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1IntroductionPolymerfilmsareusedinawidevarietyofapplications.Theirtoughnessisoftenabasicrequisitetomeetsomeindustryneeds.
TheLinearElasticFractureMechanics(LEFM)approachisusedtostudyfracturesoccurringatnominalstresseswellbelowthematerialyieldstress.Thedissipatedenergyisconfinedinasmallareanearthecracktip,andthe
fractureisbrittle.TheLEFMapproachisnotapplicablewhentheplasticityaroundthecracktipbecomeslarge;inthosecasestheElasticPlasticFractureMechanics(EPFM)isapplied.Whenthecrackpropagationoccursthrougha
highlydeformedandyieldedmaterialthenPost-YieldFractureMechanicscanalsobeappliedandtheEssentialWorkofFracture(EWF)isasuitablemethodology.
TheEWFapproachhasbecomeverypopulartocharacterisefractureofpolymerfilmsandisincreasinglyusedduetoitsapparentsimplepreparationandeasytesting.TheEWFcharacterisestheplanestresstoughnessin
modeI,generallyusingthedoubleedgenotchedtension(DENT)configurationforthespecimens.
InspiteoftheapparentsimplicityoftheEWFtest,someaspectsofthevalidityofthistechniqueremaincontroversial;thereareintricatedetailsthatseemtoplayanimportantroleintherepeatabilityandreproducibilityofthe
test.Thisproblemhasbeenandstillisatopicofmuchdebate,andthesequestionsindicatethattheEWFprocedureisnotyetsufficientlywell-definedtobestandardised.Someoftheaspectsofthetestvalidityarerelatedtothe
specimenmanufacture,particularlythequalityofthenotches.
Twosetsofspecimenshavebeenprepared,thefirstonesharpenedbythefemtosecondlaserablationtechnique,andthesecondonesharpenedbytheclassicalrazorbladeslidingtechnique.Thesetwosetsofspecimenshave
TestMethod
Thefracturetestingofductilepolymerfilms:Effectofthespecimennotching
N.Leóna,∗
noel.leon@estudiant.upc.edu
A.B.Martíneza
P.Castejóna
D.Arencóna
P.P.Martínezb
aCentreCatalàdelPlàstic,DepartamentdeCiènciadelsMaterialsiEnginyeriaMetal-lúrgica,UniversitatPolitècnicadeCatalunya,BarcelonaTech,C/Colom114,08222Terrassa,Spain
bNUDECSA,C/PintorVilaCinca,24-28,Pol.Ind.CanHumetdeDalt,08213Polinyà,Spain
∗Correspondingauthor.
Abstract
The fractureofaductilepolymer film,aheterophaseethylene-propyleneblockcopolymer,hasbeenstudied, combininga rangeof characterisationmethods inanattempt toprovideabetterunderstandingof the
intricate details that play an important role in the repeatability and reproducibility of the essentialwork of fracture test. The experimental factors that have a strong influence on the resulting parameters are clearly
explained,withparticularattentiontotheeffectofthequalityofthenotches,thenon-collinearityofthetwoedgenotchesindoubleedgenotchedtensionspecimens,andthelackofalignmentofthespecimenwiththeload
axis once it ismountedon the load train.Furthermore, the influenceof theseexperimental factors on the registered stress-displacement curves is also studied, anda criterionand themethod for separatingnon-valid
specimensareestablished.
Keywords:Fracture;Essentialworkoffracture;J-integral;Polymerfilm
beencharacterisedbycombiningtheEWF,J-integral,andcracktipopeningdisplacement(CTOD)methodsinanattempttoprovideabetterunderstandingoftheEWFfractureapproachforcharacterisingthefracturetoughnessofa
ductilepolymerfilm.Theconnectionbetweenthequalityofthenotchesandtheshapeandsizeoftheregisteredstress-displacementcurveshasbeenestablished.Thiswasdoneinordertofindacriterionandamethodtoeliminate
non-validspecimens.Furthermore,ithasbeenstudiedindetailhowthesizeandshapeofthestress-displacementcurvesarerelatedtotheEWFfractureparameters.
Theeffectonthestress-displacementcurvesofspecimenswithnon-collinearnotches,specimenswithdifferentqualitybetweenthetwoedgenotches,andspecimenshavingalackofalignmentwiththeloadaxisoncemounted
onthetestingmachinegripshavebeenalsostudied.
Moreover, there is a limited understanding of the polymers towhich theEWFapproach can be applicable. TheEWFapproachhas been successfully applied to polymers that undergo necking before crack propagation.
However,thereissomecontroversyovertheapplicabilityoftheEWFapproachtoheterophasepolymers,whichcandeformbyothermechanisms.Forthisreason,averyductilegradeofanethylene-propyleneblockcopolymer(EPBC),
whichispronetoplasticdeformationandthusproblematicforthenotchsharpening,wastested.
ThemainobjectiveofthisworkistocontributetoabetterunderstandingandtoclarifysomeofthecontroversialfactorsinvolvedintheEWFtest.
2TheEWFapproach2.1TheEWFconcept
TheEWFapproach[1]isbasedonthehypothesisthatthetotalenergyinvolvedduringtheductilefractureofapre-crackedspecimen(Wf)canbeseparatedintotwoterms.
whereWe, theessentialworkof fracture, represents theenergy required for the creationof twonewsurfacesduring the crackpropagation,whereas the second term,Wp, is called theplasticworkor thenon-essentialworkof
fractureandcollectsallothersourcesofenergyproducedthroughoutthefractureprocess.ThetermWeisconsideredtobeproportionaltotheareaoftheFractureProcessZone(FPZ)whileWpisproportionaltothevolumeofthe
OuterPlasticZone(OPZ).ThesezonesareschematisedinFig.1foraDENTspecimen.
RewritingEq.(1)usingspecificterms,
wheretisthespecimenthickness,loistheoriginalligamentlengthandβisafactorthatdependsontheshapeoftheOPZ.
ItispossibletoassessEq.(2)byperformingaseriesoftestsonspecimenswithdifferentligamentlengths,andsubsequentlyplottingthespecifictotalworkoffracturevalues,wf,asafunctionoftheirligamentlengths.A
(1)
Fig.1DENTspecimengeometry.
alt-text:Fig.1
(2)
simpleregressionanalysisofthisplotshowsthatthespecificessentialworkoffracture,we,andthespecificnon-essentialworkoffracture,βwp,aretheinterceptforazeroligamentlengthandtheslopeofthelinearregressionline,
respectively.
