信息對抗技術(shù)專業(yè)畢業(yè)設(shè)計(jì)英文翻譯說明

Theultrasonicwavepropagationincompositematerial

anditscharacteristicevaluation

JunjieChang,ChangliangZheng,Qing-QingNi

1.Introduction

FRPcompositematerialswereappliedtovariousfields,suchasaircraftandspacestructures,becauseoftheexcellentcharacteristics,e.g.,light-weight,highratioofrelativeintensityandhighratioofrelativerigidity.DespiteFRPhavingsuchoutstandingcharacteristic,cracksinthematrixandfracturesofthefibermakedebondingsuchkindofdamageeasytooccurbetweenthefiberandthematrix,orthemulti-layers.Thesedamagesaredifficulttobedetecteddirectlybyvisualinspectionfromthesamplesurface,causingtroubletoensurethereliabilityandsafetyofthecompositematerialandstructures.Meanwhile,healthmonitoringtechnologiesofmaterialsareindispensable.Amongthem,theultrasonichealthmonitoringtechnologyattractslotsofattentionsinrecentyears.Simulationsbyfiniteelementmethodhavebeenperformedforthedevelopmentofapparatusforultrasonicdamage-detection,suchasultrasonicpictureinspectionandultrasoniclaser,andfortheverificationoftheirsafetyandvalidity.Researchesandcalculationsonthepropagationanalysisoftheultrasonicwaveinfiberstrengtheningcompositematerialshavebeenwellconductedandreported[1–8].

Onthesolidinterface,twokindsofboundariescanbeconsidered.Oneisliquidcontactinwhichthinlubricantisplaced,andonlypowerandpositionmovementperpendiculartotheinterfacearetransmitted.Theotheroneiscompletesolidcombination,whichpowerandpositionmovementbothperpendiculartoandparalleltotheinterfacearetransmitted.

Fiberstrengtheningcompositematerial,theinterfacebetweenthefiberandthematrixcanbeconsideredtobesolidcontact.Inthecaseof,debondingexistingbetweenthematrixandthefiber,fewliteratureswerefound,sincetheconversionsofthetransmittedwavemode,reflectionwavemodeandreflectionpulsephase(waveform)maketheanalysisverycomplicated.Providedthisproblemtobesolved,thequalityofthematerials,tosomeextent,canbeestimatedfromthesoundimpedanceofthereflectorandthetransmissionobject,andtheoptimaldamage-detectionmethodcanbealsoassumedinasimulation.

Inthisresearch,inthesimulationofthetechniquemonitoringthehealthbyanultrasonicwavemethod,theultrasonicwavedistributionpatternwasanalyzedwiththebasictheoryforwavepropagationbyusingthemodelforfiberstrengtheningcompositematerial.Namely,itaimsatobtainingtheamplitudeofthereflectionwaveandtheamplitudeofatransmittedwave,whenthelongitudinalwavehasunitamplitudeincidenceinmodelcompoundmaterial.Inthecaseofanultrasonicwavepropagationinsideamodelmedia,theratesofthereflectivelongitudinal,reflectivetraversewave,transmissionlongitudinalwaveandatransmissiontraversewavegeneratedatageneralincidenceangleintheinterface(afiberandexfoliation)wereanalyzedandreflectivecoefficientandatransmissioncoefficientweregotten,

respectively.Visualizedstudiesseparatingintoalongitudinalwaveandatraversewavewerecarriedout,andthemechanismsofalongitudinalwavedistributionandatraverse-wavedistributionwereelucidatedwhentheultrasonicwavepropagatedinsideacompositematerial.

2.Ultrasonicwaveequations

Considerasinglefibercomposite,i.e.,asinglefiberisembeddedinamatrix.TwodimensionsanalysisisconductedasshowninFig.2.Inthiscase,whenanultrasonicwavepropagatesinthissolidmedia,fromHooke’slaw,thestress–strainrelationshipfortwo-dimensionalplanestraininanisotropicmediaiswrittenasfollows[2]:

（1）

（2）

（3）

（4）

WherekandlareLame′constants,andtheTsuperscriptdenotesthetransposition.

Theultrasonicwaveequationsofmotionfortwodimensionalplanestraininanisotropicmediaareasfollows:

（5）

Where,thefirsttermontheleft-handsideofEq.(5)correspondstoalongitudinalwave,andthesecondtermcorrespondstoatransversewave.

isdensity.Ifthelongitudinalwavevelocity

andtransversewavevelocity

areintroducedtheultrasonicwaveequationsofmotionfortwo-dimensionalplanestraincanberewrittenby

（6）

Inthecaseofaplaneadvancingwave,thefollowingformulaisusedtocalculatefortheoscillatingenergygeneratedbytheultrasonicwaveperunittime:

