butfailuresurelydoes.Withallthedefects,onecouldquestionhowanycompositematerialcouldperformatasatisfactorylevel.Despitethemanydefects,thespecialpropertiesofthefibersandtheamelioratingroleofthematrixcombinetogiveanextraordinarybalanceofpropertiesthatremainsataveryhighlevelforthehigherqualityproducts.Tobesure,thesecompositepropertieswouldnotbepossiblewithoutasuperiorcapabilityofthefiberphaseortheenablingpropertiesofthematrixphase,botharevitalandessential.Nextonthescaleofimportanceisthematterofscaleitself.Oneofthemajorfulcrumsofdissensionistheuncertaintyastothescaleatwhichtocharacterizefailure.Allfailuremodeshaveascaleofaction.Thecentralproblemistorecognizethescaleforaparticularmodeoffailureandthentocharacterizeit.Damageoccursatallscalesfrommolecularonup.Perhapsanextremeexamplewillbestillustratethepoint.MoleculardynamicscannotpredicttheEulerbucklingofamainstructuralmember.Thismismatchinscalesisridiculouslygreat.Whileitisgenerallytakenthatsmallerscalesrevealmorefundamentaleffectsthandolargerscales,thereareimportantandcriticalexceptionstothisoversimplification.Manyormostmaterialscomposingloadbearingstructuresfallundertheexceptionalcategory.Theseengineeringmaterialsarestronglydistinguishedfromothermajorclassessuchaselectronicmaterialsandbio-materialswhichhavefardifferentprimaryfunctionsfromthatofmainlysupportingloadwithoutfailurebutwithminimaldeformation.Compositeslaminateshavefailuremodesthatinherentlyrelatetothescaleofthelaminate.Forexample,delaminationismeaningfulonlyatthelaminatescale.ThedifferentbutverybroadscalesofconceivablerelevancehereareAtomic–angstroms10-9mFibersize–microns10-6mLaminathickness–mils10-4mLaminatethickness–millimeterstoinches10-1mConcerningscaledependence,kinkbandsforexamplecannotbepredictedfromfiberscalefailure.Moregenerally,contrarytomanyclaims,macroscopicfailurecannotbepredictedbymoleculardynamics.Thereisa6or7ordersofmagnitudegapthatisanimposingbarrier.Realisticmacroscopicfailurepredictionsmustoriginatefromacarefulassessmentoftheproperscaleforthefailuremode.Many,butnotnecessarilyallmacroscopicfailuremodesoriginateatthemacroscopicscale.Greatcareisneededinmakingthisdetermination.Takingmacroscopicfailuretobeatthelaminaandlaminatescales,theoriginofthefailuremodesthendependsupontheparticularsofthelayupofthelaminawithinthelaminate.Althoughinterestingasconceptsandcertainlyusefulindevelopingnewmaterials,trulyusingnano-mechanicsand/ormicromechanicseffectstopredictmacroscopicfailurewouldrequireanimmensecommitmentandbynomeansisitanestablishedapproach.Somemicroornanoscaleapproachesarethatinnameonlysincethey“backout”constituentpropertiestogivedesiredmacroscopicscaleresults.Infact,evenjusttryingtopredictlaminatefailurebehaviorfromlaminalevelbehaviormayhaveseverelimitations,aswillbeshownlater.Duetothecomplicationsofdamageandofthescaledependenceofthefailuremodes,failurecharacterizationbaseduponnano-scaleandmicroscaleidealizations(eitherfullyorpartiallyso)willnotbeconsideredinthetwomethodstobegivenhere.Thereisaverylargeliteratureonthesubjectofdamageandfailureinfibercompositelaminates.Allconceivableapproachesarebeingtried,afewtypicalapproacheswillbementionedhere.Hinton,KaddourandSoden[1]compliedaveryusefulcollectionandassessmentofmanydifferentapproaches.PuckandSchurmann[2]giveanapproachoriginallybaseduponCoulomb-Mohrtypebehavior.MayesandHansen[3]descriptivelydesignatetheirmethodasMCT(Multi-ContinuumTheory).Daniel[4]treatsmanyaspectsoffailure.RobbinsandReddy[5]giveanapproachusinginternalvariables.Tsaiandcolleagues[6]giveanduseMMF(MicromechanicsofFailure).AfiniteelementapproachtodamageandfailureisgivenbyTayetal[7],EFM(ElementFailureMethod).Notonlyaretheremanyresearchsourcesandreferences,almostallofthemrepresentdistinctlydifferentandindividualizedapproaches.Consideringthedifficultyofthetopic,itisnotsurprisingthatthereisnothingthatisevenwithinproximityofbeingaunified,verified,andreasonablyrecognizedmethodology.Thepresentinterestsandmethodswillberestrictedtocarbonfiber–polymericmatrixsystems,whicharegenerallythehighestperformancesystems.Assuch,theseapproachesmaybesomewhatlessapplicabletoglass–polymersystems,althoughthepossibilityremainsopen.Thetechnicalstar