Thevaluewhichrepresentsthetoughness,namely,we,isaninherentmaterialparameteronlyiftheligamentyieldsfullybeforetheonsetofcrackpropagation.
2.2KeyassumptionsIntheEWFanalysis,thefollowingthreebasickeyassumptionsaremade:
a) Theloisfullyyieldedpriortotheonsetofcrackpropagation.
InaDENTspecimen,itcouldbeestimatedthatlowillbecompletelyyieldedpriortotheonsetofcrackpropagationifitislessthantwicethesizeoftheplasticzoneradius,rp.Underplanestressconditions,foralinearplastic
zone
andforacircularplasticzone
whereEistheelasticmodulusandσyistheuniaxialyieldstress.
Althoughhavinglo≤2rpisareasonablesizecriterion,itappearstobetoorestrictive.
b) Fractureoccursunderplanestressconditions.
Aspolymerfilmshaveathicknessoflessthan1mm,apracticallowerlimitof5mmforlohasbeenacceptedwhenpreparingDENTspecimenstobeproperlyhandled.Theupperlimitforlorequiresfull-ligamentyieldingbefore
crackpropagation.Hence,lohastobelessthantwicerpinDENTspecimens.
Anotherupperlimitisgivenbytherelationship:
whereWisthespecimenwidth.Thislastconditionisnecessarytopreventedgeeffects.
c) Goodqualitynotches.
Goodqualitymeans identicalandrepetitivesharpnotcheswithoutplasticdeformation in frontof thenotchtip.Thisrequirementguaranteesself-similar load-displacementand ligament length-displacementcurves for the
testedspecimens[2,3].
Thenotchsharpeningisofcriticalimportanceinobtaininggoodresults[4–6].Thelargernotchtipradiusorplasticdeformation,thehigherwevalues.
2.3OtherconsiderationsWhenthekeyassumptionsaresatisfied,weisthespecificenergyjustbeforecrackinitiation.Thatis,aninitiationvaluewhichcoincideswiththeJ-integralvalueatinitiation,Jo[2].
Hillhasdemonstrated[7]thatintheDENTgeometryunderplanestressconditions,nostresscanexceedthevalueof1.15σy.Thus,themaximumstressregisteredduringtheDENTtest,σmax,hastobebetweenσyand1.15σy,
anditsvalueisequalforalltheligaments.Theoretically,atsmallvaluesoflo,thespecimencanbeinamixedstateofstress,whichincreasesσmax.Therefore,thisHillcriterioncouldbeusefultodeterminethelowerlimitoflo. In
practice,theexperimentalvariabilityintheσmaxvaluescreatesdifficultiesfortheapplicationofthiscriterion.Clutton[4]hassuggestedanothercriterion,whichutilisesthemeanofthemaximumstresses,where
(3)
(4)
(5)
Thiscriteriononlyremovesdatawhereanerrorindimensionalmeasurementorinloadexists.
3Experimentaldetails3.1Material
ThestudyhasbeenconductedonacommercialgradeofEPBC.Themicrostructureconsists[8]ofelastomericethylene-propyleneparticlesembeddedinapolypropylenematrix.
Polypropylenerequiresimprovedtoughnessatbothroomandlowtemperaturestofulfilsomeindustryrequirements.Themechanismresponsibleforthetoughnessreinforcementistheformationofshearbandsaroundthe
elastomericparticles,whichabsorbsmostofthedeformationenergy.
TherawmaterialintheformofpelletswaskindlysuppliedbyREPSOL.Filmsthatwere0.5mmthickwerecast-extrudedfromthepellets.
3.2SpecimenpreparationTwokindsofspecimenswereprepared:dumbbellshapedandDENTspecimens.Allthespecimenswerepreparedandtestedinthemachinedirectionorientation.
DumbbellshapedspecimenswereobtainedinacuttingpresswiththeshapeanddimensionsofISO527-3typeVspecimen.
TheDENTspecimenswereusedtoperformthefracturetests.EPBCfilmswerecutinrectangularcoupons(Fig.1),whichwerepre-notchedformingsawcutslots.Thenotcheshadtobecollinear,andplacedoppositeone
anotheratthemidpointofthespecimenheight.
Themostpopularmethodusedtosharpennotchesistherazorbladeslidingtechnique.Inthistechnique,thenotchesaresharpenedbydrawingafreshrazorbladeacrossthepre-notch.Itisadvisabletodothisinasinglepass
sothattherazorbladefollowsthesametrack,avoidingbifurcations.Insteadofarazorblade,scalpelshavealsobeenused.Coolingthespecimensbelowtheirglasstransitiontemperature(Tg)priortotheslidingtechniquecanbe
helpful.Verysmallnotchtipradiiofaround1μmcanbemanufactured.Unintentionaldevelopmentofaplasticzoneaheadofthenotchtipcanbeinducedbythecompressivecomponentofthesidewaysslidingforce.Thenotchquality
isdependingonthetechniqueused,andevenontheoperatorskill.
The femtosecondpulsed laserablation technique (femtolaser)canbeused tomicromachinepracticallyanymaterial,withnegligible thermaldamage to thesurfacesurrounding theablatedareas.Withproperset-up, this
techniqueallowsobtainingconsistentnotchesthathavenegligiblethermaldamage,noplasticdeformation,andanotchtipradiusofapproximately1μm[2,3,6].
Thesharpeningofthepre-notchedEPBCspecimenswascarriedoutusingtwodifferentmethods,thefemtolaserablationtechniqueandrazorbladesliding.
Inonesetof18specimens,themachinedpre-notchwasextendedbytheapplicationofthefemtolaserablationtechniquewiththesameset-upandothervariables,asdefinedforanotherEPBCgrade[6].
Thesecondsetof18specimenswassharpenedbymanuallyslidinganewrazorbladeacrossthepre-notchinasinglepass.
Theloofeachspecimenwasmeasuredaftertestinginanopticalmicroscope.
Onesurfaceofeachspecimenwasadequatelysprayedwithaspecklepatternbeforebeingtested.
