The Effects of Prestrain and Subsequent Annealing on Tensile Properties of CP-Ti

15 Pages·2017·9.14 MB·English

metals
Article
The Effects of Prestrain and Subsequent Annealing
on Tensile Properties of CP-Ti
LeChang,Chang-YuZhou*andXiao-HuaHe
SchoolofMechanicalandPowerEngineering,NanjingTechUniversity,Nanjing211816,China;
[email protected](L.C.);[email protected](X.-H.H.)
* Correspondence:[email protected];Tel./Fax:[phone]
AcademicEditor:MarkT.Whittaker
Received:14February2017;Accepted:14March2017;Published:17March2017
Abstract: The aim of the present work is to investigate the effects of prestrain and subsequent
annealingontensilepropertiesofcommercialpuretitanium(CP-Ti). Accordingtotensiletestresults,
yieldstrengthandultimatetensilestrengthincreasewiththeincreaseofprestrain. Elongationand
uniformstraindecreaselinearlywithprestrain. Inthecaseofprestrainthatishigherthan3.5%,the
macro-yieldofspecimenschangesfromgradualyieldingtodiscontinuousyielding. Itissupposed
thatconsiderablenumbersofdislocationsintroducedintothematerialleadtotheappearanceof
yieldplateau. Thequantitativeanalysisofthecontributionofdislocationhardeningtothestrain
hardeningshowsthatdislocation-associatedmechanismsplayanimportantroleinstrainhardening.
Moreover,amodifiedFields-Backofenmodelisproposedtopredicttheflowstressofprestrained
CP-Tiatdifferentstrainrates.Bothstrainratesensitivityandstrainhardeningexponentdecreasewith
prestrain. Fracturesurfacesofthespecimensshowthatfracturemechanismofalltestedspecimensis
dimplefracture. ThemoreductiledeformationinprestrainedCP-Tiafterannealingindicatesthatits
ductilityisimprovedbyannealing.
Keywords: CP-Ti;prestrain;yieldplateau;tensileproperties;flowstress;fracture
1. Introduction
Duringthemanufactureofmaterials(stamping, coldrolling, equalchannelangularpressing,
bending) and the installation and service history of the equipment components (such as creep,
overload),differentdegreesofplasticdeformationwillhappeninthematerials. Theextentofprior
plastic strain introduced into the material can significantly change the mechanical properties and
consequentlyaffecttheplasticdeformationbehavior. Atpresent,theinvestigationoftheinfluence
of prestrain on the materials has been focused on steels [1–7], titanium alloys [8–10], aluminum
alloys[11,12],magnesiumalloys[13–15],Zr-basedalloys[16]andsoon.Usually,priorheavycold
workleadstoaconsiderableincreaseinstrengthbycreatingdislocationbarrierstoinhibitsubsequent
dislocationmovementduringplasticdeformationatroomtemperature. Forinstance,Zhangetal.[2]
foundthatbypre-strainingandbakehardening,thestrengthofC–Mn–SiTRIPsteelwasenhanced.
Further, they supposed that the unlocking from weak carbon atmospheres of dislocations newly
formed during prestraining led to the appearance of yield point on the stress–strain curve [3].
Leeetal.[6,7] found that work hardening rate and strain rate sensitivity (SRS) of 304 L stainless
steelweredependentonthevariationofprestrain. Sarkeretal.[13,14]suggestedthatthevariation
of strain hardening rate of AM30 magnesium alloy with pre-straining was related to deformation
twinninganddetwinning.Thus,itcanbeseenthatprestrainhasimportanteffectsonthesubsequent
plastic deformation behavior for many materials. Also, it provides that the effects of prestrain
on the performance of hexagonal close-packed materials are associated with twinning structures
producedinthepriordeformation[13–15]. Manyresearchershavestudiedtheeffectsofpriorsevere
Metals2017,7,99;doi:10.3390/met7030099 www.mdpi.com/journal/metals
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deformation, such as cold rolling and equal channel angular pressing (ECAP) on mechanical
plasticdeformation,suchascoldrollingandequalchannelangularpressing(ECAP)onmechanical
properties of CP-Ti [17–19]. The activation of twinning in CP-Ti is affected by many factors, such as
properties of CP-Ti [17–19]. The activation of twinning in CP-Ti is affected by many factors, such
deformation temperature, strain rate, deformation value, deformation direction [20,21]. Prior
as deformation temperature, strain rate, deformation value, deformation direction [20,21]. Prior
deformation (cold rolling and ECAP) produces many twins in the initial microstructure of CP-Ti,
deformation(coldrollingandECAP)producesmanytwinsintheinitialmicrostructureofCP-Ti,which
which is different from tensile prestrain [18,19,22–24]. The effects of stretching prestrain on the
isdifferentfromtensileprestrain[18,19,22–24]. Theeffectsofstretchingprestrainonthemechanical
mechanical properties of CP-Ti have not been examined. Thus, in this paper, different amounts of
propertiesofCP-Tihavenotbeenexamined. Thus,inthispaper,differentamountsofprestrainwere
prestrain were applied to CP-Ti and a uniaxial tensile experiment was conducted to investigate the
appliedtoCP-Tiandauniaxialtensileexperimentwasconductedtoinvestigatetheeffectsofprestrain
effects of prestrain on mechanical properties, work hardening rate, flow stress and fracture
onmechanicalproperties,workhardeningrate,flowstressandfracturemechanism.
mechanism.
2. ExperimentalMaterialsandProcedures
2. Experimental Materials and Procedures
ThematerialsusedinthepresentstudywereCP-Tiintheformofacold-rolledandannealedplate.
The materials used in the present study were CP-Ti in the form of a cold-rolled and annealed
ThechemicalcompositionwasgiveninTable1. Thespecimenswith3mmthickness(seeFigure1)
plate. The chemical composition was given in Table 1. The specimens with 3 mm thickness (see Figure
weremachinedfromtheas-receivedplatebywireelectricaldischargemachining. Inordertoexclude
1) were machined from the as-received plate by wire electrical discharge machining. In order to
theeffectofsurfaceroughness,thespecimensweregroundandpolishedbymetallographicabrasive
exclude the effect of surface roughness, the specimens were ground and polished by metallographic
paper. The tensile testing was carried out by Instron tensile experimental equipment (INSTRON,
abrasive paper. The tensile testing was carried out by Instron tensile experimental equipment
Norwood,MA,USA).Thestrainwasautomaticallymeasuredbyextensometer(INSTRON,Norwood,
(INSTRON, Norwood, MA, USA). The strain was automatically measured by extensometer
MA, USA). Different levels of pre-deformation along rolling direction were applied at the same
s(ItNraSinTRraOteN(, 0N.0o0r0w5oso−d1), MwiAth, UthSeAc)o. nDtirfofleroefnetx lteevneslos mofe tperre.-Tdhefeonr,mthateiosnp eacliomnegn rsowllienrge duinrelocatidoend waenrde
raeplpoalideedd atto thfrea scatumree .sTtrhaeins trraatien (0ra.0te00d5u sr−i1n) gwriethlo tahdei ncgonrtarnogl eodf efrxotemns0o.0m00e0te5rt. oT0h.e0n0,4 ths−e 1s.pIencaimddenitsio wn,etroe
unloaded and reloaded to fracture. The strain rate during reloading ranged from 0.00005 to 0.004 s−1.
investigatetheeffectsofsubsequentannealingontensilepropertiesofprestrainedsamples,isothermal
In addition, to investigate the effects of subsequent annealing on tensile properties of prestrained
heat-treatment was conducted using a vacuum furnace equipped with an auto tune temperature
csaomntprolellse, ris(oHthUeArmHaOl NheGa,t-Sturezahtomue,nCt hwinaas) .coTnhdeuacntendea ulisninggt eam vpaecruautumr efsurwnearcee 5e0q0u◦ipCpaendd w6i0t0h ◦aCn wauittho
tune temperature controller (HUAHONG, Suzhou, China). The annealing temperatures were 500 °C
dwell times ranging from 30 min to 1 h. The detailed annealing experimental scheme was listed
and 600 °C with dwell times ranging from 30 min to 1 h. The detailed annealing experimental scheme
inTable2. Themicrostructurewascharacterizedusingopticalmetallography.Thespecimenswere
was listed in Table 2. The microstructure was characterized using optical metallography. The
mechanically ground and chemically etched in a solution consisting of 10 mL nitric acid, 2 mL
specimens were mechanically ground and chemically etched in a solution consisting of 10 mL nitric
hydrofluoricacidand88mLdistillatedwater. Studyonthefracturesurfaceoftensilespecimenswas
acid, 2 mL hydrofluoric acid and 88 mL distillated water. Study on the fracture surface of tensile
carriedoutusingaJSM-6360LVscanningelectronmicroscope(JEOL,Tokyo,Japan).
specimens was carried out using a JSM-6360LV scanning electron microscope (JEOL, Tokyo, Japan).
Table1.Chemicalcompositionofusedcommercialpure(CP)-titanium(wt.%).
Table 1. Chemical composition of used commercial pure (CP)-titanium (wt. %).
Element Ti Fe C N H O
Element Ti Fe C N H O
CompositioCnomBpaolsainticoen Ba0l.a0n6ce 0.060. 010.01 <<00..0011 0.0010 .0001.12 0.12
TTaabbllee 22.. AAnnnneeaalliinngg eexxppeerriimmeennttaall sscchheemmee..
Annealing
PPreressttrraaiinn ((εεpprree))//%% 500 °C, 30 min 500 °C, 40 mAinnn ea5li0n0g °C, 60 min 600 °C, 30 min
500◦C,30min 500◦C,40min 500◦C,60min 600◦C,30min
1 √√ √√ - √√
1 -
2 √√ √√ √√ -
2 -
√ √ √ √
33.5.5 √ √ √ √
√ √ √
55 √ √ √ --
√ √ √
66.5.5 √ √ -- √

