On the mechanistic basis of deformation at the microscale in hexagonal close-packed metals

29 Pages·1.129 MB·English

by  Britton T.B., Dunne F.P., Wilkinson A.J.

Downloaded from http://rspa.royalsocietypublishing.org/ on June 3, 2015
On the mechanistic basis of
deformation at the microscale
rspa.royalsocietypublishing.org
in hexagonal close-packed
metals
Review
T.B.Britton1,F.P.E.Dunne1andA.J.Wilkinson2
Citethisarticle:BrittonTB,DunneFPE,
WilkinsonAJ.2015Onthemechanisticbasisof 1DepartmentofMaterials,ImperialCollegeLondon,
deformationatthemicroscaleinhexagonal
PrinceConsortRoad,LondonSW72AZ,UK
close-packedmetals.Proc.R.Soc.A471: 2DepartmentofMaterials,UniversityofOxford,ParksRoad,
20140881.
OxfordOX13PH,UK
http://dx.doi.org/10.1098/rspa.2014.0881
TBB,0000-0001-5343-9365;AJW,0000-0002-8801-4102
Received:13November2014
This is anoverviewof micromechanicaldeformation
Accepted:30April2015
mechanisms in hexagonal close-packed metals. We
start with an in-depth discussion of single-crystal
behaviour concerning crystallographic slip, plastic
SubjectAreas:
anisotropyanddeformationtwinning.Wemoveonto
energy,materialsscience,
discusssomecomplexitiesinvolvedinpolycrystalline
mechanicalengineering
deformation and modelling approaches, focusing on
rateeffectsintitaniumalloysthatarethoughttoplay
Keywords: asignificantroleindwellfatigue.Wefinishourreview
deformation,metals,mechanics,alloy with a brief commentary on current understanding
andstate-of-the-arttechniques,andoutlinesomekey
areaswherefurtherstudyisrecommended.
Authorforcorrespondence:
T.B.Britton
e-mail:[email protected]
1. Introduction
Hexagonal close-packed (HCP) metals1 are used in a
widevarietyofengineeringsectors,includingaerospace,
nuclear,automotive,scientificinstrumentation,chemical
engineering and bioengineering. The metals and alloys
are used owing to the combination of excellent
mechanical properties, corrosion resistance and the
ability to engineer new chemistries and thermo-
mechanicaltreatmentstotailortheirmicrostructure,and
henceproperties,foraparticularapplication.
TheengineeringuseofHCPmetalsiswidespread,for
example: titanium is used in fan blades in jet engines,
1WenotethatHCPmetalsarenotstrictlyclosepacked,accordingtothe
idealrigidballmodel(seetable1),butwestickwiththeterm‘hexagonal
closepacked’orHCPasperconventionwithinthisfield.
2015TheAuthors.PublishedbytheRoyalSocietyunderthetermsofthe
CreativeCommonsAttributionLicensehttp://creativecommons.org/licenses/
by/4.0/,whichpermitsunrestricteduse,providedtheoriginalauthorand
sourcearecredited.
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corrosion-resistantpipingandbiomedicalimplants;zirconiumisusedinfuelcladdinginnuclear
2
fissionreactors;magnesiumisusedinautomotiveapplicationssuchassteeringwheelsandintake
manifolds;zincisusedasacoatingforsteels;andberylliumisusedinscientificinstrumentation
.rs
and nuclear fusion reactors. The other HCP metals (cobalt, cadmium, rhenium, hafnium and ..pa
ruthenium)areusedlessextensively. ....roy
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This review describes mechanistic studies and insight into the deformation of HCP alloys ...rg
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continueswithabriefdiscussionontwinning,focusingonthreeofthemetals—Zr,TiandMg— ...R
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used in high-value engineering applications. To demonstrate industrial relevance and promote ..So
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components. ..81
2. Single-crystalanisotropy
(a) Theslipsystems
Hexagonal symmetry leads to considerable anisotropy in the elastic and plastic mechanical
properties of HCP metals, as well as other physical properties. The slip systems, illustrated in
figure1,havebeenidentifiedasplayingasignificantroleintheplasticdeformationofHCPmetals
andalloys.
