Constitutive Modeling for Flow Behaviors of Superaustenitic Stainless Steel S32654 during Hot Deformation

Constitutive Modeling for Flow Behaviors of Superaustenitic Stainless Steel S32654 during Hot Deformation

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JOURNALOFIRON ANDSTEELRESEARCH,INTERNATIONAL􀆰2 0 1 6,2 3( 2):1 7 8 G 1 8 4

􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉􀪉 􀪉

Con s t i t u t i v eMod e l i ngf o rF l owBe ha v i o r so fSupe r au s t e n i t i cS t a i n l e s s S t e e lS32654du r i ngHo tDe f o rma t i on , En G x i angPU1 2 ,  HanFENG1 ,  Mi nLIU1 ,  Wen G i eZHENG1 , j 1 HanDONG1 ,  Zh i G gangSONG

( 1.Cen t r a lI r onandS t e e lRe s e a r chI ns t i t u t e,Be i i ng100081,Ch i na;  2. Schoo lo fMa t e r i a l sSc i enc eand j , , , ) Eng i ne e r i ng Ts i nghuaUn i ve r s i t i i ng100084 Ch i na y Be j Ab s t r a c t:Ho tde f o rma t i onbehav i o ro fsupe r aus t en i t i cs t a i n l e s ss t e e lS32654 wa si nve s t i t edwi t hho tc omp r e s s i on ga t e s t sa tt empe r a t u r e so f950-1250 ℃ ands t r a i nr a t e so f0 􀆰001-10s-1 .Above1150 ℃ ,wi t hs t r a i nr a t el owe rt han 0 􀆰1s-1 ,t hef l owcu r ve sexh i b i tne a r l t e ady G s t a t ebehav i o r,wh i l ea th i rs t r a i nr a t e,c on t i nuousf l ows o f t en i ng ys ghe , o c cu r s.Top r ov i deap r e c i s ep r ed i c t i ono ff l owbehav i o rf o rt hea l l oy t hec ons t i t u t i vemode l i ngc ons i de r i nge f f e c to f s t r a i nwa sde r i vedont heba s i so ft heob t a i nedexpe r imen t a lda t aandc ons t i t u t i ver e l a t i onsh i i chi nc o r r a t edAr G pwh po r hen i ust e rmandhype r bo l i c G s i net t i on.Thema t e r i a lc ons t an t sα,n,Q andl nA a r ef oundt obef unc t i onso f ypee qua t hes t r a i nandc anbef i t t edemp l oy i nge i t h G o r de rpo l a l.Thede ve l opedc ons t i t u t i vemode lc anbeemp l oyedt o gh ynomi de s c r i bet hede f o rma t i onbehav i o ro fsupe r aus t en i t i cs t a i n l e s ss t e e lS32654. Ke r d s:S32654;supe r aus t en i t i cs t a i n l e s ss t e e l;ho tde f o rma t i on;c ons t i t u t i vemode l i ng ywo