FFiigguurree 11.. TThhee ggeeoommeettrryy ooff tthhee tteesstt ssppeecciimmeennss..
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33.. RReessuullttss aanndd DDiissccuussssiioonn
3.1. TensilePropertiesofAs-ReceivedCommercialPure(CP)-Ti
3.1. Tensile Properties of As-Received Commercial Pure (CP)-Ti
According to uniaxial tensile experiment, mechanical properties of CP-Ti were determined.
According to uniaxial tensile experiment, mechanical properties of CP-Ti were determined.
Engineeringstress–straincurvesoftheas-receivedmaterialweregiveninFigure2. Plasticdeformation
Engineering stress–strain curves of the as-received material were given in Figure 2. Plastic
processcanbedividedintothreestagesbythethreecharacteristicpoints(A,B,C)onthetensilecurve.
deformation process can be divided into three stages by the three characteristic points (A, B, C) on
Thefirstfeaturepointisyieldstrengthpoint(pointA),deformationbeforethispointistheelastic
the tensile curve. The first feature point is yield strength point (point A), deformation before this
deformationstage. Obviously,intherangeof0.00005–0.004s−1,theyieldofCP-Tiiscontinuousas
point is the elastic deformation stage. Obviously, in the range of 0.00005–0.004 s−1, the yield of CP-Ti
noyieldplateauappears. Thesecondfeaturepointisthehighestpoint(pointB).Generally,when
is continuous as no yield plateau appears. The second feature point is the highest point (point B).
maximumtensileforcereaches,sampleneckingstarts,thecorrespondingpointBisthedemarcation
Generally, when maximum tensile force reaches, sample necking starts, the corresponding point B is
betweenuniformplasticdeformationandnon-uniformplasticdeformation. Whenplasticdeformation
the demarcation between uniform plastic deformation and non-uniform plastic deformation. When
isconcentrated,load-bearingcapacitydecreasesquickly,thecorrespondingfeaturepointispointC.
plastic deformation is concentrated, load-bearing capacity decreases quickly, the corresponding feature
Thestrainofdiffuseneckingandlocalizedneckingwereexpressedasfollows:
point is point C. The strain of diffuse necking and localized necking were expressed as follows:
εεd𝑑==n𝑛 (1(1) )
εεl𝑙==22n𝑛 (2(2) )
wwhheerree εεd iiss iinniittiiaall ssttrraaiinn ooff ddiiffffuussee nneecckkiinngg,, εεl iiss iinniittiiaall ssttrraaiinn ooff llooccaalliizzeedd nneecckkiinngg aanndd nn iiss ssttrraaiinn
d l
hhaarrddeenniinngg iinnddeexx.. TThhee ssttrreessss––ssttrraaiinn ccuurrvvee iinn ppllaassttiicc ssttaaggee iiss ddiivviiddeedd iinnttoo tthhrreeee ssttaaggeess,, vviiaa uunniiffoorrmm
ddeeffoorrmmaattiioonn,, ddiiffffuussee nneecckkininggs tsataggeea nanddlo lcoaclaizliezdedn encekciknignsgt asgtaegbey btyh ethtwe otwpoe rppeernpdeincudliacrullianre lsi.nAess. tAhes
wthoer wkohrakr dhaenrdinegnienxgp eoxnpeonnteinst disi fdfeifrfeenrtenutn udnedredri dffiefrfeernetnstt srtarianinr artaetse,s,d disitsitningguuisishha arreeaa ooff ssttrreessss––ssttrraaiinn
ccuurrvvee wwaass oonnllyy ggiivveenn aatt ssttrraaiinn rraattee ooff 00..00000055 ss−−11, ,aass sshhoowwnn iinn FFiigguurree 22.. IItt ccaann bbee sseeeenn tthhaatt CCPP--TTii hhaass
oobbvviioouuss ssttrraaiinn rraattee sseennssiittiivviittyy.. WWiitthh tthhee iinnccrreeaassee ooff ssttrraaiinn rraattee,, tteennssiillee ssttrreessss––ssttrraaiinn ccuurrvvee ooff CCPP--TTii
aasscceennddss.. MMoorreeoovveerr,, tthhee yyiieelldd ssttrreennggtthh aanndd tteennssiillee ssttrreennggtthh iinnccrreeaassee aanndd tthhee eelloonnggaattiioonn ddeeccrreeaasseess..

