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Effects of Pre-strain and Temperature on Bake Hardening of TWIP900CR Steel
JOURNALOFIRON ANDSTEELRESEARCH,INTERNATIONAL２ ０ １ ５,２ ２( ４):３ ６ １ Ｇ ３ ６ ５
Ef f e c t so fPr e Ｇ s t r a i nandTempe r a t u r eonBakeHa r d e n i ngo f TWIP９００CRS t e e l Su l eymanKILIC１ , Fahr e t t i nOZTURK２ , Tay f unS IGIRTMAC３ , GokhanTEKIN３
( １．Depa r tmen to fMe chan i c a lEng i ne e r i ng,Ah i Ev r anUn i ve r s i t r s eh i r４０２００,Tu r key; ２．Depa r tmen to f y,Ki Me chan i c a lEng i ne e r i ng,ThePe t r o l eumI ns t i t u t e,AbuDhab i２５３３,UAE; ３．TheCo skunö zMe t a lFo rm, Bu r s a１６１４０,Tu r key) Ab s t r a c t:Th ee f f e c t so fp r e Ｇ s t r a i na ndb a k i ngt emp e r a t u r eonb a k eh a r d e n i ngb e h a v i ou ro fTWI P９００CRs t e e lwe r ei nv e s t i Ｇ a t e d．Th er e s u l t sr e v e a lt h a tt h eb a k eh a r d e n i ngp r o c e s sc on t r i bu t e st oani nc r e a s ei ny i e l ds t r eng t hupt o６５ MPaa tt he g bak i ngt empe r a t u r eo f２００ ℃．Thed i f f e r enc ei ny i e l ds t r eng t hbe twe enbak i ngt empe r a t u r e so f１７０and２００ ℃i sa l Ｇ mo s ti ns i i f i c an t． I ti sc l e a r l e r vedt ha tbak i nga tah i empe r a t u r edoe sno tr e su l ti nas i i f i c an ti nc r e a s ei n gn yobs ght gn i e l ds t r eng t h．Fo rar e a s onab l ebakeha r den i ng,agoodc omb i na t i ono fp r e Ｇ s t r a i nandbak i ngt empe r a t u r ei sne c e s s a Ｇ y r s i de s,t het oughne s so ft hema t e r i a li sf oundt ode c r e a s ewi t hi nc r e a s i ngp r e Ｇ s t r a i n． y．Be Ke r d s:twi nn i ng Ｇ i nduc edp l a s t i c i t t e e l;TWIP;bakeha r den i ng;s t r a i nha r den i ng;t oughne s s ys ywo
Hi i lp r i c e s,env i r onmen t a lr egu l a t i ons,and gho l i twe i tde s i e su l ti n mo r eapp l i c a Ｇ gh gh gndemandsr t i ono fadvanc ed h i t r eng t hs t e e l s (AHSS)i n gh s s t ruc t u r a lc omponen t so fau t omo t i ve．The s es t e e l s , haveh i t r eng t h imp r ovedf o rmab i l i t r a sh ghs yandc wo r t h i ne s s．No rma l l i t r eng t hi sa c comＧ y, h gh s l i shed wi t ht he expens eo f duc t i l i t i l et he p y．Wh s t r eng t hi si nc r e a s ed,t he duc t i l i t i s u s u a l l d Ｇ y y e , , c r e a s ed andv i c eve r s a． I nr e c en tye a r s h i Ｇ gh man an e s ea u s t e n i t i ctw i nn i ng Ｇ i ndu c e dp l a s t i c i t P) g y (TWI
t fs t e e lont hebodyo ft hec a ri no rde rt or educ e ypeo , i t swe i t． Bumpe rbe am c r a shboxo rs imi l a rcomＧ gh t sf o ri t sh i n e r s o r t i onande l ong a t i on ponen ghe gyab p r a t i oma t e r i a lc anbeg i vena scur r en tapp l i c a t i onsi n , au t omo t i vei ndus t r Ba s i c a l l e s samoun to fshe e t y． yl ma t e r i a l sa r eus eddu et oh i t r e ng t ht owe i tr a t i o ghs gh o ft hes t e e l． I ns he e tme t a lp a r tp r oduc t i on,she e tme t Ｇ a l sa r es t ampedf i r s tandt henpa i n t i ngp r oc e s si nc l u Ｇ d i ngcoa t i ngsi spe r f o rmed．Bak i ngp r oc e s si sdone [] f o l l owi ngt hepa i n t i ngp r oc e s sa t１７０ ℃ ５ ．Dur i ng h i sope r a t i on,c a rbonandn i t r ogena t omsd i s so l ved s t e e lh a sb e e nd e v e l op e di no r d e rt oimp r o v es t r e ng t h t nt hef e r r i t es t ruc t ur eandd i f f us edt od i s l oc a t i ons． andduc t i l i t oge t he r．TheTWIPs t e e l sc on t a i nh i yt gh i [] l l owi ng t he d i f f us i on p r oc e s s, Co t t r e l la tmos Ｇ mangane s ei nt heaus t en i t e pha s e１ ．Un l i keo t he r Fo , h e r eo c c u r r e di nt h e m i c r o s t r u c t u r ea n dt h i sl e a d s h i h Ｇ s t r e n t hs t e e l s TW I Ps t e e l s c o n t a i ns l i d i s l o Ｇ p g g p [ [ ６] ２, ３] oani nc r e a s ei nt hey i e l ds t r eng t h ．Th i sp r oc e s si s c a t i on and twi nn i ng de f o rma t i on me chan i sms ． t a l l ed bake ha rden i ng．A bake ha rden i ng p r oc e s s TheTWIPs t e e l s wh i ch haveh i t r eng t habove c ghs r ov i de sas i i f i c an ti nc r e a s ei ns t r eng t ht hr ough ８００ MPaa r ea c c omp l i shedbyt hetwi nn i ng me cha Ｇ p gn , hecomb i na t i ono fwo rkha rden i ngdur i ngs t amp i ng n i sm． I nt h i st fs t e e l ah i rs t r a i n Ｇ ha r den i ng t ypeo ghe t r a i nag i ngdur i ngpa i n tbak i ngp r oc e s s． coe f f i c i en tde l aysne ck i ng．The r e f o r e,ah i t ands ghamoun Bakeha rden i ngi scons i de r eda st hep r oc e s so f o fe l onga t i on (mo r et han ４０％ )i sa ch i eved．Al Ｇ , nc r e a s i ngy i e l ds t r eng t h．F i r s tt hep r oc e s swa sde Ｇ t hought heTWIPs t e e lha sve r t t r a c t i ves t r eng t h i ya l opedf o rt hel owc a rbons t e e l s． Seve r a lr e s e a r che s andduc t i l i t omb i na t i on,sp r i ngba cko ft hes t e e li s ve yc enconduc t edr ega rd i nge f f e c t so fp r e Ｇ s t r a i ns, i t eh i ompa r ed wi t ho t he r advanc ed h i qu gh,c gh havebe [] t empe r a t ur e,andt empe r a t ur eexposur et imeont he s t r eng t hs t e e l s４ ． Au t omo t i vei ndus t r si n t e r e s t edi nus i ngt h i s yha
r f o rmanc eo fbakeha rden i ngp r oc e s sf o r AHSS． pe
B i o r aphy: Su l eymanKILIC,Ma s t e r,As s i s t an tRe s e a r che r; E Ｇma i l: su l eymank i l i c＠ah i ev r an edu t r; Re c e i v e dDa t e: Ma r ch７,２０１４ g Co r r e s i ngAu t ho r:Fahr e t t i nOZTURK,Do c t o r,As s o c i a t ePr o f e s s o r; E Ｇma i l:f o z t urk＠p i a c a e pond