3.3TestconditionsAlltestswerecarriedoutat23±1°Cusingacrossheadspeedof2mm/minonaZwickservo-hydraulictestingmachine,whichwasfittedwithatwo-cameradigitalimagecorrelation(DIC)systemandAramissoftware(GOM,
Germany).
Ingeneral,DICisbasedontheprincipleofcomparingspecklepatternsonthesurfaceofthedeformedsamples,orbetweenanytwodeformationstates.Surfaceswithhighcontrastarerequiredtoavoidimagedistortionand
thereforeinaccuratedata.Hence,beforetesting,onesurfaceofeachspecimenwascoveredwithathinwhitecoatingbeforebeingsprayedinordertoobtainblackpoints,asrequiredbytheDICsystem.
Uniaxialtensiletestswereperformedonthedumbbellshapedspecimens.TheloadwasregisteredbytheloadcellandthedisplacementsbytheDICsystem.
(6)
TheDENTspecimensweretested,inmodeI,untilcompletefailure.ThespecimenswereproperlyclampedwithanoriginaldistancebetweenclampsofZ=60mm.Foreachspecimen,theloadasafunctionofthecross-head
displacement,dz,wasregistered.
DICsystemimagesobtainedduringthetestswererecordedforallthespecimens.Theseimageswerealsoanalysedwiththesoftwareformeasuringthedeformationandtheligamentlengthevolutionthroughoutthetest.The
displacementdopzwasmeasuredwithtworeferencepointsveryneartoeachother,butoutsidetheouterplasticzone,whichcorrespondstothelargestlospecimen.Thedistancebetweenthesetworeferencepointswasalwaysthe
sameforallspecimensofagivenset.Then,byusingtheregisteredloads,displacements,andligamentlengths,twosetsofdata,foreachspecimen,canbeplotted.Specifically,theloadisplottedasafunctionofthedisplacement,and
theligamentlengthlasafunctionofthedisplacement.
4Resultsanddiscussion4.1Uniaxialtensiletest
TheσyandEvaluesoftheEPBCfilmweremeasuredon5dumbbellshapedspecimensfollowingtheISOstandard527,resultinginE=1.24±0.1GPaandσy=25.0±0.2MPa.Thespecimensshowedawhiteningzoneinthe
deformedarea,whichischaracteristicoftheheterophasepolymers.
4.2NotchqualityThenotchesoftwospecimensfromeachsetwereobservedbyopticallightmicroscopyandalsobyscanningelectronmicroscopy(SEM).
Observationoftherazorbladesharpenednotchesunderthelightmicroscope(Fig.2a)revealedsomestresswhiteningaheadofthenotchtip,indicatingthatsomeplasticdeformationhadtakenplace.Thisphenomenonwasnot
presentinthenotchesofthefemtolaserspecimens(Fig.2b).
Fig.2Opticalmicrographs:a)Femtolasernotch,b)Razorbladenotch.
TheSEMmicrographsoftherazorbladenotches(Fig.3)revealedvolumeaccumulationofplasticallydeformedmaterialatthenotchtip.Thenotchtipradiuswaslessthan1μmandthesharpeningextensionvariedbetween
900and1300μm.
All the femtolasernotchesobservedthroughtheSEMturnedout tobevirtually identical (Fig.4),withanotch tipradius less than1μmanda sharpeningdepthof750μm. Itwasalsoobserved that therewasnoplastic
deformationandnegligiblethermaldamageatthenotchroot.
alt-text:Fig.2
Fig.3SEMmicrographsofarazorbladespecimen:a)Extendednotch,b)Notchtipdetail.
alt-text:Fig.3
Both typesofnotcheswerevery sharp,withpractically the samenotch tip radius,but thereweredifferences in theplasticdeformationat thenotch root,whichwasvisible in the razorbladenotchesandabsent in the
femtolaserones.
ThesecondphaseparticlesoftheEPBCactasstressconcentrators,andsoonlyasmallcompressivecomponentoftheslidingforceisneededtoproduceplasticdeformation,whichisvisualisedaswhitening.
4.3FemtolaserspecimensTheloadversusdisplacement(dopz)curvesobtainedthroughtestingarerepresentedinFig.5,foreachoneofthe16specimenstested.Here,apartialoverlapofthecurvescorrespondingtolo=5.89mmandlo=6.45mmas
wellasthecurveslo=19.37mmandlo=20.39mmcanbeobserved.
Fig.4SEMmicrographsofafemtolasernotch:a)Generalview,b)Detailofthecracktip.
alt-text:Fig.4
Theligamentlengths(l)asafunctionofthedisplacement(dopz)arerepresentedinFig.6forthesame16testedspecimens.AsinFig.5,apartialoverlapisalsoobservedforthesamelocurves.
Eq.(2)canbeevaluatedasexplainedbefore.InFig.7,wfasafunctionofloisrepresented,using,dzanddopz,twodifferentwaysofmeasuringthedisplacements.Thewevalues,127.05±12.64kJ/m2(dz)and130±9.59kJ/m2
(dopz),arepracticallycoincidentbuttheslopes,21.35±0.90MJ/m3(dz)and19.94±0.70MJ/m3(dopz),changeslightly.
Fig.5Registeredload-dopzcurvesforthe16femtolaserspecimens.
alt-text:Fig.5
Fig.6Registeredlversusdopzcurvesforthe16femtolaserspecimens.
alt-text:Fig.6
ThedopzwasmeasuredusingtworeferencepointscloselylocatedtotheOPZ,andinthiswaytheOPZwascontainedwithinthesetwopoints,forallspecimens.Thedistancebetweenthesereferencepointswasconstantforall
specimens.Thedisplacementsat rupturemeasured fromthecrosshead (dz)are larger than thedisplacementsmeasured fromthe limitsdefinedby theouterplastic zone (dopz).Theelasticdeformationoutside theplastic zone is
recoveredonunloadingsothatbothrupturedisplacementswouldbeexpectedtobeequalatleastthatthetotalrecoveryofotherdisplacements,asviscoelastic,doesnothappenbeforespecimenrupture.
Oncewe,σy,andEwereobtained,therpwascalculatedandEqs.(3)–(5)wereaccomplished.Thus,twoofthekeyassumptionsoftheEWFaresatisfied,i.e.,theligamentlengthiscompletelyyieldedpriortotheonsetofcrack
initiation,andfractureisunderplanestressconditions.
