Nonlinear ultrasonic evaluation of the fatigue damage of adhesive joints

NDT&EInternational70(2015)9–15ContentslistsavailableatScienceDirectNDT&EInternationaljournalhomepage:www.elsevier.com/locate/ndteintNonlinearultrasonicevaluationofthefatiguedamageofadhesivejointsGuoshuangShuia,n,Yue-shengWanga,n,PengHuanga,JianminQubabDepartmentofMechanics,BeijingJiaotongUniversity,Beijing100044,ChinaDepartmentofCivilandEnvironmentalEngineering,NorthwesternUniversity,Evanston,IL60208-3109,USAarticleinfoArticlehistory:Received24April2014Receivedinrevisedform12November2014Accepted17November2014Availableonline18December2014Keywords:NonlinearultrasonicsFatiguedamageAdhesivejointsNon-destructiveevaluationabstractAnexperimentalmethodbasedonthenonlinearultrasonictechniqueispresentedtoevaluatefatiguedamageofanadhesivejoint.Inthispaper,specimensmadefromAZ31magnesium–aluminumalloybondedthroughanepoxylayeraresubjectedtoafatigueload.Theultrasonicharmonicsgeneratedduetodamagewithintheadhesivelayeraremeasured;andtheacousticnonlinearityparameter(ANP)basedonthefundamentalandsecondharmonicsisdetermined.TheresultsshowthatthenormalizedANPincreaseswiththefatiguecycles.Furthermore,atheoreticalmodelwithdifferentinterfacialcompressionandtensionstiffnessisproposedtointerpretthegenerationofsecondharmonics.&2014ElsevierLtd.Allrightsreserved.1.IntroductionAdhesivejointsarewidelyusedinvariousindustrialapplications,suchassafety-criticalstructuresintheaerospaceandautomotiveindustries.Adhesivelybondedstructuralcomponentsusuallyprovidemanyadvantagesoverconventionalmechanicalfasteners.Amongtheseadvantagesarelowerstructuralweight,lowerfabricationcost,andimproveddamagetolerance[1,2].Forexample,advancesinaerospacetechnologyhavebeenmadepossiblethroughtheuseoflightweightmaterialsandweight-savingstructuraldesigns.Joints,inparticular,havebeenandcontinuetobeareasinwhichweightcanbetrimmedfromanairframethroughtheuseofnovelattachmenttechniques.Withtheincreasinguseofadhesivebondedstructures,corre-spondingmethodsforevaluationandtestingofthestructuralintegrityandqualityofbondedjointshavebeenwidelyinvestigatedanddevelopedforthepurposeofstructuralhealthmonitoring[3–5].Non-destructivecharacterizationforqualitycontrolandremaininglifepredictionhasbeenakeyenablingtechnologyfortheeffectiveuseofadhesivejoints.Conventionallinearultrasonictechniquescandetect?awssuchasdelamination,cracks,andvoidsintheadhesivejoints.However,moreimportanttothebondqualityistheadhesivestrength.Althoughinprinciple,strengthcannotbemeasurednon-destructively,theslightnonlinearityinthematerialmayindicatematerialdegrada-tionortheonsetoffailure[6].Furthermore,microstructuralvariationsCorrespondingauthors.E-mailaddresses:gsshui@bjtu.edu.cn(G.Shui),yswang@bjtu.edu.cn(Y.-s.Wang).http://dx.doi.org/10.1016/j.ndteint.2014.11.0020963-8695/&2014ElsevierLtd.Allrightsreserved.nduetoagingmayalsocausechangeinthethirdorderelasticcon-stants,whicharerelatedtotheacousticnonlinearparameter(ANP)ofthepolymeradhesive.Ithasbeenobservedthathigherharmonicsofthefundamentalfrequencyaregeneratedwhenaharmonicultrasonicwavepropa-gatesthroughanonlinearmaterial[7].Itisproposedthatthematerialdegradationcreatesnonlinearitywhichcanbedetectedinthewavepropagationcharacteristics[8,9].Severaltheorieshavebeendevel-opedtomodelthisnonlineareffect.Forexample,AchenbachandParikh[10]presentedtheirtheoreticalinvestigationtoobtaininfor-mationontheadhesivebondstrengthfromultrasonictestresults.Usingthepostulatethatfailureoftheadhesivebondisprecededbynonlinearbehaviorattheinterface,theyobtainedanonlinearparameterthatcorrelatestojointstrength.Basedonamicroscopicdescriptionofthenonlinearinterfacebindingforce,aquantitativemethodwaspresentedbyPangrazandArnold[11].Tangetal.