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Timokh i nae ta l ７ s t ud i e d５％ p r e Ｇ s t r a i n e ddu a lpha s e ( DP)a nd t r a n s f o rma t i on Ｇ i ndu c e dp l a s t i c i t P) y (TRI s t e e l si no r de rt os e et hei nc r e a s ei ny i e l ds t r eng t h whenho l d i ngt hes t e e l sa t１７５ ℃ f o r３０ mi n．The i r r e su l t sshowedt ha tt hei nc r e a s e so fwo rkha r den i ng andbakeha r den i ng we r eabou t８０ MPaf o rDPand , ６０ MPaf o r TRIP s t e e l s r e spe c t i ve l y．The bake ha rden i ngbehav i ou ro fTRIPs t e e lwi t handwi t hou t Nband Mowi t h４％ p r e Ｇ s t r a i n wa si nve s t i a t e db g y [] Pe r e l omae ta l ８ ．A９０ MPai nc r e a s ewa sme a sur ed a f t e radd i ng Nband Moanda７０ MPai nc r e a s ewa s s e enf o rTRIPs t e e lwi t hou tNbandMo． Dehghan ie t [] a l ９ eva l ua t edt hebakeha r den i ngo f３％ －９％ p r e Ｇ s t r a i nedAl ７０７５ma t e r i a lh e l da t１１５－２８５ ℃ f o r１１－ ３５mi n．Th e t a i n e dt h eb e s tr e s u l t sa f t e rp r e Ｇ s t r a i Ｇ yob n i ngo f６％ andho l d i nga t２００ ℃ f o r２３ mi nus i ng op t imi z a t i ont e chn i s．I no t he rs t ud i e s,Dehgha Ｇ que [ １０] n i exami nedt hee f f e c to fg r a i ns i z eonbakeha rd Ｇ en i ng．Att hes amet ime,t hec ond i t i ono fbe s tbake ha rden i ng us i ng a r t i f i c i a lneu r a lne two rk (ANN ) []
wa sp r ed i c t ed ． Du r r enbe r re ta l i nve s t i t ed ge ga t hee f f e c to fpr e Ｇ s t r a i nand bakeha r den i ng ont he co l l i s i onpr ope r t i e s．Theyexpo s edTRIP７８０s t e e lt o bakeha r den i ng p r o c e s sa t１７０ ℃ f o r２０ mi nand demons t r a t edt ha tt ens i l es t r eng t hi nc r e a s e swi t hi n Ｇ c r e a s i ngp r e Ｇ s t r a i nandy i e l ds t r eng t hi nc r e a s e sand t hens t a r t sde c r e a s i nga f t e rac e r t a i nr a t e．Kva cka j [ ] and Mamuz i c１３ expo s edBH２２０s t e e lt obakeha rd Ｇ en i ngp r o c e s sa t１７０ ℃ f o r２０ mi nandt heyshowed t ha tt he r ei sani nc r e a s ei nt her angeo f７３t o８２MPa [ ] wi t h wo rk ha r den i ng．Momen ie ta l １４ c onduc t ed t her e s e a r chonbakeha r den i ng o fS t １４s t e e lwi t h , , , ４％ ６％ and８％ p r e Ｇ s t r a i nf o r２０mi na t１５０ １８０, and２１０ ℃．Re su l t sr eve a lt ha ts t r eng t hi nc r e a s e s wi t hi nc r e a s i ng bak i ngt empe r a t u r eand p r e Ｇ s t r a i n． [ ] S imi l a rr e s e a r chwa spe r f o rmedby Wange ta l １５ i n ２％ ,６％ ,and８％ p r e Ｇ s t r a i nc ond i t i onsf o rl owc a r Ｇ bons t e e lhe l da t１７０ ℃ f o r２０ mi n． I na no t h e rs t udy, e f f e c t so fb a k eh a r d e n i nga ndwo r kha r den i ngwe r eex Ｇ ami nedf o r TRIP,DP,and HSLA ( h i t r eng t h ghs [ ] l owa l l oy)s t e e l s． I nt hes t udy１６ ,t hes amp l e swe r e he l da t２％ p r e Ｇ s t r a i nand１７０ ℃ f o r３０ mi n．Ther e Ｇ s u l t sr e v e a lt h a tt h eb a k eh a r d e n i ngp r op e r t fTRI P yo s t e e l si sbe t t e rt hant ha to fDPand HSLAs t e e l s． [ ] Wagene r１７ s t ud i edt hes t r eng t hi nc r e a s ea f t e r t hepa i n t i ngp r o c e s s．Ther e su l t si nd i c a t et ha tt he s t amp i ngandpa i n t i ngp r o c e s so fac a rdoo ri nc r e a s e i e l ds t r eng t ho ft hema t e r i a lg r adua l l y y． I np r e s e n tr e s e a r c h,t h ee f f e c t so fp r e Ｇ s t r a i nand b ak i ngt emp e r a t u r ewe r es t ud i e df o rTWI P９００CRand r e su l t swe r ed i s cus s edi nde t a i l． [ １１]
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１ Exp e r imen t a lPr o c e du r e I nt h i ss t udy,aTWIP９００CRs t e e lo f１ ３mmi n t h i ckne s swa sus edi no rde rt ode t e rmi nee f f e c t so f r e Ｇ s t r a i nandbak i ngt empe r a t ur eonma t e r i a lpr op Ｇ p e r t i e s．Thechemi c a lcompos i t i ono ft he ma t e r i a li s i veni nTab l e１． g Tab l e１ Ch emi c a lc ompo s i t i ono fTWIP９００CRs t e e l ma s s％ C
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Te s ts amp l e sshowni nF i １we r ep r epa r eda c Ｇ g co rd i ngt o ASTM E８s t anda rdby wa t e rj e tcu t t i ng a l ong r o l l i ng d i r e c t i on．The a s Ｇ r e c e i ved and p r e Ｇ s t r a i neds amp l e swe r eus ed．Thep r e Ｇ s t r a i nso f２％ , ４％ ,and６％ we r eapp l i edbySh imadzu Au t og r aph
１００kNt e s t i ng ma c h i n e．Thes amp l e swe r epu ti nf u r Ｇ n a c ef o rbakeha rden i ngp r oc e s s． F i r s t l hef urna c e y,t wa ss t ab i l i z edf o r４ha t１７０and２００ ℃．Then,t he s amp l e swe r epu ti ns i det hef urna c eandexpos edf o r ２０ mi n．Thens amp l e swe r epu tou t s i det hef urna c e andcoo l eddownt or oomt empe r a t ur e( RT)．F i na l Ｇ , / l ens i l et e s twa sconduc t eda taspe edo f２５ mm yt mi n．De f o rma t i on wa s me a sur ed wi t hav i deot ype ex t ensome t e r me a sur emen t s s t e m． M e c h a n i c a l y , r ope r t i e ssucha sy i e l dandt ens i l es t r eng t hs s t r a i n p ha rden i ngands t r eng t hcoe f f i c i en t s,un i f o rmandt o Ｇ t a le l onga t i ons,andt oughne s swe r ede t e rmi ned．
F i １ Ten s i l et e s ts e c imend imen s i on s( Un i t:mm) g p
２ Re s u l t sandDi s c u s s i on Af l ow cur veshowst her e l a t i onsh i ft rue po ̇ s t r a i n( t r a i nr a t e( empe r a t ur e( ε),s ε)andt Ti n ) K ．Th i sf unc t i onc anbeexp r e s s edi nagene r a lf o rm i nEq ( １)． ̇ ( σ＝f( ε, ε, T) １)
