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1、Statistical Tensile Strength for High Strain Rate of Aramid and UHMWPE Fibers46材料工程/2006年5期StatisticalTensileStrengthforHighStrainRateofAramidandUHMWPEFibersYANGBin.XIoNGTao,XIONGJie(KeyLaboratoryofAdvancedTextileMaterialsandManufacturingTechnology,MinistryofEducation,ZhejiangSciTechUniversity,Hangz
2、hou310018,China)Abstract:Dynamictensileimpactpropertiesofaramid(Technora)andUHMWPE(DC851)fiberbundleswerestudiedattwohighstrainratesbymeansofreflectingtypeSplitHopkinsonBar,andstressstraincurvesoffiberyarnsatdifferentstrainrateswereobtained.Experimentalresultsshowthattheinitialelasticmodulus,failure
3、strengthandunstablestrainofaramidfiberyarnsarestrainrateinsensitive,whereastheinitialelasticmodulusandunstablestrainofUHMWPEfibervamsarestrainratesensitive.Afiber-bundlestatisticalconstitutiveequationwasusedtodescribethetensilebehaviorofaramidandUHMWPEfiberbundlesathighstrainrates.Thegoodconsistency
4、betweenthesimulatedresultsandexDerimenta1dataindicatesthatthemodifieddoubleWeibullfunctioncanrepresentthetensilestrengthdistributionofaramidandUHMWPEfibersandthemethodofextractingWeibullparametersfromfiberbundlesstressstraindataisvalid.KeywOrds:aramidfiber;UHMWPEfiber;impactbehaviour;statisticalprop
5、erties;statisticalconstitutiVeequationCLCnumber:TB33Documentcode:AArticleID:1001-4381(2006)05004605Technora,madefromaramidfibersandsomewhatsim订artothecommonlyknowKevlar,andUltrahighlyorientedhighmolecularweightpolyethvlene_UHMWPEfibersarealloftenusedinflexiblearmourapplicationsandhencesubjectedtohig
6、hratesofloading.Theutilizationoftheirreinforcedcompositesarmourincertainballisticapplicationsisincreasinglypreferredoverconventionalrigidmetalarmoursystemsbecauseofitssuperiorstrength.toweightratioandflexibility.Todate,thedesignanddevelopmentofsuchfabricarmoursystemshavelargelybeenapproachedempirica
7、lly卜.Theballisticresistanceoffiberreinforcedcompositeisessentiallydependentonthemechanicalbehaviorofthereinforcingcomponentandthematrix.Fibersandfiberbundlescarrythebulkoftheappliedloadinafiber-reinforcedcomposite.Thustheunderstandingofthestrainratesensitivityofthefibersisveryimportantfortheuseandde
8、signofthefiberreinforcedcomposites.Nevertheless,forTechnoraandUHMWPEfibersandfiberbundles,fewexperimentalresultsonthehighstrainratehavebeenreported.ItiswellknownthatengineeringfibersoftenexhibitabrittlefracturebehaviorandtheirtensilestrengthobeyWeibullstatisticaldistribution.Twoexperimentalmethodsca
9、nbeusedtodeterminethestrengthstatisticaldistributionparametersoffibersunderquasistaticloading.Oneisthesinglefibertestandtheotheristhefiberbundletest一.Thefiberbundletestingmethodisincreasinglyusedtoday.Ontheotherhand,duetothetechniquedifficulty,nosuitableexperimentaltechniqueisavailabletoperformthedy
10、namicsinglefibertensiontests.Therefore,thefiberbundletestingmethodistheonlychoicefordeterminingthedynamictensilestrengthdistributionoffibersunderimpactloadingconditions.一.Inthispaper.tensileimpacttestsofaramid(Technora)andUHMWPE(DC851)fiberbundlesarecarriedoutundertwohighstrainratesbyusingaSplitHopk
