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

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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

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(4)

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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.

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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.

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Fig.9DeterminationofCTODforthe16femtolaserspecimens.

alt-text:Fig.9

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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

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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

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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

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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

Fig.26Femtolaserandrazorbladespecimenswithlo=17mm:a)σversusdopz,b)lversusdopz.

alt-text:Fig.26

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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