Seve r a lemp i r i c a lmode l swe r epr opos edi nl i t e r Ｇ , a t ur e s．Themos twi de l u s e dm o d e l s a r eH o l l o m o n y ( ) , ( Swi f t Krupskowsky andLudwi t i on PowＧ gequa e rl aw)mode l s．The Ho l l omonequa t i oni sg i veni n Eq ( ２)．Th i sequa t i ondependsontwopa r ame t e r s:
I s sue４ Ef f e c t so fPr e Ｇ s t r a i nandTempe r a t u r eonBakeHa r den i ngo fTWIP９００CRS t e e l
s t r eng t hc oe f f i c i en t( K )ands t r a i nha r den i ngexpo Ｇ nen to rc oe f f i c i en t( n)． ( σ＝Kεn ２) ( Theo t he rmode li st heSwi f tmode la l s oc a l l ed Swi f t ＧKrupkowskyl aw)g i veni n Eq ( ３)．I nt h i s hei n i t i a ls t r a i n( ε０ )shou mode l,K ,n andt l dbe de f i ned． n ( ε０ ＋ε) ３) σ＝K (
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s． Theva r i a t i ono fs t r a i nha rden i ngexponen tv t rues t r a i ni sd r awna sshowni nF i ３us i ngt hede Ｇ g s c r i bed mode l s．Ther e su l t sr eve a lt ha tacon f o rmＧ ab l et endenc sob t a i nedus i ngt heLudwi l． yi g mode Asi ti squ i t eknownt ha tt hes t r a i nha rden i ngexpo Ｇ nen ti si nc r e a s edwi t hi nc r e a s i ngs t r eng t hands t r a i n．
Theo t he rmo s twi de l ed mode li st heLud Ｇ yus ( ) ( ) wi t i on Powe rl aw t ha ti sg i veni nEq ４． gequa Themode lc ons i s t so ft hr e epa r ame t e r s:K ,n,and t hema t e r i a ly i e l ds t r eng t h( σ０)． n ( σ＝σ０ ＋Kε ４)
Thes t r a i nha r den i ngc oe f f i c i en to ft hema t e r i a l i sde f i neda ss t r e s s Ｇ c a r r i ngab i l i t ft hema t e r i a la s y yo s e eni n Eq ( ５)．The h i l uei nd i c a t e sh i gh n va gh f o rmab i l i t fma t e r i a l s． yo ( ( ) n dl og σ dl σ) εd σ ( ５) n＝ ( )＝ ( )＝ ε dl ε σd ε dl og n Theha r den i ngr a t e( d σ/d ε)i sanimpo r t an tpa Ｇ r ame t e rt ode t e rmi nes t r eng t hen i ngo ft he ma t e r i a l a sshowni nEq ( ６)．Th i si sno ti den t i c a lt os t r a i n ha rden i ngexponen t,g i veni nEq ( ５)． σ d σ ( ６) ＝n d ε ε Trues t r e s sv s．t rue s t r a i n cu r ve f o ra s Ｇ r e c e i ved TWIP９００CRs t e e lwa sp l o t t edandme chan i c a lpr op Ｇ e r t i e swe r ede t e rmi neda sshowni nF i ２． Cu r vef i t Ｇ g t i ngana l s i sw a s e r f o r m e df o rs e v e r a lw e l l Ｇ k n o w n y p mode l ssucha s Ho l l omon,Swi f t (Krupskowsky), andLudw i Powe rl aw)a sd e s c r i b e dp r e v i ou s l e n g( y．Ev t hougha l lt he mode l shaver e a s onab l ep r ed i c t i ons, t heLudwi lha st hebe s tpr ed i c t i onc apab i l i t g mode y o ft hef l owcu r vef o rTWIP９００CRs t e e l．Thema t e r i Ｇ ( ) a lmode l sa r epr a c t i c a l l u s e d i nf i n i t ee l e m e n t F E y , s o f twa r e．Th e r e f o r et h eLudw i e lshou l dbecon Ｇ g mod s i de r edi nt heFEana l i s． ys
F i ３ Va r i a t i ono fs t r a i nha r d en i nge xpon en tv s． t r u es t r a i n g
S imi l a r l he wo rk ha rden i ng r a t e wa sa l so y,t s t ud i edus i ngt hep r ev i ous l s c r i bed mode l s．The yde r e su l t sa r ei l l us t r a t edi nF i ４． I ti nd i c a t e st ha tt he g ne ck i ngs t a r t sa tt hei n t e r s e c t i ono ft het rues t r e s s v s． t rues t r a i ncur veandt hewo rkha rden i ngcur ve． The Ludwi ve showst ha t ne ck i ng wi l lt ake g cur l a c ea tt hel a t e rs t age． p
F i ４ Ef f e c to fwo rkha r d en i ngr a t ev s． t r u es t r a i n g
F i ２ Tr u es t r e s sv s． t r u es t r a i nc u r v e so fd i f f e r en t g ma t e r i a lmod e l sf o rTWIP９００CRs t e e l
F i ５summa r i z e st heva r i a t i ono ft hes t r eng t h g coe f f i c i en t sandt hes t r a i nha rden i ngexponen twi t h r e spe c tt os eve r a lp r e Ｇ s t r a i nedva l ue s． I ti si nd i c a t ed t ha ts imi l a rr e su l t s we r eobs e r veda td i f f e r en tf ur Ｇ na c et empe r a t ur e s．Thes t r eng t h coe f f i c i en ts t a r t s i nc r e a s i nga tt hebeg i nn i ngandt hens t a r t sde c r e a Ｇ s i nga t４％ p r e Ｇ s t r a i n．Howeve r,t hes t r a i nha rden Ｇ i ngexponen ti nc r e a s e swi t hi nc r e a s i ngp r e Ｇ s t r a i n i ng va l ue sf o rbo t ht empe r a t ur e s．Theh i rt empe r a Ｇ ghe t ur e( ２００ ℃ )he a t i ngdo e sno tc on t r i bu t et os t r a i nha r Ｇ
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F i ５ Va r i a t i ono fs t r a i nha r d en i nge xpon en tand g s t r eng t hc o e f f i c i en tv s． bak i ngt emp e r a t u r e
F i ６ S t r a i nha r d en i nge xpon en tv s． t r u es t r a i n g
den i ngc oe f f i c i en t s． I ts e emst ha t１７０ ℃ i sani de a l t empe r a t u r ef o rbakeha r den i ngp r o c e s so ft h i sma Ｇ t e r i a l． Thes t r a i nha r den i ngc oe f f i c i en tv s． t rues t r a i n ( ) i sp l o t t edus i ngt heLudwi l F i ６ ．Re su l t s g mode g i nd i c a t et ha th i rt empe r a t u r edoe sno tp r oduc e ghe h i rva l ue．Theh i s tva l ue s we r eob t a i neda t ghe ghe e Ｇ s t r a i no f２％ andbak i ngt empe r a t u r eo f１７０ ℃． pr
s． t rues t r a i ncur ve swe r ep l o t t ed Trues t r e s sv ( ) a sshowni nF i ７ a f o r v a r i o u s r e Ｇ s t r a i n s a n d t w o g p , bak i ngt empe r a t ur e so f１７０and２００ ℃ r e spe c t i ve l y． Theg r aphwa sz oomedi nF i ７( b)． g Ther e su l t si nd i c a t et ha tt heh i rbak i ngt emＧ ghe r a t ur edoe s no tcon t r i bu t et os t r eng t hi nc r e a s e pe s i i f i c an t l I t me anst ha th i rbak i ngt empe r a Ｇ gn y． ghe , t ur ei sno tn e c e s s a r xp e c t e dt heh i rc u r v ewa s y．Ase ghe