[12]measuredtheonsetofnonlinearityinadhesivebondsbysubjectingtostaticloadssimultaneouslywiththeultrasonictesting.Thedegrada-tionoftheadhesivebondwasinducedbycyclicfatigueloading.Thedeteriorationduetocyclicfatigueisidenti?edbythereductionofthelinearportionofthestress–straincurvewithoutanychangeinslopeinthelinearrange.Furthermore,Delsantoetal.[13,14]developedaspringmodeltosimulatetheultrasonicwavepropagationinnon-classical(hysteretic)nonlinearmedia.Vanaverbekeetal.[15]pro-posedamultiscalemodelforthetwo-dimensional(2D)nonlinearwavepropagationinalocallymicrodamagedmedium,andpresentednumericalsimulationsinviewofnondestructivetestingapplications.Anetal.[16]developedarigorousnonlinearspringmodelunderthenormalincidenceofbothlongitudinalandSHwaves.Thenumericalsimulationsshowtheaccuracyandapplicabilityoftheirmodelfora10G.Shuietal./NDT&EInternational70(2015)9–15thinlayerbetweentwosolidsundertheconditionofsmallratioofthicknesstowavelength.Inthemeanwhile,ultrasonicguidedwaveshavebeenusedtoanalyzeadhesiveordiffusionbondedjoints.Forexample,NagyandAdler[17]studiedguidedwavesinadhesivelayersbetweentwohalf-spaces,demonstratingthattheresultingdispersioncurvesarerela-tivelyinsensitivetothepropertiesoftheadhesivelayer.RohklinandWang[18]examinedLambwavesinlap–shearjoints,includingthedevelopmentofananalyticalspringmodel.Roseetal.[19]developeddispersioncurvesfortitaniumdiffusionbondsandexaminedfre-quencyshiftsandspectralpeak-to-peakratiosofdifferentbondedstates.LoweandCawley[20]analyzedthesensitivityofadhesivebondpropertiesonguidedwavesusingathree-layeredmodel.Helleretal.[21]combinedlaserultrasonictechniqueswiththe2DfastFouriertransform(FFT)tocharacterizeadhesivebondproperties.Seifriedetal.[22]usedanalyticalandcomputationalmodelstodevelopaquanti-tativeunderstandingofthepropagationofguidedLambwavesinmulti-layered,adhesivebondedcomponents.Inthispaper,theANPisusedtocharacterizethedegradationofanadhesivejointmadefromepoxyresinbetweentwoaluminumplates.Ultrasonicthrough-transmissiontestswereconductedonsamplescuredundervariousconditions.ThemagnitudeofthesecondorderharmonicwasmeasuredandthecorrespondingANPwasevaluated.TheseexperimentallymeasuredANPs,asfunctionsofdegradation,arethenusedtoquantitativelycharacterizetheconditionoftheadhesivebond.AfairlygoodcorrelationbetweenthefatiguecycleandtheANPisobserved.Furthermore,theexperimentallyobservedsecondhar-monicgenerationisinterpretedbydevelopingananalyticalmodel.TheresultsshowthattheANPcanbeusedasagoodindicatoroftheadhesivestrengthforadhesivejoints.2.ExperimentalprocedureAsshowninFig.1,thetestsampleisanoverlapjointoftwoaluminumplatesbondedtogetherbyanadhesivelayer.Theadhesiveisakindofbisphenolepoxyresinwithepoxyvalueof0.441mol/100g.ThealuminumplateismadeofAZ31magnesium–aluminumalloy,withtheyieldingstress199MPa,elasticmodulus46GPa,Poisson’sratio0.27anddensity1770kg/m3.AsillustratedinFig.1,thebondedareaofthespecimenis30mm?24mm.Theadhesive(bondline)thicknessisgenerallylessthan1mmandtheadherend’sthicknessisabout6.5mm.Thealuminumplateswereanodizedandprimedpriortoapplicationoftheadhesive.Thejointswerethenputintoatemperature/pressureovenforcuring.Theywere?rstlycuredfortwohourswithatemperatureof801C,andthencuredforanothertwohourswithatemperatureof1601C.Allsamplesusedinthisstudywerepreparedunderthesameconditions.AschematicdiagramfortheexperimentalsetupisshowninFig.2.Thetransmittingtransducerwasdrivenbyatoneburstsignalof6cyclesat5MHz.ThereceivingtransducerwasusedtoAdhesive layer3130200454423Fig.1.Dimensionoftwoaluminumplatesbondedthroughanadhesivelayer(unit:mm).