11、insonTensileBar(SHTB),andtheexperimentaldataareusedtoderivestatisticalconstitutiveequationofaramidandIIHMPEfiberbundles.Foundationitems:supportedbytheNationalNaturalScienceFoundationofChina(10372092).E-mail:StatisticalTensileStrengthforHighStrainRateofAramidandUHMWPEFibers471ExperimentalApparatusand
12、TensileImpactTestTensileimpacttestswereconductedonthereflectedindirecttensileimpactapparatusfrommodifiedSHPB(SplitHopkinsonPressureBar).Aschematicofthesetupandstresswavepropagation.z-tschemearepresentedinFig.1.Throughtheimpactofthestrikerbarontheoutputbar,producingastresswavevialiningblocktransmitst
13、hroughtheinputbar.Suchstressimpulsetravelsdowntheinputbarandispartiallyreflectedattheinputbar/specimeninterfaceandpartiallytransmittedtothespecimenandtheoutputbar.Measurementsofthereflectedandtransmittedwavesweremadeusingstraingagesarrangedontherespectivebarsofthesystem.Theincidentstraini(t),reflect
14、edstrain(t)andtransmittedstraint(t)arerecordedatstraingagesmountedontheinputbarandoutputbars,respectively.Accordingtotheone-dimensionalsimple-wavetheory,thedynamictensilestress口.(t),dynamictensilestrain.()andstrainrate()inthespecimencanbeobtainedfromthefollowing:伪,l</L2l,:.,一一一一一!A.A1-strikerbar;
15、2-outputbar;3一inputbar;4一absorbingbar;5-superdynamicamplifier;6-transientconverter;7-computer;8-speedometer;9-liningblock;10一specimenFig.1Tensileapparatussketchandstresswavepropagationx-tscheme)(1)(r)(r)dr)一2LC.oi()一()(2)(3)whereEandA0aretheYoungsmodulusandthecrosssectionalareaoftheinput/outputbar,C
16、oisthelongitudinalwavevelocityofthebar,A.andL0arethecrosssectionalareaandgagelengthofthespeci-men,respectively.ThematerialinvestigatedinthispaperareTech-nora(producedbyTeijininJapan)andDC851(UPMWPE,producedbyNingboDacheninChina)fiberbundle.Aschematicdiagramofthefiberbundlespecimenanditsconnectionwit
17、htheinput/outputbarsisshowninFig.2.Thetwoliningblocksaregluedtothesupplementplate.Thefiberbundlesarewoundedcontinuouslyontoeachsideoftheliningblocksinparallelanduniformwindings.Thentheliningblockswiththebundlesarebondedintotheslotsoftheinput/outputbarsusinghighshearstrengthadhesive.Thesupplementplat
18、eisremovedfromtheliningblocksbeforethetensileimpacttest.Thespecimengagelengthis8ram.茴眚1一supplementplate;2-liningblock;3-fiberbundles;4-outputbar,5-inputbarFig.2Fiberbundlespecimenanditsconnectionwithinput/outputbarsThetensileimpacttestswereconductedattwohighstrainrates,1700/sand2500/sforTechnoraand2
19、200/sand2500/sforUHMWPEfiberbundles.Fig.3andFig.4showtheintegraltensilestressstraincurvesofthetwofiberbundles,respectively.ThetensilepropertiesofinitialYoungsmodulusE,themaximumvalue(failurestress)andunstablestrainb(correspondingtothefailurestress)forTechnoraandUHMWPEfiberbundlesattwostrainratesarel
20、istedinTable1.ItisseenthattheinitialYoungsmodulus,strainofTechnorafiberfailurestressandunstabledoesnotapparentlywiththechangeofstrainrate,SOTeehnorafibercanbe48材料工程/2006年5期regardedashighstrainrateinsensitivemateria1.ForUHMWPE(DC851)fiber,theinitialYoungSmodulusincreasesapparentlywithincreasingstrain
21、rate,whereastheunstablestraindecreasesapparentlywiththestrainrateincreases,andthefailurestressincreasesslightly,SOtheinitialYoungSmodulusandunstablestrainofUHMWPE(DC851)fiberarehighstrainratesensitivemateria1.ThatSbecausethehighstrengthandhighmoduluspolyethylenefiberpossessescharacteristicwithahighd
