metallic
Hui,
20
25
Thee?ectsofdrawingonthestructureandmechanicalpropertiesofaCo-basedmetallicglassundertensionwerethoroughlyinves-
tigated.Surfacechangesinducedbydrawing,includingremovalofsurfaceflaws,surfacechemicalhomogenizationandgenerationof
duetotheirintriguingpropertiesincludinghighstrength
capability,BMGshavegreatpotentialasmaterialfor
small-sizedcomponents,inparticularformicro-electro-
mechanicalsystems(MEMS)[4–6].
hausene?ect[11]andMatteuccie?ect[12]—andthese
understandingthedeformationmechanismsofBMGs.
Frombothtechnologicalandscientificpointsofview,
therefore,itisofgreatimportancetoinvestigatethe
mechanicalpropertiesandthereliabilityofBMGsamples
atsmallscales,suchasglassywires,aswehavedonein
thecurrentstudy.
Correspondingauthor.Fax:+861062332508.
E-mailaddress:luzp@ustb.edu.cn(Z.P.Lu).
Availableonlineatwww.sciencedirect.com
ActaMaterialia58(2010)2564–2576
andelasticitycombinedwithhighcorrosionresistance[1–
3].AbovetheglasstransitiontemperatureT
g
inthesuper-
cooledliquidregime,BMGsusuallyremainstableagainst
crystallizationandsoftenintoaviscousliquid,whichmake
themmalleablelikeathermosettingpolymer.Moreimpor-
tantly,BMGsalwaysshowlowshrinkageduringsolidifica-
tionduetothenatureoftheirrandomatomicpacking,
whichpermitsmoldingofintricate,nearnet-shapedparts
withmicroscaleprecisionandsmoothsurfaces[4–6].
Therefore,duetotheirexcellentnet-shapefabrication
havebeenemployedinsomeMEMSapplications.How-
ever,variousissuesregardingapplicationsofMGsas
MEMShaveyettobesolved,suchasflawtolerances(i.e.
thereliabilityunderloading).Inaddition,itwasfoundthat
MGsatsmallsamplesizesexhibiteddi?erentdeformation
behaviorascomparedwiththebulk-sizedones[13–20].
Homogeneousdeformationhasbeenreportedinnano-
sizedspecimensofZr-andPd-basedBMGs[19,20]and
micro-sizedMg-basedglassywires[21].Systematicstudies
ofthesizee?ectswoulddefinitelyshednewinsightsinto
compressiveresidualstresstendtoincreasethefracturestrength,whilstopenvolumescreatedduringdrawing,particularlynano-voids,
arelikelytosoftenthewires.Initially,thesurfacechangesaredecisivefactors,butasdrawingproceeds,theopenvolumesgradually
becomedominant,yieldingamaximumfracturestrengthinthewireswithanareareductionratioof22%.Moreover,itwasfoundthat
thefracturestrengthreliabilitywasenhancedbythedrawing,whichisduenotonlytothesurfaceperfectionbutalsototheincreaseof
plasticdeformationcapability,manifestedbythedecreaseintheactivationenergyofindividualsheartransformationzones.Ourresults
implythatthedrawingtechniquecouldbeapromisingapproachtocontinuouslyproducingsmall-sizedglassywireswithimprovedover-
allproperties.
C2112009ActaMaterialiaInc.PublishedbyElsevierLtd.Allrightsreserved.
Keywords:Metallicglasses;Drawing;Tensiontest;Strengthreliability
1.Introduction
Bulkmetallicglasses(BMGs)areofcommercialinterest
Metallicglassesatsmallsamplesizeshavedemonstrated
excellentmagneticproperties—e.g.giantmagnetoimped-
ancee?ect[7,8],giantstress-impedance[9,10],largeBark-
E?ectsofdrawingonthetensilefracture
ofsmall-sized
Y.Wu,H.H.Wu,X.D.
StateKeyLaboratoryforAdvancedMetalsandMaterials,University
Received3October2009;receivedinrevisedform
Availableonline
Abstract
1359-6454/$36.00C2112009ActaMaterialiaInc.PublishedbyElsevierLtd.All
doi:10.1016/j.actamat.2009.12.043
strengthanditsreliability
glasses
G.L.Chen,Z.P.Lu
ofScienceandTechnologyBeijing,Beijing100083,China
December2009;accepted22December2009
January2010
www.elsevier.com/locate/actamat
rightsreserved.
ibrateandmeasurethestrainduringloading,andaspecial
grip(seeFig.1b)wasdesignedtoensureproperspecimen
alignment.Nano-indentationexperimentswereconducted
withaMTSDCMnano-indentationsystematvarious
loadingratesrangingfrom8C210
C03
to2C210
C01
s
C01
.Each
datapointwasanaveragefromninetestssothatartifacts
canbeminimized.Positronannihilationlifetimespectros-
copy(PALS)measurementsofthewirespecimenswere
performedusingafast–slowcoincidentmethodanda
22Napositronsourcesandwichedbetweentwo
10C210mmglassplates.Theas-castanddrawnwireswere
preparedandthenlineduponeafteranothercloselyonthe
twoglassplatesforthePALSanalysis.Stressdistribution
inducedbydrawingaftereachstepwascharacterizedby
thefiniteelementmethod(Ansyssoftware).Numericalcal-
culationsabouttheactivationenergyofsheartransforma-
tionzones(STZs)wereperformedintheMatLabprogram.
High-resolutiontransmissionelectronmicroscopy
(HRTEM)specimenswerepreparedbyionmillingunder
liquidnitrogenandtheHRTEMobservationwascon-
ductedonaJEM2010Fwithafieldemissiongun,operated
atavoltageof200kV.HRTEMimageswereobtainedwith
thesameconditionsasreportedbyLiandcoauthors
[30,31],i.e.adefocusvalueof–200nm,toensurethesame
contrasttransferfunction(CTF)fortheas-castanddrawn
wires.Imageanalysiswascarriedoutusingthesoftware
DigitalMicrograph3.5.2ofGatanInc.
