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Physics,Mechanics&Astronomy
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Correspondingauthor(email:luzp@ustb.edu.cn)
?ResearchPaper?
March2010Vol.53No.3:394–398
SpecialTopiconBulkMetallicGlassesdoi:10.1007/s11433-010-0136-8
EffectsofcoolingratesonthemechanicalpropertiesofaTi-based
bulkmetallicglass
XIAOYueHua,WUYuan,LIUZhiYuan,WUHongHui&LüZhaoPing
StateKeyLaboratoryforAdvancedMetalsandMaterials,UniversityofScienceandTechnologyBeijing,Beijing100083,China
ReceivedDecember29,2009;acceptedJanuary22,2010
MechanicalpropertiesoftheglassyspecimensfabricatedatdifferentcoolingrateswithacompositionofTi
40
Zr
25
Cu
12
Ni
3
Be
20
weresystematicallyinvestigated.Itwasconfirmedthatfastercoolingratescausednotonlyalargeramountoffrozen-infree
volumebutalsoahigherglasstransitiontemperatureinthebulkglassyalloy.Increaseinthefreevolumewasfoundtofavor
plasticdeformationandthentogiverisetolargercompressiveplasticity,whilsttheriseintheglasstransitiontemperature
seemedtobecloselyrelatedtothehigheryieldstrength.Moreover,theincreaseofyieldstrengthandplasticityinducedbyfast
coolingratesmayalsobeassociatedwiththeresidualstressgeneratedduringthefabricationprocess.Ourresultssuggestthat
thedeformationbehaviorofbulkmetallicglassesissensitivetovariousfactorsandinfluencesfromtheotherfactorsshouldbe
excludedasfarascooling-rateeffectsonbulkmetallicglassesareconsidered.
bulkmetallicglasses,mechanicalproperties,cooling-rateeffects,residualstress
PACS:61.43.Dq,65.60.+a,81.05.Kf
Bulkmetallicglasses(BMGs)areusuallyfabricatedby
rapid-quenchingtechniquesinwhichthecoolingrateisa
keyprocessingfactor.Asdiscussedinliterature,glassfor-
mationability(GFA)ofBMGsisbestdescribedbythe
criticalcoolingrate,R
c
[1–3].Inadditiontoitsroleasone
ofthedecisivefactorsinthevitrificationprocessofBMGs,
thecoolingratealsoinfluencesthefinalmicrostructure
[4,5]
andphysicalproperties[6].Boththeoreticandexperimental
resultshavedirectlyshownthatmechanicalpropertiesof
BMGswerecloselyrelatedtocoolingratesappliedduring
thesamplepreparationprocess[7,8].Anincreaseinthe
coolingrateislikelytogiverisetoalargerplasticityand
loweryieldstrength[9].However,furtherinvestigationsare
neededforafullunderstandingofthecooling-rateeffects
onmechanicalpropertiesofBMGs.
Recently,thedeformationbehaviorofamorphoussolids
wasfoundextremelysensitivetotheotherfactorssuchas
Poison’sratio[10],residualstress[11],andtestingspeci-
mensizes[12,13].Assuch,effectsofthecoolingrateare
oftenoverlappedwiththesefactorsinBMGs.Itisthusnec-
essarytoexcludeinfluencesfromtheotherfactorsinterms
ofthecooling-rateeffects.Inthispaper,weattempttoin-
vestigatethecooling-ratedependenceofmechanicalprop-
ertiesinBMGsandtherelatedmechanismsviacarefully
designedexperiments.
1Experiment
MasteralloyswithnominalcompositionsofTi
40
Zr
25
-
Cu
12
Ni
3
Be
20
(at.%)[14]werepreparedbyarc-meltinga
mixtureofrawmetalsincluding99.999%Ti,99.5%Zr,
99.99%Cu,99.99%Niand99.99%BeinaTi-getteredargon
atmosphere.Thealloyingotsweremeltedsixtimestoen-
sureacompositionalhomogeneity.Rod-shapedsamples
wereobtainedbysuction-castingthemoltenalloysinto
coppermoldswithdiametersof2,5,8and10mminhelium
atmosphere.Theamorphousstructureoftheas-castsamples
XIAOYueHua,etal.SciChinaPhysMechAstronMarch(2010)Vol.53No.3395
wasascertainedbyX-raydiffraction(XRD)usingCu-Kα
radiation.AsdemonstratedinFigure1,compressivespeci-
menswithadiameterof2mmandanaspectratioof2:1
(height/diameter)werepreparedfromtheas-castrodswith
differentdiametersbyanelectricaldischargemachine.Lat-
eralsurfacesofallthecompressionsampleswerecarefully
polishedtoeliminatesurfacedefects.Aspeciallydesigned
devicewasusedtogrindbothendsofcompressionsamples
forensuringagoodalignment.Uniaxialcompressiontests
wereconductedbetweentwoWCplatensatanengineering
strainrateof2×10
?4
s
?1
inaSANStestingmachinewitha
maximumloadof300kN.Thermalpropertieswereana-
lyzedbydifferentialscanningcalorimetry(DSC)(Netzsch
STA449C)ataheatingrateof20K/min.