22、egreeofcrystalandorientation,mostmoleculesparticipateinstraightchaincrystal,andallthestraightchaincrystalmoleculesparticipateinhighrateimpacttensile,thustheinitialelasticmodulusandunstablestrainofhighstrengthandhighmoduluspolyethylenefiberyarnsarestrainratesensitiveonmacroscopic.磬403.53.02.52.O1.5l0
23、0.50Fig.3Stress-straincurvesofaramid(Technora)fiberbundlesattWOhighstrainrates(a)strainrate一1700/sl(b)strainrate一2500/sTable1MechanicalandDC851propertiesofTechnorafiberbundles矗0西山0Fig.4Stress-straincurvesofUHMWPE(DC851)fiberbundlesattWOhighstrainrates(a)strainrate一2200/sl(b)strainrate一2500/s2Statist
24、icalConstitutiveModelofFiberBundlesFig.5showsthemechanicsmodeloffiberbundles.Thebasicassumptionsusedinthismodelarepresentedas.一引:?NFig.5Modeloffiberbundles(1)AbundleiSconsistedofNparallelfiberswiththelengthofL,crosssectionalareaAandmodulusEfasshowninFigure5.(2)Everyfiberislinearlyelasticbeforebroken
25、.Therearenointeractionsamongfibers.When/-gfibersarebroken.theloadwillbeevenlydistributedtOtherestoffibers.(3)Thetensilestrengthoffibersfollowsaparticularstatisticaldistribution.Usually,thetwoorfourparameterWeibulldistributionexpressedinEq.(4)andEq.(5)areadopted.日02StatisticalTensileStrengthforHighSt
26、rainRateofAramidandUHMWPEFibers49G()一1一唧一(singleWeibulldistribution)G()一p一LooLd堡ro2AnLJJ(4)(5)(doubleWeibulldistribution)whereG()isfailureprobabilityofsinglefiberunderanappliedstress,EisYoungSmodulesoffiberbundles,whichcanbeexperimentallyevaluatedfromthestressstraincurveoffiberbundles.iSstrainoffibe
27、rbundles,oand卢arethescaleandshapeparametersofWeibulldistributionfunction,respectively.Thusthestatistiealconstitutivemodeloffiberbundiescanbeexpressedby:Eexp一等(singleWeibulldistribution)Eexp一等(doubleWeibutiondistribution)(6)(7)Basedontheexperimentalstressstraindata,theexperimanta1weibu11curveIn一1n(丧)
28、against1n(EE)canbeobtained.Fig.6andFig.7showtheexperimentalWeibullcurvesatstrainratesfrom1700/sto2500/s.ItisindicatedthattheexperimentalWeibullgraphisnotastraightlineandexhibitsanonlinearcharacteristic.Obviously,itisimpropertouseastraightlinetoextrapolatethisexperimentalWeibullcurve.Thetwo-parameter
29、Weibullfunctionisnotappropriatefordescribingthestrengthstatisticaldistributionoffibers,eventhoughithasasimpleform.HereamodifieddoubleWeibulldistributionfunctionisintroducedtoincorporatesuchnonlinearcharacteristicasshowninequation(8).一ao+E一导(8)Analgorithmfornonlinearleastsquareestimationofparametersi
30、susedtosimulatetheexperimentalpointsandestimatethefiveWeibullparameters,dr0;0oi;Pl;002;J8z.TheWeibullparametersoftheTechnoraandUHMWPEfiberbundlesattwostrainratesarelistedinTable2.ThecomparisonofthesimulatedstressstraincurvesandWeibullcurveswiththeexperimentaldataisshowninFig.3andFig.4,respectively.I
31、tcanbeseenthatthesimulatedFig.6WeibulldistributioncurvesofTechnorafiberbundlesattwohighstrainrates(a)strainrate=1700/s;(b)strainrate=2500/s=b一匕Fig.7WeibulldistributioncurvesofDC851fiberbundlesattwohighstrainrates(a)strainrate=2200/sI(b)strainrate=2500/sresultsagreewellwithexperimentaldata,whichconfi