  Supe r aus t en i t i cs t a i n l e s ss t e e lS32654i sb r oad l y us edi nve r s t i l eenv i r onmen t sowi ngt oi t sexc e l G yho [ 1] l en tco r r os i onr e s i s t anc eandh i t r eng t h . I nt h i s ghs a l l oy,t headd i t i ono fh i on t en t so fa l l oy i nge l e G ghc men t schr omi um,mo l i t r ogende c r e a G ybdenumandn s e ss t a ck i ngf au l tene r o f t h ea l l o a n d l o w e r sd i f G gy y , f us i oncoe f f i c i en to ft hea l l oy andt hush i empe r G ght [] a t u r es t r eng t ho ft hea l l oyi si nc r e a s ed2 .Compa r ed wi t ho rd i na r t en i t i cs t a i n l e s ss t e e lsucha s304L yaus , and316L S32654i smo r ed i f f i cu l tt ode f o rmandi s vu l ne r ab l et oho tc r a ckbe c aus eo fi t spoo rho two rk G ab i l i t r e f o r e,ho tp r o c e s s i ngpa r ame t e rf o rt h i s y.The a l l oyshou l dbede s i a r e f u l l oc onduc tt heho t gnedc yt de f o rma t i ono ft hes t e e l.Howeve r,wi t hr ega r dt o t her e s e a r chonS32654,mucha t t en t i onha sbe enf o G cus edont hec o r r o s i onr e s i s t anc eand p r e c i i t a t i on p behav i o r, wh i l e on l imi t ed i nve s t i t i ons have yl ga [ ] be enpe r f o rmedonho tde f o rma t i ono ft h i sa l l oy3G6 .   I no rde rt oe s t ab l i sht hef i n i t ee l emen t( FE) s imu l a t i onmode l sf o rt heho tde f o rma t i ono fme t a l s anda l l oys,t hec ons t i t u t i ver e l a t i onsh i c o n s i d e r i n p g e f f e c to fs t r a i ni sa lwaysus eda sani npu tt ot heFE [ ,] c ode7 8 . I nav i ewo ft heme chan i c sandme t a l l u r gy,

t hea c cur a t emode l i ngo fho tf l ows t r e s sus i ngcon G s t i t u t i ver e l a t i onsh i sas i i f i c an te f f e c tont he p ha gn [] me t a lf o rmi ng p r oc e s s e s9 .The r e f o r e,i nr e c en t , a r sr e s e a r che shavebe enpub l i shedonp r opos i ng ye o rmod i f i ngt hecons t i t u t i ve mode lf o rt hes imu l a G y t i ono ft heho tf o rmi ngp r oc e s s e so fme t a l so ra l l oys. [ ] Pue ta l 􀆰 10 de r i vedacons t i t u t i veequa t i ont oco r r e G l a t ef l ow s t r e s s wi t h de f o rma t i on t empe r a t ur e, s t r a i nr a t eands t r a i n,andt hecons t i t u t i ve mode l

wa se f f e c t i vef o rp r ed i c t i ngt hef l ows t r e s so fbo r on mi c r oa l l oyedTi GAl GCr GVa l l oysdur i ngho tde f o rma G t i on.La t e r,someo t he ri nve s t i a t o r s e s t a b l i s h e d t h e g cons t i t u t i veequa t i onsf o rva r i ous me t a l sanda l l oys [ ] i nco r r a t i ngt hee f f e c to ft hes t r a i n11G18 .Hane t po [ ] a l 􀆰 13 pr opos edacons t i t u t i ver e l a t i onsh i i n c o r o r a G p p t i ngt hee f f e c to fs t r a i n,andt hemode lcou l de f f e c G t i ve l eve a lt heh i empe r a t ur ef l ow behav i o ro f yr ght Cr20Ni25Mo4Cusupe r aus t en i t i cs t a i n l e s ss t e e l.Pue t [, ] a l 􀆰 6 14 deve l oped t he cons t i t u t i ve r e l a t i onsh i p by s t udy i ng t he ho t de f o rma t i on behav i o ro f supe r G aus t en i t i cs t a i n l e s ss t e e lS32654and254SMO,bu t , i nt hecons t i t u t i ve mode l t hee f f e c to fs t r a i n on f l ows t r e s swa sno tcons i de r ed.

B i o r aphy: En G x i angPU,Do c t o rCand i da t e; E Gma i l: 􀆰c om; Re c e i v e dDa t e:De c embe r1,2014 pexyunda@163 g Co r r e s i ngAu t ho r: Wen G i eZHENG,Pr o f e s s o r i a t eEng i ne e r;  E Gma i l:sxzwj@s ohu 􀆰c om j pond

I s sue2 Cons t i t u t i veMode l i ngf o rF l owBehav i o r so fSupe r aus t en i t i cS t a i n l e s sS t e e lS32654du r i ngHo tDe f o rma t i on 

