AmajorpurposeoftheTechni-calInformationCenteristoprovidethebroadestdisseminationpossi-bleofinformationcontainedinDOE’sResearchandDevelopmentReportstobusiness,industry,theacademiccommunity,andfederal,stateandlocalgovernments.Althoughasmallportionofthisreportisnotreproducible,itisbeingmadeavailabletoexpeditetheavailabilityofinformationontheresearchdiscussedherein.LA-UR-85-3026.....eLA-UR--85-3O26...DE85017533TITLEHIGHSTRAINRATEDEPOKMATI~INFCCMETALSANDALUXSAUTHOR(SIP.S.Follanebeeq85’,InternationalConferenceonMetallurgicalSUBMITTEDTO:~~~tApplicationsofShock-WaveendHigh-Strain-RatePhenomena,Portland,OR,July28-August1,1985.DISCLAIMERTbb~~~duM-ntofwork~byM~aftbaUpitdBtsta-rent.NdtktblJnltdStataGww0m8ntnaramy~tb4d,nwAOy’itbdrUmkmakaMym.mty,~wImptbd,w~MY~Ilab!lhyaraplA-JJmtyfwllla-my,almpbt4namwudullmmofMyInfammkm,qppmtw,prdm%amdti.m~tk~tkumWOUldmMlafdnppimdyownalri@u.Rdwrnkw8intomyc@flcoomnmroWtmdwt,~ofmwkabytrdnamqtrdtnimk,mmubdurw,orOUmrw&daoot~titutgwimplyIU-~~~.Ormyapoylbmllf,mnvi,mmddon,offwotin#byth9udtalsma(lINwnmsataDdl#nba90fmkamuzhudndowvunm4ntUdtdSt4tmorMyquwytke#d.OotnsaudyamcorrdkottlmdtkaLamkarums&&Na’ii%%%%‘HICNSTRAINRATEDEPORHATIOI9INFCC!YETAMANDALLOYSP.S.FollanebeeLoaAlamosNationalLaboratoryLooAlamoe,NewHexico,USA,87545Theeffectofetrainrate,qndparticularlyofhighstrainrates,ondeformationmechanismsinmaterialslaoffundamentalinteresttothosewhouodelqndanalyzedynamicloading.InmanymaterialathestrainrateqenaitivityISknowntoincreaaedramaticallywhentheotrainrateimraieedqbove’103q-l.Thisincreaeehaebeeninterpretedpreviouslyqeqtran-mitionindeformationmechanismfromthermalqctivationcontrolqtlWstrainratetodislocationdra~controlqthiahretrainrate,Incopper,copper-aluminumqlloyaqndqtainleoaqteel,recantmeamramentmhaveqhewnthattheincreaaedrateqeneitivityfoundqthighstrainratemlanotduetoatransitionindeformationmechaniombutrathercanbcqxplainedwithqtandardthermalqctivationtheory.Themfindingsqndtheirimplicationre8ardin8thefo-lationofconmtitutlvebehaviorwillqrepresented.1.INTRODUCTIONAlthou6hthehighstrainratedeformationbehaviorofmostcomonmetalshaebeenstudiedumlngoneofqvarietyofqxporlmentaltechnique-[1],qtudioaofFCCmetal-umingtechnique-baeedonthnHopkinmonbarhavei.dominatedtheliterature.SomeoftheeeInvectigationaarelistedinTable1.ThistabulationISnot-anttobeallinclusive,b.:rathertolistthoeeinvestigationswheretheconstantstrain,retrainrateqenmitivity,whichISdefinedqa,.(1)couldbeqvaluatedoverawiderangeofstrainratee.Thehighstrainratedatainmo~toftheseInvestigationhavebeenmeaeuredincompressionusingthesplitHopkinaonpreesurebar.InmanyofthereferenceslistedinTable1,theconstantstrain,otrainrateeeneitivityI@foundtoIncreasewhentheatrafnrateinraisedaboveroughly103S-l.Whenthemaximum#trainrateInvestigatedj?limitedto103S-l,suchanincrease10usuallynotseen[3,5,10].ThieincreameortransitionInrateqeneitivityhaabeenthetopicofwchdiacueaion.Althoughinpolycryotallinecopper,moatpreviousInveotigatorahavenotedsuchatransitionwhenretrainrateaofthe“rder104areachieved,Lindholm[11]havedidnotmeaaureanyincreaseinrateaeneitivityatqtrainrateeaehighma6xi04q-l.Thishaaledtoqueetionsconcerningthevalidityofexperimanr.altechniquesattheachighetrainratea.WhetherornotthereexistsanIncreaoeintherateaenaitivityqthigh#trainratealaanimportantquestion.Manyimpactphenomenaleadtodeformatio~.atstrainrateaqxceeding103q-l;theabilitytouodelth~seproceoeeacomputatienallyrequirestheknowledseandunderstandingofthematerialconatitutivebehaviorqthighstrainratam.Explanationfortheincreaeedrateaencitivityhavebeenproposedwhichqrebaaedonqtransitioninratecontrollingdeformationmechanismfromthermalqctivationatlowqtrainrate-tosomeformofdislocationdrag,duetotheinteractionwithphononaatroomtemperature[22],at#trainratesexceeding103c-l.T!lepredominanceofdislocationdragcontrolleddeformationhaabeenuoedtoexplainthetxp~rimentallyoboervedrelationshipbetweenflowstressa(atconstantqtrain)qndatrainrste;-(2)wherethebackatreaeobqndtheconstantt!arat.