Recently,variouspre-treatmentmethodshavebeenver-
ifiedtobee?ectiveinimprovingmechanicalpropertiesof
MGs.RemarkablecompressiveplasticityofseveralZr-
basedBMGshasbeenachievedbycold-rolling[22],surface
shot-peening[23],high-pressureprocessing[24],surface
mechanicalattritiontreatment[25]andotherpre-straining
methods[26].However,thesepre-treatmenttechniques
wereusuallyappliedtolarge-sizedZr-basedBMGsamples
andonlytheire?ectsoncompressivepropertieswere
reported.Drawingisaproductivewaytoproducemicrom-
eter-sizedwiresandwasverifiedtohaveremarkablee?ects
onthemagneticandmechanicalpropertiesofMGs[27,28].
Unfortunately,therelatedmechanismshavenotbeen
clearlyrevealeduntilnow.TofacilitatetheuseofMGs
assmall-sizedcomponentsandprovideacontinuouspre-
treatmenttechnique,thee?ectsofdrawingonthestructure
andtensilepropertiesofMGsmeritfurtherinvestigation.
Inthispaper,weselectaCo-basedMGasanexampleto
thoroughlyinvestigatethee?ectsofwiredrawingonthe
structureandmechanicalproperties.Specificattention
waspaidtothedrawinge?ectsonthefracturestrength
anditsreliability,andunderstandingoftheunderlying
mechanisms.
2.Experimental
Masteralloyswithanominalcompositionof
Co
69.5
Fe
4.5
Cr
1
Si
8
B
17
(inat.%)werefabricatedbyinduc-
tion-meltingamixtureofrawelementshavingapuritylevel
above99.99%.Amorphouswireswithadiameterof125lm
wereproducedbythein-rotating-waterquenchingtechnique
usingthemasteralloys[29];themasteralloysweremelted
usingargonaspurginggasinaquartztubeandthenejected
totherotatingcoolingwaterinanairatmosphere.Noseri-
ousoxidationwasobservedduetotherapidsolidification
andrelativelygoodoxidationresistanceofthechosenCo-
basedalloy.As-quenchedamorphouswiresweredrawn
throughmultiplediamonddieswith2–3lmreductionin
diameterperstepatroomtemperature.Aschematicillustra-
tionofthediamonddiesispresentedinFig.1.
Theamorphousnatureoftheas-quenchedanddrawn
wireswasexaminedbyX-raydi?raction(XRD)usingCu
K
a
radiation.Thermalpropertieswereanalyzedbydi?er-
entialscanningcalorimetry(DSC)(NetzschSTA449C)at
aheatingrateof20Kmin
C01
.Anelectronprobemicro-
analysis(EPMA)(JEOLJXA-8100)wasusedtoinspect
theelementaldistributiononcross-sectionsofthewires.
Priortomechanicaltests,theas-castanddrawnwireswere
observedbyscanningelectronmicroscopy(SEM,
SUPRAe55)toverifytheintegrityofthecircumference,
andonlythoseamorphouswireswithgoodroundness
andnolargecastingdefectsand/orotherimperfections
werechosenfortensiletesting.Theactualwirediameters
werealsomeasuredbySEM.
TensionexperimentswereconductedonanInstron5848
Y.Wuetal./ActaMaterialia
micro-testerwithagaugelengthofC2410mmandastrain
rateof2C210
C04
s
C01
.Asmallstraingaugewasusedtocal-
(a)
(b)
(1)-30ConeAngle
(2)-16-18SecondaryAngle
(3)-20-30%BearingLength
(4)-30ReliefAngle
(1)(2)(3)(4)
Fig.1.Schematicillustrationofthediamonddie(a),andthegripforthe
wiretensiletesting(b).
58(2010)2564–25762565
Inordertocharacterizelocalizedorderingoftheas-
quenchedanddrawnglassywires,aprocessnamedauto-
correlationfunction(ACF)wasappliedfortheobtained
HRTEMimages.TheACFtreatmenthasbeenconsidered
asastatisticalinterpretationofHRTEMimages,often
appliedtothequantitativeestimationofthedegreeof
orderinginnon-periodicobjects[32,33].
Tocharacterizenano-scalevoidsinourspecimens,a
methoddevelopedbyMillerandGibson[34],andlater
extendedbyLiandcoauthors[30,31],wasusedinthepres-
entstudy.Inthismethod,thekeyistoidentifydensityfluc-
tuationsonHRTEMimagesanddeterminethelocations
withstatisticallysignificantlylowerdensitiesthantheaver-
age,whichcanbereferredtoasnano-voidsaccordingto
theauthors[30,31,34].
3.Results
3.1.Drawinge?ectsonthewirestructureandlateralsurfaces
Comparisonofthelateralsurfacesbetweentheas-
quenchedanddrawnwiresisshowninFig.2a.Allofthe
as-quenchedanddrawnwiresshowagooduniformityin
shape.However,flawscanbeseenoccasionallyonthesur-
faceoftheas-quenchedwires,whichwereformedduring
thefabricationprocessinairatmosphereduetoimpurities
and/oroxides.Duringthedrawingprocess,theflawswere
removedandthedrawnwiresshowalmostflawlesssurface,
asillustratedinFig.2a.Theamorphousnatureoftheas-
2566Y.Wuetal./ActaMaterialia
quenchedanddrawnwiresisascertainedbytheX-raydif-
30405060708090100
R=82%
R=71%
R=58%
R=41%
RelativeIntensity,a.u.