（7）

3.Resultsofanalysisandsimulation

3.1.Transmissionenergyindifferentinterfaceshapes

Whenanincidentverticalwaveisobliquelyirradiated,fourwavesasshowninFig.3,i.e.,reflectedlongitudinalwave,reflectedtransversewave,transmittedlongitudinalwaveandtransmittedtransversewave,wouldappearontheinterface.Inotherwords,theshapeoftheinterfacebetweenepoxyandglassmayinfluencethepropagationoftheultrasonicwave.Forthisreason,themodelwithdifferentinterfaceshapesasshowninFig.1wasusedtoinvestigatetheinfluenceofinterfaceshapeonwavepropagationbehavior.Thevolumefractionproportionofbothmaterialsis1:1,despiteofthedifferentinterfaceshapesofthethreemodels.Thatistosay,theglass-volume-percentageofallthemodelsis50%.ThepropertiesofeachmediumusedintheanalysisareshowninTable1.Asaboundaryconditionofthemodel,absorptionisconsideredontherightandleftedge,whileitissymmetrical(theroller)ontheupanddowndirection.TheanalyticconditionandtheinputparameterswereshowninTable1.

Fig.2showsthetransmissionenergyoftheultrasonicwavepropagationforthesefourmodelsshowninFig.1.

Fig.1.Fourdifferentinterfaceshapesbetweenepoxyandglass.

Herethetransmissionenergywasdefinedbytheaverageenergyperunitarea,lJ/mm2,atthereceiveredge.Asseen,inModel1,theincidentultrasonicwaveisperpendiculartotheplaneinterface,andtransmittedwaveoccursalongwholeplane,sothatthetransmissionenergyisfarlargerthanthatintheothermodels.Thefull-reflectiontakesplaceinpartofinterfaceinbothModel2andModel3whentheincidenceangleislargerthanthecriticalanglebecausetheultrasonicwaveradiatesobliquelyonaconvexorconcaveinterface.Aboutonethirdoftheincidentwaveexperiencesfull-reflectioninModel2andModel3.However,thetransmissionenergyofModel3islargerthanthatofModel2.AsecondpeakappearsinthetransmissioncurveofModel3.Peak1isareflectedwavethatpropagatesasasecondarywavesourceneartheup-down-wardinterface(intheglassregion),whilepeak2isatransmittedwaveinthecentralpartoftheglassregion.Thereasonmightbethatneartheinterface,arefractiveindexdistributionoccurs,resultingintheappearanceofthescatteredwaves,includingrefractionandreflectionwaves.

Thefull-reflectiontakesplaceininterfaceofModel4(incidenceangleis45_).Allprimaryincidentwaveswerereflected,andtheverysmalltransmissionenergythatshowsasfigureisbecausethedispersionwaveandthereflectedwavepenetratedthepartassecondarywavesourcefromtheverticalneighborhood.

3.2.Influenceofdifferentfiberconditions

Refractiveindexdistributionoccursnearthesecondphaseboundaryduetothesecondphasecompounding,resultingintheappearanceofthescatteredwaves,includingrefractionandreflectioninthecompositematerialsstrengthenedbyfibers.Inthenext,thescatteringoftheultrasonicwaveshowninFig.1willbetakenintoconsideration.Thescattersoccurduetofibersembeddedincompositematerials.Theincidentwave

,propagatinginmatrixregion,isasinusoidalwave.Whentheincidentwavereachesthefiber,someistransmittedintothefiber,andtheotherisreflectedonthefiber/matrixinterface,andbecomesasecondarywavesource.Accordingtotheoverlappingprincipleofwavefunctions,thewholewavefunction

canbeexpressedasasumoftheincidentwave

andthescatteredwave

.

（8）

Wherethescatteredwave

includesallthewavesscatteringcomponentsgeneratedduetotheinterfacefromtheknownwave

.

ThemodelfigureofthecompositematerialsfortheinvestigationofthescatterswasdesignedaswhatshowninFig.3,wherethreefiberswithdifferentshapeswereembeddedinthematrix.Thesizeofthemodelwas

.Theboard-shapedglassfiberwiththickness

wasembeddedinthecenterofthematrixofepoxyinModel1,andwasobliquelyembeddedinModel2.Acolumnshapedglassfiberwithadiameter

wasembeddedinthecenterofmatrixinModel3.Theabovethreemodelshadacommonfiberpercentageof20.TheanalyticconditionandtheinputparameterswereshowninTable1.

ForthemodelsinFig.3,whentheincidentwaveontheleft-handsideoftheglassregionarrivedatthefirstinterfacebetweentheepoxyandglass,thetransmittedwaveandthereflectedwavearose.Thenthereflectedwavepropagatedtotheincidenceside,whilethetransmittedwavepropagatedtothereceiversideandarrivedatthesecondinterfaceoftheglassandepoxythroughtheglassregion.

Thesecondtransmittedwaveandthesecondreflectedwavearoseatthesecondinterface,andamultiplexreflectionoccurredintheglassregion.Fortheboard-shapedfiber(planefiber)andthecolumn-shapedfiber(cylindricalfiber),Fig.4showsthecomparisonsoftheanalyticresultsinthecasesofModel1(fiberthickness

),Model2(fiberthickness

,

_)andModel3(fiberdiameter

)inFig.3,withanequivalentfibervolumefractionbutwithadifferentshape.Asseenfromthefigure,thetransmissionenergyoftheModel1isfarlargerthanthatModel2andModel3.