Thea/3(cid:2)112¯0(cid:3)or(cid:2)a(cid:3)directionsaretheclose-packeddirectionsandarethustheshortestBurgers
vectorpossibleforperfectdislocations.(cid:2)a(cid:3)typedislocationshavebeenshowntosliponseveral
different slip planes including (0001) basal, {101¯0} prismatic and {101¯1} pyramidal. The three
(cid:2)a(cid:3)Burgersvectorsareco-planarwithinthebasalplaneandsoonlyoffertwoindependentslip
directions.Tofullysupportanarbitraryplasticstrain,andsosatisfythevonMisesdeformation
criterion,modesthatgeneratesheardisplacementoutofthebasalplanearerequired.Dislocations
with a/3(cid:2)112¯3(cid:3) or (cid:2)c+a(cid:3) Burgers vectors have been found in many HCP metals and these
alongwithdeformationtwinning(see§4)providetheadditionaldeformationmodes.The(cid:2)c+a(cid:3)
dislocations have Burgers vectors that are significantly longer than for the (cid:2)a(cid:3) dislocations and
henceareenergeticallylessfavouredandtendtohavehigherresistancetomotion.
(b) Determiningcriticalresolvedshearstresses
Themostdirectwaytoestablishthecriticalresolvedshearstress(CRSS),whichisthepreferred
measure of resistance to slip on a given slip system, is to conduct a macroscopic tension or
compression test on a suitably oriented single-crystal sample. A considerable body of work of
this type has been undertaken, predominately in the 1950s, 1960s and 1970s, to establish the
fundamentalsofCRSSvaluesfortheimportantslipsystemsinthepureHCPmetals[1–4].Growth
ofthesinglecrystalsisitselfamajorundertaking,especiallywhereasolid-stateallotropicphase
transformation occurs (e.g. in Zr and Ti). The orientation of the crystal is typically determined
usinglaboratory-basedLaueX-raydiffraction(XRD)inthereflectiongeometry.Thecrystalcan
then be cut at a suitable orientation so that loading causes a large resolved shear stress on the
selectedtargetslipsystemwhileminimizingthestressonothers.Thesehigh-puritysinglecrystals
are typically very soft and have to be treated carefully. Growth of large single crystals of the
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〈112–3〉 c 3
{0001} basal slip plane ..rsp
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a {101–0} prismatic slip plane ...ro
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a2 〈1a112–0〉 {101–1} pyramidal slip plane ...........alsocietypub
alpha titanium (HCP) ...lish
Figure1.SlipsystemsinHCPmetalsandalloys. ....ing.o
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morehighlyalloyedsystemshasoftenprovedprohibitivelydifficultandnowthatdataforthe ...R
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pure metals and lightly alloyed systems have been established the approach has seen limited ..So
subsequentapplication. ...c.A
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scheme, so that a good fit is obtained to the bulk stress–strain response, and to the lattice ..81
strain evolution for various grain orientation families probed by the diffraction experiment.
The ‘grain families’ consist of all the grains within the diffraction volume that contribute to
a given diffraction peak and so average over a range of possible grain orientations that are
dispersed through the material in grains with differing nearest neighbour environments. The
simulations are seeded with grain orientations that represent the macroscopically measured
texture.Turner&Tome[5]appeartohavebeenthefirsttotakesuchanapproachusinganelasto-
plastic self-consistent (EPSC) model to extract CRSS values for slip modes in Zircaloy-2 from
neutron diffraction measurements of residual stresses. Previous related work by Lebensohn &
Tome [6] used a viscoplastic formulation along with texture development to imply yield and
hardening behaviour over much larger strains again in Zircaloy materials. These early works
used models in which grains are considered as ellipsoidal inclusions in a homogenized matrix
which are analysed using a framework developed by Eshelby [7,8]. The scheme is iterated, so
that the average behaviour of the individual grain inclusion is consistent with the properties
of the homogenized equivalent matrix. The EPSC approach is computationally very efficient, but
theeffectsoftheindividualgrainenvironmentsare‘smearedout’,andstressvariationswithin
thegrainsareremovedthroughuseoftheEshelbyellipsoidalinclusionresult.Thisproblemis
exacerbated in low-symmetrymaterialssuch as the HCP metals, as local neighbour effects can
bequitestrong.Ascomputingpowerhasincreased,theEPSCmodelhastendedtobereplaced
with a crystal plasticity finite-element analysis (FEA) simulation, or most recently with fast
Fouriertransform(FFT)image-basedsimulations[9–11].Thesemoremodernapproachesremove
some of the shortcomings of the EPSC model by allowing intragranular stress variations and
grain–graininteractions.However,theapproachreliesonsimultaneouslyfittingmultiplemodel
parameterstomulti-variableexperimentaldatasets.Errorsinthebest-fitmaterialsparametersare
difficulttoassessastheycombinebothlimitationsofthemodelassumedanduncertaintiesinthe
experimentalmeasurementswhicharelinkedincomplexways.