2θ,degree
as-cast
R=22%
(b)
(a)
Fig.2.SEMimagesoflateralsurfacesoftheas-castanddrawn
amorphouswires(a),and(b)X-raydi?ractionpatternsoftheas-
quenchedanddrawnamorphouswires(Ristheareareductionratio).
InsetistheTEMimageanditsSAEDdi?ractionpatternofthedrawn
wireswithR=82%.
fractionandTEMimageshowninFig.2b.Onlyabroad
di?usepeakwithoutanyevidenceofcrystallinephasesis
seenforallthesamples,indicatingthatthesewiresare
mostlyamorphous.TheTEMimageandthecorrespond-
ingselected-areaelectrondi?raction(SAED)pattern
shownintheinsetofFig.2bfurtherconfirmnooccurrence
ofanycrystallizationeventeveninthewiredrawntothe
largestareareduction,i.e.R=82%.
Itwasarguedthatmechanicaldeformationcouldinflu-
encetheatomicstructuresatsmallscalessuchasstress-
inducedlocalizedordering[35,36].Tofurtherverify
whetherlocalizedordering(atthelengthscaleof1–2nm
butwithoutaclearinterfacewiththeamorphousmatrix
[37])hasoccurredduringthedrawing,theACFtechnique,
whichiscapableforaquantitativemeasurementofthe
extentoflocalizedordering,hasbeenappliedtoelectron
microscopeimageanalysis.HRTEMimagesoftheas-cast
anddrawnsampleswithR=22%and82%wereshownin
Fig.3a,c,ande,respectively.Toconductlocalizedorder-
inganalysis,theHRTEMimagesweredividedinto64sub-
images,eachofwhichhasadimensionof
1.895C21.895nm
2
.Onesub-imagewithcoordinates(1,4)
inFig.3b,whichshowssomeclearcrystal-likedi?raction
spotsinitsfastFouriertransformation(FFT)pattern
(notshown),waschosenasareferencepatterntodepict
thelocalizedorderinginthisstudy.Allthesub-images
whoseatomicarrangementsexhibitaclearerfringethan
thereferencepatternwereconsideredasbeingordered.
Statisticalanalysisofallthesub-imagesinFig.3b,d,and
frevealsthecontentsoflocalizedorderingonthescaleof
1–2nminthethreewiresare12.5%,10.9%,and14.1%,
respectively.Thereisnoobviousdi?erenceofthelocalized
orderingbetweentheas-castanddrawnwires,thusthepos-
sibleinfluenceofthelocalizedorderinginducedbydefor-
mationonthefracturestrengthcanberuledout.
3.2.Drawinge?ectsonthechemicalandmicro-mechanical
homogenization
Detailedelementalanalysesoncompositionfluctuation
fromthecircumferencetothecenteronthecross-section
oftheas-quenchedanddrawnamorphouswiresareshown
inFig.4.Fortheas-quenchedsample(Fig.4a),theconcen-
trationsofCoandBremainroughlyconstantfromthesur-
facetocenter,whilsttheFeconcentrationdecreases
graduallyfromthesurfacetoadepthofC247.5lmandthen
remainsconstantatitsnominallevelof4.5%.Incontrastto
theFedistribution,siliconisdepletedonthesurfacebut
graduallyincreasestoitsdopinglevelof8%atasimilar
depthof7.5lm.AccordingtoLiuetal.,thecompositional
inhomogeneitynearthesurfaceoftheas-quenchedamor-
phouswirecanbeattributedtotheSorete?ectinduced
bytemperaturegradientduringcooling[38].Afterfurther
drawingtoanareareductionlargerthan22%,i.e.more
than7.5lmreductioninradius,alltheconstituentele-
58(2010)2564–2576
mentsshowahomogeneouscompositiondistribution
alongtheradius,asshowninFig.4bandc.
Y.Wuetal./ActaMaterialia
Nano-indentationexperimentswerecarriedouttochar-
acterizemicro-mechanicalpropertiesofthedrawnamor-
phouswires.Fig.5illustratesthehardnessdi?erence
betweenthecenterandsurfaceofthedrawnwireswithdif-
ferentareareductionratiosmeasuredatthesameloading
rateof5C210
C02
s
C01
.Itcanbeseenthatthehardnessdi?er-
encebetweenthesurfaceandcenterdecreasesmonotoni-
Fig.3.HRTEMimagesoftheas-cast(a)anddrawnamorphouswireswith
images(b),(d),and(f).
58(2010)2564–25762567
callywiththeincreaseoftheareareductionratio,
indicatinganincreasedhomogeneityinthemicro-struc-
ture.Similarly,di?erenceoftheelasticmodulusbetween
thesurfaceandcenteralsodiminisheswithdrawing.Thus,
itcanbeinferredthatthemicro-structureinthewires
becamemoreandmorehomogeneousasthedrawingpro-
cessproceeds.
R=22%(c),andR=82%(e),respectively,andthecorrespondingACF
70
72
Co
2568Y.Wuetal./ActaMaterialia
3.3.Drawinge?ectsonthemacroscopictensilefracture
strength
Thestress–straincurvesforthewireswithR=0%,22%,
and82%areshowninFig.6a,b,andc,respectively.For
010203040506070
15
18
21
B
Distancefromsurface,μm
7.5
8.0
8.5Si
4.2
4.5
4.8
Fe
concentration,%
0102030405060
15
18
21
B
concentration,%
Distancefromsurface,μm
7.5
8.0
8.5Si
4.2
4.5
4.8
Fe
70
72
Co
(b)
(a)
-50510152025303540
15
18
21
B
concentration,%
7.5
8.0
8.5Si
4.2
4.5
4.8
Fe
70
72
Co
Distancefromsurface,μm
(c)
Fig.4.Elementaldistributionfromthesurfacetocenterfortheas-cast
amorphouswire(a),thedrawnwireswithR=22%(b),andR=82%(c).