F i ７ Tr u es t r e s sv s． t r u es t r a i nc u r v e sf o rv a r i ou sp r e Ｇ s t r a i n sandbak i ngt emp e r a t u r e s g
obs e r veda t６％ pr e Ｇ s t r a i n． Theva r i a t i oni ny i e l ds t r eng t hi si l l us t r a t eda s r a h i c a lb a r si n F i ８． I ts h o w st h a t h i h e ri n Ｇ g p g g c r e a s ewa sde t e rmi neda s６５ ８ MPaa t６％ p r e Ｇ s t r a i n and２００ ℃．Theva l uewa s５５ ３ MPaf o r１７０ ℃．A ３０ ℃ t emp e r a t u r ed i f f e r e n c e ma d ea１０ ５ MPad i f f e r Ｇ e n c ei ns t r eng t hva l ue s． De t e rmi n i ngt he y i e l ds t r eng t h,０ ２％ o f f s e t ru l ewa sus ed．Yi e l ds t r eng t hi nc r e a s e swi t hani n Ｇ c r e a s eo fp r e Ｇ s t r a i nr a t i o．Whenbakeha r den i ngwi t h ２％ pr e Ｇ s t r a i ni sapp l i edt ot hea s Ｇ r e c e i veds amp l e,
app r ox ima t e l ５ MPai nc r e a s ei ny i e l ds t r eng t h ya９９ wa sobs e r ved．A ８１ ３ MPapa r to ft h i si nc r e a s ei s c aus edby wo rkha r den i ng,andt heo t he r１８ ２ MPa r to ft h i si nc r e a s ei sowi ngt obakeha r den i ng．The pa l owe s tv a l u ewa sd e t e rmi n e da t２％ p r e Ｇ s t r a i nf o rbo t h
bak i ngt empe r a t ur e s．I nc r e a s i ng p r e Ｇ s t r a i ns me ans add i t i ona ld i s l oc a t i ons．The s er e su l t si nd i c a t et ha t add i t i ona ld i s l oc a t i onsa r ene ededf o rasu i t ab l eha rd Ｇ
F i ８ Yi e l ds t r eng t hv s． r e Ｇ s t r a i n sandbak i ngt emp e r a t u r e s g p
I s sue４ Ef f e c t so fPr e Ｇ s t r a i nandTempe r a t u r eonBakeHa r den i ngo fTWIP９００CRS t e e l
３６５
en i ngbehav i o r． Theva r i a t i oni nt ens i l es t r eng t hv s．pr e Ｇ s t r a i n andbak i ngt empe r a t u r ei sg i veni nF i ９． T h er e Ｇ g su l t sc l e a r l ha tt hec omb i na t i on o fp r e Ｇ y showedt s t r a i nandbak i ngt empe r a t u r eha snopo s i t i vee f f e c t ont ens i l es t r eng t h．
F i １１ Sp e c i f i cen e r s o rp t i onv s． r e Ｇ s t r a i n sand g g yab p bak i ngt emp e r a t u r e s
F i ９ Ten s i l es t r eng t hv s． r e Ｇ s t r a i n sand g p bak i ngt emp e r a t u r e s
Ass e eni nF i １０,t het o t a le l onga t i onwa sde Ｇ g c r e a s edwi t hi nc r e a s i ngp r e Ｇ s t r a i na sexpe c t ed．The s imi l a rbehav i o rwa sobs e r veda tbo t hbak i ngt emＧ r a t u r e s． pe Thet oughne s so ft he ma t e r i a lwa sa l s ode t e r Ｇ mi nedus i ngt hea r e aunde rt het rues t r e s sv s． t rue s t r a i ncu r ve．Th i sva l uei nd i c a t e st ha tt heamoun to f ene r i s a b s o r b e du n t i l t h e f r a c t u r e ． T h e r e s u l t s a r e gy summa r i z edandd i sp l ayedi nF i １１．Ther e su l t sr e Ｇ g ve a lt ha ti nc r e a s i ngp r e Ｇ s t r a i nha sanega t i vee f f e c t ont het oughne s s． I ti sa l s oobv i oust ha ti nc r e a s i ng bak i ngt empe r a t u r eha sanega t i vee f f e c ti nt e rmso f t oughne s sva r i a t i on．
F i １０ To t a le l ong a t i onv s． r e Ｇ s t r a i n sand g p bak i ngt emp e r a t u r e s
３ Conc l u s i on s ( １)Th eLudw i e lh a sb e t t e rp r e d i c t i on st han gmod
t heSwi f tandt heHo l l omon mode l s．The r e f o r e,t he Ludwi lshou l dbecons i de r edi nFEana l i s． g mode ys ( ２)Hi i ngt empe r a t ur edoe sno tr e su l t ghbak i nas i i f i c an ti nc r e a s ei ny i e l ds t r eng t h． gn ( ３)Hi i ngt empe r a t ur eha sanega t i ve ghbak e f f e c tont hema t e r i a lt oughne s s． ( ４)Agoodcomb i na t i ono fp r e Ｇ s t r a i nandbak Ｇ i ng t empe r a t ur ei s ne c e s s a r o r a su i t ab l e bake yf ha rden i ng． Re f e r enc e s:
[ １] VH． Schumann,NeueHü t t e１７ ( １９７２)６０５ Ｇ ６０９． [ ２] O．Gr a s s e l,L．Kr uge r,G．Fr ommeye r,L W．Meye r,I n t． J． P l a s t i c i t ２０００)１３９１ Ｇ １４０９． y１６ ( [ ３] J K． Jung,OY． Le e,YK． Pa rk,D E．Kim,KC． J i n,S K． Kim,KH． Song,J．Ko r． I ns t．Me t．Ma t e r．４６ ( ２００８)６２７ Ｇ
６３３． [ ４] MG．Le e,D．Kim,C．Kim,ML．Wenne r,K． Chung,I n t． J． P l a s t i c i t ２００５)９１５ Ｇ ９５３． y２１ ( [ ５] S． Da s,I．Timokh i na,S B． S i ngh,E． Pe r e l oma,ON．Mohan Ｇ t e r． Sc i．Eng．A５３４ ( ２０１２)４８５ Ｇ ４９４． t y,Ma [ o c．Phys．So c．LondonSe c t．A ６] AH．Co t t r e l l,B A．B i l by,Pr ６２ ( １９４９)４９ Ｇ ６２． [ ７] I B．Timokh i na,E V．Pe r e l oma,S P．Ri nge r,R K．Zheng, P D．Hodgs on,I S I JI n t． ５０ ( ２０１０)５７４ Ｇ ５８２． [ ８] E V．Pe r e l oma,KF．Rus s e l l,MK．Mi l l e r,I B．Timokh i na, Sc r i t a Ma t e r． ５８ ( ２００８)１０７８ Ｇ １０８１． p [ ９] K．De hgh a n i,A．Ne k a h i,MA M．Mi r z a i e,Ma t e r．De s． ３ １( ２ ０ １ ０) １７６８ Ｇ １７７５． [ １０] K．Dehghan i,Ma t e r． Sc i．Eng．A５３０ ( ２０１１)６１８ Ｇ ６２３． [ １１] K．Dehghan i,A． Sha f i e i,Ma t e r．Le t t． ６２ ( ２００８)１７３ Ｇ １７８． [ １２] L．Du r r e nb e r e r,X．Lemo i n e,A．Mo l i n a r i,J．Ma t e r． Pr o c e s s． g Te chno l． ２１１ ( ２０１１)１９３７ Ｇ １９４７． [ １３] T．Kva cka i c,Me t a l ur i a４５ ( ２００５)５１ Ｇ ５５． j,I．Mamuz g j [ １４] A．Momen i,K．Dehghan i,S．Abba s i,M．To rkan,Me t a l ur i Ｇ g a１３ ( ２００７)１３１ Ｇ １３８． j [ Sh i,YL．He,X G．Lu,L．L i,J． I r onS t e e l １５] H．Wang,W． Re s． I n t． １９ ( ２０１２)No １,５３ Ｇ ５９． [ １６] Adv a n c e dHi t r e ng t hS t e e l( AHSS)App l i c a t i onGu i d e l i n e s, ghS /p //www Ve r s i on４ １ [ ２００９ Ｇ ０６ Ｇ ０１]h t t wo r l d a u t o s t e e l o r r o Ｇ p: g /ah /． e c t s s s Ｇ i d e l i n e s j gu [ １７] HW．Wagene r,J．Ma t e r．Pr o c e s s．Te chno l． ７２ ( １９９７)３４２ Ｇ ３５７．