AfurtherclassofmethodstoobtainCRSSvaluesarebasedondeformingsmallvolumesof
materialwithinindividualgrainsofapolycrystal.Mersonetal.[12]andViswanathanetal.[13]
noted the marked change in hardness when performing nanoindentation into selected grains
within Ti alloys with surface normal parallel (harder and more stiff) or perpendicular (softer
andlessstiff)tothebasalplane.Here,thedifficultyliesinextractingtheexactslipsystemsthat
are operating in the very complex loading environment surrounding the indenter tip. A more
detailedinvestigationbyBrittonetal.[14]linkednanoindentationdatatohigh-resolutionelectron
backscatter diffraction(EBSD)measurements of the lattice curvatureand residual stresses, and
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atomic force microscopy (AFM) measurements of the surface topography to better understand
4
theflowfieldsnearindentsindifferentlyorientedgrains.Theyalsoconductedcrystalplasticity
FEA simulations using a strain gradient plasticity formulation with CRSS values adjusted to
.rs
give a good fit to the experimental load–displacement data for differently oriented grains, and ..pa
made comparison with topography, lattice rotation and strain fields obtained experimentally. ....roy
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EZBamSDbaalnddieAtFaMl.[1to5]sthuadvyedaelsfoorumsaedtiocnryasrtoaulnpdlacsotinciitcyalminoddeenlltisnign,coorimenmtaetricoinallmyepausruereTmi;ehnotwsewviethr, .....lsocie
itacnhlelceiartoertllameysiehsddisgeiuomhnn.ocFoneufrsrttatarnhainyetetrsysmizoaoennreeitfs,hfoaeetcrlCtoasRcpikySnSotihffnoemrihretahsariesdmu(cid:2)nurceel+smastaieoa(cid:3)nnnttyssdpmweceirstyahlinsptlsaostlaylhodsagittnertmaghpe.ahAlCioclRnthgSeofStfuhevgceathls(cid:2)ucte(cid:3)hosneaexnxtiahstnremaocfliatnyeoddwreemnsfituaaeyltltidobisnne, ............typublishing.o
extractionofreliablequantitativeCRSSvaluesisdifficultowingtothecomplexstressandstrain ...rg
fieldsduringindentationwhichleadtomultipleslipandhardeningfromslip-systeminteractions, ...Pro
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aswellastheindentationsizeeffectfromtheimposedstraingradients. ...R
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Inordertoisolatetheplasticresponseintoasingletargetedslipsystemitispossibletouse ..So
afocusedionbeam(FIB)tomachinemicrometre-scaledtestpieces(compressionpillarsorbend ...c.A
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btteheseatmetadss)kinforaofmninatnienordp-iirnveditdienungateltrhpeoorllyoocatrdhye–srdtaibslsepslopafcoepkmaerestnmictuadllala-rtsaccarclyoesmttaeplslatoirngegrdaapwphipticharonaratiunesno.tianTtdhioeisnngtatrhteiaaottnlcyaasnnidmthopenlnilfiybeaes ........71:20140
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singleCRSSvalueneedbeextractedfromagiventest.Themajorissueswithtestingsuchsmall ..81
volumesarethe‘smallerisstronger’sizeeffectsandthestochasticnatureoftheplasticflow[16].
In the bending geometry, the strain gradients and retention of dislocations in the low-stress
regions near the neutral axis tend to reduce the relative size of the strain bursts or load drops
seencomparedwiththecompressioncase.Therealsoseemstobegoodagreementonthenature
andcauseofthesizeeffectseeninmicro-cantilevertesting,allowingextrapolationtobulkvalues
to be made with more confidence. Gong and co-workers [17–20] have made extensive use of
micro-cantilevers to study CRSS values for the major slip systems in various Ti alloys. This
has included work with Ding et al. [21,22] using FIB on deformed micro-cantilevers to make
thin foils for post-mortem transmission electron microscopy (TEM) analysis of the dislocation
structures obtained. The bending geometry requires that crystal plasticity FEA simulations are
usedtoobtaintheCRSSvaluesthroughaprocedureusingforwardmodellingandcomparison
with experiment. Recent work by Tarleton et al. [23] has linked these types of experimental
single-crystalmeasurementsofmicro-cantileverbendingwithaplanartwo-dimensionaldiscrete
dislocationdynamics(DDD)modelanddemonstratedthattheremaybeastrongsizedependence
notonlyinheritedfromsoftpile-upsinthezerostressregion,butalsoowingtothedensityof
sourcesintheselimitedvolumes.
