evaluation of k1c

JOURNALOFMATERIALSSCIENCELETTERS1(1982)13-16Evaluationof1Kicofbrittlesolidsbytheindentationmethodwithlowcrack-to-indentratiosK.NIIHARA*,R.MORENA,D.P.H.HASSELMANDepartmentofMaterialsEngineering,VirginiaPolytechnicInstituteandStateUniversity,Blacksburg,Virginia24061,USAThefracturetoughness,orcriticalstressintensityfactor,isanimportantparameterrequiredforthepredictionofthemechanicalperformanceofstructuralmaterials.Foritsmeasurementalargevarietyofexperimentalmethodsareavailable[1-5].Onesuchmethodisthehardnessinden-tationmethodwhichyieldsvaluesfortheModeIcriticalstressintensityfactor,K[e.Thismethodisparticularlyusefulforbrittlematerialswithlowfracturetoughnesssinceitisbothsimpleandrapidandpermitssmallsamplesizes.Inprinciple,theindentationmethodrequiresmeasurementofthesizeofcracksformedaroundtheindentatloadsinexcessofthecriticalload,Pc,requiredtoinitiatecracksaroundtheindent.Becauseofthehighversatilityoftheinden-tationtechnique,numerousstudieshavebeendevotedtothedeformationprocessandfracturephenomenaduringindentation[2,5-23].EvansandCharles[1],onthebasisofadimensionalanalysisoftheunderlyingfracture-mechanicalprinciplesandexperimentaldata,showedthattherelationbetweenfracturetoughnessandratioofcrack-to-indentsizeexhibiteduniversalbehaviour.Ascurve-fittedbyBlendell[24],thisuniversalbehaviourcanbeexpressed:(KIeCHHal/2)(H/E¢~)2Is=0.055log(8.4a/c),(1)whereKieistheModeIcriticalstressintensityfactor,~istheconstraintfactor(23),Histhehardness,EistheYoung'smodulus,aisthehalf-diagonaloftheVickersindentandeistheradiusofthesurfacecrack(seeFig.2a).ForagivenmaterialwithaknownYoung'smodulusthefracturetoughness,KIe,canbereadilyevaluatedwhentheindentationloadandcorrespondingvaluesofcandaareknown.EvansandCharles[1]concludedthattheiranalysiswasapplicabletomaterialswithhardnesses,toughnessesandPoisson'sratiosrangingfromatleast1to30GNm-:,0.9to16MNm-3/2and0.2to0.3,respectively.ThepresentwritersinvestigatedtheapplicabilityoftheEvansandCharlesmethodtorangesofpropertyvalueslargerthantheselattervalues.Itwasfoundthatliteraturedata[7]fortheindentationbehaviourofWC-CocompositesdidnotagreewellwithEquation1.Itisthepurposeofthiscommunicationtopresentarationalefortheobserveddeviation.Fig.1showsthedataofDawihlandAltmeyer[7]forWC-CocompositestogetherwithEquation1plottedas(Kxe(~/Hal/2)(H/E())2/sagainstc/a.Atlowvaluesofc[a,considerabledeviationsappeartoexistbetweentheexperi-mentaldataandEquation1.InordertoprovideanexplanationforthisdeviationitshouldbenotedthatimplicitinplottingthedatashowninFig.1istheassumptionthatthecracksobservedaroundtheindentationtaketheformofmedian(half-penny)cracks,whichcompletelysurroundtheindentation,asshowninFig.2a.Anothercracksystem,so-calledPalmqvistcracks,however,havebeenfoundatlowvaluesofc/a[5,6,15].Suchcracksbeginonlyattheendofthediagonalsoftheindentation,asillustratedinFig.2b.Theexistenceofsuchcrackshasbeenascer-tainedforanumberofmaterialsbyasectioningtechnique[15,19],byfractographyofasurfacethroughanindentation[17,23],orbydirectobservationofcrackformationprocessusingopticalmicroscopy[10].Ogilvyetal.[15]observedthatforreasonably-toughmaterialssuchasWC-Cocompositeswithmorethanabout6wt%Co,Palmqvistcrackswereformedonlyevenathighloads.Haganandco-workers[17,23]*NowwiththeResearchInstituteforIron,SteelandOtherMetals,TohokuUniversity,Sendal,980Japan.0261-8028/82/010013--04502.40/0©1982ChapmanandHallLtd.130.080.060.04~t0.010.0080.006II'lIIc~oal-%&Charles&WC-Co(6%)AlzxwC-Co(6%)BI\....~.Oawihl&Altmeyer•WC-Co(,I%)~E]WC-Co(15%)jIfIII246c/eFigure1ComparisonoftheindentationfracturedataforWC-Cocomposites[7]withtheuniversalcurve[24]fortiledataofEvansandCharles[1].andLankfordandDavidson[18]observed,forsoda-limeglassandsiliconcarbide,respectively,thatthesurfaceradialcracksformedatlowloadswerenotassociatedwiththemedian(haitipenny)cracks.EvansandWflshaw[10]confirmedthatforanumberofbrittlematerialsthePalmqvistcrackswereformedinthelow-loadregime.ItissuggestedthatthecracksfortheWC-CoalloysshowninFig.1,atleastatthelowervaluesofc/a,actuallyhavethegeometryofPalmqvistcracksratherthanmediancracks.If,indeed,thiswerethecase,itwouldbemoreappropriatetoevaluatethefracturetoughnessfromindentationdataintermsofl/aforPalmqvistcracks,ratherthanc/aforthemediancracks.Ascanbeascer-tainedfromFig.2,thedimensionsofthePalmqvistandmediancracksarerelatedby:lla=c/a-1.(2)Thevalidityoftheabovesuggestionisdemon-stratedinFig.3whichshowstheliteraturedatafortheindentationfracturebehaviourofanumberofbrittlematerialsandtheWC-CocompositesofFig.1plottedintermsof(KIe¢/Hal/2)(H/E~)°'4againstl/aorc[a.Itisclearlyevidentthatallthedatafallintotwoseparatesets,bothshowingexcellentlinearity.Atthelowervaluesofthecrack-to-indentratiosandlowerslope,thedatashowexcellentcorre-lationwithl/aforPalmqvistcracks.Atthehighervaluesofcrack-to-indentratioandhigherslope,bettercorrelationisobtainedwithc]aforthemediancracks.Becauseoftheclosespacingofthedatatothelinearfit,itappearsthatthenormalizingparameter(HIES)°'4proposedbyEvansandCharles[1]formediancracks,isappro-priateforPalmqvistcracksaswell.Forth