Hall-Petch relationship in a nanotwinned nickel alloy

Hall–Petchrelationshipinananotwinnednickelalloy

LeonL.Shaw,a,*AngelL.OrtizbandJuanC.Villegasc

aDepartmentofChemical,MaterialsandBiomolecularEngineering,UniversityofConnecticut,Storrs,CT06269,USAbDepartamentodeIngenierı´aMeca´nica,Energe´ticaydelosMaterialesUniversidaddeExtremadura,06071Badajoz,SpaincIntelCorporation,Chandler,AZ85226,USA

Received5November2007;revised4January2008;accepted14January2008Availableonline26January2008

TheHall–Petchrelationshipinananotwinnedalloywithabsenceofdislocationpile-upsisinvestigatedforthefirsttime.Itisshownthat,whenthetwinspacingislarge(d>150nm),thehardnessexhibitsadÀ1/2dependence.However,whenthetwinspacingissmall(d<100nm),adÀ1dependenceresults.Thesephenomenaareinterpretedbasedondislocation-mediatedmechanismscorroboratedbytheanalysisofelectronmicroscopyandX-raydiffractometry.Ó2008ActaMaterialiaInc.PublishedbyElsevierLtd.Allrightsreserved.

Keywords:Hardness;Plasticdeformation;Twinning;Nanocrystallinemicrostructure;Hall–Petchrelation

Grainrefinementhasbeenatopicofintensivere-

searchforseveraldecades.Thedrivingforcebehind

theseenduringeffortsistheenhancementofstrength

asthegrainsizedecreases,asdescribedbytheempirical

Hall–Petch(H–P)relationship[1,2]

ry¼riþkyDÀ1=2ð1Þ

whereryistheyieldstrengthofapolycrystallinemate-

rial,Distheaveragegraindiameter,riistheoverall

resistanceoflatticetodislocationmovementandkyis

theH–Pslopemeasuringtherelativestrengtheningcon-

tributionofgrainboundaries(GBs).Eq.(1)hasbeen

foundtobeapplicabletoawiderangeofcoarse-grained

materials(DP$1lm),includingapplicationstothe

flowstressatagivenstrainandthehardnessofthe

material[3],thedislocationcellsofheavilydeformed

materials[4],thematerialswithseverallevelsofsub-

structures,e.g.theco-presenceoflow-anglecellbound-

ariesandhigh-anglecellblockboundaries[5],and

materialswithmicrosizedtwins[6,7].

Recently,theapplicabilityoftheH–Prelationto

ultrafine-grainedmaterials(100nm

andnanograinedmaterials(D<100nm)[10–12]has

beenstudiedextensivelybecauseoftheirpotentialsto

offersubstantialimprovementsinmechanicalproperties

overcoarse-grainedmaterials.Manyofthestudiesin

thisareahavebeensummarizedinarecentreviewarticle[13],whereacomprehensivelistofreferencescanbe

found.However,studiesontheH–Prelationinnano-

twinnedmaterialsareextremelyscarce,withonlyone

investigationonsingle-phasenanotwinnedmaterialsre-

portedintheopenliterature[14].Inthatstudy,Eq.(1)is

foundtobevalidforelectrodepositedCuwithtwin

thicknessassmallas13nm.Furthermore,theHall–

Petchslopeisnearlythesameasthatdeterminedfrom

coarse-grainedCu,suggestingthatthestrengtheningef-

fectoftwinboundaries(TBs)isanalogoustothatof

conventionalGBseveninthenanometerscale[14].

TheapplicabilityoftheH–Prelationtothenanotwin-

nedCuhasbeenexplainedbydislocationpile-ups

againstTBs[14].However,itiswellknownthatmany

materialsdonotexhibitdislocationpile-ups[15],and

theirH–Prelationshavebeenexplainedbytheactiva-

tionofGBdislocationsources[16]orotheralternative

mechanisms[17–19].Inthisstudywehaveinvestigated,

forthefirsttime,thedependenceofthehardnessof

nanotwinnedmaterialsonthetwinspacingwithabsence

ofdislocationpile-ups.Theabsenceofdislocation

pile-upscanbeattainedfromlowstackingfaultenergy

materialswhenthetwinthicknessistoosmalltosupport

dislocationpile-ups,asrevealedinthisstudy.

Anickel-baseHASTELLOYC-2000Òalloy1witha

lowstackingfaultenergy(1.22mJmÀ2)[20]waschosen

forthisstudyinordertoproduceagradientof

1359-6462/$-seefrontmatterÓ2008ActaMaterialiaInc.PublishedbyElsevierLtd.Allrightsreserved.

doi:10.1016/j.scriptamat.2008.01.025*Correspondingauthor.Tel.:+18604862592;fax:+18604864745;e-mail:

leon.shaw@uconn.edu1HASTELLOYandC-2000areregisteredtrademarksofHaynesInternational,

Inc.Available online at www.sciencedirect.com

ScriptaMaterialia58(2008)