FFiigguurree 22.. EEnnggiinneeeerriinngg ssttrreessss––ssttrraaiinn ccuurrvveess ooff aass--rreecceeiivveedd CCPP--TTii..
33..22.. TTeennssiillee PPrrooppeerrttiieess ooff PPrreessttrraaiinneedd SSppeecciimmeennss
TThhee pprreesstrtaraininw wasatsa kteankefrno mfrothme uthneif ourmnifpolramst icpdlaesftoircm daetifoonrmzoantieonan dzotnhee dainspde rtshieo ndiinssptearbsiiloitny
irnegstiaobnil(i1ty% r,e2g%io,n3 .(51%%,, 52%%,, 63..55%%,, 150%%, ,61.55%%,, 1r0e%sp,e 1c5ti%ve, lrye)s.pAecctciovredlyin).g Atcoctoerndsiinleg sttor etesns–ssilter asitnrecsus–rvstersaoinf
cduifrfvereesn otfp rdeisftfreariennetd psrpeesctrimainenesd, asspeshciomwennsin, aFsig suhroew3an, iitnc aFnigbuerese 3ena, thita tc,aanf tebre psreee-nst rtehtacht,i nagft,etre npsriele-
ssttrreestcsh–sintrga,i ntecnusrivlee asstrceesnsd–ss.trBaointh cyuiervlde satrsecnegntdhs.a nBdotuhl tiymiealtde tsetnresnilgetsht reanngdt huilnticmreaatsee .teTnhseilset rsetnrgenthgtohf
iCnPc-rTeiaissee. nThhaen scterdenagttthh eofc oCsPto-Tfid ius cetinlihtay,nacsedfr aactt uthree sctorsati nofd decurcetaislietsy,a also tfrwaictthuprer essttrraaiinn .dBeycrceoamseps aar ilnogt
wthiethe npgriensetreariinn.g Bsytr ceosms–pstarraiinngc tuhrev eensgoifn3e.e5r%in,g5 %straenssd–6st.5ra%inp cruesrtvreasi noefd 3.s5p%ec, i5m%e nans,di t6c.5a%n bperesseternaitnheadt
sepnegcinimeeernisn,g its tcraenss –bset rsaeiennc uthrvate senofgitnheeesreinspge sctirmesesn–sstarraeinc locuser,vtehsa otfm tehaenses wspheecnimperensst raarien cislorsaen, gtihnagt
mfroeman3s. 5w%hteon6 p.5r%es,tflraoiwn sistr erassnignicnrge afsreosms li3g.5h%tly two i6th.5p%r,e sfltorawin s.tWrehsse ninpcrreesatsraeisn srleigahchtleys w10i%th apnrdesatbroavine.,
Wtheheunlt ipmreastetrsatirne nregathchiessr a1p0%id laynrde aacbhoevdea, nthdey uieltlidmsatrteen sgtrtehnigstvhe irsy rcalposideltyo rteeancshileeds tarnendg ythie.ldIt sistrwenogrtthh
inso vtienrgy thclaotsaes tpor etesntrsaiilne rsetarecnhgesth3.. 5I%t i,st hweomrtahc rnoo-tyiinegld thchaat nagse psrferostmraginr ardeuaachlyesie l3d.5in%g, ttohed imscaocnrtoin-yuioeulds
ychiealndginegs ,fraosmsh gorwadnuianl Fyiigeuldrein3gb t.oT dhiescdoinsctionnutoinuuso yuieslidnicnrge,a asse sohfoflwonw isnt rFeisgsusrhe o3wb.s Tthhee adpispceoanrtainnuceouosf
yinieclrdeapslea toefa fulo.w stress shows the appearance of yield plateau.
Metals2017,7,99 4of15
Metals 2017, 7, 99 4 of 15