IftheloadinFig.5isdividedbytheareaofitsinitialligament,astressversusdopzrepresentationisobtained.ThisnewplotisrepresentedinFig.8.Thehatchedareaundertheσ-dopzcurvesisequaltowe=130kJ/m2.Asetof
overlappingcurves(heads)canbeobservedinthelowdisplacementrangeuptoafairlyrecognizablevalue,di,fromwhichthecurves(tails)starttodiverge.Thehatchedareabeginsatdopz=0untilthedisplacementdi,wherethe
crackinitiationbegins.Whenthedisplacementsarelargerthandithenthereiscrackpropagation.FromtheanalysisofFig.8thecrackinitiationdisplacementdi=4.94±0.11mm,themaximumstressσmax=28.75±0.74MPa,and
thecrackinitiationstressσi=25.89±0.46MPacanbeidentified.
Theσmaxvaluesarebetweenσyand1.15σyandthereforeEq.(6)isalsovalidforallspecimens.TheCluttonandHillcriteriaarenowsatisfied.
InFig.8someoftheframesregisteredbytheDICcamerasarealsoschematised.Theexactframewherecrackinitiationbeginscannotbevisuallydetected,butthearrowsintheframeofFig.8showthatinthisframethecrack
Fig.7EWFplotforthe16femtolaserspecimens:●)Displacementdopz,▲)Displacementdz.
alt-text:Fig.7
Fig.8Stressversusdopzcurvesforthe16femtolaserspecimens.
alt-text:Fig.8
initiationhasbeeninitiated.TheframesdisplayedinFig.8indicatethatpriortodithereisnocrackpropagationandafterwards,thecrackgrowthhasalreadybegun.Thecrackinitiationcorrespondsverywellwithcoordinates(di,σi),
confirmingtheonsetofcrackinitiation.Then,weisthespecificenergyjustuptocrackinitiation.TheframesinFig.8followasequenceofeventsleadingtofractureoftheDENTspecimens.Theprocessbeginswiththeopeningand
bluntingofthenotchandtheyieldingoftheligamentarea,followedbycrackinitiationandpropagationuntilcompletefailure.
Thecracktipopeningdisplacementattheonsetofcrackinitiation,CTODis
wheredristhedisplacementatcompleterupture.
InFig.9theobtaineddrvalues(Fig.2)infrontofloareplottedforthe16specimens.AsimplelinearregressionanalysisofthisplotshowsthattheCTODvalueistheinterceptforazeroligamentlength.TheCTODvalueof
4.94mmiscoincidentwithdithedisplacementattheonsetofcrackinitiation(Fig.8).
Thecracklengthincrementduetoblunting,Δab,justpriortocrackinitiationisgiven(Fig.1)by
where li is the ligament length at the onset of crack initiation. When li is represented as a function of lo, there is a linear dependence between the two variables. The li values can be determined in Fig. 6 from the di values
correspondingtoeachlospecimen.InFig.10thelivaluesobtainedforeachlospecimenaregraphed.AsimplelinearregressiononthisgraphresultsinaninterceptΔab=1.42mmandaslopeof1,aspredicted.
(7)
Fig.9DeterminationofCTODforthe16femtolaserspecimens.
alt-text:Fig.9
(8)
Fig.10DeterminationofΔabforthe16femtolaserspecimens.
alt-text:Fig.10
Toensurethatthefracturemechanismisthesame,irrespectiveoftheligamentlength,thespecimensmustshowacommonandsteadyfracturephenomenologyduringcrackgrowth.
InFig.6,thecrackgrowthiscomprisedbetweentheCTODanddrvalues.ThecrackgrowthrangeofFig.6canbenormalisedusingtheΔabandCTODvalues.Thenormalisedresultscanberepresentedinaplotliketheone
showninFig.11.Here,allthecurvesoverlapexceptforthespecimenswithlo=5.89mmandlo=19.37mm,whichshowslightdeviations.Inthiswaythesametwospecimensareidentified,whichalsohavedeviationsinFigs.5and6.
Thesetwospecimenswereexcludedandalltheworkwasrecalculated.Attheendofthenewanalysis(we=128.81kJ/m2andβwp=19.87MJ/m3usingdopz),theinfluenceofthesetwospecimensonthepreviousresultswas
insignificant.
Now,thelastofthekeyassumptionsissatisfiedbecausetheremaining14specimenshadrepetitivesharpnotcheswithoutplasticdeformationaheadofthecracktip.Assuch,weisaninherentmaterialproperty.
Duringthecrackpropagation,theloadPversusthecracklengtha[2]isrepresentedby
anditsderivative
Thus,ifPisrepresentedasafunctionofa,astraightlinewithslope–tσishouldbefound.
Thecracklength(Fig.1)isgivenby
Then,bycombiningEq.(11)withFigs.5and6,PasafunctionofaisdepictedinFig.12forthetails.ThetwocurvesthatdeviatedfromtheothersinFig.12aredirectlyrelatedtothetwopreviouslydiscardedspecimens.The
lineardependenceindicatesthatallpropagationsfollowthesametrendexceptatthehigheravalues,nearthecompletespecimenfracture,wheretheslopeincreases.Fromtheslopecalculatedofthe14validspecimens,itisfound
thatσi=25.20±0.96MPa,whichagreeswiththepreviouslydeterminedvalueinFig.8.
Fig.11Normalisationofcrackgrowthforthe16femtolaserspecimens.
alt-text:Fig.11
(9)
(10)
(11)
TheJ-integralconceptrepresentsanenergycontourpathintegralthatisindependentofthepatharoundthecrack.TheJ-integralcanberepresented[9]as
whereU is theexternalworkdoneup toagivenconstantdisplacementd, anda is thecrack length.TheLandesandBegleyexperimentalmethod [9] is usedhere.Thismethod requires two steps.The first step consists of the
graphicalrepresentationoftheenergydividedbyt,asafunctionofa,whendisfixed.TheresultantplotisshowninFig.13.Thepointsbelongingtothesamedisplacementshowlinearityandcanbefittedbyastraightline.ByEq.(12),
theresultantslopeoftheregressionlineis-J.ThesecondstepconsistsofplottingtheJvaluesversusdisplacement,asillustratedinFig.14.