JOURNALOFIRON ANDSTEELRESEARCH,INTERNATIONAL２ ０ １ ５,２ ２( ４):３ ６ １ Ｇ ３ ６ ５
Ef f e c t so fPr e Ｇ s t r a i nandTempe r a t u r eonBakeHa r d e n i ngo f TWIP９００CRS t e e l Su l eymanKILIC１ , Fahr e t t i nOZTURK２ , Tay f unS IGIRTMAC３ , GokhanTEKIN３
( １．Depa r tmen to fMe chan i c a lEng i ne e r i ng,Ah i Ev r anUn i ve r s i t r s eh i r４０２００,Tu r key; ２．Depa r tmen to f y,Ki Me chan i c a lEng i ne e r i ng,ThePe t r o l eumI ns t i t u t e,AbuDhab i２５３３,UAE; ３．TheCo skunö zMe t a lFo rm, Bu r s a１６１４０,Tu r key) Ab s t r a c t:Th ee f f e c t so fp r e Ｇ s t r a i na ndb a k i ngt emp e r a t u r eonb a k eh a r d e n i ngb e h a v i ou ro fTWI P９００CRs t e e lwe r ei nv e s t i Ｇ a t e d．Th er e s u l t sr e v e a lt h a tt h eb a k eh a r d e n i ngp r o c e s sc on t r i bu t e st oani nc r e a s ei ny i e l ds t r eng t hupt o６５ MPaa tt he g bak i ngt empe r a t u r eo f２００ ℃．Thed i f f e r enc ei ny i e l ds t r eng t hbe twe enbak i ngt empe r a t u r e so f１７０and２００ ℃i sa l Ｇ mo s ti ns i i f i c an t． I ti sc l e a r l e r vedt ha tbak i nga tah i empe r a t u r edoe sno tr e su l ti nas i i f i c an ti nc r e a s ei n gn yobs ght gn i e l ds t r eng t h．Fo rar e a s onab l ebakeha r den i ng,agoodc omb i na t i ono fp r e Ｇ s t r a i nandbak i ngt empe r a t u r ei sne c e s s a Ｇ y r s i de s,t het oughne s so ft hema t e r i a li sf oundt ode c r e a s ewi t hi nc r e a s i ngp r e Ｇ s t r a i n． y．Be Ke r d s:twi nn i ng Ｇ i nduc edp l a s t i c i t t e e l;TWIP;bakeha r den i ng;s t r a i nha r den i ng;t oughne s s ys ywo
Hi i lp r i c e s,env i r onmen t a lr egu l a t i ons,and gho l i twe i tde s i e su l ti n mo r eapp l i c a Ｇ gh gh gndemandsr t i ono fadvanc ed h i t r eng t hs t e e l s (AHSS)i n gh s s t ruc t u r a lc omponen t so fau t omo t i ve．The s es t e e l s , haveh i t r eng t h imp r ovedf o rmab i l i t r a sh ghs yandc wo r t h i ne s s．No rma l l i t r eng t hi sa c comＧ y, h gh s l i shed wi t ht he expens eo f duc t i l i t i l et he p y．Wh s t r eng t hi si nc r e a s ed,t he duc t i l i t i s u s u a l l d Ｇ y y e , , c r e a s ed andv i c eve r s a． I nr e c en tye a r s h i Ｇ gh man an e s ea u s t e n i t i ctw i nn i ng Ｇ i ndu c e dp l a s t i c i t P) g y (TWI
t fs t e e lont hebodyo ft hec a ri no rde rt or educ e ypeo , i t swe i t． Bumpe rbe am c r a shboxo rs imi l a rcomＧ gh t sf o ri t sh i n e r s o r t i onande l ong a t i on ponen ghe gyab p r a t i oma t e r i a lc anbeg i vena scur r en tapp l i c a t i onsi n , au t omo t i vei ndus t r Ba s i c a l l e s samoun to fshe e t y． yl ma t e r i a l sa r eus eddu et oh i t r e ng t ht owe i tr a t i o ghs gh o ft hes t e e l． I ns he e tme t a lp a r tp r oduc t i on,she e tme t Ｇ a l sa r es t ampedf i r s tandt henpa i n t i ngp r oc e s si nc l u Ｇ d i ngcoa t i ngsi spe r f o rmed．Bak i ngp r oc e s si sdone [] f o l l owi ngt hepa i n t i ngp r oc e s sa t１７０ ℃ ５ ．Dur i ng h i sope r a t i on,c a rbonandn i t r ogena t omsd i s so l ved s t e e lh a sb e e nd e v e l op e di no r d e rt oimp r o v es t r e ng t h t nt hef e r r i t es t ruc t ur eandd i f f us edt od i s l oc a t i ons． andduc t i l i t oge t he r．TheTWIPs t e e l sc on t a i nh i yt gh i [] l l owi ng t he d i f f us i on p r oc e s s, Co t t r e l la tmos Ｇ mangane s ei nt heaus t en i t e pha s e１ ．Un l i keo t he r Fo , h e r eo c c u r r e di nt h e m i c r o s t r u c t u r ea n dt h i sl e a d s h i h Ｇ s t r e n t hs t e e l s TW I Ps t e e l s c o n t a i ns l i d i s l o Ｇ p g g p [ [ ６] ２, ３] oani nc r e a s ei nt hey i e l ds t r eng t h ．Th i sp r oc e s si s c a t i on and twi nn i ng de f o rma t i on me chan i sms ． t a l l ed bake ha rden i ng．A bake ha rden i ng p r oc e s s TheTWIPs t e e l s wh i ch haveh i t r eng t habove c ghs r ov i de sas i i f i c an ti nc r e a s ei ns t r eng t ht hr ough ８００ MPaa r ea c c omp l i shedbyt hetwi nn i ng me cha Ｇ p gn , hecomb i na t i ono fwo rkha rden i ngdur i ngs t amp i ng n i sm． I nt h i st fs t e e l ah i rs t r a i n Ｇ ha r den i ng t ypeo ghe t r a i nag i ngdur i ngpa i n tbak i ngp r oc e s s． coe f f i c i en tde l aysne ck i ng．The r e f o r e,ah i t ands ghamoun Bakeha rden i ngi scons i de r eda st hep r oc e s so f o fe l onga t i on (mo r et han ４０％ )i sa ch i eved．Al Ｇ , nc r e a s i ngy i e l ds t r eng t h．F i r s tt hep r oc e s swa sde Ｇ t hought heTWIPs t e e lha sve r t t r a c t i ves t r eng t h i ya l opedf o rt hel owc a rbons t e e l s． Seve r a lr e s e a r che s andduc t i l i t omb i na t i on,sp r i ngba cko ft hes t e e li s ve yc enconduc t edr ega rd i nge f f e c t so fp r e Ｇ s t r a i ns, i t eh i ompa r ed wi t ho t he r advanc ed h i qu gh,c gh havebe [] t empe r a t ur e,andt empe r a t ur eexposur et imeont he s t r eng t hs t e e l s４ ． Au t omo t i vei ndus t r si n t e r e s t edi nus i ngt h i s yha
r f o rmanc eo fbakeha rden i ngp r oc e s sf o r AHSS． pe
B i o r aphy: Su l eymanKILIC,Ma s t e r,As s i s t an tRe s e a r che r; E Ｇma i l: su l eymank i l i c＠ah i ev r an edu t r; Re c e i v e dDa t e: Ma r ch７,２０１４ g Co r r e s i ngAu t ho r:Fahr e t t i nOZTURK,Do c t o r,As s o c i a t ePr o f e s s o r; E Ｇma i l:f o z t urk＠p i a c a e pond