Micro-pillar compression has been used for measurements on Mg alloys in basal slip and
twinning [24–27] and in Ti alloys for prismatic slip and twinning [28,29]. Generally, no FEA
modellingisundertaken,andloadanddisplacementaresimplyconvertedtoengineeringstress
and strain from measurements of the pillar cross-section and height, although the strains are
typicallyoverestimatedowingtodeformationbelowthepillarwhicheffectivelyactsasablunt
punch.Acommonshortcomingininterpretationofmuchofthemicro-pillarcompressiondata
hasbeenaninsistenceonusingasimplepower-lawscalingforanalysingthelength-scaleeffects;
thisisunphysicalasextrapolationtothebulkleadstozerostrength.Thishasbeenemphasized
byDunstan&Bushby[30],whohavereanalysedmicro-pillarcompressiondatatoincludefinite
bulkstrength.
(c) Criticalresolvedshearstressesforpuremetals
(cid:2)a(cid:3) dislocations are the dominant dislocation types and the naive-expectation of near-exclusive
slip on the close-packed plane is to some extent borne out [2 ] astable 1 shows that basal slip
tends to be preferred when the c/a ratio is close to the ideal value obtained for close packing
of hard spheres. However, the relative ease of slip on the (cid:2)a(cid:3) basal slip system decreases as
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Table1.c/aratio,preferredslipsystemandcriticalresolvedshearstressesofpureHCPmetals.
5
preferred (cid:2)a(cid:3)basal (cid:2)a(cid:3)prism
.rs
metal c/aratio slipsystem purity CRSS(MPa) CRSS(MPa) references .p
.a
Cd 1.886 (cid:2)a(cid:3)basal 99.996 0.2 Roscoe[31] ....roy
.a
....Z....n........................................1.......8....5....6......................................(cid:2)....a....(cid:3)......b....a....s....a..l..................................9....9.......9....9....9..............................0.......2......................................................................................................................J..i..l..l..s....o....n......[..3....2....]...................................... .....lsocie
....iM..d....eg....a....l..............................11........66....23....43......................................(cid:2)....a....(cid:3)......b....a....s....a..l..................................9....9.......9....9....6..............................0.......8....h....a....r..d......s..p......h....e....r..e......m......o....d....e....l........................................................B....u....r..k....e......&......H......i..b....b....a....r..d......[..3....3....]...... ........typublish
..C..o....................1....6..2..3...................(cid:2)..a..(cid:3)...b..a..s..a.l.......................................................................................................................................... ....ing.o
Re 1.615 (cid:2)a(cid:3)basal 9.0 16.5 Jeffery&Smith[34] ..rg
..Z..r....................1....5..9..3...................(cid:2)..a..(cid:3)...p..r.i.s..m..................9..9....9..8.................>....2.4..........................6....4............................R..a..p..p..e..r.p..o..r..t..[.3..5..]........... ....Pro
.......................................................................................................................................................................................................... ..c.
Ti 1.588 (cid:2)a(cid:3)prism 99.95 92 23.5 Levine[36] ..R.
........RHB........u....ef............................................................................111...............555........688........812............................................................................(cid:2)(cid:2)(cid:2)........aaa........(cid:3)(cid:3)(cid:3)............ppb........rra....ii....sss........amm....l....................................................................999........989...............96........2....................................................................2.........3....................................................................................................................212....4....00..........7....6........................................................................................................DTS....u....na........ros....n....w&....e........r....&M....&........iB....tW....rc........eh....he....e....id....tl....lei....s....[....[3....[3....83....9....7]....]....]................ ..............471:20140Soc.A
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..81
the c/ a ratio decreasest(able 1). A distinct anomaly in this is Be, which has a particularly low
c/a ratio but still exhibits (cid:2)a(cid:3) basal slip as its easiest slip system. Bacon & Vitek [40] point
out that d-electrons may play a significant role in promoting (cid:2)a(cid:3) prism slip over basal slip.