   I nt hepr e s en ts t udy,i s o t he rma lc omp r e s s i on t e s t swe r econduc t edi nawi der angeo fs t r a i nr a t e s , andde f o rma t i ont empe r a t u r e s wi t hav i ewt odeve l G op i ng t he c ons t i t u t i ve r e l a t i onsh i i ch c oup l e s p wh f l ows t r e s swi t hs t r a i n,s t r a i nr a t eandde f o rma t i on t empe r a t ur e.Thea c cu r a c ft hec ons t i t u t i vemode l yo wa sve r i f i edbyt hec ompa r i s onbe twe ent hep r ed i c G t edandexpe r imen t a lr e su l t s.

179

f r om t hecomp r e s s i ont e s t s we r eus edt ocons t ruc t t het rues t r e s s G t rues t r a i ncur ve s.

2 Re s u l t sandDi s c u s s i on

2 􀆰1 S t r e s s G s t r a i nbeha v i o ro fS32654   F i 􀆰1exh i b i t st het i c a lf l owcur ve so fS32654 g yp s t e e lcomp r e s s ed unde rd i f f e r en t ho t de f o rma t i on cond i t i ons. I tc anb es e e nt ha tt hes ha eo f f l o wc u r v e s p r ema rkab l het empe r a t ur eands t r a i n ydependsont 1 Exp e r imen t a lPr o c e du r e r a t e.Obv i ous l t h pe aks t r e s sand pe aks t r a i n y,bo ( t hes t r a i n co r r e spond i ng t ot he pe ak s t r e s s)i n G   Th ec h emi c a lc ompo s i t i o n( ma s s%)o fS 3 2 6 5 4s t e e l : , , r e a s ewi t hde c r e a s i ngt het empe r a t ur eandi nc r e a s G us edi nt h i ss t ud sa sf o l l ows C0 􀆰0 1 7 S i0 􀆰3 6 Mn c yi ngt hes t r a i nr a t e.Thef l ows t r e s si nc r e a s e sr ap i d l 2 􀆰88,Cr24 􀆰51,Ni22 􀆰35,Cu0 􀆰36,Mo7 􀆰24,N i y tt hei n i t i a ls t ageo fho tde f o rma t i on,f o l l owedbya 0 􀆰45,and Feb a l a n c e.Th es amp l ep r epa r a t i on wa s a [ 14] , l ow i nc r e a s e i nd i c a t i ng t ha tt he wo rk Gha rden i ng r f o rmeda st he me t hod de s c r i bed p r ev i ous l pe y . s a t ede c l i ne swi t hi nc r e a s i ngs t r a i n.Att het empe r a G Ho tc omp r e s s i ont e s t swe r ec a r r i e dou tu s i ng Gl e e b l e G r ur eh i rt han1150 ℃ ands t r a i nr a t el e s st han 3800 ma ch i nea td i f f e r en tt empe r a t u r e sf r om950t o t ghe 􀆰1s-1 ,t hef l owcur ve sexh i b i tt hene a r l t e ady G 1250 ℃ ands t r a i nr a t e sf r om 0 􀆰001t o10s-1 wi t h 0 ys t a t ebehav i o r.I tshou l d be no t edt ha ta th i r c l i nd r i c a lcompr e s s i onspe c imenso f8 mmi nd i amG s ghe y t r a i nr a t e,con t i nuousf l ow so f t en i ng oc cur sa f t e r e t e rand15 mmi nhe i t.Al lt hespe c imens we r e s gh e a ch i ngape ak,wh i chmaybea t t r i bu t edt ot hedy G r ehe a t edt o1200 ℃ a tahe a t i ngr a t eo f30 ℃/sand r cr e c r t a l l i z a t i on (DRX)o rf l ow i ns t ab i l i t he l df o r180 s be f o r et he ho tc omp r e s s i on t e s t s. nami ys y. , Thei n i t i a li nc r emen to fs t r e s sa sar e su l to fwo rk Then t hey we r ehe a t edt oo rc oo l edt ode f o rma t i on rden i nganddynami cr e cove r sa t t r i bu t edt oan t empe r a t ur ew i t hah e a t i ngo rc o o l i ngr a t eo f10 ℃/s ha yi nc r e a s ei nd i s l oc a t i ona s we l la st hef o rma t i on o f andhe l df o r30s.Al lspe c imenswe r ede f o rmedt oa i r a i nbounda r i e s. I tshou l dbeno t edt ha tt heoc G t rues t r a i no f0 􀆰7.Thel oad G s t r oke da t a ob t a i ned subg