eachsize,morethan20tensiletestswerecarriedout.All
thetensilestress–straincurvesshowatypicalnon-linear
deformationbehaviorafterapparentyielding[39,14,17],
whichmaybeduetotheformationofnano-metervoids
fromcoalescenceoffreevolume[40].Asshownin
Fig.6a,theapparentfracturestrengthoftheas-quenched
amorphouswirerangesfrom2816to3228MPa,witha
variationof412MPa(i.e.thedi?erencebetweenthemax-
imumandtheminimumstrength).Thefracturestrength
rangesfrom3430to3740MPawithavariationof
310MPaforthedrawnwirewithR=22%,whilstthewires
withthelargestareareduction(R=82%)showafracture
strengthbetween2996and3260MPa,withavariationof
264MPa.Theaveragefracturestrengthr
f
asafunction
ofthereductionratioRisshowninFig.6d.Ascanbeseen,
thefracturestrengthr
f
increaseswithRinitially,reachesa
maximumaroundR=22%,andthendecreaseswithfur-
therincreaseofR.Theoriginsofthefracturestrength
dependenceontheareareductionratiowillbediscussed
020406080
0.0
0.5
1.0
1.5
2.0
HDifference,
GPa
AreaReduction,%
10
20
30
EDifference,
GPa
Fig.5.Micro-mechanicalpropertydi?erencebetweenthesurfaceand
centeronthecross-sectionsoftheamorphouswiresasafunctionofarea
reductionratioR.
58(2010)2564–2576
lateron.
3.4.Drawinge?ectsonthetensilefracturestrength
reliability
Weibullstatisticalanalysishasbeenintroducedtochar-
acterizethestrengthreliabilityofMGs[17,19,41].TheWei-
bullequationusuallyusedtoplottheWeibullmodulusisin
thedoublelogarithmicform:
lnfln?1=e1C0P
f
TC138g?lnVtmlnrC0mlnr
0
;e1T
wheremistheWeibullmodulusthatrepresentsthe
strengthreliability,r
0
isascalingparameter,Visthevol-
umeofthetestedsample,P
f
isthefractureprobabilityat
agivenuniaxialstress,andcanbecalculatedusingthe
equation:P
f,i
=(iC00.5)/n,wherenisthetotalnumberof
thesamplestestedandiisthesamplerankinginascending
orderoffailurestress.
Fig.7ashowstheWeibullplotsinthefashionsuggested
byEq.(1)fortheas-quenchedandthedrawnwireswith
0
1000
2000
3000
4000
Stress,MPa
Strain
as-cast
2%
1000
2000
3000
4000
2%
Stress,MPa
R=22%
(a)
(b)
Y.Wuetal./ActaMaterialia
R=22%and82%.Alinearcorrelationbetweenlnln[1/
(1C0P
f
)]andlnrisobtainedforallthethreetypesof
wires,andthelinearleast-squaresfittingwithEq.(1)to
theseexperimentaldatayieldstheWeibullmodulusmas
31.7fortheas-quenchedamorphouswires,51.0and57.1
forthedrawnwireswithR=22%and82%,respectively.
TheWeibullmodulus,m,actuallyreflectsreliabilityof
thetestedsamples,andahighermvaluerepresentsanar-
rowerdispersionofthefracturestrengthandthushigher
reliability.Themvaluefortheas-quenchedamorphous
wiresislargerthanthatofbrittleceramics,similartothat
ofFe-basedBMGs[42]andMg-basedBMGs[43],but
smallerthanthatofZr-basedBMGs[44].Itisinteresting
topointoutthatadistinctincreaseofthemvalueoccurs
withdrawing,asdemonstratedinFig.7b,implyingthat
thewiredrawingprocesscouldenhancethereliabilityof
themacroscopictensilestrength.
4.Discussion
4.1.originsforthefracturestrengthdependenceonthewire
drawingprocess
Aselaboratedearlier,noapparentlocalizedordering
andcrystallizationhasoccurredduringthewiredrawing
process,butdefectconcentrationeitheronthesurfaceor
0
Strain
Fig.6.Tensilestress–straincurvesfortheamorphouswireswithdi?erent
Dependenceofthefracturestrengthoftheas-quenchedanddrawnamorphou
0
1000
2000
3000
Stress,MPa
Strain
2%
R=82%
(c)
(d)
3000
3300
3600
σ
f
(MPa)
58(2010)2564–25762569
insidethewires,freevolumecontentsandsurfaceresidual
stressofMGwirescouldbechanged,whichallinfluence
thefinalfracturestrength.Normally,fewerdefectsand
largecompressivesurfaceresidualstressarelikelyto
increasethefracturestrengthwhilemorefreevolumetends
tosoftenMGwires.
4.1.1.E?ectsofsurfacestatesonthefracturestrength
First,ithasbeenverifiedthatsurfacedefectshavesignif-
icantinfluencesontheplasticityandstrengthofMGs;sur-
facedefectswitharadiusassmallas1nmcouldtrigger
rapidfailure[45].Fig.2ashowsrandomlydistributedsur-
facedefectsonthevirginwireresultingfromthein-rotat-
ing-waterquenchingprocess,whichcouldinitiatecracks
undertensionandthusreducethetensilestrengthofthe
wires.Afterthesurfaceflawswereremovedbywiredraw-
ing,theaveragefracturestrengthshouldbeincreased.In
addition,itiswellknownthatthefractureofbrittleengi-
neeringmaterialsdependsonthestressnecessarytoprop-
agateacritical-sized“weakestlink”anywhereinthe
samples.Asthedrawingprocessproceeds,theinhomoge-
neouselementaldistributionhasbeeneliminated(Fig.4),
andthedi?erenceofmicro-mechanicalpropertiesbetween
thesurfaceandcenterisdiminished(Fig.5),indicatingthat
“weakestlinks”becamefewerinthesamples[20],andthe
appliedstresscanbedistributedmorehomogeneouslywith
020406080
AreaReduction,%
areareductions:(a)R=0(as-cast),(b)R=22%,and(c)R=82%.(d)
swiresontheareareductionratioR.