Fig.12Loadversusaforthe16femtolaserspecimens.
alt-text:Fig.12
(12)
Fig.13Inputenergydividedbythicknessversusaforthe14validfemtolaserspecimens.
alt-text:Fig.13
Foranon-workhardeningmaterialandfullyieldingoftheligament[2],U/tisalinearfunctionofaataconstantdisplacement,asithasbeenverified,then
InFig.14,theslopeoftheregressionline,σi=22.76MPa,agreesreasonablywellwiththepreviouslyfoundσivalues.TheJvalueatcrackinitiation,Jo,isobtainedbyintroducingtheCTODvalueintheJ-integralplot,asshown
inFig.14.ThisprovidesavalueofJo=126.49kJ/m2thatmatcheswellwithwe.
TherelationshipbetweenJoorweandCTODgiven[2]by
issatisfied.
4.4RazorbladespecimensTheloadversusdopzcurvesdeterminedduringtestingareshowninFig.15foreachofthe16specimenstested.Here,thereisnooverlapofcurvesobserved.
Fig.16accountsfortheregistereddataoflasafunctionofdopz.Apartialoverlapofthespecimenswithlo=19mmandlo=17.86mmisobserved.
Fig.14J-integralplotforthe14validfemtolaserspecimens.
alt-text:Fig.14
(13)
(14)
Fig.15Registeredloadversusdopzcurvesforthe16razorbladespecimens.
alt-text:Fig.15
TheEWFplotofthe16specimens,whendopzisused,isdisplayedinFig.17.Theinterceptatdopz=0oftheregressionlineyieldswe=175.97kJ/m2.
ThestressversusdopzcurvesaredepictedinFig.18a.Twodifferentpopulationsofcurvescanbeobserved.Onepopulationhasthe4specimenswiththeshorterlospecimens,whiletheotheronecontainstheremaining12
specimens.
Fig.16Registeredlversusdopzcurvesforthe16razorbladespecimens.
alt-text:Fig.16
Fig.17EWFplotfortherazorbladespecimens:●)dopz16specimens,▲)dopz11specimens,■)dz11specimens.
alt-text:Fig.17
Forthiscase,themeanvalueofσmax(Fig.18a)surpassestheupperlimitoftheHillcriterion.Theσmaxvaluesforthe4shorterloarelargerthan1.15σy, indicatingthepossibilitythattheycouldbeinamixedmodestate.
However,thisisnotthecasebecausetheshorterfemtolaserspecimens,whichhavesimilarlo,wereinapureplanestressstate.TheCluttoncriterion(Eq.(6))issatisfied.
Toinvestigatewhetherthefracturemechanismisthesameforallthe16specimens,itisconvenienttoperformthestudyofcrackgrowthrange,aswasdonebefore(Fig.11)forthefemtolaserspecimens.TheCTODandΔab
valuesweredeterminedthroughFigs.19and20,respectively.Now,withΔabandCTOD,thecrackgrowthrangeofthesespecimenscanbenormalised.InFig.21thenormalisedcurvesarerepresented.Itcanbeclearlyobservedthat11
specimensoverlap,4specimenspresentlargedeviations(lo=5.11mm,lo=5.85mm,lo=6.96mmandlo=8.29mm),andthespecimenwithlo=20.38mmhasaslightdeviation.
Fig.18Stressversusdopzcurvesfortherazorbladespecimens:a)16specimens,b)11specimens.
alt-text:Fig.18
Fig.19DeterminationofCTODfortherazorbladespecimens:●)dopz16specimens,▲)dopz11specimens.
alt-text:Fig.19
Fig.20DeterminationofΔabfortherazorbladespecimens:●)dopz16specimens,▲)dopz11specimens.
alt-text:Fig.20
Fig.21Normalisationofcrackgrowthforthe16razorbladespecimens.
alt-text:Fig.21
TheframescollectedbytheDICsystemofthese5specimenswerecarefullyexamined.Inthe4specimenswiththeshorterlo,itisobservedthatthetwonotchesofthesamespecimendonotinitiatethepropagationatthesame
time.Thisfacthasbeenalsoseeninotherpolymerfilms[2,3]andcanbeoriginatedbyqualitydifferencesbetweenthetwonotchesofthespecimen.Suchdifferencesareprobablyproducedduringtheslidingoftherazorbladein
specimenswithshortlo,beingmoredifficulttosharpenthatinspecimenswithlargelovalue.
Intentionally,onespecimenhasbeenpreparedusingadifferentcompressivecomponentoftherazorbladeslidingforceonthetwonotches.Fig.22showstheopticalmicrographsofbothnotches.Here,thedifferentextentof
plasticdeformationcanbeobserved.Aframeofthetestedspecimenshowingthenon-simultaneouspropagationofbothcracksisalsoshown.
Theonlyonedifferenceobservedinthespecimenwithlo=20.38mm,whencomparedwiththeother11validspecimens,wasthatalongertimewasrequiredforcrackinitiation.ThiscanalsobeobservedinFig.18awhereits
divalueislargerthanotherspecimens.Thedivaluecorrespondstoaninitiationstressof25.35MPa.Bothnotchespropagateatthesametime,buttheircomparativelylargerdisplacementandlongertimetocrackinitiationcanbe
attributedtoeithertheirlargercracktipradius,ortheincreasedplasticdeformationaheadofthecracktip,despitetheparityofthenotchquality,whencomparedtotheother11validspecimens.
Now,afterdiscardingthe5anomalousspecimens,theworkwasentirelyrecalculatedwiththe11validspecimens.ThesespecimenssatisfiedEqs.(3)–(5)andtwoofthekeyrequirementswerefulfilled,i.e.,theligamentlengths
arecompletelyyieldedpriortotheonsetofcrackinitiationandfractureisunderplanestressconditions.However,inspiteoftherepetitivesharpnotches,thesespecimenshaveplasticdeformationaheadofthecracktip,andtherefore
thethirdkeyrequirementisnotaccomplished.Thus,wewithavalueequalto168.44kJ/m2isnotaninherentmaterialproperty.