FFiigguurree 33.. EEnnggiinneeeerriinngg ssttrreessss––ssttrraaiinn ccuurrvveess ooff ddiiffffeerreenntt pprreessttrraaiinneedd ssppeecciimmeennss.. ((aa)) 00%%––1155%% pprreessttrraaiinneedd
CCPP--TTii aanndd ((bb)) tthhee aappppeeaarraannccee ooff yyiieelldd ppllaatteeaauu..
In order to evaluate the variation of flow stress with true strain, work hardening rate θ (dσ/dε)
Inordertoevaluatethevariationofflowstresswithtruestrain,workhardeningrateθ(dσ/dε)
is derived from the true stress–strain curve. Figure 4 displays variations of θ with true strain for as-
is derived from the true stress–strain curve. Figure 4 displays variations of θ with true strain for
received and prestrained CP-Ti. An often reported feature for pure titanium, in particular in
as-received and prestrained CP-Ti. An often reported feature for pure titanium, in particular in
compression conditions, consists in a three-stage character of deformation curve [25,26]. Work
compression conditions, consists in a three-stage character of deformation curve [25,26]. Work
hardening rate of as-received CP-Ti shows three decrease stages (A, B and C stage), as shown in
hardening rate of as-received CP-Ti shows three decrease stages (A, B and C stage), as shown in
Figure 4a. Work hardening rate decreases sharply at the beginning of plastic deformation (stage A)
Figure4a.Workhardeningratedecreasessharplyatthebeginningofplasticdeformation(stageA)
and then decreases gradually at moderate strain (stage B). In stage C, work hardening rate decreases
andthendecreasesgraduallyatmoderatestrain(stageB).InstageC,workhardeningratedecreases
slowly with strain, as the slopes flatten with the increase of true strain. Between stages A and B the
slowlywithstrain,astheslopesflattenwiththeincreaseoftruestrain. BetweenstagesAandBthe
transition occurs at a true plastic strain of 0.018, between stages B and C at a true plastic strain of
transitionoccursatatrueplasticstrainof0.018,betweenstagesBandCatatrueplasticstrainof0.096.
0.096. The transition points between stages A and B and that between stages B and C of as-received
ThetransitionpointsbetweenstagesAandBandthatbetweenstagesBandCofas-receivedCP-Tiare
CP-Ti are consist with results of Becker et al. [27] and Hama et al. [28]. For prestrained CP-Ti in Figure
consistwithresultsofBeckeretal.[27]andHamaetal.[28]. ForprestrainedCP-TiinFigure4b,itsθis
4dbe,p ietns dθe nist odneptreunedsetnrat ionna ntrdupe rsetsrtarainin a.nWdi tphrtehsetrianicnr.e Wasietho ftphree sintrcariena(sεe of≥ p2re%st)r,aainri s(eεpsrtea ≥g e2%B)o,f aw roisrek
pre
stage B of work hardening rate occurs. Stage B is characterized by an increasing strain hardening rate
hardeningrateoccurs. StageBischaracterizedbyanincreasingstrainhardeningratewithtruestrain
with true strain at the range of 0.5%–2%. With increasing prestrain, the rise tendency in stage B is
attherangeof0.5%–2%. Withincreasingprestrain,therisetendencyinstageBismoreremarkable.
mInotrhee rceamsaerokfaεble. ≥In 3th.5e% c,asster aoifn εphrea ≥r d3e.5n%in, gstrraatien ahtatrhdeeneinndg oraftset aagt ethAe eisnnde ogfa sttiavgee, aAls ios ninedgiactaivtees, athlsaot
pre
indicates that yield plateau appears in tensile stress–strain curves, which is consist with Figure 3b.
yieldplateauappearsintensilestress–straincurves,whichisconsistwithFigure3b. Additionally,
Additionally, compared with as-received CP-Ti, θ of prestrained CP-Ti decreases, indicating the
comparedwithas-receivedCP-Ti,θofprestrainedCP-Tidecreases,indicatingthedecreaseofwork
decrease of work hardening ability. Li et al. [29] and Ghaderi et al. [30] investigated the effect of grain
hardeningability. Lietal.[29]andGhaderietal.[30]investigatedtheeffectofgrainsizeonthetensile
size on the tensile deformation mechanisms of CP-Ti and found that as grain size decreased to about
deformationmechanismsofCP-Tiandfoundthatasgrainsizedecreasedtoabout26µm,yieldplateau
26 μm, yield plateau occurred. In this paper, the grain size of CP-Ti is about 30 μm, as shown in
occurred. Inthispaper,thegrainsizeofCP-Tiisabout30µm,asshowninFigure5a,determined
Figure 5a, determined by linear intercept method. Li et al. [29] supposed there were two possible
bylinearinterceptmethod. Lietal.[29]supposedthereweretwopossiblereasonsfortheobserved
reasons for the observed variation of the macro-yield. First is the high number of dislocation tangles
variationofthemacro-yield. Firstisthehighnumberofdislocationtanglesandthemobiledislocation
and the mobile dislocation density. The second reason is the presence of deformation twinning.
density. Thesecondreasonisthepresenceofdeformationtwinning. However,asgrainsizedecreases
However, as grain size decreases to 30 μm, the activation of twinning in CP-Ti during tensile
to30µm,theactivationoftwinninginCP-Tiduringtensiledeformationisnon-significant[29]. Thus,
deformation is non-significant [29]. Thus, ascribing the initial yield plateau of CP-Ti during tensile
ascribingtheinitialyieldplateauofCP-Tiduringtensiledeformationtothepresenceoftwinningis
deformation to the presence of twinning is unreasonable. It is no doubt that dislocation structure
unreasonable. Itisnodoubtthatdislocationstructureexistsintheprestrainedsamplesanditsdensity
exists in the prestrained samples and its density increases with prestrain. However, the volume
increaseswithprestrain. However,thevolumefractionoftwinningistremendouslysmall,asshownin
fraction of twinning is tremendously small, as shown in Figure 5b–f, though its density increases with
Figure5b–f,thoughitsdensityincreaseswithprestrain. Almostnotwinningstructurecanbeobserved
prestrain. Almost no twinning structure can be observed in 2%–3.5% prestrained samples and few
in2%–3.5%prestrainedsamplesandfewtwinsexistsin5%–15%prestrainedsamplesindicatedby
twins exists in 5%–15% prestrained samples indicated by white arrows. According to quantitative
whitearrows. Accordingtoquantitativestatisticalanalysisofmicrostructureintheprocessoftensile
statistical analysis of microstructure in the process of tensile deformation along rolling direction [31–
deformationalongrollingdirection[31–34],thetwinvolumefractionisalwaysconsiderablysmalland
34], the twin volume fraction is always considerably small and the plastic deformation can be
theplasticdeformationcanbeattributedtodislocationslip. Therefore,asprestrainreaches3.5%,high
attributed to dislocation slip. Therefore, as prestrain reaches 3.5%, high dislocation density in the
dislocationdensityintheinitialmicrostructureleadstothepresenceofyieldplateau.
initial microstructure leads to the presence of yield plateau.
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Metals 2017, 7, 99 5 of 15