The dislocation core structures cannot be predicted unless simulations correctly capture the
interatomic bonding and in particular the directional covalent-like nature to which d-orbitals
contribute significantly. Calculations for (cid:2)a(cid:3) screw dislocations in Ti showed two low-energy
configurationswiththecoreeithersplittingintotwodistinctShockleypartialsonthebasalplane
orspreadingmorecontinuouslyontheprismplane.Finnis–Sinclair-typepotentialsdonotfully
capture the directional effects and tend to under-predict the basal plane stacking fault energy,
andthuswronglypredictbasalplanesplittingasthelowerenergyconfiguration.However,when
the more realistic bond-order potentials are used, which better represent d-electron effects on
directional bonding, higher basal stacking fault energies are predicted and the preferred low-
energyconfigurationiscorrectlyidentified,withthecorespreadingontheprismplane[41].More
recentdensityfunctionaltheory(DFT)calculationsforTihaveconfirmedthatthelowerenergy
core configurations involve dissociation on the prism plane [42,43]. Like Ti, the metals Zr and
Hf are also group 4 d-block elements and prism slip occurs more readily for similar reasons.
Theabsenceofanyd-electronsinBemayresultinalowerbasalplanestackingfaultenergyand
stabilizedissociationintoShockleypartialsonthebasalplane.Adhikari&Mukhopadhyay[44]
suggestthatbondingwithinthebasalplaneofBeismetallicbutalongthe(cid:2)c(cid:3)axistendstohavea
morecovalentcharacter.
Deformation temperature and strain rate have significant effects on CRSS values. Strain-
rate and temperature jump tests have been used to extract CRSS data from single crystals
over a wider range of conditions and to allow activation volumes to be probed in addition to
activation energies [45]. Figure 2 shows CRSS values as a function of temperature for pure Ti
[2,36,46,47,49], Zr [1,3,4,45 ] and Mg4[8] at very low interstitial impurity levels. Basal slip in
Mg has a markedly lower CRSS value than either prism or basal slip in Ti and Zr, as shown
infigure2.ThebehaviourofTiandZrisverysimilarwithCRSSvaluesfor(cid:2)a(cid:3)prismslipbeing
radically lower than for (cid:2)a(cid:3) basal slip at low temperatures but becoming more similar at high
temperatures.Theactivationenergyfor(cid:2)a(cid:3)basalslipislargerthanfor(cid:2)a(cid:3)prismslipinthesetwo
metals.Athighpurities([Oeq]<0.2at%,seeequation(2.1)),thereareanomalouspeaksinboth
the activation energies and activation volumes reported for both basal and prism slip close to
roomtemperature[50].However,athigherinterstitialcontents,typicalofcommercialmaterials,
this anomalous behaviour is supressed [50]. Thermal activation, particularly in relation to the
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Tanaka & Conrad [47] 6
160 Paton & Backofen [46]
Ti prism
Levine [36] .rs
140 ..pa
Akhtar [1] ...ro
RSS (MPa) 11802000 ZTri pbraissaml LAASoekkvohhi tt&naaerr H[[&31i g6]Tg]e ignhs t[s4o5o]nian [4] ...............yalsocietypublish
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Mg basal Sheely & Nash [48] ..rg
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20 ...R
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0 200 400 600 800 1000 1200 ....4c.A
Figure2.CRSSvaluesforbasalandprismslipinTi[2,36,4t6e,m47p],eZrra[t1u,3r,e4 ,4(K5])andMg[48]singlecrystalswithverylowinterstitial ........71:20140
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content. ..81
near-room-temperaturecreepbehaviour,isofparticulartechnologicalinterest,asdiscussedin§6.
Thereisaclearneedforfurtherresearchtounderstandtheatomisticmechanismscontrollingthe
slipratesensitivityofthedifferentslipsystemsandhowtheyareinfluencedbyalloying.
Atlowstrains(stageI),prismslipisassociated withwell-separatedplanarsliplinesonthe
samplesurface.AsstageIIisreached,othersecondaryslipfeaturescanbeobserved.Diffraction
contrastinTEMrevealslongdislocationlinespredominatelyofscrewcharacteralignedalongthe
(cid:2)112¯0(cid:3)directions,withdensitiesof1012–1013m−2typicalfordeformationofafewpercentstrain
[50].Surfacesliplinesobservedforbasalsliporientations,withscreworientationstendingtobe
alignedwith(cid:2)112¯0(cid:3),havebeenreportedinbothTiandZrasmorewavyinnatureandassociated
withcross-slipontotheprismplaneforwhichdissociationintopartialsismorefavoured[1,2].