TheEWFplotofthe11validrazorbladesharpenedspecimensisdepictedinFig.17forthemeasureddisplacementsdzanddopz.Thewevaluesforbothdisplacementsarepracticallyidentical,167.29±10.49kJ/m2(dz)and
168.44 ±10.91kJ/m2 (dopz), but the slopes change slightly, 22.33 ±0.73MJ/m3 (dz) and 21.33 ±0.76MJ/m3 (dopz), as in the femtolaser specimens (Fig. 7). Thewe=168.44kJ/m2 for the 11 specimens is slightly less than the
we=175.97kJ/m2obtainedfromthe16specimens.
InFig.18bthecurvesσversusdopzarerepresentedforthe11validspecimens.Theσmaxis28.26±0.25MPa,andeachσmaxvaluemeetsHillandCluttoncriteria.Thehatchedareaundertheσ-dopzcurvesisequalto168.44kJ/m2
(wevalue).Thishatchedareabeginsatdopz=0andextendsuntildi=6.54±0.04mm.Inthislowrangeofdisplacements,allthecurves(heads)overlap.Fromdi,thecurves(tails)starttodivergeuntildr.So,inFig.18b,diisidentified
asthedisplacementattheonsetofcrackinitiationanditscorrespondingstressvalue,σi=25.35±0.15MPa,asthestressattheonsetofcrackinitiation.Thisbehaviourhasbeenpreviouslyfound[2,3]forrazorbladeandfemtolaser
sharpenedspecimens.
TheCTODvalue(6.34mm)isdeterminedinFig.19.Asexpected,thisvalueiscoincidentwiththedivalueidentifiedinFig.18b,andΔab=1.59mmisobtainedinFig.20forthe11specimens.
Proceedingasbeforewiththefemtolaserspecimens;theloadduringthecrackpropagationisrepresentedinFig.23foreachoneofthe16testedrazorbladesharpenedspecimens.Discardingthe4shorterlospecimens,and
thespecimenwithlo=20.38mm,astraightlineaspredictedbyEq.(10),results.The5curvesthatdepartfromtheotherinFig.23correspondtothe5specimensdiscardedbefore.ByapplyingEq.(10)totheslopeofthestraightline
obtainedfromthe11validspecimensshowninFig.23,itisfoundthatσi=25.06±0.88MPa,avaluethatagreesverywellwiththeσivaluesdeterminedbefore.
Fig.22Non-simultaneouscrackpropagation.
alt-text:Fig.22
TheJ-integralprocedurewasperformedasdescribedbefore.ThetwostepsoftheexperimentalmethodareshowninFigs.24and25.InFig.24,thepointsbelongingtothesamedisplacementshowlinearityandcanbefittedby
aregressionline.Theslopeofthislineis-J(Eq.(12)).TheseslopesaredisplayedinFig.25asafunctionofthedisplacement.Here,followingEq.(13),theslopeoftheregressionlineσiresultsin22.04MPa,whichagreesreasonably
withtheσivalueencounteredinFig.18b.UsingthedisplacementattheonsetofcrackinitiationgivesJo=166.01kJ/m2,whichalsoagreeswithwe.
Fig.23Loadversusaforthe16razorbladespecimens.
alt-text:Fig.23
Fig.24Inputenergydividedbythicknessversusafortherazorbladespecimens.
alt-text:Fig.24
The11selectedspecimenshaverepetitivesharpnotches,butwithplasticdeformationaheadofthenotchtip,thissetofspecimensdoesnotfulfilthekeyrequirementofconsistent,highqualitynotches.Asaconsequence,weis
notaninherentmaterialproperty.However,therelationshipbetweenwe,Jo,CTODandσi,givenbyEq.(14),iscompletelyfulfilled.Thesevaluesdependonthenotchqualityandtheirrelationshipsaremaintained.
4.5FemtolaserversusrazorbladeTherearedifferencesinthenotchqualitybetweenthefemtolaserandtherazorbladesharpenedspecimens.Theplasticdeformationleadstohighervaluesofwe,CTODandJo,althoughtheirvaluessuccessfullyaccomplishEq.
(14).
Inpolymerfilms[2,3]lessductilethanEPBC,ithasbeenpossibletogeneratenotchesusingtherazorbladeslidingtechniquewithandwithoutplasticdeformationinfrontofthenotchtip.Oncespecimenscontainingplastic
deformationwerediscarded,thefractureparameterswerecoincidentwiththoseobtainedinfemtolaserspecimens.
Themeanσmaxandσivaluesforthefemtolaserandrazorbladespecimenshavethesamevalues.However,theCTODandΔabvaluesarelargerfortherazorbladesharpenedspecimens.
Foramorethoroughanalysisoftheσ-dopzcurves,inFig.26atheregisteredcurvesobtainedfromtwoequalligamentlengthsaredisplayed,onesharpenedbyfemtolaserandtheotherbyrazorblade.Forthesamespecimens,
thel-dopzcurvesareshowninFig.26b.InFig.26aandbcanbeobservedthatthedrvalueislargerfortherazorbladesharpenedspecimen.Anotherwaytorepresentthesedatacanbeperformedbyshiftingtheσ-dopzandl-dopzcurves
alongthedisplacementaxissothattherupturedisplacementscoincide,asshowninFig.27afortheσ-dopzcurvesandinFig.27bforthel-dopzcurves.Doingso,thedivalues fall in thesameplace,andthetailsoverlap.Withsuch
representation,itcanbededucedthatthecrackgrowth,andthepropagationenergy,arethesameforbothsharpeningmethods,andthentheslopeβwpoftheEWFplotwouldhavethesamevalueforbothsetsofspecimens,asis
observed.InFig.26a,itcanbeseenthatthetwocurvesoverlapintherangecomprisedbetweenthedisplacementsdopz=0andthedisplacementcorrespondingtoσmax.InFig.27b,itcanbeobservedthatthetailsalsooverlap.The
differencebetweenbothcurvesoccursintherangecomprisedbetweenthedisplacementcorrespondingtoσmaxanddi.Inspiteofthis,σiisthesameforbothnotchsharpeningprocedures.
Fig.25J-integralplotfortherazorbladespecimens.
alt-text:Fig.25
Thesametrendshavebeenobservedinotherductilepolymerfilms[2,3].Itisclearthattheshapeofthestress-displacementcurvesisgreatlyinfluencedbythequalityofthenotches.