7000 6000
676000000000 ((aa)) ssttrraa iin0n . r0raa0tt0ee05s-1 565000000000 ((bb)) 00..00000055ss--11 pprreesst t0rraa%iinn
5000 00..000000055ss-1-1 4000 01%%
/MPa/MPa 34534000000000000000 AA 000...0000000445ss-s-11-1 /MPa/MPa23423000000000000000 123562356%%.%.%.%.5555%%%%
22000000 BB 11000000
1000 C 0
10000 C 0 AA BB CC
00.00 0.04 0.08 0.12 0.16 0.20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
0.00 0.04 t0r.u0e8 strain0.12 0.16 0.20 0.00 0.02 0.04 0t.0ru6e s0t.r0a8in0.10 0.12 0.14 0.16
true strain true strain
FigFuigreur4e. T4.h Tehvea rviaartiioatnioonf wofo wrkohrka rhdaerndiennginragt erawtei twhittrhu etrsutera sitnr.a(ina). A(as) -rAesc-erievceedivCedP -CTiPa-Ttid aiftf edriefnfetrsetnrta in
Figure 4. The variation of work hardening rate with true strain. (a) As-received CP-Ti at different
ratsetsraainnd ra(tbe)s parneds t(rba)i nperdesCtraPi-nTeida tC0P.-0T0i0 a5t s0−.010.05 s−1.
strain rates and (b) prestrained CP-Ti at 0.0005 s−1.

Figure 5. Metallographic figures of different prestrained samples: (a) as-received; (b) 2%; (c) 3.5%; (d)
Figure 5. Metallographic figures of different prestrained samples: (a) as-received; (b) 2%; (c) 3.5%; (d)
Fig5u%r;e (e5). 1M0%et aanlldo g(fr)a 1p5h%ic pfirgesutrraeisnoedf dspifefecirmenetnsp.r Tewstrinasin aerde isnadmicpatleeds: b(ya )wahsi-tree acreriovweds ;in(b F)ig2u%r;e (5cd)–3f..5 %;
5%; (e) 10% and (f) 15% prestrained specimens. Twins are indicated by white arrows in Figure 5d–f.
(d)5%;(e)10%and(f)15%prestrainedspecimens.TwinsareindicatedbywhitearrowsinFigure5d–f.
The variations of strength and ductility of CP-Ti as functions of tensile prestrain are shown in
The variations of strength and ductility of CP-Ti as functions of tensile prestrain are shown in
Figures 6 and 7 respectively. It is observed that with the increase of prestrain, both yield strength and
FigTuhreesv 6a arinadt i7o nresspofecsttirveenlyg.t Iht iasn odbsdeurvcetidli tthyaot fwCitPh- tThiea isnfcurenacstei oonf sproefsttreanisni,l ebopthre ysiterladin starerengsthho awnnd in
tensile strength increase. The increment in yield strength with the amount of prestrain is gradually
Figteunresisle6 satnredn7gtrhe sinpcercetaivsee.l yT.hIet iisncorbesmerevnet dint hyaietlwd istthretnhgetihn wcrietahs tehoef apmreosutnrat ionf, pbroetshtryaiienl diss gtrreandgutahllayn d
slow, which can be seen from the slope of variation of yield strength with the increase of prestrain.
tenssloilwe,s wtrehnicght hcainn cbree aseseen. Tfrhoemi nthcree smloepnet oinf vyaieriladtisotnr eonfg ytihelwd istthretnhgetha mwoituhn tthoe finpcrreesatsrea ionf ipsrgesrtardaiuna. lly
The increase of yield strength with prestrain can be rationalised by following two reasons. One is that
sloTwh,ew inhcircehascea onf byeieslde esntrefrnogmth twhieths lporpesetroafinv acarina tbieo nraotifonyaielilsdedst breyn fogltlhowwiintgh ttwhoe rineacsroenass.e Oonfep irse tshtarat in.
dislocation density increases quickly with increasing prestrain. As a result, the resistance to start
Thdeiisnloccreaatisoeno dfeyniesiltdy sitnrecrnegatshesw qituhicpkrleys twraitihn icnacnrebaesirnagti opnreaslitsreadinb. yAfso all orwesiunlgt, ttwheo rreesaissotannsc.eO tno esitsartth at
plastic deformation on reloading increases sharply with increasing prestrain. The other is that as
displolacsattiico dnedfoenrmsiatytioinnc roena sreesloqaudiicnkgly inwcirtehasinesc rsehaasirnpglyp wreistthr aiinnc.rAeassianrge spurlets,ttrhaeinr.e sTihstea noctheetro isst athrtapt laass tic
prestrain increases, few twins also contribute to the increase of yield strength. The yield strength
depforremstraatiino ninocnreraesleosa, dfeinwg tiwnicnrse aaslesos schoanrtprilbyuwte ittho itnhcer ienacsrienagsep oref sytriealidn .sTtrhenegotthh. eTrhies tyhiaeltda sstprernegsttrha in
increases more and more slowly with prestrain. The logarithmic curve of the yield strength versus
incirnecarseeass,efse mwotrwe iannsda lmsoocreo nstloriwbulyt ewtoithth periensctrraeians.e Tohfey lioegldarsittrhemngict hc.uTrvhee oyfi ethlde sytireelndg stthreinngcrthea vseerssmuso re
the prestrain is linear. Thus, a power law can be used to describe the relationship between prestrain
the prestrain is linear. Thus, a power law can be used to describe the relationship between prestrain
andmoreslowlywithprestrain. Thelogarithmiccurveoftheyieldstrengthversustheprestrainis
and yield strength, expressed as follow:
and yield strength, expressed as follow:
linear. Thus,apowerlawcanbeusedtodescribetherelationshipbetweenprestrainandyieldstrength,
expressedasfollow: σσ==6688..0088εε𝑝𝑝𝑟𝑟𝑒𝑒00..4433++330055..3344 ((33))
IItt iiss sshhoowwnn tthhaatt tthhee ccuurrvvee ooff tthheeσ EEq=quua6at8tii.oo0nn8 ε((33pr))e ii0ss.4 cc3oo+nnss3iis0stt5ee.nn3tt4 wwiitthh tthhee oorriiggiinnaall ddaattaa ppooiinntt,, aanndd tthhee ( 3)
correlation coefficient R is 0.999. When prestrain is less than 6.5%, ultimate tensile strength increases
corIrteilsatsihoonw coneftfhicaitetnht eRc ius r0v.9e9o9f. WthheeEnq puraetsitornain(3 i)s ilsescso tnhsaisnt e6n.5t%w, uitlhtimthaeteo rteignisnilael sdtraetnagptho iinntc,raeansdest he
slowly with prestrain. As prestrain increases up to 10%, ultimate tensile strength increases rapidly
corsrloelwatlyio wnictohe pffirecsietrnatinR. iAss0 .p9r9e9s.trWainh einncprereassetrsa uinp itsol e1s0s%t,h ualnti6m.5a%te, tuenltsimilea stetretenngstihl einsctrreenasgetsh rianpcirdelays es
and yield strength is close to tensile strength. According to relationships between uniform strain,
and yield strength is close to tensile strength. According to relationships between uniform strain,
slowlywithprestrain. Asprestrainincreasesupto10%,ultimatetensilestrengthincreasesrapidly
anedellooynnigeglaadttiioosnntr e((εnε))g,, ttthoottiaasll ceelllooosnneggtaaottiiootennn ((sεεitltooettaall s==tr eεεpnprreeg ++th εε.)) Aaannccddo prpdrreeinssttgrraatiionn,,r ebblooattthhio uunnnsihiffoioprrmsmb ssetttrrwaaiienne anannuddn eeifllooonnrmggaattsiitoornna in,
decrease linearly with prestrain. As prestrain increases up to 10%, plastic deformation of CP-Ti
decrease linearly with prestrain. As prestrain increases up to 10%, plastic deformation of CP-Ti
eloqnugiacktiloyn de(εv)e,lotoptsa ilnetolo tnhgea dtiifofnus(eε ntoetaclk=inεgp sreta+geε.) Haonwdepvreers, ttroatainl ,elboontghatuionnif oofr mCPs-Ttria rienmaaninds ecloonnsgtaantito n
quickly develops into the diffuse necking stage. However, total elongation of CP-Ti remains constant
decarbeoauste l3i0n.e5a%rl, yswligithhtlpy relesstsr atihna.nA sthper easst-rraeicneiivnecdre amseasteuripalt,o t1h0a%t ,mpelaanstsi ctdhee fotortmala tdiounctoilfitCy Pk-Teeipqsu iicnk ly
about 30.5%, slightly less than the as-received material, that means the total ductility keeps in
developsintothediffuseneckingstage. However,totalelongationofCP-Tiremainsconstantabout
30.5%, slightly less than the as-received material, that means the total ductility keeps in constant.