~thfunction-ofstrain.Therehasbeenwideumageof“vimcous”or“linear”law-suchq-Eq.2todescribeconatitutlvebehaviorqthighetrainratea..ThepurposebehaviorIlopkinoonquestionobtainablecertaincopper,beroleofqofthisfewpaperistodescribewewillthatqventhedynamicreviewteetre~ult~deformationtheeplitaddreseresults10hateelae-lobtainedtheareifinwillratetheofFCCmetals.validity.ratesqreFirst,brieflyvalidpreaeureofxperimentalbarqtechniquesandandspecificallyexceedingqtainleaatestWeconcludeapproachingtaken.SomeandfiveInSectionmechanisms,reviewed.atstrainprecautioncoppe~aluminuminqxperimentalauetenitic4theqlloys,3.presentedqtSectionoriginoftheincreasedtoinvestigateunderstandingatreesthatertreee,aene~tivityofhighstrainratesdragieladiecuaaed.theInordercurrentthreeholdconcludedsensitivityAnon5.dislocationglidekineticsetatedislocationDynamicflowisueasurementsarecomparedwithmeasurementsusedaaar,internaldraguechanismsInvestigatedfortheproposed.donotcontributeratesratelawisofthemechanicalandittotheratethan10wherepreesureloadinghavebeenD16us-cm-liswave.the,diameternaturallyTechniquesbyofthepressuredecrensetoFrantzwave(4)(5)bar.Dispersiontheriaetimeitintheelasticbarwilltheelopealthatetrain[27];intheleadingisnotwithqdgeofofthisthewavetofurtheretconditionincreaeedescribeddifficultapproximateThecriteriapressurtperformednomalresultsstrainifthetrA~ZOidalbars,teetresultsratioofimposedforratesisteetschosenofbyBertholfandKarnes.ofEqs.4and5eu~gestsateretheteetratesthel/d5mmdiameterifaehighInspectionEq.4aa104ti-~canbeoftheactufiluaytheepecimencriteriavaliditytomatchEq.3andbeOlightlylubricationin[26]techniquethatifetreinstrainqmployed.euggeotsIndeed,overconservative.Anotherinterpretationadvantaseoandetrainbarmeasurementspreueureinhadbeenevaluatedbarqtahigherthan4%,higherofwouldhavebeenqllowed.intheHopkineonsiflnalo.qreproblemwithexperimentsthegageqrisesintheRecallthatthatsplitoneofthegagewaveoftesttechniquesthedeformingbasedontheHopkinmonbarietheetrestHopklneouqampleqimplyralatedForthe1,theinitialtoqtratncompressivemadeontheelaaticqhewnpremeurebara.inFis.schematically..El(t)qndreflectedtenoiletheqtreaewaveER(t)w~vemeasuradontheincidentaccordingtobarandthebarcanbetransmittedcombinedcompredvaET(t)meaouredonthetransmittertoyieldwithintheepecimena(t)=;:o[E1(t)+ER(t)+ET(t!]withinthesampleaccordingdt,wavevelocity,ofthespecimen,itto(6)qndthestrain=@E0E(t)1(t)-ER(t)-ET(t)](7)a.and10nndAlaISwhereEisYoung-smodulus,arethetheetre~einitialsectionalatanytime,-EI(t)*~(t)crossCoAStljelongitudinalareaandlengthbar.sectionalthecroseconstant~(t)ar?aofthepressureofthespecimenthatwhichimpliesTypicallyiaaeaumedthattk,especimen)onbothfaces(andthroughout(8)andSimplifiesd(t)-Eqa.6and7toread,E~ET(t)ao(s)and-2C0c(t)-J~E#)WhenEq.8applies,strainepecimen.precisestraineignalothreelubricantsdiapereioncomplicateinEq.10.uncertaintyinfluencejncreased,gageaignalatimingcorrelatewaveswillnndwillTheoftheTheoperationalbetweenindt.measurementproblemthesefrom(lo)ofthestrainthieUsually,a~oureareflectedbehaviorliceitinthatandtransmittedtheplacinggagetheofwavetoaniatodeterminestheetreaawithsamplewaves.theinthedeformingqstablishingthetimjngthelietedsmall~trainstrainbetweenpresenceRlafiticabove(e.g.,rateroutinesieaeaumedrhatgageaequidistantrealtraneittime.timetheHowever,throughsourcesthepreciseinterfaces,theoferrorserroristhebeinfluencedcombinecombinedT10Bawithbyimperfectepecimen.theqelectionof“zero”effecttimewithw.