Ifthereisasetofspecimenswiththesamenotchtipradius,buthassomespecimenswith,andotherswithout,plasticdeformationaheadofthenotchtip,then,aftertesting,allspecimenswouldhavethesameσmaxandσibut
differentdi.Thisresultsincrossingcurvesintheload-displacementandligamentlength-displacementplots.Thesebehaviourscanbeexpectedifthesetcontainedspecimensthathaddifferentlevelsofplasticdeformation.
Thenormalisedcrackgrowthversusdisplacementcurvesof thecrackpropagationareshown inFigs. 11and21 for the femtolaserand razorbladespecimens, respectively. If a singlegraphofboth figures ismade,after
discardingthenon-validspecimens,allthecurveswilloverlap,confirmingthatbothsetsofspecimenspresentthesamepropagationbehaviour.Thenormalisedplotsofthecrackgrowthversusdisplacementarehelpfultorejectthose
specimenswithdifferentqualitynotches.
ThisEPBCgradepresentswevaluesof130and168.44kJ/m2forthefemtolaserandrazorbladesetsofspecimens,respectively.Theirβwpvalueisapproximately21MPa/m3,consideringanaverageofthedifferentwaysto
measurethedisplacement.Martínezetal.[6]foundwevaluesof60and116kJ/m2fortwosetsoffemtolaserandrazorbladespecimens,respectively,andanaverageβwpvalueofapproximately15MJ/m3,foranotherEPBCgrade,which
hadthesame8.5%ethylenecontentbutalowermolecularweight.Thus,theincreaseinmolecularweightresultsinanincreaseintoughnessandinpropagationenergy.
4.6Theshapeofthestress-displacementcurvesTheshapeandsizeofthestress-displacementcurvesobtainedfromspecimensthatwerenotchedindifferentways,makesitpossibletoanalysetheirEWFbehaviourwhentheyarecomparedwiththetwopreviouslyanalysed
setsofspecimens,thefemtolaserandtherazorbladesharpenedspecimens.
Fig.27Femtolaserandrazorbladespecimenswithlo=17mm:a)Shiftedσ-dopz,b)Shiftedl-dopz.
alt-text:Fig.27
Fournewspecimenshavebeenmanufactured.Thefirstofthesespecimenswassharpenedbyapplyingtherazorbladeslidingtechnique,but,inthiscase,thesharpeningwascarriedoutoverspecimensthatwerefrozenin
liquidnitrogen,thatis,belowtheTgofthematerial.Reductionoftheplasticdeformationaheadofthenotchtipisexpectedwhenitiscomparedwiththerazorbladesharpenednotchesatroomtemperature.Then,equalvaluesofσmax
andσiwillbeanticipated,unlikethefemtolaserandrazorblade(roomtemperature)sharpenedspecimens,andalsoequaltailsofthestress-displacementcurves.However,intermediatevaluesfordianddrarealsoexpected,resulting
inanintermediatewevalue.
Fig.28ashowstheregisteredstress-displacementcurvesfor3specimenswithsimilarlovalues.ThecurveFcorrespondstolo=11.47mmfemtolaserspecimen,thecurveGcorrespondstolo=10.84mmrazorblade(room
temperature)sharpenedspecimen,andthecurveN2correspondstolo=10.41mmrazorblade(liquidnitrogen)sharpenedspecimen.Fig.28bshowsthesamecurvesofFig.28abutshiftedtothesamedr.Asexpected,the3curveshave
thesameσmax,σi,andtails,butthedi,theCTOD,increaseswiththeplasticdeformation,resultinginhigherwevalues.
Whereasthetwoedgenotcheswereproperlyalignedinallthetestedspecimens,inthesecondofthe4newspecimens,thetwoedgenotches,sharpenedbyrazorbladesliding,werenotcollinear.Instead,theyhad1mm
separation. The non-collinearity of the two edge notches can modify the stress distribution in the ligament zone, and the results will likely be influenced. In Fig. 29, the stress-displacement curve registered for this specimen
(lo=12.28mm)withnon-collinearnotchesispresented.Forcomparisonpurposes,arazorbladesharpenedspecimenwithcollinearnotchesandlo=12.31mmisalsopresented.These2curvesshowequalσmaxvaluesandoverlap
betweendz=0anddz=di.Ifequalσivalues(25.5MPa)arealsoconsideredforbothcurves,equalwevaluesareimplied.However,thecurveofthespecimenwithnon-collinearnotcheshasalargerdrvalue,causingthatthetailsof
bothcurvesdonotoverlap.Further,theareaoftheσ-dzcurvebetweendianddrisalsolarger,causingβwptobehigherforthespecimenwithnon-collinearnotches.
Fig.28Stress-displacementcurvesforF-femtolaser(lo=11.47mm),G-roomtemperaturerazorblade(lo=10.84mm),andN2-liquidnitrogenrazorblade(lo=10.41mm):a)Measureddisplacement,b)Displacementshiftedtodr.
alt-text:Fig.28
Thespecimenshavetobetestedwiththedirectionoftensionperpendiculartothecollinearnotches.Thatis,thespecimensmustbeproperlymountedonthegripsofthetestingmachine.Ifthespecimensaretiltedwhenthey
aremountedonthegrips,thenthecollinearnotchesofthespecimenarenotorientedperpendicularlytothedirectionoftension,andsothestressdistributionintheligamentismodified.Thethirdofthe4newspecimens,arazor
bladesharpenedspecimenwithlo=12.13mm,hasbeentestedwiththespecimentiltedby5°onthegrips.Itsstress-displacementcurveisshowninFig.29andcouldbecomparedtothespecimenwithlo=12.31mm,whichwas
correctlymountedonthegrips.Thecurvesforthesetwospecimensoverlaponlyuptoσmax.Afterthispoint,thecurveofthetiltedspecimenisgreaterandhasalargerdrvaluethanthenon-tiltedspecimen.Consideringσi=25.5MPa,
thetiltedspecimenwillhaveahigherwevaluethantheproperlymountedspecimen.