Duringtheinitialprestrainprocessthehighertheprestrainis,thelowerelongationonreloadingis.
MMeettaallss 22001177,, 77,, 9999 66 ooff 1155
cMcooenntasslsttaa2n0n1tt7.. , D7D,uu99rriinngg tthhee iinniittiiaall pprreessttrraaiinn pprroocceessss tthhee hhiigghheerr tthhee pprreessttrraaiinn iiss,, tthhee lloowweerr eelloonnggaattiioo6nno foo1nn5
rreellooaaddiinngg iiss..

555500
550000
445500
MPaMPa440000 yyiieelldd ssttrreennggtthh
stress/stress/333305050000 RR==00.9.99977 uullttiimmaattee tteennssiillee ssttrreennggtthh
225500
220000
00 22 44 66 88 1100 1122 1144 1166
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00..4400
00..3355 3300..55%%
metersmeters0000....23235050
ductility paraductility para000000......112112050050 uetuetolnolontoitanifanlfogl og srasrtmatmtrtriai oa osisinntnntrraaiinn
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MMeettaallss 22001177,, 77,, 9999 77 ooff 1155
MMeettaallss 22001177,, 77,, 9999 77 ooff 1155
stages of θ are consistent with those in Figure 4. Therefore, it is obviously demonstrated that the high
ssttaaggeess ooff θθ aarree ccoonnssiisstteenntt wwiitthh tthhoossee iinn FFiigguurree 44.. TThheerreeffoorree,, iitt iiss oobbvviioouussllyy ddeemmoonnssttrraatteedd tthhaatt tthhee hhiigghh
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aanpdp eraisrianngc estoafgey ioefl dwpolrakte haaurdoennrienlgo ardatine.g andrisingstageofworkhardeningrate.
aanndd rriissiinngg ssttaaggee ooff wwoorrkk hhaarrddeenniinngg rraattee..

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(a) two percent prestrain with annealing; (b) five percent prestrain with annealing. Twins are
(((aaa))) ttwtwwooop eppreecrreccneetnnptt rpepsrrteerssattirrnaaiwinn i twwhiiattnhhn aeaannlnnineegaal;lii(nnbgg);; fi ((vbbe)) pffeiivrvceee nppteeprrcrceeesnntttr appinrreewssttirrtahaiinann wnweiiatthhli naagnn.nnTeewaaillniinnsgga..r eTTiwwndiinnicss a taaerrdee
indicated by white arrows in Figure 8b.
biinnyddwiicchaatiteteedda bbryryo wwwhhsiiittnee aFarirgrroouwwress 8 iibnn . FFiigguurree 88bb..