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２２
３６２
Timokh i nae ta l ７ s t ud i e d５％ p r e Ｇ s t r a i n e ddu a lpha s e ( DP)a nd t r a n s f o rma t i on Ｇ i ndu c e dp l a s t i c i t P) y (TRI s t e e l si no r de rt os e et hei nc r e a s ei ny i e l ds t r eng t h whenho l d i ngt hes t e e l sa t１７５ ℃ f o r３０ mi n．The i r r e su l t sshowedt ha tt hei nc r e a s e so fwo rkha r den i ng andbakeha r den i ng we r eabou t８０ MPaf o rDPand , ６０ MPaf o r TRIP s t e e l s r e spe c t i ve l y．The bake ha rden i ngbehav i ou ro fTRIPs t e e lwi t handwi t hou t Nband Mowi t h４％ p r e Ｇ s t r a i n wa si nve s t i a t e db g y [] Pe r e l omae ta l ８ ．A９０ MPai nc r e a s ewa sme a sur ed a f t e radd i ng Nband Moanda７０ MPai nc r e a s ewa s s e enf o rTRIPs t e e lwi t hou tNbandMo． Dehghan ie t [] a l ９ eva l ua t edt hebakeha r den i ngo f３％ －９％ p r e Ｇ s t r a i nedAl ７０７５ma t e r i a lh e l da t１１５－２８５ ℃ f o r１１－ ３５mi n．Th e t a i n e dt h eb e s tr e s u l t sa f t e rp r e Ｇ s t r a i Ｇ yob n i ngo f６％ andho l d i nga t２００ ℃ f o r２３ mi nus i ng op t imi z a t i ont e chn i s．I no t he rs t ud i e s,Dehgha Ｇ que [ １０] n i exami nedt hee f f e c to fg r a i ns i z eonbakeha rd Ｇ en i ng．Att hes amet ime,t hec ond i t i ono fbe s tbake ha rden i ng us i ng a r t i f i c i a lneu r a lne two rk (ANN ) []
wa sp r ed i c t ed ． Du r r enbe r re ta l i nve s t i t ed ge ga t hee f f e c to fpr e Ｇ s t r a i nand bakeha r den i ng ont he co l l i s i onpr ope r t i e s．Theyexpo s edTRIP７８０s t e e lt o bakeha r den i ng p r o c e s sa t１７０ ℃ f o r２０ mi nand demons t r a t edt ha tt ens i l es t r eng t hi nc r e a s e swi t hi n Ｇ c r e a s i ngp r e Ｇ s t r a i nandy i e l ds t r eng t hi nc r e a s e sand t hens t a r t sde c r e a s i nga f t e rac e r t a i nr a t e．Kva cka j [ ] and Mamuz i c１３ expo s edBH２２０s t e e lt obakeha rd Ｇ en i ngp r o c e s sa t１７０ ℃ f o r２０ mi nandt heyshowed t ha tt he r ei sani nc r e a s ei nt her angeo f７３t o８２MPa [ ] wi t h wo rk ha r den i ng．Momen ie ta l １４ c onduc t ed t her e s e a r chonbakeha r den i ng o fS t １４s t e e lwi t h , , , ４％ ６％ and８％ p r e Ｇ s t r a i nf o r２０mi na t１５０ １８０, and２１０ ℃．Re su l t sr eve a lt ha ts t r eng t hi nc r e a s e s wi t hi nc r e a s i ng bak i ngt empe r a t u r eand p r e Ｇ s t r a i n． [ ] S imi l a rr e s e a r chwa spe r f o rmedby Wange ta l １５ i n ２％ ,６％ ,and８％ p r e Ｇ s t r a i nc ond i t i onsf o rl owc a r Ｇ bons t e e lhe l da t１７０ ℃ f o r２０ mi n． I na no t h e rs t udy, e f f e c t so fb a k eh a r d e n i nga ndwo r kha r den i ngwe r eex Ｇ ami nedf o r TRIP,DP,and HSLA ( h i t r eng t h ghs [ ] l owa l l oy)s t e e l s． I nt hes t udy１６ ,t hes amp l e swe r e he l da t２％ p r e Ｇ s t r a i nand１７０ ℃ f o r３０ mi n．Ther e Ｇ s u l t sr e v e a lt h a tt h eb a k eh a r d e n i ngp r op e r t fTRI P yo s t e e l si sbe t t e rt hant ha to fDPand HSLAs t e e l s． [ ] Wagene r１７ s t ud i edt hes t r eng t hi nc r e a s ea f t e r t hepa i n t i ngp r o c e s s．Ther e su l t si nd i c a t et ha tt he s t amp i ngandpa i n t i ngp r o c e s so fac a rdoo ri nc r e a s e i e l ds t r eng t ho ft hema t e r i a lg r adua l l y y． I np r e s e n tr e s e a r c h,t h ee f f e c t so fp r e Ｇ s t r a i nand b ak i ngt emp e r a t u r ewe r es t ud i e df o rTWI P９００CRand r e su l t swe r ed i s cus s edi nde t a i l． [ １１]
[ １２]
１ Exp e r imen t a lPr o c e du r e I nt h i ss t udy,aTWIP９００CRs t e e lo f１ ３mmi n t h i ckne s swa sus edi no rde rt ode t e rmi nee f f e c t so f r e Ｇ s t r a i nandbak i ngt empe r a t ur eonma t e r i a lpr op Ｇ p e r t i e s．Thechemi c a lcompos i t i ono ft he ma t e r i a li s i veni nTab l e１． g Tab l e１ Ch emi c a lc ompo s i t i ono fTWIP９００CRs t e e l ma s s％ C
０ ３７
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Cr
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Te s ts amp l e sshowni nF i １we r ep r epa r eda c Ｇ g co rd i ngt o ASTM E８s t anda rdby wa t e rj e tcu t t i ng a l ong r o l l i ng d i r e c t i on．The a s Ｇ r e c e i ved and p r e Ｇ s t r a i neds amp l e swe r eus ed．Thep r e Ｇ s t r a i nso f２％ , ４％ ,and６％ we r eapp l i edbySh imadzu Au t og r aph
１００kNt e s t i ng ma c h i n e．Thes amp l e swe r epu ti nf u r Ｇ n a c ef o rbakeha rden i ngp r oc e s s． F i r s t l hef urna c e y,t wa ss t ab i l i z edf o r４ha t１７０and２００ ℃．Then,t he s amp l e swe r epu ti ns i det hef urna c eandexpos edf o r ２０ mi n．Thens amp l e swe r epu tou t s i det hef urna c e andcoo l eddownt or oomt empe r a t ur e( RT)．F i na l Ｇ , / l ens i l et e s twa sconduc t eda taspe edo f２５ mm yt mi n．De f o rma t i on wa s me a sur ed wi t hav i deot ype ex t ensome t e r me a sur emen t s s t e m． M e c h a n i c a l y , r ope r t i e ssucha sy i e l dandt ens i l es t r eng t hs s t r a i n p ha rden i ngands t r eng t hcoe f f i c i en t s,un i f o rmandt o Ｇ t a le l onga t i ons,andt oughne s swe r ede t e rmi ned．
F i １ Ten s i l et e s ts e c imend imen s i on s( Un i t:mm) g p
２ Re s u l t sandDi s c u s s i on Af l ow cur veshowst her e l a t i onsh i ft rue po ̇ s t r a i n( t r a i nr a t e( empe r a t ur e( ε),s ε)andt Ti n ) K ．Th i sf unc t i onc anbeexp r e s s edi nagene r a lf o rm i nEq ( １)． ̇ ( σ＝f( ε, ε, T) １)