(a)
7.98.08.18.28.3
-6
-4
-2
0
2
R=82%
m=57.1
R=22%
m=51.0
lnln(1/1-P
i
)
ln[σ
f
(MPa)]
as-quenced
m=31.7
40
50
60
(b)
2570Y.Wuetal./ActaMaterialia
fewerstressconcentrationsites,whichcanalsoresultina
higherfracturestrength.
Second,surfaceresidualstresschangecouldbeanother
factorwhichaltersthefracturestrength.Toinvestigate
e?ectsoftheresidualstressofthedrawnamorphouswires
aftereachdrawingstep,afiniteelementanalysis(FEA)was
conductedinanAnsyssoftware.Fig.8ashowstheconsti-
tutedmodelsystemforthedrawingprocess,andFig.8b
showsarepresentativeVonMisesstressdistributionon
thecross-sectionofthedrawnamorphouswire.Itiseasily
seenthattheamorphouswireexperiencedloadingand
unloadingofacompressivestressalongtheradiusdirec-
tionduringeachdrawingstep.Whentheamorphouswire
wasdrawnoutofthediamonddie,residualstresseswere
leftupontheunloadingofthecompressivestressalong
theradiusdirection.Forsimplicity,theresidualstresson
thesurfaceoftheas-castamorphouswireswastakento
bezero,andthenthechangeofthesurfaceresidualstress
asafunctionoftheareareductionratioisinafashion
showninFig.8c.Thecompressivesurfaceresidualstress
increasesinitiallyandreachesamaximumvalueabout
40MPaaroundR=25%,decreaseswithfurtherdrawing,
andeventuallyturnsintotensileresidualstressafter60%
areareduction.Ithasbeenpointedoutthatthecompres-
020406080
30
Weibullmodulus
AreaReduction,%
Fig.7.Weibullplotsofthetensilefracturestrengthfortheas-castand
drawnwireswithR=22%and82%(a),and(b)theWeibullmodulusasa
functionoftheareareductionratiofortheas-castanddrawnamorphous
wires.
sivesurfaceresidualstressisbeneficialwhilethetensile
residualstressisdetrimentalfortheincreaseofhardness
andstrength[11,46,47].Thecompressiveresidualstress
onthesurfacehasasimilartrendtothatofthefracture
strengthshowninFig.6d,suggestingthatitcouldbea
dominantfactora?ectingthefracturebehaviorofthe
drawnwires.
4.1.2.Evolutionofopenvolumesduringdrawing
Itisalsooftenconsideredthatmechanicalpropertiesof
BMGsarecloselyassociatedwithflowdefectswhichhavea
goodcorrelationwithenthalpychangebeforeglasstransi-
tioninDSCmeasurements[48].Toassesstheinfluenceof
drawingonflowdefectsevolution,DSCmeasurements
werecarriedoutforamorphouswireswithR=0%,22%,
and82%.AsshowninFig.9,allwiresexhibitsimilarther-
malbehaviorwithnosignofanyglasstransitionprocess
butaverysimilarcrystallizationevent.Thedisappearance
ofglasstransitioneventisdueprobablytothefactthatit
occurredtoocloselywiththecrystallizationandwascov-
eredbythestrongsignalfromthelaterreaction[49].How-
ever,theexothermicsignalsbeforethecrystallizationin
DSCcurvesaredi?erentamongthesesamples,asclearly
indicatedinFig.9b.Theexothermicsignalsusuallycorre-
spondtotheenthalpyreleaseduetostructurerelaxationof
theamorphousstructure,whichisproportionaltothe
amountofexcessflowdefectscontainedintheamorphous
alloy[48].Thereisonlynegligibleexothermicsignalforthe
as-castwireandaslightincreaseforthedrawnwirewith
R=22%,buttheheavilydrawnwirewithR=82%shows
anobviousexothermicenthalpyofabout3.3Jg
C01
,indicat-
ingthatconsiderableamountofflowdefectshavebeencre-
atedandstoredinthiswires.Thecreatedflowdefectslead
toalessdenselypackedstructureandweakera?nity
betweenatoms,andthereforeadecreaseinhardness,elas-
ticmodulus,andfracturestrength.
Ithasbeenverifiedthatsizesof“openvolumedefects”
inBMGsrangedfromthesubatomiclengthscaleto
nano-meterscale.Floresetal.havecategorizedtheseopen
spacesintothreecategories[50,51],i.e.interstitialholes,
flowdefects,andnano-metervoids.Thethreetypesof
theopenvolumesplayimportantrolesindeformation
behaviorsofBMGs[40].Toexploreevolutionoftheopen
volumesduringdrawing,wefirstadoptedthequantitative
HRTEManalysismethoddevelopedbyMillerandGibson
[34]andlaterextendedbyLietal.[30]andJiangandAtz-
mon[31],toidentifynano-meterscaledefectsintheas-cast
anddrawnamorphouswires.Fig.10a–cshowsthecon-
vertedimagescorrespondingtoFig.8a,c,ande,respec-
tively.Thesmalldarkspotsintheimagesrepresentnano-
metervoidsassuggestedbyMillerandcoauthors
[30,31,34].Byanalyzingthecontrastfromtheseimages
usingcomputersoftware,theareafractionofthenano-
voidsshowninFig.10isestimatedtobe0.49%,0.58%
and1.29%fortheas-castanddrawnwireswithR=22%
58(2010)2564–2576
and82%,respectively.Apparently,thereisnosignificant
changeinthenumberofnano-voidsduringtheinitial
(a)
Y.Wuetal./ActaMaterialia
drawingstage(R=22%),whilstanappreciableincrease
canbeobservedforthewireheavilydrawntoR=82%.