F i 􀆰1 Tr u es t r e s s G t r u es t r a i nc u r v e sf o rS 32654s t e e la td i f f e r en ts t r a i nr a t e sandd i f f e r en tt emp e r a t u r e s g

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    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 􀆰23 

cu r r enc eo fs i ng l epe aksi nt hecu r ve si nd i c a t e st ha t [ , ] DRXi swe l lunde rway19 20 . 2 􀆰2 E s t a b l i s hme n to fc o n s t i t u t i v er e l a t i on s h i tpe ak pa s t r a i n    Thepe aks t r e s so ft hea l l oyde f o rmedunde rd i f G f e r en tde f o rma t i on c ond i t i onsc an be p r ed i c t ed by emp l oy i ng c ons t i t u t i ve equa t i ons, wh i ch de s c r i be t hedependenc eo fs t r e s sonde f o rma t i ont empe r a t u r e [ ] and s t r a i nr a t e21 .Thef o l l owi ng equa t i ons we r e us edt oe s t ab l i sht hec ons t i t u t i ver e l a t i onsh i f o rh o t p : de f o rma t i ono fS32654a tpe aks t r a i n ̇ ( / ) (   Z =εexp Q RT 1)

Tak i ngi nve r s ef unc t i ono fEq 􀆰( 5)g i ve s 1 1/n 2/n 1/2 } (   σp= l n{( Z/A ) + [( Z/A ) +1] 6) α   I ti swe l lknownt ha tEq s 􀆰( 2)- ( 4)a r ewi de l y us edi nde s c r i b i ngt het he rma l l c t i va t edp r oc e s so f ya ( ) ho tde f o rma t i onf o r me t a l so ra l l oys.Eq s 􀆰 2 and ( 3)a r esu i t ab l ef o rr e l a t i ve l ows t r e s sr eg imeand yl , , h i hs t r e s sr e i m e r e s e c t i v e l w h i l eE 􀆰 4)c an g g p y q( beapp l i edi nawi der angeo ft empe r a t ur e sands t r a i n r a t e s.The r e f o r e,i nt h i ss t udy,Eq 􀆰( 4)wa semG l oyedt odeve l opt hecons t i t u t i ver e l a t i onsh i G p p.Tak ( ) i ngna t ur a ll og a r i t hmf r om bo t hs i d eo fEq 􀆰4 y i e l d s t hef o l l owi ngequa t i on:

1Q 1 ̇ 1 ( ε- l 7)   l n[ s i nh( α σp)]= + l n nA nRT n n   Thev a l u e so fn1andβa r ed e t e rmi n e dt ob e6 􀆰917 ( 4) and0 􀆰0358r e spe c t i ve l b l i n e a rr e r e s s i o no ft he y y g ̇ ( ) ( ) , ; , aks t r e s sda t aba s edonEq s 􀆰 2 and 3 andt h i s st h eZe n e r GHo l l omonp a r ame t e r εi ss t r a i n pe wh e r e Zi i v e st hev a l u eo fα=β/ n1 =0 􀆰0052.Theme ans l op e s r a t e;Qi st heappa r en ta c t i va t i onene r fde f o rma G g gyo -1 -1 , 􀅰 􀅰 ; ; ̇ st hega sc ons t an t8 􀆰31J mo l K t i on R i ( fp l o t so fl n εa k1 andk2 )o a i n s tl n[ s i nh( α σp)]and g 4 Ti st emp e r a t u r e;σpi sp e a ks t r e s s;A1,A2,A ,n1, l [ ( ) ] ( / ) ns i nh α σp aga i ns t 10 T we r e4 􀆰794 and n,βandα (≈β/n1)a r eappa r en tma t e r i a lc ons t an t s. 1 􀆰219,r e s e c t i v e l ss howni nF i s 􀆰2( a)and2( b). p y,a g    Ac co rd i ngt ot hede f i n i t i ono ft hehyp e r bo l i c G s i n e Theva l ueo fQ i sg i vena sQ =104R 􀅰k1 􀅰k2 =486 l aw,Eq 􀆰( 4)c a nb er ewr i t t e na st h ef o l l owi ngf o rm: /mo kJ l.Ac co rd i ngt oEq s 􀆰( 1)and ( 4),t hep l o to f 1/n   s i nh( α σp)= ( Z/A ) =[ exp( α σp)- l nZ aga i ns tl n[ s i nh( α σp )]wa sob t a i ned,whe r eby /2 ( exp(-α σp)] 5) theva l ue so fn andA we r ec a l cu l a t edas4􀆰73and   Z =̇ εexp( Q/RT )=A1σnp1   Z =̇ εexp( Q/RT )=A2exp( σp) β n   Z =̇ εexp( Q/RT )=A [ s i nh( α σp)]

( 2) ( 3)

̇ ( a)l n εv s. l n[ s i nh( α σp)];  ( b)l n[ s i nh( α σp)]v s. 104/T ;  ( c)l nZv s. l n[ s i nh( α σp)];  ( d)l nZv s. l n εp.

F i 􀆰2 Re l a t i on s h i r ame t e r s g pamongpa

I s sue2 Cons t i t u t i veMode l i ngf o rF l owBehav i o r so fSupe r aus t en i t i cS t a i n l e s sS t e e lS32654du r i ngHo tDe f o rma t i on 

1 􀆰07408×1017 ,r e s e c t i v e l si nd i c a t e di nF i 􀆰2( c). p y,a g The r e f o r e,t hepe aks t r e s sc ons t i t u t i ver e l a t i onsh i p o fho tde f o rma t i onf o rS32654s t e e lc anbeob t a i ned bysubs t i t u t i ngt heva l ue so fα,n,Q and A i n t o Eqs 􀆰( 4)and ( 6),exp r e s s eda sf o l l ows. æ 86000ö÷ ç4 ÷÷ =1   Z =̇ εexpçç 􀆰07408× è RT ø 4 􀆰73 ( σp)] 8) 1017[ s i nh( 0 􀆰0052 /