Figure 9. Engineering stress–strain cures of prestrained specimens after annealing (500 °C, 40 min).
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Figure 10. Three stages of work hardening rate in prestrained specimens after annealing: Sharp
FFFiiiggguuurrreee 111000... TTThhhrrreeeeee ssstttaaagggeeesss ooofff wwwooorrrkkk hhhaaarrrdddeeennniiinnnggg rrraaattteee iiinnn ppprrreeessstttrrraaaiiinnneeeddd ssspppeeeccciiimmmeeennnsss aaafffttteeerrr aaannnnnneeeaaallliiinnnggg::: SSShhhaaarrrppp
decrease in stage A, moderate decrease in stage B and slow decrease in stage C.
dddeeecccrrreeeaaassseee iiinnn ssstttaaagggeee AAA,,, mmmooodddeeerrraaattteee dddeeecccrrreeeaaassseee iiinnn ssstttaaagggeee BBB aaannnddd ssslllooowww dddeeecccrrreeeaaassseee iiinnn s sstttaaagggeee C CC...
Metals2017,7,99 8of15
Furtherquantitativeanalysisofthecontributionofdislocationhardeningtothestrainhardening
of the material was made. In this paper, two parameters (∆σ , ∆σ ) were introduced, expressed
1 2
asfollows:
∆σ =σ −σ (4)
1 R RA
∆σ =σ −σ (5)
2 RA S
∆σ ,∆σ representshardeningcontributionsfromdislocationsassociatedmechanismsandother
1 2
mechanisms, respectively. σ , σ andσ refertoyieldstrengthofas-receivedCP-Ti, prestrained
S R RA
specimensandprestrainedspecimenswithannealing,respectively. FromFigure11,itcanbeseen
thatbelowthestrainoftwopercent,thehardeningmainlycomesfromthedislocationsassociated
mechanismsandotherhardeningmechanismsarenotimportantatthisstage(about3–4MPa).Asstrain
increasesto3.5%,∆σ (about21–31MPa)increasesfast. Withtheincreaseofstrain,thecontributionon
2
strainhardeningfromboththedislocationsassociatedmechanismsandothermechanismsincreases.
Nevertheless,accordingtothevariationof∆σ /(∆σ +∆σ )withprestraininFigure11,despitethe
1 1 2
decreaseofcontributionfromdislocationhardening,dislocationsassociatedmechanismsstilloccupy
80%oftheoverallstrainhardening. Therefore,dislocationsplayanimportantroleinstrainhardening
ofCP-Tiduringroomtemperaturetensilealongrollingdirection. Also,itindicatesthatdislocationslip
isthepredominantplasticdeformationmechanism. ThisisconsistentwiththeresultsofAmouzou[31]
andRothetal.[33]. BasedonTaylor-typerelationsbetweendislocationdensityandlocalflowstress,
thequantifiedcontributionofdislocationdensitytotheincreaseofstrengthisexpressedasfollows:
σ = σ +MαGbρ1/2 (6)
p 0
where M, α, G and b are the Taylor factor, Taylor constant, shear modulus and Burgers vector,
respectively;andσ isthelatticefrictionstress. Accordingtotheliterature[31],therelationbetween
0
dislocationdensity(ρ)andtensilestrain(ε)islinear:
ρ= a +a ε (7)
1 2
wherea anda areconstants. Thus,thevariationofdislocationhardeningstress(∆σ )withprestrain
1 2 1
(ε )shouldsatisfythefollowingrelationship:
pre
∆σ = c +c (cid:0)a +a ε (cid:1)1/2 (8)
1 1 2 1 2 pre
wherec andc areconstants. FromFigure11,itisobviouslythattherelationshipbetween∆σ and
1 2 1
ε satisfiesEquation(8)andthecorrelationcoefficientRis0.97. Afterannealingtreatment,ultimate
pre
tensilestrengthdecreases, comparedwithprestrainedspecimens.Thedecreaseofultimatetensile
strength in the 3.5% prestrained specimen is maximum, as shown in Figure 12. The elongation of
prestrainedspecimensincreasesafterannealing,asshowninFigure13. Whenprestrainislessthan
3.5%,theelongationofprestrainedspecimensafterannealingishigherthantheas-receivedCP-Ti.
However,whenprestrainisabovefivepercent,theelongationofprestrainedspecimensafterannealing
startstodecreasecomparedwiththeas-receivedCP-Ti. Thisindicatesthatbyproperheattreatment
andcertainpriorplasticdeformation,boththestrengthandductilityofCP-Ticanbeimproved.
Metals2017,7,99 9of15
MMMeeetttaaalllsss 222000111777,,, 777,,, 999999 999 ooofff 111555

FFFFiiiigggguuuurrrreeee 11111111.... TTTThhhheeee qqqquuuuaaaannnnttttiiiiffiffiiieeeedddd aaaannnnaaaallllyyyyssssiiiissss ooooffff eeeeffffffffeeeeccccttttssss ooooffff ddddiiiissssllllooooccccaaaattttiiiioooonnnnssss aaaassssssssoooocccciiiiaaaatttteeeedddd mmmmeeeecccchhhhaaaannnniiiissssmmmmssss ((((∆ΔΔΔσσσσ1111)))) aaaannnndddd ooootttthhhheeeerrrr
mmmmeeeecccchhhhaaaannnniiiissssmmmmssss ((((Δ∆ΔΔσσσσ2222)))) oooonnnn ssssttttrrrraaaaiiiinnnn hhhhaaaarrrrddddeeeennnniiiinnnngggg....

FFFFiiiigggguuuurrrreeee 11112222.... DDDDeeecccelllciiinlnnieene eooofffo uuuflllttutiiimmlmtiaaamttteeea tttteeeennntssseiiinllleees issslttetrrreeesnnntrgggetttnhhhg aaatffhfttteeearrr f aaatennnrnnneeaeaanalllniiinnneggga:l:: i σσσnbbbg---RRR:,,, σσσσbbbb----RRRR---AAA,,,, σΔΔΔbσσσ- Rrrre-eeAppp,rrreee∆sssσeeennnrttte tttpeeenrnnessssiiilelleeen sststttrtrreeeennnnsgggitttlhhhe
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pppprrrreeeessssttttrrrraaaaiiiinnnneeeedddd aaaannnndddd pppprrrreeeessssttttrrrraaaaiiiinnnneeeedddd ssssppppeeeecccciiiimmmmeeeennnnssss wwwwiiiitttthhhh aaaannnnnnnneeeeaaaalllliiiinnnngggg....