Tofurthercharacterizetheevolutionoftheopenvolumes
aftertheheavydrawing,PALSmeasurementswerecon-
ductedfortheas-castandheavilydrawnamorphouswires
withR=82%,andthecorrespondingresultsaregivenin
(b)
(c)
0204
-20
0
20
40
AreaReduction
Compressiveresidualstress,MPa
Fig.8.(a)Finiteelementmodelusedfornumericalcalculation,(b)VonMises
drawnamorphouswires,and(c)variationofthesurfaceresidualstresswiththe
58(2010)2564–25762571
Fig.11.Followingdetailedexplanationso?eredbyFlores
etal.[50],theshortlifetimes
1
ands
2
areattributedtoposi-
tronannihilationininterstitialholesofthedenselypacked
bulkandflowdefectsofthealloy,respectively,whilstthelon-
gestlifetimes
3
isassociatedwiththeannihilationinnano-
metervoids.Asshown,thethreelifetimecomponents
06080
-FEAsimulation
,%
ο
stressdistributionafterdrawingtoR=22%asarepresentationforthe
areareductionratioR.Thelineistoguidetheeyes.
4006008001000
R=82%
R=22%
as-cast
exothermic,a.u.
Temperature,K
(a)
(b)
2572Y.Wuetal./ActaMaterialia
increaseafterheavydrawing,indicatingthatactualsizesof
allthetypesoftheopenvolumedefectsaredilated,which
isincontrasttowhathasbeenobservedinrollingofmetallic
glasses[50].Thenormalizedintensitiesareindicativeofthe
relativeconcentrationofeachpositrontrap.Afterheavy
drawing,thes
1
intensitycorrespondingtothenumberof
interstitialholesandthes
2
intensityassociatedwiththecon-
centrationofflowdefectsslightlydecrease,whilethes
3
inten-
sitycorrespondingtothenumberofnano-metervoidsis
surprisinglyincreasedfrom1.3%to6.8%.Therefore,itseems
thatsomeofflowdefectsconglomeratetogetherduringthe
heavilydrawingandformthenano-metervoids.Ourpresent
resultssuggestthatthereexisttwocompetingmechanisms
fortheopenvolumeevolutionduringtheheavydrawing:
freevolumecreationthroughdeformationandfreevolume
coalescenceandthenano-voidformation,whichisconsis-
tentwithpreviousreports[52].
Therefore,onecanspeculatedthatthetensilefracture
strengthofthedrawnwiresisdeterminedbythecom-
binede?ectsoftheseveralfactors.Thefirsttypeoffac-
torsisbeneficialfortheincreaseofthefracture
strength,includingremovalofsurfaceflaws,surface
600700800
R=82%
R=22%
as-cast
exothermic,a.u.
Temperature,K
Fig.9.DSCcurvesoftheas-castanddrawnwireswithR=22%and82%
(a),and(b)istheblow-upcorrespondingtothecircledareain(a).
58(2010)2564–2576
homogenizationandthegenerationofthecompressive
residualstresses.Thesecondtypeoffactorstendsto
softenthewiresbecauseofalooseratomicpackingstruc-
tureand/orweakeratomica?nityresultingfromthefree
volumeandnano-voidscreatedduringmultiple-steps
drawing.DuringtheinitialdrawingtoaroundR=22%,
thefirsttypeoffactorsisdecisive,leadingtotheincrease
inthefracturestrength.Asthedrawingproceeds,the
compressiveresidualstressonthesurfacestartsto
decreaseandmoreandmoreopenvolumeswerecreated,
theincreaseofthetotalopenvolumesbecamedominant,
leadingtothedecreaseinthefracturestrength.
Fig.10.Fourier-filtered,thresholdfilteredandinvertedimagesthat
correspondtoFig.8(a),(b),and(c),respectively.Thedarkspotsrepresent
nano-voids.
0.0
0.7
1.4
2.1
τ3τ2
Lifetime,ns
Defecttype
as-cast
R=82%
τ1
80
(a)
Y.Wuetal./ActaMaterialia
4.2.Mechanismsfortheenhancedfracturestrength
reliability
4.2.1.Surfaceperfection
Asmentionedearlier,fractureofbrittlematerialsusu-
allyinitiatesfromthe“weakestposition”anywhereinthe
material.Theweakpositionssuchaschemicalimpurities
andsurfacedefectscouldbethestressconcentrationsites
andmaytriggerrapidfailureofBMGsundertension
[45].Inotherwords,therandomlydistributedsurfaceflaws
andthemacro-scalechemicalandmechanicalinhomogene-
ityoftheas-castamorphouswireswouldincreaseuncer-
taintyofthefracturestrengthandthereforereducethe
Weibullmodulusoftheas-castwires.Whenthesurface
flawsandthemacro-scaleinhomogeneitywereremoved
bysubsequentdrawing,thetensilereliabilityisincreased
consequentlyforthedrawnamorphouswires.Neverthe-
less,itisworthnotingthattheWeibullmoduluskeeps
increasingafterthesurfacehomogenizationandremoval
ofsurfaceflaws(i.e.R>22%),asshowninFig.7b,which
0
20
40
60
Intensity,%
as-cast
R=82%
Ι3Ι2
Defectstype
Ι1
(b)
Fig.11.Positronannihilationspectrumoftheas-castanddrawnwires
withR=82%.Lifetimecomponents(a)thatreflectsizes,andintensities
(b)thatrepresenttherelativeconcentrationofthethreetypesoftheopen
volumes.
impliesthattherearesomeotherfactorsa?ectingthe
strengthreliabilityduringdrawing.