~ichtostartoftheserelationship),curveaatheintegrationinthetimingetreasteetetrainbutcanhavealargeonthepredictedoraethetotaltheeetimeiodecreaeed.wehaveaddedeeveralcalibrationTouinimizeerrors.,ourSIIPBteatE1procedure.bar.Firstofall,wee-tablishactualqctualtimingbetweenandERbyfiringETbywithfiringtherunwethestriknrthestrikeitransmitteral~uthegivenverifystrikerbarattheincidentweeetablish(i.e.,ga8ebar[3].veloci~ynofactorabarattheincidentbarbarwhichittimingqeparatedE1thisbyfromthetransmitterandcontactcalibrationaccuratelybalancecomputethisisbetweenThetrulyprocedures,thatSecondly,betweenDuringbarwhichioindirectcpecimen).forbothretraingaseameasuringexpressionatreaaitandueingtothemomentumbyLindholmtoueeEqs.withinInadditionthesecalibration9and10toofthethe.largerdowehavechooenandetrainreduces6and7ratherinthewave,isthatstraincorrection[28].curve2.measuredThetimingthanEqa.sinceitthedeformin~established.risingtheqtre~sspecimen.Theadvantagetheallws“zero”whichofthisthreetheuncertaintytimingE1andERhasbeenaccuratelyofSecondly,toestablishitcurveonalluaeofE1,whichisthemostsharplydisadvantagerepresentthiswithinPochhamme~ChreecanbeminimizedAnstrainFig.whichrateapchooee2exampleiaelvesoscillationbehavior.~yperformingofaetreeaiederivedintoprocedureintroducesnotpecimen.theqTheextentproblemwavea40ataehowncurveinieadiepereionstrainueingto“move”themtotheapec!,meninterfacerateof-6000S-ltheresultderivedusingconfidenceshowninFig.InNitroniccurvethedaahedinthietheeehiehhighaocaseAthigheranalyaia.asolldEqe.6and7whileTheagreementandresult.proceduretheresultEqe.9and10.inthetestlaRoodstrainweofthetwocurvedthe3-wavethetheWithSomet.meadonotagreeoutlinedreaulteabove,etatralnaaWell;inwerateshaveaaresultscaeesdegree(Eqe.6and7)ratherthanthe2-waveproced~reanextqectionconfidence-1In0.metalswillinourSHPBtestbepresented.-105X104ofFCCsomenxperimantalonavariety111.EXPERIIIENTAI.RESULTSINSONEFCCMETALSstrainbehavioralloysoxygen-freeelectronicstainleearatea.uoingrateoqteeluThestraeecopperfromofcopperandstrainseveralhaaratesaluminum103n-landausteniticincompressionqtbeendetermineddescribedoverawiderangeofstraint~-1.5x10UDatafromq-lwerewaouradsecticn.StraintheSIIPBtemtprocedure10-”U8-1i~,theprwioueto10-1q-l..woreqchievedqtinqqtandardqcrew-drivenmechanicaltoteetingmachineExtentof30%.withwhileusingaofP.11datastrainwagrateotesting8enerallyfrom10-10-11020-1weremeasuredqxtensometer.servo-hydraulicdeforutionmaterialagrainstecloICIqremachinewithl$mitedqnopticaltolesmthanatrueThecampooitionsotrainwere&nveoti8atedintherecrystallizedconditionaveragedimeneionWhentestingatransitionoforder30urnto50um.overthewiderangefromisothermalcase,workintotheofthestainlessabovetheretemtdueepeclmenshowninTable2.ofstraintestl,eattemperaturelagivenrateerioeby(11)Cpis(Y“1).andtheheatTableNitroniccapacity3listsandVIStheapproximatetoastrain(SeeFigs.estimatedItisfractionofof0.20ofPcpindicatedtointheconditionsadiabaticconditions.toconversion‘T-lq-’whereandstrainIncluded15b.thereandP*Inthelatterofplaetic(u(c)de,i~thedensity,intoforheatcoppertableworkconverted~o(e)dcratesvalues40deformedrespectively.increaseesection).stressatof6X103e-land5X103s-linflow3and4).fromEq.1114thatinandtheinthisdataarethetemperaturedecreaaesinthefollowingincrementsteel.thatandthecorrespondingtemperaturemuchisri~elargernotbelow.strainrates(estimatedfromEqs.evidentsmallteatspresentedandflowstresqinthestainlesstests)arerelativelyrisecopper(andinreportedcurvesThusinthecopperinthestainlessevidentLhecopper-aluminumcannotbeneglected.presented40stainlesscurvesrates.r~sultstheqasierthetemperaturewhereasbecomeintheexperimentssteelinthestresswithcopperinthoseFig.andthestraf.nsignificant,experimentsThi~willcurveslesshighercurvesSomestresssteelisforforxperimentstheq3and4.s-lratetrend.ofheatinterceptandNitronic4thatthestrainthethatTtisstressplotisofareshowninFigs.than10-2strainconsequenceNoteatstrainThisathigherIncontrast40indicaterates.ofadirectthestrainthisceveralgenerationexperiments.increasingtemperatureforcopperstrainratestraindonotshowthiqsensitivityincreasestrainoetsversusisThestressforbothcopperincreasingrat~.andNitronicathighplotastraintovisualizebyIncludinainasemi--logarithmicAnothersuchaplotalloweflowatthatconstantadvantageofthisofdatareparation.’qffecteetremo.duetoexperimentalSemi-logarithmic8forscatterplotsfromthooeduetorealarechangesinof102inflowFige.inratsthethatE-l.SHPBtheItintheThus,foundinnextatvariouaitemted.isfoundreeulteatetrainstrainsatetrainshownrates5throughsenaitivltyallmaterialsbyEq.1eteelbeginenoneofIneachcameanincreaoeinFigs.7and8quggeeterrorsratedeecribeddefinedratebesectionexperiment6i.IncreaeedshouldpreviousthieTheetainleeaaeneitivitythatnotedratemaelowaatheexperimentalratestheincreaoedanexperimentalareimportantevidenc~ratherOCthisierealatstrainthatthanas“low”MP102O-;.aenaitivitywillartifact.Inthepr~videematerialsthefurtheroriginthesenectionincreasedratesensitivitybeqxaminedinmoredetail.IV.ORIGINCFTHEINCREASEDRATESENSITI?WVATHIGHSTRAINRATEStheSHPBdatashowninFigs.anequationehowninofFig.is9.thatThetowithTofurther5-8,ItisAnyof5-8maybepiottedbyEq.2.rateagreementdragthewhichwithonlinearforhaeaxeaandthecopperledaosomeWaeofofthanaoffitdatatotheformgivenAnexampleEq.2menaitivityinve6tigatoreregimedescribedabtoconcludeinSectiontheIncreaeedHowever,foundinthisfoundvalueratherieduetoabeenoftransition1[7,14].Interaetione,controlledtheoreticaldictateathedeformation,understandingasmall,hplicationetheexperimentallyhasinconeietentUbdislocation/obstaclelargereeultevalueshown[29,30].understandworthwhiletheofinFigs.toreviewcomefeatureedislocation/obetacleAechematicbytheanforce.interaction.ofadislocationdistance~istoproceedpastrestrictedshowninFig.theobstaclebyseveral10.arraybarriers,separatedandatOK;Atequilibriumaveragerequiredis~andtheetreaelawritten(12)Thieioaeetobstacleetreeeueaeure10calledofthethresholdintrinmicOnceproce~datreesorthemechanicaldeterminedbreakssetbythresholdtheandfircttheitwillstrengthtotfienextparticularconfiguration.thedislocationqwayfromtheofob~-+~cleswherethesameequilibrium.conditionqppliem.6ietribtion[31]Forofdialocmt20n/dialacationinteractionandforaqtatiatlcalbecomesdinlocationethemechanicalthresholdstrea~(13)wherePImthetotalgreaterdislocationdenmityandaisactivationlarequiredstressaconstantaesi-tstoforceoforder0.5.appliedAttemperaturesqtressthanOKthermaltheandthuealowertheobstacle.strainrateqppliedetreeathedi~locatio~laregivenbyanpactandThevaluedependent;oftheappliedtheactualnowbecomeetemperaturedependenciesArrheniusqxpreeoionoftheform(14)where~.i~aconstanttheactivation~whereTaylorener8yand,forInteraction[31]withehortrangeobetaclea,AGiewritten312,MlJ(T)b380{1-(~)1’~}a~isthenormalizeddonot8iveetrainfound(15)activationaatener8yand~=M;whereMisincreaain8ratestoEqs,etrainthataofatrequireetheratethenewisthesomefactor(M=3.C6).dramaticallySHPBetrainrateathigheeneitivityrates,whichwouldappeartoimplyquationeTheseqneneitivityincreaeeddeformationthatuniquestrainStrainstrainqrrorsrateuechanism.However,therestrictionandstrainor“structure”,thisto14and15abovetheydeocribeobstacleinFi8s.raterateinherenttothetemperatureconfigurationdependenciesresultsetructuretheconstantetressthemeaaureofwhichisreatrictlon.mechanicalthreshold.jumpteatssensitivitythoeeThecomparisonhavebeenueedofexperimentalconstantproberates.exhibitrateconstantstructurethethese5-9maynoteatiafyatlowerstrainmaterialsstructurehiehqtrainIntheSHPB,however,limitalar8econstantcanto?hemeasurementofthedynamicyieldthattechniquesstructurenotaplotbeatetrainrateSincet3enr.itivity.theconctantstrainrates,aenaitivityatthevalidityofueingmeaeureddirectlyI-,constant6traintoapproximateoneatconstantetructurecanbeInvestigatedeaeuringbyuthemechanicalthresholdetreee.A.MEASUREMENTOFTHEMECHANICALTHRESHOLDthetheTheprocedurerat?formeaauring[19,32].tomechanicalofinterest