14 􀆰73 úù êé Z ú + 􀆰307 l n{êêê   σp=192 17 úú 􀆰07408×10 û ë1 􀆰73 ö2/4 ù1/2 éæ ú êç Z ÷ ú êç } ( ÷ 9) +1 úú êê ç 􀆰07408×1017 ÷ø û ë è1    Appa r en ta c t i va t i onene r sagoodi nd i c a t o r gyi o ft hedeg r e eo fd i f f i cu l t ft he ho tde f o rma t i on yo r o c e s sf o rt h e me t a l so ra l l o s. I ti s we l le s t a b l i s h e d p y t ha tt heva l ueo fappa r en ta c t i va t i onene r o rt he gyf ho tde f o rma t i oni sa s s o c i a t edwi t ht hei n t e r a c t i ono f t en t i a l l i l ed i s l o c a t i ons wi t ho t he rd i s l o c a G po y mob t i ons,so l u t e,g r a i nbounda r i e sandp r e c i i t a t e s. I n p , add i t i on t hepe r i od i c a lf r i c t i ono ft hel a t t i c ei t s e l f [ 22] maycon t r i bu t et ot hechangei na c t i va t i onene r gy . I nEq 􀆰( 8),t he me anva l ueo ft hea c t i va t i onene r gy ( / ) f o rho tde f o rma t i ono fS32654s t e e l 486kJ mo li s muchl a r rt hant ha to ft hes e l f G d i f f us i ono fγ GFe ge [ , ] ( /mo /mo 268kJ l)andNi ( 280kJ l)23 24 . I tusua l l y doe sno tcon f o rm wi t ht hes e l f G d i f f us i ona c t i va t i on ene r fa l l oy i nge l emen t s.Th i si s ma i n l c aus e gyo ybe t hes t r e s si nEq 􀆰( 7)i sno tno rma l i z e dbyt h eYoung ′ s modu l us wh i ch s t r ong l f o rma t i on y depends on de [ ] t empe r a t ur e25 .   I tha sbe enr epo r t edt ha tt hedependenc eo ft he ) ( heZ pa r ame t e ri sdemons t r a t ed aks t r a i n εp ont pe [ ] a sf o l l ows26 : m (   Z =Kεp 10) whe r e,t hepa r ame t e r sK andm dependont hea l l oy c ompo s i t i on,a ndc a nb eob t a i n e dbyr e r e s s i ona n a l s i s g y ( ) , o ft heexpe r imen t a lda t a.Ass howni nF i 􀆰2 d i ti s g

obv i oust ha tεpi nc r e a s e swi t hi nc r e a s i ngZ pa r ame G t e r.Theequa t i onf o rZ pa r ame t e rv s.pe aks t r a i n c anbeexp r e s s eda sf o l l ows: 21 3 (   Z =1 􀆰30436×10 εp􀆰61 11)

  I tha sbe enf oundt ha tt hes t r a i nf o ri n i t i a t i ono f DRXi sa ta r ound0 􀆰65-0 􀆰85t ime so fpe aks t r a i n [ ] unde rag i vende f o rma t i onc ond i t i on27 .Ac c o r d i ng G , l t h ec r i t i c a ls t r a i nf o rt h eo c c u r r e n c eo fD R Xi s y expe c t edt or educ ewi t hi nc r e a s i ngt empe r a t u r eand de c r e a s i ngs t r a i nr a t e. S i nc et heDRXnuc l e ibe c ome s , e a s i e rt of o rm a th i h e rd e f o r m a t i o nt e m e r a t u r e s g p t hec r i t i c a ls t r a i nf o ro c cu r r enc eo fDRX de c r e a s e s. Mo r eove r,t he mob i l i t fg r a i nbounda r i e sc anbe yo enhanc ed wi t hi nc r e a s i ng de f o rma t i ont empe r a t u r e