32、rmsthatthemodifieddoubleW.eibulldistributionfunctioncanrepresentthestrengthdistributionofTechnoraandUHMWPEfiberbundlessubjectedto50材料工程/2006年5期highstrainrateloading.UsingtheparametersinTable2andEquation(8),weobtainstatisticalconstitutiveequationsoffiberbundlesattwodifferentstrainrates.Table2Weibullp
33、arametersestimatedfromfiberbundletests一0.43+l11.7唧一r一r(Technora,一1700Is)一0.23+114.01e唧一r一expI一【I一【.jIu(Technora,=2500/s)一0.38+56.48e唧一r一r(DC851,一2200/s).xp一LL一0.54+103.35e103.35e?.r103.35e13.02.JL4.82(DC851,一2500/s)3Conclusioni0.69Ic2(1)TensileimpacttestsonTechnoraandUHMWPEfiberbundleswerecarriedout
34、attwohighstrainrates.ExperimentalresultsshowthatTechnorafibercanberegardedashighstrainrateinsensitiremateria1.andtheinitialYoungsmodulusandunstablestrainofUHMWPE(DC851)fiberarehighstrainratesensitivemateria1.(2)ThefiberbundleconstitutiveequationcanintegrallydescribethetensilebehaviorofTechnoraandUHM
35、WPEfiberbundlesathighstrainrates.ItisappropriatetousethemodifieddoubleWeibulldistributionfunction?tocharacterizethestrengthdistri-butionofTechnoraandUHMWPEfibers.ThefiberbundletestingmethodisvalidtoderivethedynamicWeibullparametersfromfiberbundlestressstraindata.References:1SHIMVPW,LIMCT,tiesoffabri
36、carmourJ.neering,2001,25:115.FOOKJ.DynamicmechanicalproperInternationalJournalofImpactEngi一2SHIMVPW,TANVBC,TAYTE.ModellingdeformationanddamagecharacteristicsofwovenfabricundersmallprojectileimpactJ.IntJImpactEngng,1995,16(4):585605.3PARGALANDAB,HERNANDEzoLIVAREsF.Ananalyticalmodeltopredictimpactbeha
37、viourofsoftarmoursJ.IntJImpactEngng,1995,16(3):455466.4CUNNIFFPM.AnanalysisofthesystemectsinwovenfabricsunderballisticimpactJ.TextileResJ,1992,62(9):495509.5CHIZF,CHOUTW,SHENGY.DeterminationofsinglefiberstrengthdistributionfromfiberbundletestingsJ.JMaterSci,1984,19:33193324.r6WATSONAS,SMITHRL.Anexam
38、inationofstatistica1theoriesforfibrousmaterialsinthelightofexperimentaldataJ.JMaterSci,1985,20:32603270.7GoDAK,FuKuNAGAH.Theevaluationofthestrengthdis-tributionofsiliconcarbideandaluminafibersbyflmulti-moda1weibul1distributionJ.JMaterSci,1986,21:44754480.8PHANIKK.Evaluationofsingle-fiberstrengthdist
39、ributionfromfiberbundlestrengthJ.JMaterSci,1988,23:941945.9WILSONDM.StatisticaltensilestrengthofNextel610andNextel720fibersJ.JMaterSci,1997,32:25352542.103ANDERSONSJ,JoFFER,H0JoM,eta1.GlassfiberstrengthdistributiondeterminedbyCOl$11onexperimentalmethodsJ.ComposSciTechno1,2002;62:131145.11ASTMD,1989,
40、standardtestmethodfortensilestrengthandYoungsmodulusforhigh-modulussingle-filamentmaterialsS.12XIAYM,YUANJM,YANGBC.Astatisticalmodelandexperimentalstudyofthestrain-ratedependenceofthestrengthoffibersJ.ComposSciTechnol,1994,52:499504.r13wANGY,XIAYM.Theeffectofstrainrateonthemechanica1behaviorofkevlar
41、fiberbundles:finexperimenta1andtheoretica1studyJ.ComposPartA,1998,29A:14l11415.14WENHUANG,YANGWANG,YUANMINGXIA.StatisticaldynamictensilestrengthofUHMwPE_f.bersJ.Polymer,2004,45:37293734.15DANIELsHE.ThestatisticaltheoryofthestrengthofbundlesofthreadsJ.ProcRoySOc,19441945,A183:405435.16coLEMANBD.OnthestrengthofclassicalfiberandfiberbundlesJ.JMechPhysSolids,1958,7:6070.