Fracture-characteristics-of-three-metals-subjected

EngineeringFractureMechanicsVol.21,No.I,pp.3148.1985PrintedintheU.S.A.0013-7944/85$3.00+.ooPergamonPressLtd.FRACTURECHARACTERISTICSOFTHREEMETALSSUBJECTEDTOVARIOUSSTRAINS,STRAINRATES,TEMPERATURESANDPRESSURESGORDONR.JOHNSONHoneywellInc.,DefenseSystemsDivision,Edina,MN55436,U.S.A.andWILLIAMH.COOKAirForceArmamentLaboratory,EghnAirForceBase,FL32542,U.S.A.Ahstrac-ThispaperconsidersfracturecharacteristicsofOFHCcopper,Armcoironand4340steel.Thematerialsaresubjectedtotorsiontestsoverarangeofstrainrates,Hopkinsonbartestsoverarangeoftemperatures,andquasi-statictensiletestswithvariousnotchgeometries.Acumulative-damagefracturemodelisintroducedwhichexpressesthestraintofractureasafunctionofthestrainrate,temperatureandpressure.Themodelisevaluatedbycomparingcomputedresultswithcylinderimpacttestsandbiaxial(torsion-tension)tests.INTRODUCTIONWHENMATERIALSaresubjectedtodynamicloadingconditionssuchashighvelocityimpact,explosivedetonationormetalformingoperations,awiderangeofstrains,strainrates,temperaturesandpressuresmaybeexperienced.Insomeinstancestherehasbeenatendencytodistinguish“dynamic”materialpropertiesfrom“static”materialproperties.Theunderlyingassumptionisthatthedifferencesbetweenthe“dynamic”and“static”propertiesmustbeduetostrainrateeffectsonly.Oftenassociatedwithhighstrainrates,however,arelargestrains,hightemperaturesandhighpressures.Therefore,itisimportantthattheeffectsofeachvariablebeproperlyassessed,ratherthanassumingalldistinguishingcharacteristicsareduetostrainratealone.ThispaperconsidersfracturecharacteristicsofOFHCcopper,Armcoironand4340steel.Aseriesoflaboratorytestshasbeenperformedtodeterminetheeffectsofstrainrate,temperatureandpressureonthestraintofracture.Acumulative-damagefracturemodelisdevelopedandevaluatedwithanindependentseriesoftestsandcomputations.TESTDATAAdescriptionofthethreematerialsisgiveninTable1.AllofthetestspecimenswerefabricatedfromthesamematerialstockandtheheattreatmentwasalwaysasspecifiedinTable1.ThetorsiontestdataareshowninFig.1.ThetorsiontesterisdescribedinRef.[I]andtheprocedureforanalyzingthedataisgiveninRef.[2].DataforawiderangeofothermaterialsarepresentedinRefq.[3]and[4].ForthedatainFig.1theaverageshearstrain,7,isassumedtooccuronlyinthethintestsection,andtooccuruniformlyalongthatsection.Atthehigherstrainrates,however,theremaybesomelocalizationsofstrainduetoadiabaticheating[2].TheaverageshearstrainsatfractureareclearlyshownfortheArmcoironandthe4340steel.NoneoftheOFHCcopperspecimensinFig.1fracturedduetorotationallimitationsofthetorsiontester.Anothershorter-gage,OFHCcopperspecimenwastestedat3=0.008s-’anditfracturedat7=8.7.MetallographicsectionsofthreetorsionspecimensareshowninFig.2.TheOFHCcopperspecimenappearstoexhibitastrainlocalizationnearthecenterofthegagesection.Therearenovoidsevidentinanyofthesections.ThetensileHopkinsonbardataareshowninFig.3.ArepresentativeHopkinsonbarapparatusanddataforvariousmaterialsarepresentedin[5].ThespecificHopkinsonbarusedforthedataofFig.3islocatedattheAirForceArmamentLaboratory(AFATL)atEglinAirForceBase.Theelevatedtemperatureswereobtainedbysurroundingthein-placetestspecimenbyanovensuchthatthetemperatureswereappliedforseveralminutespriortotesting.ThetruetensilestraininFig.3isbasedontheassumptionthatthereisuniformaxialstraininthetensilespecimen.Thestress-straindataareshownonlyforrelativelysmallstrainsbecausethey3132G.R.JOHNSONandW.H.COOKTableI.PhysicalpropertiesofOFHCcopper,Armcoironand4340steelHEATTREATMENTTEMPERATUREtK)TIMEATTEMPERATURE(MINUTES)-__HARDNESS~OCKWELL~GRAINSIZE(mm1___~ELASTICPROPERTIESELASTICMODULUS,E(GPaJPOISSON’SRATIO,YSHEAR~DULUS,E/2(1+VIIGPalBULKMODULUS.E/3(1-2Yi(GPa)_”THERMALPROPERTIESDENSITY.ikqlm3)CONDUCTIVITY,k(W/ml0SPECIFICHEAT,cpUlkqKIDiFFUSiViN,k/pi+,h2idEXPANSIONCOEF.NOL.).a(K-l1MELTINGTEMPERATURE,TMELT(K)e-jF-30jF-72c-30-__0.060-0.090o.D%-0.1500.010d2072000.34I0.290.29-.cannotbeaccuratelyevaluatedafterneckingoccursinthetensilespecimen.Whilethesedatacanbehelpfulinexaminingstrengthcharacteristics,fracturecharacteristicscanbedeterminedonlybyexaminingpost-testedspecimensasshowninFig.4.ThephotographsofFig.4andthemetallographicsectionsofFig.5bothshowtherelativelyductilefractureoftheOFHCcopperandArmcoiron,whencomparedtothe4340steel.InFig.5,voidsaremostevidentintheArmcoironandsomearepresentintheOFHCcopper.The4340steelalsoshowssomevoidformationatelevatedtemperatures.Quasi-statictensiledataareshowninFig.6.Thenotchedgeometryspecimensareidenticaltothoseusedelsewhereandgiveaconcentrationofhydrostatictensioninthetestspecimen[6].ThisisclearlyshowninthedataofFig.6.Foraspecifiedtruestrain,thestress(includinghydrostatictension)increasesasthenotchbecomesmoresevere.Itcanalsobeseenthatthepresenceofthehydrostatictensionsignificantlydecreasesthestrainatwhichthematerialfractures.Figure7showsmetallographicsectionsofthequasi-statictensiletestspecimens.TheOFHCcopperandArmcoironfailinamoreductilemannerthanthe4340steel,asexpected.TheformationofvoidsisapparentintheunnotchedOFHCspecimenandalloftheArmcoironspecimens.Novoidsareevidentinthe4340steelspecimens.DATAANALYSI