.thresholdareatreaedeforuwdhaabeenattheiaandescribedstrainpreviouslyMultiplestrainapecimene“~fintereetTheneachspecimenreloadedextrapolateCombiningquaai-8taticallyoniamadeandrearrangingattemperaturestoEqs.determineof76K,’180thereloadiZand295KandstressyieldatOK.14and15yields(16)whichindicateebythattheaplotofthe8quarerootofehear~hearthereloadmoduluB,,yieldvereueraisedetreap,testtoathenormalizedtemperature,powerof2/3,temperaturenormalizeda8traighttheslopedependentbytheline.ofgo.chosen2000,0.05,tothiowhich16alsogivewhileactivationmodulu6andatehouldTheinterceptlineisOKgivesproportional..mechanicaltotheAStrainspecimensofthesethresholdinverselynormalizedlargeratesoftestenergywas1,100,ofmatrix10-2,toinvestigateand95000.15,S(E,s-l~)ineoPPer”andeach10-4,loadedrates.50000.10,stressshockwerechosenand0.25rateathistorieswerestrainstrainsThus0.2035separateoneandstrainwaveAleesrecoverywereinvestigated.atashockthresholdweredeformedInaddition,ofexperimentserieswasof40.performedmechanicalSamples13-1.Thepressureatrees10GPa[33].extensiveueasurementwaeatstrainperformedrateBofinNitronic10-3toastrainof0.10and6X103resultsofthesestudieshal~ebeendescribedforin[32].Figureatat11ashowsthenormalizedstrain18eeenbehaviormeasuredstraightratetoIncreaneexpectedmechanicallineoftheplotwithsugResteda-lincreaelng13.byEq.16atreine.strain,copperdeformedof0.000145tovariout3Theinterceptlacon~istentcomputedinT=OKthewhichwithfromEq.thresholdformThedislocationandEq.density13arefromthe12.Aatresse~shownFig.(17)where?!-11x1014E-2qndp.EOcanbefitontheoreticalthedislocationthroughqntheresultsequationmeaeureableinFig.iaentical12.toGihanEq.[34]hasproposed8roundsHi-17whereM10termed-ltiplicationqconstant.AlthoughpurameterMisfoundinmphasizedGilmanhasqthatmayvaryHiswithtoliecoefficientexperiRantallyoverFig.strainweretheAsthethatgreaterstresseasierbetweenpoeaiblethresholdthatthecoefficientperceivedtemperaturewithin[34](and,thus,withstrainrate),theaeaconstant.whichqgreesstresswithForcopper,thevalueofF!=5X1014to15x1914m-2[1S]foundgenerallytherangeawiderangeofqtzain12.Thedependencerates,ofthetiweeholdof0.10structure,thereaxeeisinFig.5.aforcopper13.deformedIfthresholdofatvariouastrainorrate.totheonshowofratestoastrain19showninFig.18shoulddefinite14.IncludedthresholdiathecomgtantstraintoimplyconstantInterceptshown,how~ver,threshold.p:.ottedthenthemechanicalstrainof0.10stress,atT=OKinFig.beindependentrateand0.20depentiencearemechanicalatreaeThedataatstrainsinFig.Theresultsareplottedclearlythateemi-logar:l.thmicvalueatheincreakethantotointhisfigureinthisatreseratefigureparallelaatsensitivitytheflowtheflowi~lainthemechanicalinterestwhereinattheflowstreos.Ofparticular103s--lbythatbehaviorthresholdOfstrainofthethisratestheincreasing~ftheuechanicalline~rofiaaccompaniedvisualizetheteatqtreaeatrese;ratea,theplotaxeaetrainflow~igm15.Byinterpolatingitmechanicalresultsvereuadifferentrat~andatresa16.etrainThisgenerateatconstantplotrateastrainrateshowninFig.atstrainehowanodramaticwhichFig.5.increaseinsensitivityqxceeding#train103a-l,mhuwningaveshockrateashouldbecontrastedinwiththebehaviorsamplerateaatconstantMeaourementaanevenhigherqtthecopperqtrainshockdeformedstreaeinfact,theyieldat10GPa[33]thanthevaluestrainsofthemechanicalatthresholdto104a-l.and,betweenhowever,waastrainueaauredequivalentdifferThehistoryloadin~aduringandwelldeformatlo~lmayandreleasebyTheisverycomplicatedofmagnitudedoes,proceaaordersshockrelaamedefinedprocesmes.equivalentplueticetrain[35],whichincoppershockdeformedat10GPais.,0.0825.atFigureretrainisfrom17showsthecomplriaonofthemechanicalTheqtrainrate-103e-lthresholdratestrascthisauafunctionaowimedtoliethisfigureofretrainw~thinthattherate.fortheshockItimintof~rthetoofthedeformationqviolenttherange-l.105E-lto107qsensitivitycontinuesstressincreasadthresholdtheqtreseatreeenotedatstrainrate-qxceedingweshockregime.Unfortunately,Withoutdonotknowthevaluethretholdqtreseoftheflowwhichaccompaniesdeformedsample.themeasuredmechanicaltheflowshockqvaluatetheitienotpoaaibledeformationthecontributiondefamation.results.IechanicallemsthanofdislocationNitronic40otreasdragcontrolledshownwithinstrainrateFig.Thisthat18duringshockThefortheqlsoindicatethethatinqnincreaaii.,~10theabrvptshouldlargeFig.strainTheetreaemuchthresholdincreacerate,butimpliesinincreaaewhereasdueThus,atoanrateveryto40isinflowwithntrezm.atralnmo~toftherateprimarilyincreasesensitivityinflowstressofstructurerateratefromincopperbyEq.13.uopparraterateqvolition,aquasi-staticinflowstresssteel.Nitronicduetointrinsicinstrainsensitivitydescribedinchangeyield19forincreasedof0.10,increaeedwithtoadynamicretrainbutThereuulteof10-3ofaverysmellaNitronicincreaseflowatreeeunloaded,rateintheatainlesedeformedsensitivityatstrainincreaeeshownin40sampleatastrainataetrainratesinq-lqthenreloaded3X103s-lioa-ltendtoverifythatuaterialmeetoftherateinthimmaterialintrineic.inthiethresholdneedstootreaeotretiaqensitiwitytotheqxceedingtheThis,-102ialikelywithrelatedadditionalqtrainmechanicalhowever,@trainrate,aswaefoundforcopper.measurementsmeasurementsandNitronicstreeedragieofbeverifiedTohavethemechanicalthresholdthreoholdtateoatintermediateehownratee.oummerize,theoetherateflowofthemechanicalqtthats-l,thatforcopperdislocationeet~sitivityrate40deformednotplotteaponJibleof@trainforleeewhichthandynamic10”ioleeothantnethreeholdmateriala.strewofqtqtrees,theIncopper,IndicateapredominantvereuoInNltronlcincreae-dtheqtrain@trainratestrainqeneitivityfoundintheseqeeeninrateconetantthaieduetotherateyieldthebehaviorqenaitivitycombinesshowninFiE.structureqvolition.40thimlattertoqenmitivitywith18.threoholdintrinnlcenmitlvityrateqOneoftheconclusionsbasedonthemechanicalmeaourementmqndqnalyaiaThispreeentedofhereiethatEq.17,amitiewritten,10notavalidratee.descriptionetatedislocationtreatavariable,40.generationplasticstraintheoverasawiderangeofetrainastructure,17uustrelatlonorforbeathermodynamicbothcopperfunctionofwhichwehaveehown10notappropriateClearlyconetantMinEq.andNitronicstrainrate,orperhapsstress,theaewaaoriginallydieloca~ion[15]postulateddeneitieeininCuin[34].ueingPrevioustransmissionstraininveetigator~qlectronratewhereasItehoulddensitieserrors.;=10-4fromEq.wasonlyhaveueasureddeformedquasj-staticallyanddynamicallycopperandaluminum[12,36]P[12]withmicroscopy.ueasuredinAAlincreaselargesingleincreasecryataleincreaeln~polycrystalscrystalsdeterminesubjecttoonlytheandtoare[36],[15].dislocationtolarge(atasmallbenoted,Inheavilywasueasuredthateinglehowever,(C>0.01)theTEMtechnique8uetalsdeformedtheTheratioofmaximum(forthresholdstreeeratio10GPachock)inofFig.17lauinimum1.8a-1)mechanical13,impliesieonhighonlywhich,that-3.2.theThisdislocationoutsidethethedenaitieaprecisiondislocationevidenceehouldlimiteddislocationforoftheetitwohir+torieabaaedaregeneralwitheomaybeinFortechniquedislocation(PofucountingTEHwhenreason,densitiesforthe1014Eq.u-z).17baaed18isgiveathisvalidityonTEMobaervationaanapproximateroughestimatebutofberegardedrulethatsomeauapicion.Equationonlyto~houldratesbeLsedgenerationinFCCuetals.v.