FFFFiiiigggguuuurrrreeee 11113333.... EEEElllloooonnnnggggaaaattttiiiioooonnnn ooooffff pppprrrreeeessssttttrrrraaaaiiiinnnneeeedddd ssssppppeeeecccciiiimmmmeeeennnnssss wwwwiiiitttthhhh aaaannnnnnnneeeeaaaalllliiiinnnngggg....
3333....4444.... CCCCoooonnnnssssttttiiiittttuuuuttttiiiivvvveeee MMMMooooddddeeeellll ooooffff PPPPrrrreeeessssttttrrrraaaaiiiinnnneeeedddd CCCCPPPP----TTTTiiii
TTTThhhheeee FFFFiiiieeeellllddddssss----BBBBaaaacccckkkkooooffffeeeennnn mmmmooooddddeeeellll [[[[33336666]]]],,,, eeeexxxxpppprrrreeeesssssssseeeedddd aaaassss ffffoooolllllllloooowwwwssss::::
σσσσ====𝑘k𝑘𝑘εεεεn𝑛𝑛𝑛εε.εε̇ṁ𝑚̇𝑚𝑚 (((999()9)) )
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AAAccccccooorrrdddiiinnnggg tttooo tttrrruuueee ssstttrrreeessssss–––ssstttrrraaaiiinnn cccuuurrrvvveeesss ooofff ppprrreeessstttrrraaaiiinnneeeddd CCCPPP---TTTiii aaattt dddiiiffffffeeerrreeennnttt ssstttrrraaaiiinnn rrraaattteeesss,,, ttthhheee vvvaaarrriiiaaatttiiiooonnn ooofff
ssstttrrraaaiiinnn rrraaattteee ssseeennnsssiiitttiiivvviiitttyyy iiinnndddeeexxx mmm(((lllooogggσσσ⁄⁄⁄lllooogggεεε̇̇)̇)) wwwiiittthhh ppprrreeessstttrrraaaiiinnn iiisss ppprrreeessseeennnttteeeddd iiinnn FFFiiiggguuurrreee 111444aaa... SSSRRRSSS ooofff ppprrreeessstttrrraaaiiinnneeeddd
Metals2017,7,99 10of15
coefficient,nisthestrainhardeningexponent,andmisthestrainratesensitivityexponent. According
totruestress–straincurvesofprestrainedCP-Tiatdifferentstrainrates,thevariationofstrainrate
Metals 2017, 7, 99 10 of 15
.
sensitivityindexm(logσ/logε)withprestrainispresentedinFigure14a. SRSofprestrainedCP-Ti
dCePc-rTeia sdeesclrienaesaersl ylwinietahrlpyr ewstirtahi np.rSetsrtarianinh.a rSdtreaniinn gheaxrdpeonnienngt ne(xlpogonσe/nlto gn(ε)loagnσd⁄lsotgreεn) gathndc osetfrfiecniegntht
kc(oσe/ffεicniε.emn)t okf(σp⁄rεe𝑛sεṫr𝑚a)i noef dprCePst-rTaiinatedd iCffPer-Teni tats tdraififnerreantet sstarraeinc arlactuesla atered cianlcFuiglautered 1i4nb F,cig.uTrhee 1v4abl,uc.e Tshoef
svtarlauinesh oafr dsternaiinn ghaerxdpeonnienngt eaxnpdonsternetn agnthd csotreeffingcitehn ctoaelfmfiocisetnkt eaelpmcoosnt skteaenpt caotndsitfafenrte antt dstifrfaeirnenrat tsetsr,aains
srhatoews,n asin shFoigwunre in14 Fbi,gcu.rBeo 1th4bn,ca. nBdotkhd ne carnedas ke dweictrheapsree swtriathin p.rBeassteradino.n Beaxspeedr iomn eenxtpdearitma,emn,t ndaatnad, mk,a ns
faunndc tki oans sfuonfcptrioesntsr aoifn pwreesrterafiitnte wdearse ffoitltloedw as:s follows:
𝑚=−0.17ε +0.03 (10)
m = −0.17ε𝑝𝑟𝑒+0.03 (10)
pre
n𝑛==−−11..1199εε𝑝𝑟𝑒00.8.877++00..1144 (1(111) )
pre
𝑘k ==−−44444400..7700εεp𝑝r𝑟e𝑒++885599.4.499 (1(122) )

Figure 14. Variation of parameters with prestrain: (a) Strain rate sensitivity; (b) strain hardening
Figure 14. Variation of parameters with prestrain: (a) Strain rate sensitivity; (b) strain hardening
eexxppoonneenntt aanndd ((cc)) ssttrreennggtthh ccooeefffificciieenntt..
Thus, the modified Fields–Backofen model containing prestrain is finally obtained as follows:
Thus,themodifiedFields–Backofenmodelcontainingprestrainisfinallyobtainedasfollows:
σ=(−4440.70ε +859.49)ε−1.19ε𝑝𝑟𝑒0.87+0.14ε̇−0.17ε𝑝𝑟𝑒+0.03 (13)
𝑝𝑟𝑒
σ= (cid:0)−4440.70ε +859.49(cid:1)ε−1.19εpre0.87+0.14ε.−0.17εpre+0.03 (13)
pre
In order to investigate the prominence of the modified constitutive model, comparisons between
the experimental data and the flow stress predicted by the modified constitutive model at different
Inordertoinvestigatetheprominenceofthemodifiedconstitutivemodel,comparisonsbetween
strain rates are shown in Figure 15. In addition, the predictability of the constitutive equation is
theexperimentaldataandtheflowstresspredictedbythemodifiedconstitutivemodelatdifferent
verified via employing standard statistical parameters, such as absolute deviation (ΔA) and
strain rates are shown in Figure 15. In addition, the predictability of the constitutive equation is
vcoerrirfieeladtivoina ceomepffliocyieinngt (sRta),n adsa srhdoswtanti isnti cFaiglupraer a1m5ae–tedr.s A,stu dcihffearseanbts sotlruatien draetveisa,t itohne v(∆aAlu)easn odf ccoorrrreellaattiioonn
coefficient R in Figure 15a–d are above 0.97, hence the modified Fields-Backofen model shows a very
coefficient(R),asshowninFigure15a–d. Atdifferentstrainrates,thevaluesofcorrelationcoefficient
high degree of goodness of fit. It is found that the absolute deviation of flow stress obtained from the
R in Figure 15a–d are above 0.97, hence the modified Fields-Backofen model shows a very high
modified constitutive model varies from 1.87 to 6.88 MPa. The constitutive equations gives the least
degree of goodness of fit. It is found that the absolute deviation of flow stress obtained from the
absolute deviation of 1.87 at 0.004 s−1 of as-received CP-Ti and the largest absolute deviation of 6.88
modifiedconstitutivemodelvariesfrom1.87to6.88MPa. Theconstitutiveequationsgivestheleast
aabt s0o.0lu00te05d esv−1i aotfi o3n.5%of p1.r8e7starta0in.0e0d4 ssa−m1polfea. sT-hreucse,i vtheed pCrPop-Toisaendd cothnestliatrugteivset aebqsuoaltuitoend perveisaetniotns ao fg6o.o8d8
estimate of the plastic flow stress for prestrained CP-Ti at different strain rates.