(cid:2)a(cid:3)sliponprismandbasalplanesisnotsufficienttosatisfythevonMisescriterionandthus
accommodate an arbitrary plastic strain. For example, tension or compression along the c-axis
cannotbeachievedwithoutslipofdislocationswithBurgersvectorsalong(cid:2)c+a(cid:3)or1/3(cid:2)112¯3(cid:3)
ortwinning(see§5).(cid:2)c+a(cid:3)sliphasbeenshowntobeasignificantdeformationmodeinmany
HCPmetalsincludingTi[51]andZr[52].TheCRSSvaluesfor(cid:2)c+a(cid:3)slipareconsiderablylarger
thanforthe(cid:2)a(cid:3)slipsystemsandcomparabletothosefortwinningsothatbothmodesareoften
activated,whichcomplicatesinterpretationofmechanicaltestdata.Williamsetal.[53]showed
thatalloyingwithAlincreasestheCRSSfor(cid:2)c+a(cid:3)slipbutinhibitstwinningmore.
TheuseofCRSSanddislocationactivitycanbeusedtoinformDDDmodelsintwoandthree
dimensions, and these models can be used to understand mechanisms involved in hardening
andmicro-plasticityinvolvingtheinteractionsofmultipledislocationsinrealstructures.Monnet
et al. [54] constructed a three-dimensional DDD model of Zr, involving both crystal slip and
thermallyactivatedprocesses,tounderstandlimitedforesthardeningatlowtemperaturesowing
to the continuous multiplication of screw dislocations of a well-oriented single slip system.
Observationsofthistypecanbeusedtoinformmodelsatlongerlengthscales(see§6and,for
example,[55]).
(d) Effectsofalloying
The small atomic radii of oxygen, nitrogen and carbon atoms allow them to adopt octahedral
interstitial sites in the HCP metals [56] and these have very pronounced effects even at low
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180
7
slip 160
·ÒaCRSS prism and basal in Ti and Zr (MPa) 11124680240000000 TTZZiiri r ···caaaaÒÒÒl obppyarri-iss2samm l·aÒ prism ........................rspa.royalsocietypublishing.o
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0 0.2 0.4 0.6 0.8 1.0 1.2 ...Pro
equivalent oxygen content (at%) ..c.
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Figure3.EffectofinterstitialcontentonCRSSvaluesofTi[18,36,50,56,58]andZr[4,5,35,45,59]atroomtemperature. ....oc.A
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concentrations on the CRSS values. The oxygen-equivalent content can be used to group .......71:2014
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strengtheningcontributionsfromoxygen,nitrogenandcarbonaccordingtotheirpotency[57]: ..81
[Oeq]=[O]+2.0[N]+0.75[C], where[X]istheat%ofelementX. (2.1)
Figure 3 shows CRSS values obtained by different authors for basal and prism slip at room
temperatureinTiandprismslipinZroverarangeofoxygenequivalentconcentrations.Although
increased oxygen content increases the strength of both prism and basal slip in Ti the effect is
muchmoremarkedfortheeasierprismslip.VeryrecentworkbyYuetal.[60]hasshownthrough
advancedscanningtransmissionelectronmicroscopy(STEM)imagingandDFTcalculationthat,
althoughthecoreofedgedislocationsinTiwasrelativelyunaffectedbyincreasingtheoxygen
contentfrom0.1to0.3wt%(approx.0.3–0.9at%),thecoresofscrewdislocationswereprofoundly
altered, narrowing significantly as the oxygen content increased. DFT suggests very intense
localized repulsion between a screw dislocation and interstitial oxygen on octahedral sites on
thesameprismaticplaneasthedislocation,whichmaypromotecross-slipclosetotheoxygento
removethedislocationfromthisenergeticallyundesirablesiteandgeneratingedgesegmentsthat
areunabletoglideontheprismaticplane.ForcommercialTialloysthelowestinterstitialcontent
isforASTMgrade1,whichhasamaximumallowableoxygenequivalentofalittleover1at%
(summingcontributionsfromoxygen,nitrogenandcarbon);thisincreasesthroughgrades2and
3tograde4,whichcanhaveanoxygenequivalentofupto1.8at%.Atthesehigherinterstitial
levels, there is relatively little difference between the CRSS values for prism and basal slip in
Ti, though of course prism slip offers more slip planes and so predominates in deformation of
polycrystals.Atincreasedoxygenlevels,thereisalsoachangeinslipmodefromwavytoplanar
slipatlowertemperaturesowingtoincreaseddifficultyofcross-slip[61,62].