Figure1Schematicillustrationofthesamplepreparationforcompres-
siontestingsamples.Forlargesizecasting,specimenswithadiameterof2
mmwerecutfromcentersoftheas-castrods.
2Results
AccordingtoJohnsonetal.
[15],achievedcoolingrate,T
?
foranas-castdiameterRcanbeestimatedas:T
?
=10/R
2
(cm).Asmentionedearlier,fourkindsoftheas-castrods
withdiametersof2,5,8and10mm,whicharedenotedas
R-2,R-5,R-8andR-10,respectively,wereprepared.Thus,
theachievedcoolingrateinthesamplesR-2,R-5,R-8and
R-10couldbeestimatedtobe1000,160,63and40K/s,
respectively.Obviouslythesmallertheas-castdiameter,the
largerthecoolingrateisachieved.X-raydiffraction(XRD)
patternsinFigure2(a)verifytheamorphousnatureofall
theas-castsamplesandthecorrespondingDSCresultsof
theseas-castrodswithdifferentcastingdiametersare
showninFigure2(b).Allfourkindsofthesamplesexhibit
anendothermiceventatlowtemperatures,followedbya
glasstransitionreactionandtwoexothermicpeaksassoci-
atedwithcrystallizationeventsathightemperatures.Note
thattheglasstransitiontemperatureisincreasedastheas-
castdiameterisdecrease(i.e.,thecoolingrateisincreased),
asshowninTable1.
Tominimizeinfluencesfromtheotherfactorsondefor-
mationbehavior,wepreparedthespecimensforcompres-
siontestsasillustratedinFigure1.Forthecastingdiameter
largerthan2mm,testingsampleswerecutfromcentersof
theas-castrods.Sinceallthecompressivespecimenshave
thesamediameterof2mm,thereportedsizeeffects[12,13]
couldbeeliminated.Furthermore,samplesurfaceswere
carefullypolishedtoeliminatepossibleeffectsofsurface
roughnessanddefects.Figure3showsrepresentativecom-
Figure2X-raydiffractionpatterns(a)andDSCcurves(b)ofthetestingsampleswithdifferentas-castdiameters.
Table1Thermalandmechanicalpropertiesforthesamplespreparedunderdifferentcoolingrates
SamplesT
g
(K)T
x
(K)Yieldstrength(MPa)Plasticity(%)Structuralrelaxationenthalpy(Jg
?1
)
R-262365018028.57.07
R-561665017513.04.51
R-861065117201.84.06
R-1060265116750.83.65
396XIAOYueHua,etal.SciChinaPhysMechAstronMarch(2010)Vol.53No.3
Figure3(a)Representativecompressivestress-straincurvesofthe2mmdiametertestingsamplespreparedfromtherodswithdifferentcastingdiameters;
(b)dependenceofthecompressiveplasticityandyieldstrengthoncoolingrate.
pressivestress-straincurvesofthesamplesR-2,R-5,R-8
andR-10.Appreciabledifferencesinboththeplasticityand
yieldstrengthwereobservedinthesesamples.Asthe
as-castdiameterisdecreased,i.e.,thecoolingrateisin-
creased,boththecompressiveplasticityandyieldstrength
areincreased,asdemonstratedinFigure3(b).