(Forinterpretationofthereferencestocolorinthis?gurelegend,thereaderisreferredtothewebversionofthisarticle.)detectthefundamentalandsecondharmonicsoflongitudinalultrasonicwavespassingthroughtheadhesivejoint.Thecentralfrequenciesoftransmittingandreceivingtransducersare,respec-tively,5MHzand10MHz.ThetoneburstsignalwasgeneratedbyRitecSNAP-0.25-7-G2nonlinearmeasurementsystemwiththehigh-powergatedampli?er.Beforedrivingthetransmittingtrans-ducer,thehighvoltagesignalpassedthrougha50Ωtermination,anattenuatorandasetoflow-pass?ltersothatthetransientbehaviorandhighfrequencycomponentfromtheampli?erweresuppressed.Thisnonlinearmeasurementsystemcanprovideamoremonochromaticultrasonicsinewavesignalwithhigherquality,andthiswilldecreasetheacousticnonlinearityfromthesignalconsiderably.Althoughthemulti-re?ectioncantakeplacebetweentheupper/lowersurfaceandinterfaceintheexperimentalsamples,there?ectedwavesreachtheReceiverabout0.6μslaterthanthelastcycleofthewavespassingthroughtheadhesivejointreachtheReceiver.Sothereisnomulti-re?ectivein?uenceinthereceivedsignal.AtypicallongitudinalwavesignalacquiredisshowninFig.3.(Oneshouldnoticethat9.0μsshowninthis?gure,whichisowingtothesettingoftheoscilloscope,isNOTthe?ighttimeofthewave.)Thesamplingrateoftheoscilloscopeis1.25GS/s.Thesignalofanentirelengthconsistsofatransientpartatthebeginning,asteadystateportion,and?nallytheturnoffringingattheend.Tomakesurethatonlythesteady-statepartofthetoneburstsignalwasused,aHanningwindowwasappliedtotheacquiredtime-domainsignalforFastFourierTransform(FFT).Therefore,onlythedatapointswithinthesteady-statepartwereselectedandthentransformedtothefrequencydomainwheretheamplitudesofthefundamentalandhigherorderharmonicsofthedetectedwavesbecomevisible.Fig.4showstheamplitudesofthefundamental(A1)andsecond(A2)harmonicsinthefrequencydomain,respectively.3.ExperimentalresultsDuringtheexperimentalmeasurements,tensamplesweresel-ectedtobefatigued.Thefatigueloadingisparalleltotheadhesivelayer,asshowninFig.2.Themaximumloadfor?veofthesampleswas2.5kN;andthemaximumloadforanother?vewas3.0kN.Thefatiguetestswereinterruptedtoperformthenonlinearultrasonicmeasurementsatdifferentnumbersoffatiguecycles.FollowingRefs.[23,24],theANPoftheadhesiveisde?nedbyβ?8A2A2e1T1hk2whereA1istheamplitudeofthefundamentalharmonicwave;A2istheamplitudeofthesecondharmonicwave;histhepropaga-tiondistance;andkisthewavenumber.Forlongitudinalwaveswitha?xedfrequencyanda?xedtransmittingdistance,theANP,β,isonlyproportionaltoA2=A21.Therefore,inthismeasurement,weuse,forconvenience,arelativeANPde?nedasβ0?A2A2e2T1Becausetherewillbesomelevelofvariabilityassociatedwiththeinitialmicrostructureofeachspecimen,themeasuredANPswillbenormalizedbythevalue(β00)measuredineachundamagedspeci-menbeforeanymechanicalloadisapplied.Thisnormalizationprocedureremovessomeofthevariabilityassociatedwiththeinitialmicrostructuresofeachspecimen,enablesadirectcomparisonoftheacousticnonlinearityevolutionofallthespecimenstested,andnormalizesthenonlinearityassociatedwiththetransmittingpiezo-electrictransducers.TheevolutionofthenormalizedANP,β0=β00,asafunctionofthenormalizedfatiguelifeisshowninFig.5(a)forspecimens1–5withthemaximumloadof2.5kN.Here,thefatigueG.Shuietal./NDT&EInternational70(2015)9–1511RitecSNAP-0.25-7-G2 OscilloscopeRF Burst High PowerReceiver ReceiverReceiverOutRF MonitorInput 1Input 2Computer50termAttenuatorHigh PassFilterPAS-0.1-40PreamplifierLow PassFilterTransmitterFatigue loadingReceiverFig.2.Experimentalsetupfornonlinearmeasurementofanadhesivejoint.0.10