4.2.2.Activationenergyofsheartransformationzones
PlasticdeformationofBMGsatroomtemperatureis
usuallyknowntobeachievedbysheardeformation.Local
eventsofcooperativeshearingofatomicclusterstermedas
STZs[53]arethebasicunitoftheplasticdeformationand
mechanicalbehaviorofBMGs,andmacroscopicdeforma-
tionbehaviorofBMGsisintrinsicallydependentonthe
actualactivationenergyofSTZs.Basedonmechanical
instabilityofindividualSTZs,aquantitativelinkbetween
themicro-plasticinstabilityandmacroscopicdeformation
ofMGshasbeenproposed[54].Inthisapproach,metallic
glasseswereregardedasanensembleofnumerousSTZ
embryoswhichcanbepossiblyactivatedtotakeplastic
sheareventswithfiniteactivationenergy.Duetothelack
ofperiodicstructureinMGs,therandomenergymodel
isadoptedwhichdescribestheenergylevelsinadisordered
systemasindependentrandomvariables.Thepopulation
ofSTZswithdi?erentactivationenergyvfortheoccur-
renceofplasticinstabilityisassumedtofollowthequasi-
Gaussiandistribution[55]:
pevT?
p
0
expC0
evC0VT
2R
2
hi
evP0T
0ev<0T
()
;e2T
whereVistheapparentaverageactivationenergyofthe
sample,Risthestandarddeviationofactivationenergies,
andp
0
isapre-factor.Basedontheanalysisofstrainen-
ergydensityandtheClausius–Duheminequality,a
stress–strainrelationshipcanbeobtainedas:
retT?Ee1C0/etTTfeeetTC0e
p
etTTC0
Z
1
0
pevTCevTdv
Z
t
0
C2exp?C0CevTetC0sTC138eeesTC0e
p
esTTdsg;e3T
whereretT;eetTande
p
etTarethestress,totalstrainandplas-
ticstrainatadeformationtimet,respectively.u(t)isa
functionusedtodescribethestrainraterelationshipbe-
tweentheplasticandtotaldeformation.C(v)istheactiva-
tionratefunctionofSTZs,andsisarandomtimethat
se[0,t].FromEq.(3),thenormalizedstressduringstress
relaxationcanbeobtainedas:
C22retT?1C0
Z
1
0
pevT?1C0expeC0CevTtTC138dv;e4T
whereC22retT?
retT
r
0
,andr
0
isthestressatthebeginningofthe
relaxation.Henceimportantparametersinthisapproach
canbeestimatedbyfittingtheexperimentaldatawith
Eq.(4).SubstitutingtheseparametersintoEq.(2),distribu-
tionoftheactivationenergyoftheSTZsinthesamplecan
thenbeestimated.Thedetailedtheoreticalanalysisand
mathematicoperationofEq.(3)canbefoundinourearlier
paper[54].
Stressrelaxationexperimentswereconductedatapreset
58(2010)2564–25762573
strainof2.5%fortheas-castanddrawnamorphouswires
withR=22%and82%.Thecorrespondingexperimental
paredwiththeas-castone.Thewiresdrawnmoreheavily
containamuchhigherproportionofSTZsthatcanbeeas-
ilyactivatedforplasticdeformationincomparisonwiththe
as-castandlightlydrawnones.Thisobservationimplies
thatthewiredrawingprocessreducedtheenergybarrier
58(2010)2564–2576
0.98
1.00
??experiment
simulation
(a)
2574Y.Wuetal./ActaMaterialia
dataandtheirfittingwithEq.(4)areshowninFig.12aby
solidlinesandtrianglesymbols,respectively.Theresultant
distributioncurvesoftheactivationenergyfortheSTZsin
allthesewiresamplesareshowninFig.12b.Clearly,the
drawnamorphouswirereachestheequilibriumstatemuch
slowerduringtherelaxationtestsandalsoshowsalower
andnarrowerdistributionoftheactivationenergyascom-
forlocalizedshearingeventsandthereforeincreasedthe
plasticdeformationcapabilityofthedrawnamorphous
wires.Theaverageactivationenergyobtainedforeach
individualspecimenisillustratedinTable1.
06001200
0.92
0.94
0.96
R=82%
R=22%
as-cast
σ/
σ
0
time,s
0123
0.000
0.005
0.010
0.015
Possibility
ActivationEnergy,eV
as-cast
R=22%
R=82%
(b)
0.010.1
8
10
12
14
as-cast
R=22%
R=82%
Hardness,GPa
StrainRate,s
-1
m
(c)
Fig.12.(a)Stressrelaxationresponses(solidline)andfittingresults
(trianglesymbol)withEq.(4oftheas-castanddrawnamorphouswires
withR=22%and82%atapresetstrainof2.5%,(b)thederivedquasi-
Gaussiandistributionoftheactivationenergyinthesespecimens,and(c)
dependenceofmicro-hardnessonstrainratesatthemiddleofthecross-
sectionoftheas-castanddrawnwireswithR=22%and82%.
TofurtherinvestigatetheSTZactivationenergyduring
drawing,arecentlydevelopedexperimentalmethod[56,57]
basedonthecooperativeshearmodel[58]wasalsoadopted
tocharacterizetheenergybarrieroftheSTZsintheas-cast
anddrawnamorphouswires.Inthismethod,thekeyisto
determinestrain-ratesensitivity,m,fromtherelationship
betweenstrainrateandmicro-hardnessmeasuredby
meansofnano-indentations.Fig.12cshowsthehardness
valueversusstrainratefortheas-castanddrawnwires
withareareductionratioR=22%and82%.Thestrain-
ratesensitivitycorrespondingtoeachtypeofwireswas
thendeterminedbytheslopeofthelinearregressionline.