Seve r a lemp i r i c a lmode l swe r epr opos edi nl i t e r Ｇ , a t ur e s．Themos twi de l u s e dm o d e l s a r eH o l l o m o n y ( ) , ( Swi f t Krupskowsky andLudwi t i on PowＧ gequa e rl aw)mode l s．The Ho l l omonequa t i oni sg i veni n Eq ( ２)．Th i sequa t i ondependsontwopa r ame t e r s:
I s sue４ Ef f e c t so fPr e Ｇ s t r a i nandTempe r a t u r eonBakeHa r den i ngo fTWIP９００CRS t e e l
s t r eng t hc oe f f i c i en t( K )ands t r a i nha r den i ngexpo Ｇ nen to rc oe f f i c i en t( n)． ( σ＝Kεn ２) ( Theo t he rmode li st heSwi f tmode la l s oc a l l ed Swi f t ＧKrupkowskyl aw)g i veni n Eq ( ３)．I nt h i s hei n i t i a ls t r a i n( ε０ )shou mode l,K ,n andt l dbe de f i ned． n ( ε０ ＋ε) ３) σ＝K (
３６３
s． Theva r i a t i ono fs t r a i nha rden i ngexponen tv t rues t r a i ni sd r awna sshowni nF i ３us i ngt hede Ｇ g s c r i bed mode l s．Ther e su l t sr eve a lt ha tacon f o rmＧ ab l et endenc sob t a i nedus i ngt heLudwi l． yi g mode Asi ti squ i t eknownt ha tt hes t r a i nha rden i ngexpo Ｇ nen ti si nc r e a s edwi t hi nc r e a s i ngs t r eng t hands t r a i n．
Theo t he rmo s twi de l ed mode li st heLud Ｇ yus ( ) ( ) wi t i on Powe rl aw t ha ti sg i veni nEq ４． gequa Themode lc ons i s t so ft hr e epa r ame t e r s:K ,n,and t hema t e r i a ly i e l ds t r eng t h( σ０)． n ( σ＝σ０ ＋Kε ４)
Thes t r a i nha r den i ngc oe f f i c i en to ft hema t e r i a l i sde f i neda ss t r e s s Ｇ c a r r i ngab i l i t ft hema t e r i a la s y yo s e eni n Eq ( ５)．The h i l uei nd i c a t e sh i gh n va gh f o rmab i l i t fma t e r i a l s． yo ( ( ) n dl og σ dl σ) εd σ ( ５) n＝ ( )＝ ( )＝ ε dl ε σd ε dl og n Theha r den i ngr a t e( d σ/d ε)i sanimpo r t an tpa Ｇ r ame t e rt ode t e rmi nes t r eng t hen i ngo ft he ma t e r i a l a sshowni nEq ( ６)．Th i si sno ti den t i c a lt os t r a i n ha rden i ngexponen t,g i veni nEq ( ５)． σ d σ ( ６) ＝n d ε ε Trues t r e s sv s．t rue s t r a i n cu r ve f o ra s Ｇ r e c e i ved TWIP９００CRs t e e lwa sp l o t t edandme chan i c a lpr op Ｇ e r t i e swe r ede t e rmi neda sshowni nF i ２． Cu r vef i t Ｇ g t i ngana l s i sw a s e r f o r m e df o rs e v e r a lw e l l Ｇ k n o w n y p mode l ssucha s Ho l l omon,Swi f t (Krupskowsky), andLudw i Powe rl aw)a sd e s c r i b e dp r e v i ou s l e n g( y．Ev t hougha l lt he mode l shaver e a s onab l ep r ed i c t i ons, t heLudwi lha st hebe s tpr ed i c t i onc apab i l i t g mode y o ft hef l owcu r vef o rTWIP９００CRs t e e l．Thema t e r i Ｇ ( ) a lmode l sa r epr a c t i c a l l u s e d i nf i n i t ee l e m e n t F E y , s o f twa r e．Th e r e f o r et h eLudw i e lshou l dbecon Ｇ g mod s i de r edi nt heFEana l i s． ys
F i ３ Va r i a t i ono fs t r a i nha r d en i nge xpon en tv s． t r u es t r a i n g
S imi l a r l he wo rk ha rden i ng r a t e wa sa l so y,t s t ud i edus i ngt hep r ev i ous l s c r i bed mode l s．The yde r e su l t sa r ei l l us t r a t edi nF i ４． I ti nd i c a t e st ha tt he g ne ck i ngs t a r t sa tt hei n t e r s e c t i ono ft het rues t r e s s v s． t rues t r a i ncur veandt hewo rkha rden i ngcur ve． The Ludwi ve showst ha t ne ck i ng wi l lt ake g cur l a c ea tt hel a t e rs t age． p
F i ４ Ef f e c to fwo rkha r d en i ngr a t ev s． t r u es t r a i n g
F i ２ Tr u es t r e s sv s． t r u es t r a i nc u r v e so fd i f f e r en t g ma t e r i a lmod e l sf o rTWIP９００CRs t e e l
F i ５summa r i z e st heva r i a t i ono ft hes t r eng t h g coe f f i c i en t sandt hes t r a i nha rden i ngexponen twi t h r e spe c tt os eve r a lp r e Ｇ s t r a i nedva l ue s． I ti si nd i c a t ed t ha ts imi l a rr e su l t s we r eobs e r veda td i f f e r en tf ur Ｇ na c et empe r a t ur e s．Thes t r eng t h coe f f i c i en ts t a r t s i nc r e a s i nga tt hebeg i nn i ngandt hens t a r t sde c r e a Ｇ s i nga t４％ p r e Ｇ s t r a i n．Howeve r,t hes t r a i nha rden Ｇ i ngexponen ti nc r e a s e swi t hi nc r e a s i ngp r e Ｇ s t r a i n i ng va l ue sf o rbo t ht empe r a t ur e s．Theh i rt empe r a Ｇ ghe t ur e( ２００ ℃ )he a t i ngdo e sno tc on t r i bu t et os t r a i nha r Ｇ
３６４
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２２
F i ５ Va r i a t i ono fs t r a i nha r d en i nge xpon en tand g s t r eng t hc o e f f i c i en tv s． bak i ngt emp e r a t u r e
F i ６ S t r a i nha r d en i nge xpon en tv s． t r u es t r a i n g
den i ngc oe f f i c i en t s． I ts e emst ha t１７０ ℃ i sani de a l t empe r a t u r ef o rbakeha r den i ngp r o c e s so ft h i sma Ｇ t e r i a l． Thes t r a i nha r den i ngc oe f f i c i en tv s． t rues t r a i n ( ) i sp l o t t edus i ngt heLudwi l F i ６ ．Re su l t s g mode g i nd i c a t et ha th i rt empe r a t u r edoe sno tp r oduc e ghe h i rva l ue．Theh i s tva l ue s we r eob t a i neda t ghe ghe e Ｇ s t r a i no f２％ andbak i ngt empe r a t u r eo f１７０ ℃． pr
s． t rues t r a i ncur ve swe r ep l o t t ed Trues t r e s sv ( ) a sshowni nF i ７ a f o r v a r i o u s r e Ｇ s t r a i n s a n d t w o g p , bak i ngt empe r a t ur e so f１７０and２００ ℃ r e spe c t i ve l y． Theg r aphwa sz oomedi nF i ７( b)． g Ther e su l t si nd i c a t et ha tt heh i rbak i ngt emＧ ghe r a t ur edoe s no tcon t r i bu t et os t r eng t hi nc r e a s e pe s i i f i c an t l I t me anst ha th i rbak i ngt empe r a Ｇ gn y． ghe , t ur ei sno tn e c e s s a r xp e c t e dt heh i rc u r v ewa s y．Ase ghe