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toconsistentlyconductthenonlinearmeasurement.Butfortu-nately,ourdataexplicitlyshowthedependenceoftheANPonthefatiguecycles.ComparisonofFig.5(a)and(b)showsthatthemaximumloadhasalittlein?uenceonthemagnitudeofthenormalizedANP.Magnitude (V)0.00

4.TheoreticalmodelanddiscussionInordertointerpretthegenerationofhigherharmonics,wepresentanonlinearmodeloftheadhesivelayerinthissection.TheultrasonicwavepropagationthroughtheadhesivejointintheabovemeasurementsmaybeillustratedinFig.6.Twoidenticalsemi-in?nitelinearelasticsolids(adherends1and2)arejoinedtogetherbyathinadhesivelayerwiththicknessh.Laméconstant,shearmodulusandmassdensityoftheadherendsareλ,μandρ,respectively;andthosefortheadhesivelayerareλ,μandρ,respectively.Foranincidentharmoniclongitudinalwavewithfrequencyωpropagatingperpendi-culartotheadhesivelayer,itwillbere?ectedbytheadhesivelayeraswellastransmittedthroughtheadhesivelayer.Wedenotetheincident,re?ectedandtransmittedwavesasP0,P1andP3,respectively,andthoseintheadhesivelayerasP2andP4.Maevaetal.[1]indicatedthatthereareexpectedtobetwopossiblesourcesofnonlinearityinanadhesivelybondedstructure.The?rstsourceistheadhesivematerialitself.Thesecondsourcemightbestructuralnonlinearitiesintheadhesivebondline,includingweakbondsorzerovolume(closed)disbonds.Aftersomeexperi-mentation,itbecomesapparentthatthematerialnonlinearityhaslittlerelevancetoagreatmanyadhesionproblems;itisanindicationofthestateofthematerialitselfotherthananindicatorofthebondstrength[1].Thestructuralnonlinearityis,however,oftenthoughtofasbeingdirectlylinkedtothestrengthorweaknessofthebonditself.Theextremeexampleofthisisthecaseofanunbonded,clappinginterface,whichhasbeenstudiedtheoreticallyandexperimentallyforsometime[1].Structuralnonlinearitiesinadhesivelybondedjointsmayariseinanumberofways.Commontoalloftheseisthelocationofthestructuraldefect,typicallyintheverythinlayerofadhesivebonding[1].Duringin-serviceconditionsadhesivejointscansufferfromanumberofdefectsduetoloading,environmentalattackorother-0.05

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Fig.3.Receivednonlinearultrasonicwaves.lifemeansthefatiguecyclenormalizedtothetotalcyclesofthewholespecimen’slife.Thespecimens1–5failedat80,91,560,281and97cycles,respectively.ShowninFig.5(b)istheevolutionofthenormalizedANPasafunctionofthenormalizedfatiguelifeforspecimens6–10withthemaximumloadof3.0kN.Forthisgroup,thespecimens6–10failedat111,91,310,102and280cycles,respectively.ItisshowninFig.5thatthenormalizedANPincreaseswiththefatiguelifeforbothsituations.Particularly,wecanseethattherateofincreaseappearstobegreaterintheearlystages,whichimpliesthatthesenonlinearultrasonicmeasurementscanbeusedtoquantitativelycharacterizetheearlydamageoftheadhesivejoints.Themeasureddatafordifferentspecimensshowincreasingscatterwithincreasingfatiguecycles,whichismostlikelyduetounc-ertaintiesinmaterialpropertiesandcureoftheadhesion.Infact,thereisaninherentrandomnessintheevolutionoffatiguedamageduringtesting,whichshouldmanifestitselfasacorre-spondingrandomnessintheresultingacousticnonlinearity.Formeasurementprocedureinthelaterstageoffatigue,thedeforma-tionassociatedwiththeincreasedfatiguecyclemakesitdif?cult12G.Shuietal./NDT&EInternational70(2015)9–15100