Table1alsosummarizestheenergybarriersofSTZsfor
eachwiremeasuredbythenano-indentationmethodin
comparisonwiththeaverageactivationenergydetermined
byourmodeldiscussedearlier.Similartotheresults
obtainedfromthecurrentmethod,theactivationenergy
ofSTZsdeterminedfromthenano-indentationmethod
alsoshowsadecreasetrendwithdrawing,confirmingthat
thewiredrawingprocesscouldenhanceplasticshearing
capability.Itistobenoticedthattheaverageactivation
energyobtainedbyourmodelisinthesameorderbut
somewhatlargerthanthatdeterminedbymolecular
dynamicsimulationbasedonthetheoryofpotentialenergy
landscape[59]andthenano-indentationmethodbasedon
thecooperativeshearmodel.Thisdiscrepancymaybedue
mainlytothefactthatmicro-plasticeventsizesmayscale
withtheoperationalvolume[60–62]involvedinthese
methods.Molecularsimulationisusuallylimitedtorather
simple,one-ortwo-componentatomicsystems,andtypical
indentationsizeisnomorethanseveralmicrons,whichis
farsmallerthanthatinourstressrelaxationmeasurements.
TheaboveanalysisoftheSTZactivationenergyofdif-
ferentwiresverifiesthattheincreaseofthestrengthreli-
abilityisalsoduetotheenhancedplasticdeformation
capabilityresultingfromthedrawingprocess.Decrease
oftheSTZactivationenergysuggeststhattheatomsor
Table1
ActivationenergyofSTZsoftheas-castanddrawnwiresdeterminedfrom
thestressrelaxationandnano-indentationmethods.
SampleAveragedactivation
energyofSTZs
a
(eV)
Strain-rate
sensitivity
STZ
volume
(A
?
3
)
STZenergy
barrier(eV)
As-cast0.750.04468060.57
R=22%0.730.04767930.56
R=82%0.630.07046130.44
a
Fromthepresentmodel.
58(2010)2564–25762575
clustersinthedrawnwirescanbemoreeasilyreshu?ed,
i.e.plasticdeformationcapabilityofthedrawnwires
enhanced,whichisequivalenttoincreasingtheflaw/dam-
agetoleranceandthengivesrisetotheincreaseofthefrac-
turestrengthreliability.Theaforementionedresultsalso
confirmthatthereexistsacorrelationbetweentheplastic
deformationabilityandthefracturestrengthreliability,
whichisusefulfordesigningBMGswithgoodengineering
propertiescombininggoodstrengthreliabilityandlarge
plasticity.
Therefore,itcanbeconcludedthatthefracturestrength
reliabilityisalsoa?ectedbytwoaspects:oneisthesurface
perfectionincludingremovalofthesurfaceflaws,the
macro-scalechemicalandmechanicalhomogenization,
andtheotheristheenhancementoftheplasticdeformation
ability,whichismanifestedbythedecreaseintheSTZacti-
vationenergyintheheavilydrawnwires.
5.Conclusions
Basedonthesystematicstudyofdrawinge?ectsonthe
fracturestrengthandthestrengthreliabilityofthe
Co
69.5
Fe
4.5
Cr
1
Si
8
B
17
amorphouswire,coupledwithcareful
investigationontherelatedmicro-structureandsurface
characteristics,thefollowingconclusionsaredrawn:
1.TheCo-basedwirescanbedrawnsmoothlywithout
appreciablelocalizedorderingandnano-crystallization.
Thedrawingprocessisane?ectivepre-treatmentto
improveboththefracturestrengthanditsreliability,
whichmayhavegreatimplicationsforengineering
applicationsofBMGsatsmallscales.
2.Thefracturestrengthdramaticallyincreasesduringthe
initialdrawingtoanareareductionratioofRC2522%,
andthendecreasesduringfurtherdrawing.Thisis
relatedtotwoaspects.Oneisthesurfacechange,caused
by,forexample,theremovalofsurfaceflaws,surface
homogenization,andcreationofcompressivesurface
residualstress.Thesesurfacechangeshelptoincrease
thefracturestrengthduringtheinitialdrawingstage.
Theotheriscreationofopenvolumes,inparticularfor-
mationofnano-voids,whichleadstoalooseratomic
packingstructureandtendstosoftenthewires.The
increaseintheopenvolumesbecameadominantfactor
duringfurtherdrawingwithR>22%andreducesthe
fracturestrength.
3.Thefracturestrengthreliability,reflectedbytheWeibull
modulus,increasesasthedrawingprocessproceeds.
Thisisduetotwofacts.Oneistheimprovementin
thesurface,causedby,forexample,removalofsurface
defectsandreductioninlocalizedstressconcentration
sitesduetochemicalandmicroscopicmechanical
homogenization,whichreducestheprobabilityoffind-
ingafertilesiteforfracture,andthereforeincreases
thefracturestrengthreliability.Theotheristheincrease
Y.Wuetal./ActaMaterialia
intheplasticdeformationcapability,manifestedbythe
decreaseintheactivationenergyofindividualSTZs,
whichincreasesthecapabilityofflaw/defectstolerance
andtheresultantfracturestrengthreliability.
Acknowledgements
ThefinancialsupportfromNationalNaturalScience
FoundationofChina(GrantNos.50725104,50841023),
the973Program(No.2007CB613903)andtheNational
HighTechnologyResearchandDevelopmentprogramof
China(No.2009AA03Z113)isgratefullyacknowledged.
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