F i ７ Tr u es t r e s sv s． t r u es t r a i nc u r v e sf o rv a r i ou sp r e Ｇ s t r a i n sandbak i ngt emp e r a t u r e s g
obs e r veda t６％ pr e Ｇ s t r a i n． Theva r i a t i oni ny i e l ds t r eng t hi si l l us t r a t eda s r a h i c a lb a r si n F i ８． I ts h o w st h a t h i h e ri n Ｇ g p g g c r e a s ewa sde t e rmi neda s６５ ８ MPaa t６％ p r e Ｇ s t r a i n and２００ ℃．Theva l uewa s５５ ３ MPaf o r１７０ ℃．A ３０ ℃ t emp e r a t u r ed i f f e r e n c e ma d ea１０ ５ MPad i f f e r Ｇ e n c ei ns t r eng t hva l ue s． De t e rmi n i ngt he y i e l ds t r eng t h,０ ２％ o f f s e t ru l ewa sus ed．Yi e l ds t r eng t hi nc r e a s e swi t hani n Ｇ c r e a s eo fp r e Ｇ s t r a i nr a t i o．Whenbakeha r den i ngwi t h ２％ pr e Ｇ s t r a i ni sapp l i edt ot hea s Ｇ r e c e i veds amp l e,
app r ox ima t e l ５ MPai nc r e a s ei ny i e l ds t r eng t h ya９９ wa sobs e r ved．A ８１ ３ MPapa r to ft h i si nc r e a s ei s c aus edby wo rkha r den i ng,andt heo t he r１８ ２ MPa r to ft h i si nc r e a s ei sowi ngt obakeha r den i ng．The pa l owe s tv a l u ewa sd e t e rmi n e da t２％ p r e Ｇ s t r a i nf o rbo t h
bak i ngt empe r a t ur e s．I nc r e a s i ng p r e Ｇ s t r a i ns me ans add i t i ona ld i s l oc a t i ons．The s er e su l t si nd i c a t et ha t add i t i ona ld i s l oc a t i onsa r ene ededf o rasu i t ab l eha rd Ｇ
F i ８ Yi e l ds t r eng t hv s． r e Ｇ s t r a i n sandbak i ngt emp e r a t u r e s g p
I s sue４ Ef f e c t so fPr e Ｇ s t r a i nandTempe r a t u r eonBakeHa r den i ngo fTWIP９００CRS t e e l
３６５
en i ngbehav i o r． Theva r i a t i oni nt ens i l es t r eng t hv s．pr e Ｇ s t r a i n andbak i ngt empe r a t u r ei sg i veni nF i ９． T h er e Ｇ g su l t sc l e a r l ha tt hec omb i na t i on o fp r e Ｇ y showedt s t r a i nandbak i ngt empe r a t u r eha snopo s i t i vee f f e c t ont ens i l es t r eng t h．
F i １１ Sp e c i f i cen e r s o rp t i onv s． r e Ｇ s t r a i n sand g g yab p bak i ngt emp e r a t u r e s
F i ９ Ten s i l es t r eng t hv s． r e Ｇ s t r a i n sand g p bak i ngt emp e r a t u r e s
Ass e eni nF i １０,t het o t a le l onga t i onwa sde Ｇ g c r e a s edwi t hi nc r e a s i ngp r e Ｇ s t r a i na sexpe c t ed．The s imi l a rbehav i o rwa sobs e r veda tbo t hbak i ngt emＧ r a t u r e s． pe Thet oughne s so ft he ma t e r i a lwa sa l s ode t e r Ｇ mi nedus i ngt hea r e aunde rt het rues t r e s sv s． t rue s t r a i ncu r ve．Th i sva l uei nd i c a t e st ha tt heamoun to f ene r i s a b s o r b e du n t i l t h e f r a c t u r e ． T h e r e s u l t s a r e gy summa r i z edandd i sp l ayedi nF i １１．Ther e su l t sr e Ｇ g ve a lt ha ti nc r e a s i ngp r e Ｇ s t r a i nha sanega t i vee f f e c t ont het oughne s s． I ti sa l s oobv i oust ha ti nc r e a s i ng bak i ngt empe r a t u r eha sanega t i vee f f e c ti nt e rmso f t oughne s sva r i a t i on．
F i １０ To t a le l ong a t i onv s． r e Ｇ s t r a i n sand g p bak i ngt emp e r a t u r e s
３ Conc l u s i on s ( １)Th eLudw i e lh a sb e t t e rp r e d i c t i on st han gmod
t heSwi f tandt heHo l l omon mode l s．The r e f o r e,t he Ludwi lshou l dbecons i de r edi nFEana l i s． g mode ys ( ２)Hi i ngt empe r a t ur edoe sno tr e su l t ghbak i nas i i f i c an ti nc r e a s ei ny i e l ds t r eng t h． gn ( ３)Hi i ngt empe r a t ur eha sanega t i ve ghbak e f f e c tont hema t e r i a lt oughne s s． ( ４)Agoodcomb i na t i ono fp r e Ｇ s t r a i nandbak Ｇ i ng t empe r a t ur ei s ne c e s s a r o r a su i t ab l e bake yf ha rden i ng． Re f e r enc e s:
[ １] VH． Schumann,NeueHü t t e１７ ( １９７２)６０５ Ｇ ６０９． [ ２] O．Gr a s s e l,L．Kr uge r,G．Fr ommeye r,L W．Meye r,I n t． J． P l a s t i c i t ２０００)１３９１ Ｇ １４０９． y１６ ( [ ３] J K． Jung,OY． Le e,YK． Pa rk,D E．Kim,KC． J i n,S K． Kim,KH． Song,J．Ko r． I ns t．Me t．Ma t e r．４６ ( ２００８)６２７ Ｇ
６３３． [ ４] MG．Le e,D．Kim,C．Kim,ML．Wenne r,K． Chung,I n t． J． P l a s t i c i t ２００５)９１５ Ｇ ９５３． y２１ ( [ ５] S． Da s,I．Timokh i na,S B． S i ngh,E． Pe r e l oma,ON．Mohan Ｇ t e r． Sc i．Eng．A５３４ ( ２０１２)４８５ Ｇ ４９４． t y,Ma [ o c．Phys．So c．LondonSe c t．A ６] AH．Co t t r e l l,B A．B i l by,Pr ６２ ( １９４９)４９ Ｇ ６２． [ ７] I B．Timokh i na,E V．Pe r e l oma,S P．Ri nge r,R K．Zheng, P D．Hodgs on,I S I JI n t． ５０ ( ２０１０)５７４ Ｇ ５８２． [ ８] E V．Pe r e l oma,KF．Rus s e l l,MK．Mi l l e r,I B．Timokh i na, Sc r i t a Ma t e r． ５８ ( ２００８)１０７８ Ｇ １０８１． p [ ９] K．De hgh a n i,A．Ne k a h i,MA M．Mi r z a i e,Ma t e r．De s． ３ １( ２ ０ １ ０) １７６８ Ｇ １７７５． [ １０] K．Dehghan i,Ma t e r． Sc i．Eng．A５３０ ( ２０１１)６１８ Ｇ ６２３． [ １１] K．Dehghan i,A． Sha f i e i,Ma t e r．Le t t． ６２ ( ２００８)１７３ Ｇ １７８． [ １２] L．Du r r e nb e r e r,X．Lemo i n e,A．Mo l i n a r i,J．Ma t e r． Pr o c e s s． g Te chno l． ２１１ ( ２０１１)１９３７ Ｇ １９４７． [ １３] T．Kva cka i c,Me t a l ur i a４５ ( ２００５)５１ Ｇ ５５． j,I．Mamuz g j [ １４] A．Momen i,K．Dehghan i,S．Abba s i,M．To rkan,Me t a l ur i Ｇ g a１３ ( ２００７)１３１ Ｇ １３８． j [ Sh i,YL．He,X G．Lu,L．L i,J． I r onS t e e l １５] H．Wang,W． Re s． I n t． １９ ( ２０１２)No １,５３ Ｇ ５９． [ １６] Adv a n c e dHi t r e ng t hS t e e l( AHSS)App l i c a t i onGu i d e l i n e s, ghS /p //www Ve r s i on４ １ [ ２００９ Ｇ ０６ Ｇ ０１]h t t wo r l d a u t o s t e e l o r r o Ｇ p: g /ah /． e c t s s s Ｇ i d e l i n e s j gu [ １７] HW．Wagene r,J．Ma t e r．Pr o c e s s．Te chno l． ７２ ( １９９７)３４２ Ｇ ３５７．