3Discussion
Figure4(a)schematicallyshowsthevolume(orenthalpy)
changeofametallicliquidasafunctionoftemperatureata
constantpressure[16].Uponcooling,ifthemetallicliquid
iscooledsufficientlyfast,crystallizationcanbeavoidedand
Figure4(a)Schematicillustrationofthevolumeorenthalpyofaliquidasafunctionoftemperatureataconstantpressure[16].Ahighercoolingrateb
leadstoahigherglasstransitiontemperatureT
gb
andalargefrozenvolume,(b)dependenceoftheyieldstrengthandplasticityonstructuralrelaxationen-
thalpy(i.e.freevolume),and(c)comparisonbetweentheyieldingstrengthexperimentallydeterminedandthatpredictedfromYang’sequation[17]with
glasstransitiontemperature.
XIAOYueHua,etal.SciChinaPhysMechAstronMarch(2010)Vol.53No.3397
thetotalvolume(orenthalpy)doesnotundergoanabrupt
changeatthefreezingpointT
m
whichusuallyoccursin
conventionalcrystallinematerialsbecauseoftheformation
ofcrystallattices.Instead,thevolume(orenthalpy)ofthe
liquidcontinuouslydecreaseswiththedecreaseoftempera-
tureuntilatacertaintemperature,termedastheglasstran-
sitiontemperature,atwhichtheundercooledliquidisfrozen
inanamorphoussolid[16].Inaddition,thehigherthe
coolingrate(linebinFigure4(a))is,theshorterthetime
availablefortheconfigurationalrelaxationateachtemper-
atureis.Thefallingoutofliquid-stateequilibriumoccurs
earlier,whichresultsinanearlierglasstransition,i.e.a
higherglasstransitiontemperature[17].Inthecurrent
Ti-basedalloy,DSCmeasurementdatapresentedinFigure
2(b)andTable1confirmthatthesamplefabricatedatthe
fastestcoolingrate(i.e.,R-2)showsthehighestT
g
valueof
623Kwhiletheonepreparedattheslowestcoolingrate
(i.e.,R-10)possessesalowestT
g
valueof602K,whichis
constantwithwhatisdemonstratedinFigure4(a).
Inadditiontothehighglasstransitiontemperature,high-
ercoolingrates(e.g.,lineb)inducealargerfrozenvolume
ofthesystem,asclearlyillustratedinFigure4(a).Forliq-
uidswiththesamechemicalcompositions,alargerfrozen
volumeindicatesalargeramountoffreevolumequenched
intheglassysamplewhichismanifestedbyDSCmeasure-
ment.Ithasbeenproposedthattheexothermiceventprior
totheglasstransitiontemperatureT
g
isstronglylinkedto
theexistenceoffreevolumeinsideBMGs[18],namely,the
enthalpyobtainedbyintegratingtheheatflow?H
r
ofthe
exothermiceventjustbeforeT
g
isproportionaltotheanni-
hilationofexcessfreevolume.BasedonFigure2(b),the
?H
r
valuesforallthetypesofthecompressionsamples
withdifferentas-castdiametersaredeterminedasshownin
Table1.Thesampleswithsmalleras-castdiametersshow
larger?H
r
values,indicatingalargeramountofthe
quenched-infreevolumeinsidethesematerials,whichis
alsoconsistentwithFigure4(a).
Asdiscussedabove,fastercoolingratescaninducea
largeramountoffreevolumeandahigherglasstransition
temperatureinBMGs.Variationsoftheyieldstrengthand
plasticityofthepresentTi-basedalloywithstructuralrelax-
ationenthalpy?H
r
areshowninFigure4(b).Withanin-
creaseoftherelaxationenthalpy(i.e.,freevolume),both
yieldstrengthandplasticityincrease.Ithasbeenwellrec-
ognizedthatfreevolumecontainedinmetallicglassesfa-
vorsplasticdeformation,andleadstoahigherplasticity[9].
Thecooling-ratedependenceoftheplasticityshowninFig-
ure4(b)canbewellinterpretedfromtheperspectiveoffree
volume.Howevermorefreevolumenormallymeansa
looseratomicstructure,whichwouldsoftenthemetallic
glass,therebyresultinginadecreaseintheyieldstrength,
contrarytothecooling-ratedependenceoftheyielding
strengthobservedinFigure4(b).
Yangetal.haveproposedaunifiedequationbetween
yieldingstrengthandglasstransitiontemperatureT
g
for
BMGs,writtenas[19]:
gg0
mm
5050
y
TTT
VV
?
??
??,(1)
whereT
0
istheambienttemperature,V
m
ismolarvolume
thatcanbecalculatedaccordingtotheruleofmixture[20].