Fundamental harmonics2.0c1.8inom80

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Fig.5.NormalizedANPasafunctionofthepercentageoffatiguelifewiththemaximumloadof2.5kN(a)and3.0kN(b).yAdherend 2 (upper half-space)P3Adhesive

hlayer

P2P4P0Px1Adherend 1 (lower half-space)Adherend 2disbondAdhesivelayercracks

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yP3P0P1xFig.6.Wavepropagationintwoadherendsjoinedbyanadhesivelayer(a),typicaldefectsinanadhesivelayerappearingduringin-serviceconditions[25](b),andillustrationofthetheoreticalnonlinearmodel(c).reasons.Thesedefectsmayincludevoids,cracks,disbond,kissingbondetc.asillustratedinFig.6(b)[25].Theoverallstrengthofthejointdependsonthebehaviorsofthesedefectsunderloading.Obviously,thetensileandcompressionalbehaviorsofthejointwillbedifferent.Forinstance,inthecrack,disbondorkissingbondregion,apotentialmechanismfornonlinearityistheopeningandclosingofthecontactasthewavepasses;thesocalled“clapping”or“slapping”mechanism,ormoregenerally,contactacousticnonlinearity[26].Forperfectly?atsurfacesincontactthisresultsinabi-linearstiffnessresponse(withzeroorlowstiffnessinthetensileregionandhighstiffnessinthecompressiveregion).Morerealistically,forroughsurfacesincontact,therewouldbeamoregradualshiftfromalow-stiffness,low-loadregiontoahigh-stiffness,high-loadregion[26].Ifapurelysineharmonicultrasonicwaveisincidentonadefectedadhesivelayerwithsuchastiffnessnonlinearitythere?ectedandtransmittedwaveswillcontainaresponseincludinghighharmonics;andthedegreeofharmonicgenerationprovidesinformationabouttheextenttowhichthedefectbehavesnonlinearly[26].BasedontheaboveanalysisofwhichthedetailscanbefoundinRefs.[1,26],weproposeanonlinearmodelbyassumingthatthedamageoftheadhesivelayerwilldecreaseitstensionmoduluswhilekeepingitscompressionmodulusunchangedduringin-service.Thatis,thetensionandcompressionmodulioftheadh-esivelayerwillbedifferent.Forsimplicityinmathematics,theadhesivelayerof?nitethicknessisreplacedbyamasslessinter-facewithzerothickness,asshowninFig.6(b).Consequently,theinterfaceismodeledasacontinuousarrayofspringswithdifferenttensionandcompressionstiffness.Attheinterface,theboundaryG.Shuietal./NDT&EInternational70(2015)9–1513conditioncanbewrittenas(σyexT?KtΔuyexT;σy;ΔuyZ0σyexT?KàΔuyexT;σy;Δuyr0;e3TwhereσyexTisthenormalstressesattheinterface;ΔuyexTisthedisplacementdiscontinuityattheinterface;andKtandKàarestiffnessoftheinterfaceintensionandcompression,respectively.Whentheultrasonicwavepropagatesthroughtheinterface,thesystemwillbehavenonlinearlybecauseofthedifferenttensionandcompressionstiffness.AsshowninFig.6(c),foranincidentharmoniclongitudinalultrasonicwaveP0propagatinginthey-directionwithfrequencyωandamplitudeAe0T,itcanbewrittenasuey0T?RenAe0Teiζo;e4Twhereζ?kyàωtwiththewavenumberk?ω=candcbeingthelongitudinalwavevelocityintheadherend.Whenthisharmonicultrasonicwaveisincidentontheabovebilinearinterface,there?ectedandtransmittedwaveswillcontainaresponseatthedrivefrequencyaswellasthehigherharmonicsduetononlinearity.ThereforethetransmittedwaveP3canbewrittenas:&ue1y3T?Re∑Ae3T'imζe5T?0memSimilartotheexperimentalway,wede?nedarelativeANPβ0basedontheamplitudeofthefundamentalharmonicwaveAe3Tt1andthatofthesecondharmonicwaveAe3T2forthetransmittedwaveP3,thatisβ0Ae3Tt?h23Ti2e6TAe1Thesolutionofβ0tispresentedinAppendixA.Here,weconsiderthespecimenusedinourexperiment,i.e.twoadherendsofAZ31bondedthroughanepoxylayer.TherelativeANP,β0t,varyingwithKà=KtisshowninFig.7.WhenKà=Kt?1,theANPiszero,whichmeansthatthereisnointerfacialdamageinthissituation.Whendamageappearswithintheadhesivelayer,thetensilestiffnessKtoftheinterfacewilldecrease,leadingtotheincreaseofKà=KtandthustheincreaseoftheANP.ThereforewecanconcludethattheANPcanbeusedtocharacterizethechangeofinterfacetensilestiffnessorthedegradationoftheadhesivelayerindirectly.5