~~LIcATIONsFOR(X)NSTTTUTTVEThemechanicaleeveralconetitutiveoverofEq.awidethresholdLAWSueasurementsincopperthechoiceandofNitronicnumericalofthese40leadmodelsmaterjaletoorconclueionelawsrangeconcerningtodescribeofutraininandtherates.theuechanicalbehaviorOneconclusionsection.it10concerningFormodelethevalidityba~edonismain17wandiscussedtheoryforoftheEq.previousdislocationunsuitableshortcomingdislocationdependenceThemicromechaniema,ofa~atclearimplicitlystrain,thatEq.The17description17areIHthat,dislocationwritten,equivalentitgeneration.aeoumeethatice.,theratedensitiesofabovedislocationqquivalentgenerationare10ignored.considerationrelatadtotheuoregeneralconclusion.,thatstrainianninappropriatevariabletoincorporateintoqconstitutivelawasapathindependentparameter.Thiei-notanewconclusion,butthedangerofaeeumingthatconetantstrainimplleaconstantqtructurehasbeendemonstratedherefortheinterpretationoftheincreaeedrateqenaitivityfoundqtntrminratesqxceeding-103e-l.Theseresultsreesphacizetheimportanceofincorporatingsomeformofqninternalstatevariableintoconmtitutivelaw.This10qne6t3entialfeatureofrecentnumericalprocedurespropocedbyBamann[37]andothers.Anotherconclusionbasedonthereeulterepo~tedhereisthattheconstantstructure(orIntrineic)strainrateeeneltlvitydoesnotincreaoedrasticallyintheFCCuetalsconsideredanthe#trainrate18~aieedabove’103e-l.Althoughtheactualatreae-strainratebehavlermaybedescribablebyanequationoftheformofEq.10thisqquationovereatimateetheactualrateqaneitivity.ThuswhenthisqquationisIncorporatedintoqnumericalmodelthatieusedtodescribdeformationinacompo~~entinwhichthestrainrateischanging,thepredictedbehavioruaydiffergreatlyfromtheactualbehaviorofthematerial.ThIomaybeimportant,forinstance,inthepredictionoftheformationofInstabilicieminplabtlcflow[39].UmeofaconstitutivelawintheformofEq.2canoverestimatetheqtabilizin8influenceofstrainrateinquchproblems.Ourreaultatuggestthatthestrainratedependenceoftheflowatreasincopper,copper-aluminumalloya,qndnuatardticatainleaaateeleehouldremainintheformatgivenbyEqa.14and15or,equivalently,intheform:“(:)mBco(18)whereu<<1.Indeed,r?centformulationsproposedbyJohnson[39]qndBammann[37]ratainthelowintrinsicratedependencegivenbythemeexpreesionasVI.SUMMARYThiopaperhaaincludedtwomajorthemeu.ThefirstconsideredthevalidttyofexperimentalraoultsdeterminedwithSHPBtechniques,Itwas,oncludedthatthaaetechniquescanyieldvaliddy.~amicstressotraindataprovidedthatCert#lnprecautionsre8ardinglubrication,qpecimanq-pact.’ratio,featuresqndlimitingofotrainrateaarepracticed.TherearetheadditionalthedatatheeereportedinSectionbelow.previously,withtwobaraizeaIIIthattheand,[19].qspportvalidityreportedreaultaoftheresults;Fi8a.Figs.ofarelistedobtained1)Although5-9notqmphasizedwerethreeSHPBreaultaforDecreasing(butnotresultsintestreaultastrainauateniticinwereresults.inrateetralnininthecopper5qnd9,thedifferentfromEq.factthediameterratio)higherwith[27],obtainedthepreaaurebar,qndthusthediametersimilarconfidencedynamicteataaincreasingfortheaapectofthespecimenntraindifferentwhetherhighshownregionqviolencerates.qllows,The4qndthediecuesionthatbardiameteraorinnotratea.Figsratewhere7thereandprovidesexiate2)ThemainquestionstrainregardingThereeultaSHPBisatateelawithanthebelowaenaitivityrate,thisalaotheatainlesawel?8showaclearbeginningconeideration~~trendwithatatrainareincreasingaenaitivityinertiathatraterateareeults.valoeaflowimportant;lafurtherahowedanthatthevaluescannotinsupportwenotejnamicactualwithofthevalidityaenaitivity.rateofthetestthresholdThisof3)Finally,increasingcorrespondingrcpreaentadecreasetheuechanicalaeneitivitybehaviorrate.iestrongtheevidenceetreaa.0/0ratioIncreaeedIncreasingmaterialstraineincetheThemajorthemeofthisincreaeedthresholdratepaperthenwaatoevaluatethesourceofthethatofthisofverauaratherutrainatreaarateqenaitivitymwithanMeasurementsthethemechanicalincreaaedcoupledfoundanalyeiaatofofkineticsstrainqvolutiondislocation-obotacleinteractionsinaplotina-l,ledtotheconclusionofflowotreosaenaitivityatainlesadragstructureqen~itivityruteconotantInstrainthanratesarlaeefromtheratealloyafromleaaThisanythanreoultintochange-104deformationdislocationthattheviscousdeacriptionelowlaqtral-nmechaniam,steelsth?copper,atqtrainnotratenotbeunderthermalhighascopper-alluminumcontrolling.undauotenticevaluatedareuechanismsimpliesconatitutivesincelawusuchasEq.2shouldofrateincorporatedtheseqctivationmatarialbehaviorofqaconditionscontrolledqeneitivitytoqtrainrate~deformationuaintained104s-linthesematerials.However,qnyde~criptionofconatitutiv?.behaviordependenceoverqwiderangeaswaaofstrainqvolition.rateshere,needetoaccountfortherateofctructureAlthoughthiscanbedoneempiricallyde~cription~andofbymeaeurin~dislocationtocompleteaawell~(~,~),generationreportedtheoretical.proceeoeeimightbeveryusefulbehaviorinqventuallyleadingalloyadescriptionsofconstitutivecrystalinFCCmetalsaainuetalsofotheretructurts.ACKNOWLEDGEMENTSIwouldlikethetoacknowledgereportedwiththemanycontributionsofW.madetotheexperimentalJ.WrightandM.LopezIamalaogratefulThisworkonwasfortheprogrambyC.E.Frantzueaaurementeandtheaesietanceinthiereport.qxteneivecollaborationU.F.KocktqndG.Regazzoni.oftheU.S.DepartmentperformedundertheauspiceaofEnergy..REFERENCES1.A.J.Hclcer,F.E.Haueer,J.Engr.Mat.Tech.101:231(1979).2.qndJ.E.Dorn,“StrainRateEffGctsinJ.A.SinonsinResponseofMetalstoHighVelocityPlaeticWavePropagation,tcDeforuaticm,P.G.ShewmonandV.F.Zackay(eda.),Interacience,NewYorkp1961.3.4.5.U.S.Lindholm,C.H.Karnes(1966).J.Mech.Phys.andE.A.SolidsJ.12:31714ech.(19).Phys.Solids14:75Rxpperger,D.L.Holt,S.G.Babcock,S.J.GreenandC.J.Maiden,“TheStrainRateDependenceoftheFlowStreeainacmeAluminumTR66-75,1966.GeneralNotorsResearchLaboratoriesAlloys,”W.G.Ferguson,(1967).A,A.6.7.8.9.KumarandJ.E.Dorn,ActsJ.Appl.Phys.16:1130:1863(1968).Kumar,F.E.HauserandJ.LindholmE,Dorn,Fleta.7J.S.andL.M.Yeakley,Exp.Mech.8:1Exp.Mech.(1968).(1970).C,K.H.DharanandF.E.Hauser,10:370F.10.S.J.Green,C.J.Maiden,S.G.BabcockandL.Schlerloh,“TheofFace-CenteredCubickletal~,’tinHighStrain-RateBehaviorInelasticBehaviorofSolids,U.Kanninm,W,Adler,A.RoaenfieldandR.Jaffee(eds.),McGraw-HillCo.,NewYork,1970,U.S,Lindholm,“DeformationMapsintheRegionofHighDisIG-cationVelocity,”ofSolids,K.inHi$hVelocityDeformationKawataandJ.Shioiri(eds.),Springer-Verlag,NewYork,1978,“StrainRateHistoryEffectsandC.Y,ChiemandJ.Duffy,OboervationaofdislocationSubstructureinAluminumSingleCrystalsFollowingDynamicDeformation,”Mat@rialsResearchl,aboratory,BrownUniversity,MRLE-137,1981.E.A.Ripperger,“DynamicPlosticBehaviorofAluminumpCopperofMaterialnUnderDynamicLoading,N.J.andIrono”inBehaviorHuffington(cd.],Am,Sot.Mech,Engr.,Chicago,1965.A.KumarandR.C.Kumble,J.Appl,J.W.Edingtc)n,Phil.Ma8.19:11J,Buchar,(1976).Phya.(1969),A.LituornandA.Piatkowski,40:3475(1969).11,12.13.14,15.16,F.Dueekp2,Jasinski,Czech.J,Phya.B26:53fl.17.%omeResultscmtheDynamicDeforma-?I.StellyandR.Dormeval,DeformationofSolids,K.tionofCopper,”inHighVelocityKswataandJ.Shioiri(edo.),Springer-Verlag,NewYork,1978.“ExperimentalStudiesonK.SatohandK.Nishimura,J.Shioiri,theBehaviorofDislocationsinCopperatHighRatesofStrain,stinHighVelocityDeformationofSolide,K.KawataandJ.Shioiri(eds.),Springer-Verlag,NewYork,1978.P.S.Follan@bee,G.RegazconiandU.F.Kocka,“TheTransitiontoDrag-ControlledDeformationj.nCopperatHighStrainRates,”inMechanicalPropertiesatHighRatesofStrain,J.Harding(cd.),InstituteofPhyaice,London,1984.M.Blalatynski18.19.20.andJ.Klepaczko,Sci.Int.14:3J.Mech.Sci.(1972).22:173(1980).21.22.T.Muller,J.Mech.Engr.A.V.Granatc,‘Microscopic?lachanismsofDislocationDrag,”inMetallurgicalEffentaatHighStrainRates,R.W.Rohde,B.M.Butch~r,J.R.HollandandC.H.Karnes(eda.),PlenumPress,NewYork,1973.U.cU.S.Lindholm,inTechniquesofMetalsResearch,Vol.5,fart1,R.F.Bunshah(cd.),JohnWileyandSons,New“fork,1971,Chap.4,p.199.P.S.Follsnsbee,inMetaleHandb[ok,NinthEdition,Sot.Metals,MetalaPark,Ohio,1985,p.198.E.D.H.Davies(1963).L.l).BertholfandS.C.Hunter,J.?3.24.25.26.Vol.SolidsSolids8,Am.11:15523:1Mach.Phys.Mech.Phys.andC.H.Karnes,J.(1975).27,C.E,Frantz,P.S.FollnnsbeaandW.J.Wright,“ExperimentalTechniqueswiththeSplitHo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