Figure4(c)showsourmeasuredyieldingstrengthforthe
samplesfabricatedatdifferentcoolingratesincomparison
withthatpredictedusingeq.(1).Ascanbeseen,eq.(1)can
correctlydescribethetrendoftheyieldingstrengthasa
functionofcoolingrateforourTi-basedBMG.Ithasbeen
arguedthatthemechanicalenergydensityforplasticde-
formationisverysimilartothethermalenergydensityfor
theglasstransitioninBMGs,andglasstransitiontempera-
tureT
g
ofBMGscanalsoreflectthedegreeofatomic
bondingstrength.HigherT
g
indicatesthattheatomsare
moredifficulttobereshuffled,thereforegivingrisetothe
higheryieldstrength.
Althoughareasonableagreementbetweentheexperi-
mentaldataandthepredictedyieldstrengthfromYang’s
equationisobtained,itisworthytonotethatdiscrepancy
betweentheexperimentalandpredicteddatabecomesmore
distinctwiththeincreaseofthecoolingrate,asshownin
Figure4(c),implyingsomeotherpossiblereasonsforthe
cooling-ratedependenceoftheyieldstrength.Ithasbeen
proposedthathighconvectionheattransfercoefficientre-
sultingfromrapidquenchingduringfabricationofBMGs
cangenerateresidualstressintheas-castsamples
[21,22].It
isalsoconfirmedthatasuitableresidualstresscouldin-
creaseyieldstrengthofmetallicglasses
[11,23].Thus,itis
reasonabletospeculatethatthehighercoolingratesinthe
thinneras-castsamplesmayinducelargerresidualstress
whichinturncontributestotheincreaseintheyield
strength.Inoneword,thelargerthecoolingrate,thelarger
theresidualstresscouldbe,thereforeleadingtohigheryield
strength.Usually,low-temperatureannealingcaneffective-
lyreduceresidualstressinas-castBMGs[24].Toconfirm
iftheresidualstressinducedbyfastcoolingratesisalso
responsibleforthehighyieldingstrengthobservedexperi-
mentally,annealingofthe2mm,as-castrodsampleatthe
temperature50Kbelowtheglasstransitiontemperaturefor
30minuteswasconducted.Thecorrespondingcompressive
stress-straincurveisshowninFigure5,ascomparedtothat
oftheas-castrod.Normally,low-temperatureannealing
embrittlesBMGsduetotheannihilationoffreevolume,but
contrarytothiscommonknowledge,theyieldstrengthof
the2mm,as-castTi-basedBMGrodslightlydecreasesaf-
terannealing,althoughtheplasticityisindeedreduced.In
otherwords,theyieldstrengthoftheseTi-basedsamples
preparedwithdifferentcoolingratesafterannealingisclos-
ertothepredictedvaluefromtheirT
g
usingeq.(1),imply-
ingthatdifferentstatesoftheresidualstressinducedby
differentcoolingratesalsoplayaroleintheobserveddis-
crepancyoftheyieldingstrengthinthepresentTi-based
BMG,whichisfurtherconfirmedinourrecentwork[25].
398XIAOYueHua,etal.SciChinaPhysMechAstronMarch(2010)Vol.53No.3
Figure5Compressivestress-straincurvefortheannealedsamplewitha
castingdiameterof2mmincomparisonwiththatoftheas-castspecimen.
4Conclusions
Insummary,cooling-rateeffectsonmechanicalproperties
ofaTi-basedBMGhavebeenthoroughlyinvestigatedby
speciallydesignedexperiments.Fastercoolingratesin-
creasenotonlythecompressiveplasticitybutalsotheyield
strength.Largeramountoffrozen-infreevolumeduetothe
fastercoolingratesshouldberesponsibleforthelarger
plasticity,whilsthigherglasstransitiontemperatureisasso-
ciatedwiththehigheryieldstrengthofthesamplesfabri-
catedathighercoolingrates.Inaddition,residualstress
generatedfromtherapid-quenchingprocessproperlyalso
affectsthemechanicalpropertiesofBMGs.Thepresent
studysuggeststhatcooling-rateeffectsondeformationbe-
haviorofBMGsarecomplexthatfurtherin-depthinvesti-
gationsareneeded.
ThisworkwassupportedbytheNationalNaturalScienceFoundationof
China(GrantNo.50725104),theNationalBasicResearchProgramof
China(GrantNo.2007CB613903)andtheProgramofIntroducingTalents
ofDisciplinetoUniversities(GrantNo.B07003).
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