Data based on theoretical model

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Fig.7.TheoreticalANPasafunctionoftheratioofcompressionstiffnesstotensilestiffness.Indamagemechanics,thedamagevariableDisusedtorepresentthedevelopmentofmicrostructuraldamageinacontinuumsense.ThisvariablecanbederivedfromthereductionoftheelasticmodulussimplyasD?1àE=E0,whereE0istheelasticmoduluswithoutdamage.Forthepresentproblem,thedamagevariableDcanbeexpressedbyusingthetensionstiffnessKtandcompressionstiffnessKàasD?1àKt=Kà.FinallywecangettherelationbetweenthedamagevariableDandtherelativeANPβ0tasshowninFig.8.WecanseethatthedamagevariableincreaseswiththerelativeANPincreasing.ManyresearcheshavebeenreportedabouttherelationbetweenmaterialdamagevariableDandfatiguecycles[27–29].Asimpleempiricalformulaswasproposedin[29], ????c!mD?1à1àNNf;e7Twherecandmareparameterstobedeterminedinanexperimentalway;NandNfarefatiguecyclesandfatiguelife,respectively.ThisequationwillbeappliedinthispapertointerprettheexperimentalresultsoftherelationbetweentheANPandfatiguecycle.WefoundinourexperimentthattheANPdoesnotvanishbeforethespecimenisloaded,i.e.β0a0whenN?0.ThisimpliesthatinitialdamagedoesexistandshouldbeconsideredinestablishingtherelationbetweenthedamagevariableDandrelativefatiguecyclesN=Nf.Therefore,wemodifyEq.(5)as ????c!mD?1àe1àDN0T1àNfe8TwhereD0istheinitialdamagevariableregardingtothewholeadh-esivestructurewhenN?0.WecanseethatEq.(6)satis?estwonecessaryconditions:D?D0whenN?0andD?1whenN?Nf.ConsideringEq.(6)andthedatainFig.8,wecangettherelationbetweenthenormalizedANPβ0t=β0t0andrelativefatiguecyclesN=Nf.Forexample,ifwetakeD0?0:1,m?0:25andc?0:003,wecangettherelationbetweenthenormalizedANPandrelativefatiguecyclesbasedonthetheoreticalmodel.Fig.9showstheexperimentmea-surementresultswiththemaximumloadof3.0kN(seeFig.5b)andthedatabasedonthetheoreticalmodel.ItisseenthattheANPbasedonthetheoreticalmodelincreasesconsistentlywiththemeasuredresults.Wecancometotheconclusionthatdifferentstiffnessoftheinterfaceintensionandcompression,causedbythedamageintheadhesivelayer,isoneofthesourcesforthenonlinearityofultrasonicwavestransmittingthroughtheadhesivestructure.Thisprovidesusa1.0

Data based on theoretical model Fitting curve0.8

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Fig.8.Damagevariableasafunctionofrelativenonlinearityparameter.

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