181

andhenc et her a t eo fDRXi nc r e a s e s. I ti sexpe c t ed t ha tt her a t eo fdynami cr e cove r DRV)a l sode G y( c r e a s e swi t hi nc r e a s i ngs t r a i nr a t e s.S i nc eDRX nu G c l e io r i i na t ef r omt hewe l l G deve l opedsubs t ruc t ur e s g duet oDRV,t hei nc r e a s ei nt hec r i t i c a ls t r a i nf o ri n G i t i a t i ono fDRX wi t hi nc r e a s i ngs t r a i nr a t ei sr e a son G ab l e.The mob i l i t fg r a i n bounda r i e s de c r e a s e s yo wi t hi nc r e a s i ngs t r a i nr a t e,andt husbo t ht hepe ak [] ands t e ady G s t a t es t r a i nsa r ei nc r e a s ed9 . 2 􀆰3 Con s t i t u t i v emode lc on s i de r i nge f f e c to fs t r a i n   Fr om F i 􀆰1,i tc anbef oundt ha tbe s i de ss t r a i n g r a t eand de f o rma t i ont empe r a t ur e,t hes t r a i na l so l aysanimpo r t an tr o l ei nt hef l ows t r e s s.Howeve r, p Eq 􀆰( 4)o rEq 􀆰( 6)doe sno tt aket hee f f e c to fs t r a i n onf l ows t r e s si n t ocons i de r a t i on.The r e f o r e,t oimG r ovet hep r ed i c t i ona c cur a c ft hecons t i t u t i ver e G p yo l a t i onsh i he compens a t i on o fs t r a i n shou l d be p,t cons i de r ed. I tha sbe enwi de l c c ep t edt ha tt hema G ya ( , , ) ( ) ( t e r i a lcons t an t s α n Q andA i nEq s 􀆰 5 and 6) [ 11] a r es t r a i n G d e e nd e n t .Fo l l owi ngt hes amep r o c e du r e p us edi ns e c t i on2 􀆰2andsubs t i t u t i ngpe aks t r e s sσpi n Eqs 􀆰( 2)- ( 6)wi t ht rues t r e s sσ a tac e r t a i ns t r a i n, o r t heva l ue so fma t e r i a lcons t an t sα,n,Q andA f t hecons t i t u t i ve equa t i ons we r e de t e rmi ned unde r d i f f e r en tt r u es t r a i n swi t h i nt her ang eo f0 􀆰10-0 􀆰65 wi t hani n t e r va lo f0 􀆰05.Tab l e1showst hec a l cu l a t G edva l ue so ft he ma t e r i a lcons t an t sa td i f f e r en tt rue s t r a i ns.The dependenc eo f ma t e r i a lcons t an t s on t rues t r a i nc anbeexpr e s s edbypo l a lwi t ho r G ynomi de rva r i ngf r omonet on i ne. I nt hep r e s en ti nve s t i G y t i on,i ti sf oundt ha tt he s eva l ue sc an bef i t t ed ga we l lbyane i t h G o rde rpo l a la sexp r e s s edby gh ynomi ( ) , Eq 􀆰1 2 a ndt h ec o r r e s ond i ngf i t t i ngc u r v e sa r es hown p i nF i 􀆰3. I ti nd i c a t e st ha tt hema t e r i a lc on s t an t shave g comp l exr e l a t i onsh i t ht r u es t r a i n.Thec o e f f i c i e n t s p wi Tab l e1 Va l u e so fma t e r i a lc on s t an t so fS 32654s t e e l und e rd i f f e r en tt r u es t r a i n s Tr ues t r a i n

α

n

0 􀆰10

0 􀆰00609

5 􀆰72

0 􀆰20

0 􀆰00605

4 􀆰33

0 􀆰15 0 􀆰25 0 􀆰30 0 􀆰35 0 􀆰40 0 􀆰45 0 􀆰50 0 􀆰55 0 􀆰60 0 􀆰65

0 􀆰00606 0 􀆰00609 0 􀆰00625 0 􀆰00637 0 􀆰00658 0 􀆰00678 0 􀆰00703 0 􀆰00723 0 􀆰00744 0 􀆰00755

4 􀆰65 4 􀆰15 3 􀆰96 3 􀆰85 3 􀆰76 3 􀆰69 3 􀆰63 3 􀆰61 3 􀆰61 3 􀆰66

Q/( kJ􀅰mo l-1)

l nA

510 􀆰46

41 􀆰89

467 􀆰38

36 􀆰95

485 􀆰16 455 􀆰71 444 􀆰78 434 􀆰51 432 􀆰59 426 􀆰27 420 􀆰81 417 􀆰44 411 􀆰34 411 􀆰74

38 􀆰43 35 􀆰98 35 􀆰05 34 􀆰19 34 􀆰05 33 􀆰53 33 􀆰06 32 􀆰79 32 􀆰28 32 􀆰34

    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 􀆰23 

182

( a)αv s. ε;   ( b)l nAv s. ε;   ( c)nv s. ε;   ( d)Qv s. ε.

