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JOURNALOFMATERIALSSCIENCE27(1991)3143-3154Interfacialdebondingandfibrepull-outstressesPartICriticalcomparisonofexistingtheorieswithexperimentsJANG-KYOKIM,C.BAILLIE,YIU-WINGMAICentreforAdvancedMaterialsTechnology,DepartmentofMechanicalEngineering,UniversityofSydney,Sydney,NSW2006,AustraliaTwocurrenttheories[11,17]ofinterfacialdebondingandfibrepull-out,whichhavebeendevelopedonthebasisoffracturemechanicsandshearstrengthcriteria,respectively,arecriticallycomparedwithexperimentalresultsofseveralcompositesystems.Fromtheplotsofpartialdebondstress,c~,asafunctionofdebondlength,threedifferentcasesoftheinterfacialdebondprocesscanbeidentified,i.e.totallyunstable,partiallystableandtotallystable.Thestabilityofthedebondprocessisgovernednotonlybyelasticconstants,relativevolumeoffibreandmatrixbutmoreimportantlybythenatureofbondingattheinterfaceandembeddedfibrelength,L.Itisfoundthatfortheepoxy-basedmatrixcompositesystems,Gaoetal.'smodel[17]predictsthetrendofmaximumdebondstress,cy*,veryweltforlongL,butitalwaysoverestimatescy*forveryshortL.Incontrast,Hsueh'smodel[11]hasthecapabilitytopredictcy*forshortL,butitoftenneedssignificantadjustmenttothebondshearstrengthforabetterfitoftheexperimentalresultsforlongL.Foraceramic-basedmatrixcomposite,o*predictedbythetwomodelsagreeexceptionallywellwithexperimentoveralmostthewholerangeofL,areflectionthattheassumedstabledebondprocessintheoryisactuallyachievedinpractice.Withrespecttotheinitialfrictionalpull-outstress,cyf,theagreementbetweenthetwotheoriesandexperimentsisexcellentforallrangeofLandallcompositesystems,suggestingthatthesolutionsforcyfproposedbythetwomodelsareessentiallyidentical.AlthoughGaoetaL'smodelhastheadvantagetodetermineaccuratelytheimportantinterfacialpropertiessuchasresidualclampingstress,qo,andcoefficientoffriction,IEt,itneedssomemodificationsifaccuratepredictionsof~*aresoughtforveryshortL.Theseincludevaryinginterfacialfracturetoughness,G~cwithdebondcrackgrowth,unstabledebondingforveryshortLandinclusionofsheardeformationinthematrixfortheevaluationofG~candfibrestressdistribution.Hsueh'smodelmayalsobeimprovedtoobtainabettersolutionbyincludingtheeffectofmatrixaxialstressexistingatthedebondedregiononthefrictionlessdebondstress,(Yo.1.IntroductionAstheuseofadvancedfibrecompositematerialsinengineeringapplicationisextended,fundamentalcon-siderationsofcostandstructuralefficiencyareaug-mentedbyimprovingdesignreliability.Thisrequiresabasicunderstandingofhowthefractureprocessinitiatesandprogressestofinalfailure.Ofparticularimportanceduringfractureisthelocalresponseofthefibre-matrixinterfacewhichhaspronouncedeffectsonthemechanicalperformanceandstructuralinte-grityofthecomposite.Experiencehasshownthatwhenacrackmovesthroughamatrixcontainingfibres,energiesareabsorbedbythefailuremech-anismssuchasmatrixcracking,fibre-matrixinter-facialdebonding,post-debondingfriction,fibrefracture,stressredistribution,fibrepull-out,etc.,am-ongwhichdebondingandfrictionalslidingduringfibrepull-outprovidemajorcontributionstothefrac-turetoughnessofmostfibrecompositeswithpolymer-andceramic-basedmatrices.Therefore,optimalconditionsfortougheningoffibrecompositesrequirethesemechanismstooccurproperly,whichinturnneedspropercontroloftheinterfacialproperties.Acomprehensivereviewonhowtheinterfacialproper-tiesinfluencethestrengthandfracturetoughnessoffibrecomposites,includingthevariousmethodsforimprovingthefracturetoughnessbymeansofinter-facecontrol,wasrecentlygivenbyKimandMai[1].Severalexperimentaltechniqueshavebeende-velopedtocharacterizetheinterracialpropertiesin-cludingthesinglefibrepull-outtest[2],thesinglefibrefragmenttest[3],themicrodebondtest[4]andthefibrepush-out(orindentation)test[5].Amongthesemethods,themostpopularandreliablemethodseemstobethesinglefibrepull-outtestwhichisthesubjectofthepresentstudy.Theoreticalanalysesof0022-246191992Chapman&Hall3143thedebondingandfibrepull-outproblemcanbeclassifiedintotwodistinctapproaches:oneisbasedonamaximumshearstresscriterionsuchthatwhentheinterfacialshearstressexceedstheshearbondstrength,completedebondingoccursunstably;andtheotherisbasedontheconceptoffracturemechanicswherethedebondedzoneisconsideredasaninter-facialcrackanditsextensionisdependentontheenergycriterionbeingsatisfied.ThefirstapproachistypifiedbytheearlyworkofCox[6],Greszczuk[7]andTakakuandArridge[8]basedontheshearlagmodel,namelythatthetensilestressesinthematrixarenegligiblerelativetothoseinthefibres,whereastheshearstressesinthefibresaresmallcomparedtothoseinthematrix.Lawrenceandco-workers[9,10]haveincludedtheeffectoffrictionalshearstressoppo-singthepull-outatthedebondedregion.TheshearstrengthcriterionhasbeenmodifiedrecentlyinaseriesofstudiesbyHsueh[11,12]whopostulatedthataprogressivestabledebondingexistsalongtheinterfaceandconsideredtheeffectofsheardeforma-tioninthematrix.RepresentativeworkofthefracturemechanicsapproachincludesthoseofGurneyandHunt[13],OutwaterandMurphy[14]andStangandShah[-15].Followingtheargumentofpreviousworkers[15,16]thatthefracturemechanicsapproachtothedebondingproblemispreferredtothemax-