Figure 3 also includes data from Zr and Zircaloy-2 recorded at room temperature, where
deformation is restricted to prism slip as deformation twinning tends to complicate extraction
ofCRSSvaluesforpurelybasalslip.InterstitialsinZrareseentohaveasimilareffectivenessin
hardening prism slip systems. Zr alloy systems tend to be less highly alloyed than Ti systems
and the oxygen interstitial content typical in commercial alloys (in the range 0.10–0.14wt%, or
approx.0.6–0.8at%)makesasignificantcontributiontostrengthatroomtemperatureasindicated
byinclusionofdataforZircaloy-2infigure3.
Interstitial strengthening is coupled with a loss of ductility. This is particularly marked at
higher concentrations, where it is linked to a change to planar slip. This can be problematic,
because exposure of Ti to elevated temperatures in oxygen-containing environments not only
causesformationofasurfaceoxidebutalsoamuchdeeperpenetratingprofileofraisedoxygen
concentration(‘α-case’).Ruggetal.[63]haveusedorientation-correctednanoindentationwithin
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(a)
8
300
250 ..rsp
.a
...ro
.y
RSS (MPa) 125000 ...........alsocietypub
C 100 ...lish
50 ....ing.o
..rg
.
...Pro
.c
0 2 4 6 8 ...R
..
aluminium content (wt%) ..So
...c.A
(b) .4
116800 .......71:2014
.0
.8
140 ..81
a) 120
P
M 100
S ( 80
S
R prism - Sakai & Fine [66–68]
C 60
prism - Williams et al. [53]
40
basal - Sakai & Fine [66–68]
20
basal - Williams et al. [53]
0 2 4 6 8
aluminium content (wt%)
Figure4.EffectofAladditiononCRSSvaluesforprismslipandbasalslipinTiat(a)roomtemperatureand(b)500K[53,66,68].
thesurfacelayertoshowsignificantchangesinhardness,aswellasmicro-cantileverscutwithin
selectedgrainsorientedforprismsliptoshowthattheCRSSinTi–6Al–4Vapproximatelydoubles
acrosstheapproximately100μmwidediffusionlayer,whereatomprobeanalysisshowsthatthe
oxygencontentincreasesfrom0.4tomorethan1wt%.Incomponents,theα-caselayercanleadto
asignificantdropinperformanceowingtoeasycrackinitiationineithertensileorcyclicloading
conditions[64,65].
Of the substitutionalalloying additionstoTi, Alis by far themost commonand important.
There have been two significant single-crystal testing campaigns by Sakai & Fine [66–68 ] and
laterbyWilliamsetal.[53].Figure4summarizestheCRSSdataobtainedforprismandbasalslip
inTi–Alalloysatroomtemperatureand500K.Thereisgoodagreementbetweenthetwostudies
for prism slip, though for basal slip the shear tests of Sakai and Fine show marked hardening
between0.5and3wt%,whereasdatafromthemoreconventionalcompressiontestingofWilliams
et al. indicate relatively little change. Sakai and Fine adopted the shear testing mode because
compression testing resulted in twinning and/or prism slip and Williams et al. also report that
deformationtwinningandprismslipwereseeninsamplescompressedwiththeaimofactivating
basal slip. Both sets of data do, however, indicate that increasing Al content and particularly
temperature tend to reduce the ratio of CRSS values for basal and prism slip. For prism slip,
considerable hardening is brought about by Al additions, and this is linked to a narrowing of
theslipbandswithdeformationbecomingmorelocalizedandplanarascross-slipismademore
Downloaded from http://rspa.royalsocietypublishing.org/ on June 3, 2015
difficult. More obviously, the basal slip which is relatively wavy in pure Ti becomes planar as
9
Alisadded.FortheirhighestAlcontent(6.6wt%),Williamsetal.showedthatprolongedageing
could generate a fine dispersion of coherent Ti3Al α2 which were destroyed by the passage of .rs
dislocations within a slip band. Under less extreme heat treatments and at lower overall Al ..pa
concentrations, clustering and short range order (SRO) in the Al distribution are thought to ...ro
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Easy(cid:2)a(cid:3)slipinHCPmaterialsdoesnotprovidethenecessaryfivedegreesoffreedomrequired ...c.A
.4
f(cid:2)oocfr+thaane(cid:3)lasalritbptii,ctrbeaurtthyarsolthueagrpnheactcirvhyeaslntyagltews.hiInenassry,osomtfetemenmscainatevnroioalvplsien,rgadteelfo.ocTrawmliaanttniooimnngicmesanhyaubbflfleesinascgicgo[n7mi1fi]mc,aownditatdhteeadfosstrhomrcoaiatutigoedhn ........71:20140
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latticereorientation. ..81
In the HCP materials, there are a number of twinning modes that can accommodate
deformation; broadly, these can be split into the contraction/compression and the extension/
tensiontwins.Thespecificlanguageheredescribesthesenseofstraingeneratedbytheoperation
ofthetwinsystemalongthe(cid:2)c(cid:3)axisoftheparentcrystalaseachtwinsystemonlyresultsinshear
inonedirection.Thiscancausesomeconfusionwithrespecttotheappliedstressstate,because
tensiontwinsareoftenfoundinspecificmicrostructuralareasofacompressiontestwherealocal
crystalhasthec-axisorientedperpendiculartothecompressionaxis,andextensionistherefore
kinematicallyrequired.