Inorder to study the influenceof thenotch tip radiuson thestress-displacementcurves,circularholesweredrilled touseasnotches.Thepressureexercisedby thedrillbitat thebeginningcausedavery largeplastic
deformation that extended to thematerial outside the hole, especially for small diameter holes. After several attempts, a specimen (lo=12.26mm)with two edge holes (diameterϕ=2mm) that had the same level of plastic
deformation inbothholeswasobtained.Toobtain thenotches thedrillingwas followedby opening the twoedgenotches.The last of the4new specimenswas tested, and the experimental stress versusdisplacement curve is
representedinFig.30a.Forcomparisonpurposes,thecurvesforthefemtolaser(lo=12.20mm)andrazorblade(lo=12.14mm)specimensarealsopresentedinthisfigure.InFig.30acanbeobservedthatthe3curvesoverlapjustup
toσmax.Fromthispointforward,thedrilledspecimenshowedlargervaluesforthestressandfordr.Thesamestress-displacementcurvesofFig.30awereshiftedalongthedisplacementaxissothattherupturedisplacementswerethe
same,andarerepresentedinFig.30b.Consideringσi=25.5MPaforthedrilledspecimenobtainedfromthefemtolaserandrazorbladespecimens,asrepresentedinFig.30aandb,itcouldbeinferredthatthedrilledspecimenwill
havehigherwe,Δab,andCTODvalues,whilethetailregionseemstobequitesimilartotheothercurves.Inanycase,theinfluenceofthenotchtipradiusonthefractureparametersisclear.
Fig.29Stress-displacementcurvesforG-razorbladecollinearnotches(lo=12.31mm),NA-razorbladenon-collinearnotches(lo=12.28mm),andT-tiltedrazorbladecollinearnotches(lo=12.13mm).
alt-text:Fig.29
5ConclusionsThefemtosecondlaserablationtechniqueenablesobtainingveryconsistent,sharpnotches,withoutplasticdeformationaheadofthenotchtip.Thisnotchsharpeningtechniqueisthemostappropriatetosharpennotchesofthe
mostductilefilmsandgivesthelowestvaluesforthefractureparameters.Thelimitationsincludetheavailabilityoftheequipmentandthehighcostpernotch.
Notchsharpeningusingtheclassicrazorbladeslidingtechniquecanyieldnotcheswithdifferentquality,whichdependsonthematerialductilityandthecompressivecomponentofthesidewaysslidingforcethatisapplied.
Sharpnotcheswithoutplasticdeformationcanbeobtained,andwillyieldvaluessimilartothefemtolaserspecimens.Normally,however,specimenswithplasticdeformationaheadofthenotchtipareobtained.Whenthetwonotches
ofthesamespecimenhavedifferentlevelsofplasticdeformation,thecrackinitiationdoesnotoccuratthesametime.Specimenswithdifferentlevelsofplasticdeformationcanbeobtained.Variabilityinthesamelaboratoryand
betweendifferentlaboratoriesofthewe,Jo,andCTODvaluescanbeexplainedbythedifferent levelsofplasticdeformationaheadofthenotchtiporthenotchtipradiusthatcanbegeneratedbyoperatorswhensharpeningthe
notches.Thelargerthelevelofplasticdeformation,thelargerwillbethedisplacementatinitiation,resultinginhighervaluesofΔabandwe.However,asthepropagationdoesnotdependontheplasticdeformation,thesameβwpvalue
willbeobtained.
Itisconfirmedthatakeyrequirementtoobtainmeaningfulresultsistohaveconsistentnotcheswithoutplasticdeformationinfrontofthenotchroot.Thenotchtipradiushasastronginfluenceonthefractureparameters.
The shape of the stress-displacement curves depends on the notch quality. Consistent notches have the sameσmax, σi, di, CTOD, andΔab values, and then the normalised curves of the propagation region overlap.Non-
overlappingcurvesbelongtospecimenswithdifferentqualitynotchesandcanbediscarded.
Thewe,Jo,andCTODvaluesobtainedfromspecimenswithplasticdeformationatthecracktip,beingthistheonlykeyassumptionnotaccomplished,satisfytherelationshipsamongwe,CTOD,Jo,andσi,butthesevaluesare
Fig.30Stress-displacementcurvesforF-femtolaser(lo=12.20mm),G-razorblade(lo=12.14mm),andD-drilled(lo=12.26mm):a)Measureddisplacement,b)Displacementshiftedtodr.
alt-text:Fig.30
QueriesandAnswersQuery:Pleasenotethatauthor’stelephone/faxnumbersarenotpublishedinJournalarticlesduetothefactthatarticlesareavailableonlineandinprintformanyyears,whereastelephone/faxnumbersarechangeableandthereforenotreliableinthelongterm.Answer:Iagreewithyourobservation.
Query:Pleaseprovidethegrantnumberfor‘NationalCouncilforScienceandTechnology(CONACYT,Mexico)’ifany?Answer:Thereisnograntnumberassociated.
Query:Pleaseconfirmthatgivennamesandsurnameshavebeenidentifiedcorrectlyandarepresentedinthedesiredorderandpleasecarefullyverifythespellingofallauthors’names.Answer:Theyareallcorrect.
notinherentpropertiesofthematerial.
Theinspectionofthenotchesinalightopticalmicroscopebeforetestingcouldbehelpfultodetectplasticdeformationinfrontofthecracktip.
Non-collinearnotches andmisalignment of the specimenson thegrips, affect the stress-displacement curves and the results. Small differencesof less than1mm in the collinearity of thenotches canbeunintentionally
generatedduringthespecimenmanufactureandhaveasmalleffectontheresults.Morecareisnecessarywhenmountingthespecimensonthegripsbecausetheshapeofthestress-displacementcurveismoreaffectedandthusthe
results.Specimenswithnon-collinearnotchesandincorrectlyalignedcanalsobedetectedbynormalisingthecurvesinthepropagationregion.
TheEWFapproachhasbeensuccessfullyappliedonanEPBC.Thisheterophasepolymerhasmultipleshearyieldingasadeformationmechanism,whichisdifferentfrompolymersthatundergoneckingbeforetheonsetof
crackpropagation.InEPBC,giventhesameethylenecontent,thefractureenergyincreasesastheaveragemolecularweightsincrease.
AcknowledgementsTheauthorsacknowledgetheMinisteriodeEconomiayCompetitividadofSpainforitsfinancialsupportthroughtheresearchprojectMAT2012-37762-C02-01.N.LeónexpresseshisgratitudetotheNational
CouncilforScienceandTechnology(CONACYT,Mexico)forthepredoctoralfellowship.
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