951–954www.elsevier.com/locate/scriptamathigh-densitynanotwinsinthesample.TheC-2000alloy

isacorrosion-resistancealloywithasingle-phase,face-

centered-cubic(fcc)structureandanominalchemical

composition(inwt.%)of23Cr,16Mo,1.6Cu,0.01C,

0.08SiandbalanceNi.Theas-receivedC-2000plates

wereinanannealedcondition.Theseannealedplates

weresubjectedtoasurfacesevereplasticdeformation

(S2PD)treatmenttocreateasurfaceregioncontaining

nanograinsfollowedbyagradientofhigh-density

nanotwinswithacontinuousincreaseinthetwinthick-

nessasthepositionmovesawayfromthetreatedsurface

oftheplate[21].TheS2PDmethodusedinthisstudy,

similartothesurfacemechanicalattritiontreatment

[22,23],entailsimpactingthesurfaceoftheplatewith

high-energyballs(e.g.WC/Coballs)repeatedlyunder

anargonatmospherefor30min[24,25].Thedetailof

otherexperimentalconditionsforS2PDcanbefound

elsewhere[21].

Themicroscopyanalysis(Fig.1)revealsthatamicro-

structuralgradienthasbeenproducedviatheS2PDpro-

cesswithagradualdecreaseinthedeformationtwin

densityasthepositionmovesawayfromtheimpacted

surface.Parallelnanotwins(3–8nmthick)withand

without60°unitdislocationsinbetweenarepresentnear

theimpactedsurface(Fig.1b),whereastwin–twininter-

sectionswithhigh-densitydislocationentanglementin

betweenarepresentbelowthenanotwinnedsurfacere-

gion(Fig.1c).Furtherawayfromtheimpactedsurface

isthedeformationregion,withsmallplasticstrains

exhibitingdislocationemissionfromtwinboundaries

(Fig.1d).BasedonthepeakbroadeninganalysisofX-

raydiffraction(XRD)patterns,thecrystallitesizeand

dislocationdensityasfunctionsofthepositionmeasured

fromtheimpactedsurfacehavebeenquantified[21].Be-

causeoftheabsenceofdislocationcellsintheS2PD-pro-cessedC-2000alloy,thecrystallitesizemeasuredvia

XRDreflectsthesizeofthesubstructuresmainlysepa-

ratedbytwinboundarieswithonlyasmallproportion

offaultandgrainboundaries,andthuscanbeapprox-

imatelyregardedasthetwinspacing[21].Furthermore,

itisfoundthatthetwinspacingdecreasesastheposition

becomesclosertotheimpactedsurface.Figure2shows

thedislocationdensityandtheaveragenumberofdislo-

cationswithineachtwinned(oruntwinned)regionasa

functionofthetwinspacing.Notethatalthoughthedis-

locationdensityincreasesasthetwinspacingbecomes

smaller(i.e.asthepositionbecomesclosertotheim-

pactedsurface),thenumberofdislocationspertwinned

(oruntwinned)regionactuallydecreases.Thisisin

excellentagreementwiththetransmissionelectron

microscopy(TEM)analysis,asrevealedbycomparing

Figure1bandc.

Figure3presentstheH–Prelationshipbetweenthe

Vickershardness,HV,andthetwinspacing,d,revealing

thattheHVÀdÀ1/2relationshipisnotlinear,butis

concavetowardsthedÀ1/2axis.Furthermore,thetrend

shownbythenanoindentationhardnessisidenticalto

thatexhibitedbytheVickershardness.However,the

nanohardnessdatahaveallowedthevalidmeasurement

ofthehardnessatlocations10lmawayfromtheim-

pactedsurface[25],andthusextendedtheevaluation

oftheeffectofthetwinspacingdownto30nm.Wepro-

posethatthenon-linearHÀdÀ1/2relationshipisdueto

thechangeinthedeformationmechanismasthe

twin

Figure1.MicrostructuresoftheC-2000alloyafterS2PDprocessing.(a)Anoverallviewofthecross-sectionfromtheimpactedsurface(indicated)tothenearlyundeformedinterior,showingagradualincreaseinthedeformationtwindensity(asindicatedbythedeformationmarkingdensity)whenthepositionbecomesclosertotheimpactedsurface.(b)AFourier-filteredlatticeimageneartheimpactedsurface,showingthepresenceofparallelnanotwinswithandwithoutdislocationsinbetween.(c)TEMbright-fieldimageatalocation$100lmfromtheimpactedsurface,showingthetwin–twinintersectionwithdislocationentanglementinbetween.(d)TEMbright-fieldimagefromalocationneartheundeformedinterior,showingemissionofdislocationsfromatwin

boundary.Figure2.Thedislocationdensityandtheaveragenumberofdisloca-tionspertwinned(oruntwinned)regionasafunctionofthetwinspacing.Notethatwhenthetwinspacingdecreasesfrom750to34nm,thepositionmeasuredfromtheimpactedsurfacechangesfrom500to10lm,respectively.

Figure3.Thehardness,H,asafunctionoftheinverseofthesquarerootofthetwinspacing,dÀ1/2.NotethattheHÀdÀ1/2relationshipisnotlinear,butisconcavetowardsthedÀ1/2axis.952L.L.Shawetal./ScriptaMaterialia58(2008)951–954