Typical shears and reorientations associated with twinning in Zr are shown in figure 5. As
the c/a ratio changes so does the associated reorientation and twinning shear (figure 6); for
example,asYoo[73]notes,thischangesthe{101¯2}(cid:2)1¯011(cid:3)systemfromanextensiontwinforlow
c/amaterials(Ti,Zr,Be,Re,Mg)toacontractiontwinforhighc/amaterials(Zn,Cd).
In addition to these geometric shear and reorientation relationships, the nature of the HCP
latticeoftenrequiresadditionalshufflestepstoaccommodatethetwinningshearattheatomic
scale[71].Ashuffleinvolveslocalatomicrearrangementandmaydominatetheselectionofthe
daughtertwinvariantandthereforetheactivetwinningmode.Foramorecompletedescription
of the precise atomic shuffles involved in HCP twins, the reader is directed to the review by
Christian&Mahajan[71].
Directobservationofthetwinningprocessisdifficultowingtotherateatwhichtwinsform.
Therefore,studieshavefocusedeitherondirectmodellingofthetwinprocess,usingtoolssuch
as molecular dynamics and observations of post-twin structures in polycrystals, or on crystal
plasticitymodellingoftexture,residualstressorpolycrystalmicrostructures.
Twinning is an important deformation mode, as, during processing, it can dominate the
formationofcrystallographictexture.Forexample,differentc/aratiosandactivetwinsystems
result in different macroscopic textures, as shown in figure 7 [72]. In Mg alloys, the lack of
easy (cid:2)c+a(cid:3) slip and predominance of twinning modes results in difficulties in forming Mg
components,asverystrongtexturescanbegeneratedwithsignificantanisotropyofmechanical
propertieswhichlimitstheirengineeringuseandavailableprocessingroutes[74].
(a) Twinningmechanisticoverview
The precise mechanisms of twinning are less well understood than for crystallographic slip. It
isthoughtthattwinningcanbebrokenintothefollowingsteps:incubation,nucleation,propagation
Downloaded from http://rspa.royalsocietypublishing.org/ on June 3, 2015
10
34.84°
.rs
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85.22° ...ro
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extension .....lsocie
.....typub
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{101–2} ·1–011Ò {112–1} ·1–1–26Ò ...rg
s=0.167 s=0.63 ...Pro
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.R
..
.S
.o
54.22° 57.05° contraction ...........471:2014c.A
.0
.8
..81
{112–2} ·1–1–23Ò {101–1} ·1–012Ò
s=0.225 s=0.104
type I type II
Figure5.TwinsystemsinHCP-Zr.(AfterTenckhoff[72].)
Be Ti Re Mg
Hf Zr Co Zn Cd
0.8
0.7
0.6 {112–1} ·1–1–26Ò
ar 0.5
e
twinning sh 00..34 {1{1–1212–2}–4}·1·12–2–23–Ò4–3Ò {10–{1111}–1–3·}10–1·–32Ò0–3–2Ò
0.2
0.1 {101–2} ·1–011Ò {10–12} ·–1011Ò
0
1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90
c/a ratio
Figure6.Twinningshearasafunctionofc/aratioinHCPcrystals;filledgreencirclesdenotereadilyactivetwinningmodes
andredopensquaresdenotelessactivetwinningmodes.(AfterYoo[73].)LabellingofeachtwinsystemindicatestheK andK
1 2
twinningplanesandtheη andη invarianttwindirections.Notetheinversionofthe{10¯12}(cid:2)¯1011(cid:3)mode,whichindicatesits
1 2
changefromanextensiontwinforlowc/amaterialstoacontractiontwinforhighc/amaterials.