FromFig.4,whichembeddedtheboard-shapedfiber,twoenergypeakswereclearlyobservedbytransmissionenergycurveinModel1andModel3.InModel1,thestrongpeakscorrespondtothefirsttransmittedwave,andfourweakpeaksareascribedtothefirstreflectedwavebytheglassfiber.InModel3,thefirstenergypeakresultedfromatransmittedwavethroughtheglassfiberregion,whilethesecondenergypeakwasduetothewavepropagatingthroughtheupperandlowerregionsoftheepoxy.Consequently,itcanbeunderstoodwhythetransmissionenergyfortheboard-shapedfiberislargerthanthatofthecolumn-shapedfiber,whenthefibervolumefractionwasthesame.

4.Behaviorofwavepropagationincompositematerial

4.1.Analysismodelandultrasonicpropagationsimulation

Mostoffiberreinforcedcompositesmaterialmaybeconsideredasaninhomogeneousbodymicroscopically,andahomogeneousonemacroscopically.Forthecompositeswithfibers,thefiberarraymodelwillbeusefultotakeintoaccountofthereflectionand/ortransmissionofmultiinterfaces.Inordertoevaluatethemacroscopiccharacteristicofsuchacompositematerial,atwo-dimensiondomainwithdifferentfiberarrayswasproposedasshowninFig.5.Inthismodel,circularglassfiberswereembeddedwithhexagonalintheinterioroftheepoxymatrix.Thesizeofthemodelwas

;thefiberdiameterisd.Anincidentwaveof100MHzwasused.Themodelforanalysiswasdividedinto

elements(1,72,80,000totalelements).Inordertoaccountforthelossofloadcarryingcapacityofthefailedelements,thestiffnessofsuchelementsarereducedbytheuseofnextmethod.

Fig.6showstheseriesofstressdispersionpatternsduringtheultrasonicwavepropagationformodeloffiberreinforcedcompositesinFig.5(fiberdiameter

,withoutattenuation).Whentheultrasonicwavewaspropagatedoutreachedthefiber,thereflectedwave,thetransmittedwave,anddispersionwavewereappearedclearly(Fig.6(a)).Ifawavemotionarrivedattheinterfacebetweenthefiberandthematrix,partofthewavewasreflectedasasecondarysourcewave,andatthesametimeadispersionwavewasgeneratedaroundthefiber.Theotherpartofthewavewastransmittedfiberandpropagatedtoreceiverside.Themultiplexreflectiontookplaceinteriorofthefiber(Fig.6(b)).Moreover,thewavewhichspreadsthecircumferenceofthefiberinterfereseachotheramongfibers,thepropagationsituationoftheultrasonicwavebecomefurthercomplicatesthanthatofbefore(Fig.6(c)–(e)).Fromtheseresults,theinfluenceoffiberonpropagationanddispersionofanultrasonicwaveinacompositematerialcouldbevisualizedandunderstood.

4.2.Influenceoffiber-volume-percentageandwithattenuationinmatrix

Whendiameteroffiberischangedby

andattenuationwith/withoutattenuationinmatrix,whichinvestigateshowthepropagationactionoftheultrasonicwaveinadistributedcompositematerialmodel.Figs.7and8haveshownthetimehistorycurveofreflectionenergywith/withoutattenuationinepoxymatrix,thatduringtheultrasonicwavepropagationformodeloffiberreinforcedcompositesinFig.5,respectively.Fig.9hasshownthetimehistorycurveoftransmittedenergywithattenuationinepoxymatrix.Fig.10hasshownthatcomparisonoftransmissionenergyratiowithand/orwithoutattenuationduringtheultrasonicwavepropagationformodeloffiber-reinforcedcompositesinFig.5,respectively.Afigureincasewithoutattenuationinepoxymatrixisomitted.

Ifthewith/withoutattenuationinepoxymatrixiscompared,thepeakvalueofreflectedenergycurve(inthecaseoffiberdiameter

)withattenuationinepoxymatrix(attenuationcoefficient120dB/m/MHz)issmallerabout30%thanthatwithoutattenuationinepoxymatrix.Moreover,althoughthereflectedenergycurveinthefigureisdisplayedonlytotwopeaks,the2ndpeakvalueislargerthanthe1stpeakvalue.The1stpeakvalueistheenergyofthereflectedwavefromafiber3,andthe2ndpeakvalueistheenergyofthereflectedwavefromfibers1and6(Fig.5).Disorderaroseonthesubsequentreflectiveenergycurve,andregularitywaslost.Moreover,itfollowsontheincreaseinfibersdiameter(fibercontent)thattheenergyofareflectedwaveincreasesirrespectiveofwith/withoutattenuationinepoxymatrix.

Inthecasewithattenuationinepoxymatrix,atforthetransmittedenergyhistorycurve,andthepeakvalue(inthecaseoffiberdiameterd=2k)inthetransmittedenergycurveisabouthalfofthatwithoutattenuation,andthegradeofinfluencebyattenuationinepoxymatrixshowup.Itbecomesclearerfromthe