F i 􀆰3 F i t t i ngc u r v e sb e twe enma t e r i a lc on s t an t sands t r a i n g

o ft hepo l a la r eshowni nTab l e2. ynomi 2 3 􀆺 α=B0 +B1ε+B2ε +B3ε + +B8ε8 n=C0 +C1ε+C2ε2 +C3ε3 + 􀆺 +C8ε8 (    12) Q =D0 +D1ε+D2ε2 +D3ε3 + 􀆺 +C8ε8 l nA =E0 +E1ε+E2ε2 +E3ε3 + 􀆺 +E8ε8 st rues t r a i n;andBi ,Ci ,DiandEi ( i= whe r e,εi

0,1,2,3,􀆺,8)a r ecoe f f i c i en t so fpo l a l. ynomi ( ) ( )   Subs t i t u t i ng Eq 􀆰 12 i n t o Eq 􀆰 6 y i e l dst he cons t i t u t i ve mode l i ng wh i ch comb i ne sf l ow s t r e s s wi t hs t r a i n,de f o rma t i ont empe r a t ur eands t r a i nr a t e f o rS32654s t e e ldur i ng h i empe r a t ur ede f o rma G ght t i on,andt heexp r e s s i oni sg i vena sf o l l ows:

Tab l e2 Co e f f i c i en tv a l u e so ff i t t i ngr e l a t i on s h i e twe enpa r ame t e r sandt r u es t r a i n pb  α

 n

kJ􀅰mo l-1)  Q/(

 l nA

 B1=0 􀆰12018

 C1=-439 􀆰038

 D1=-3325 􀆰34965

 E1=-1205 􀆰5808

 B0=0 􀆰00222

 C0=23 􀆰42024

 B2=-1 􀆰49409

 C2=4434 􀆰767

 B4=-37 􀆰563

 C4=87002 􀆰8

 B6=-123 􀆰003

 C6=242862 􀆰4

 B3=9 􀆰78505

􀆰84668  B5=87  B7=94 􀆰71996

 B8=-30 􀆰8479

 D0=675 􀆰14477

 D2=26681 􀆰35276

 E0=91 􀆰40141

 E2=11953 􀆰301

 C3=-25200 􀆰2

 D3=-132042 􀆰327

 E3=-66961 􀆰575

 C5=-186565

 D5=-723593 􀆰178

 E5=-474976 􀆰13

 D7=-490832 􀆰82

 E7=-427876 􀆰39

 C7=-175749

 C8=54234 􀆰51

 D4=396154 􀆰9991  D6=793558 􀆰6488  D8=136245 􀆰8723

1 1/n( ε) σ= ( ) l n{[ Z′/A ( ε)] + αε 2/n( ε) 1/2 ( }       〔[ 13) Z′/A ( ε)] +1〕 ù ) êéQ ( ú ε ú Z′=̇ εexp êêê ú ë RT úû whe r e,Z′i st heZene r GHo l l omonpa r ame t e rc ons i d G e r i ngt hee f f e c to fs t r a i n.

 E4=226739 􀆰37

 E6=603700 􀆰351  E8=130092 􀆰314

    Us i ngt hepo l a lf i t t i ngr e su l t sshowni n ynomi Tab l e2,t he Ar rhen i us G t t i t u t i ve equa t i on ypecons r e l a t edt os t r a i ni sob t a i ned.Me anwh i l e,t hef l ow , s t r e s sa saf unc t i ono ft empe r a t ur e s t r a i nr a t eand s t r a i nc anbea c cur a t e l r ed i c t edt hr oughEq 􀆰( 13). yp , Asp r e s en t edi nF i 􀆰 4 c o m a r i s o nb e t w e e nt h e r e G g p p d i c t edandexpe r imen t a lr e s u l t swa sc a r r i e dou ti nt h i s

I s sue2 Cons t i t u t i veMode l i ngf o rF l owBehav i o r so fSupe r aus t en i t i cS t a i n l e s sS t e e lS32654du r i ngHo tDe f o rma t i on 

183

( a)1000 ℃ ;   ( b)1050 ℃ ;   ( c)1100 ℃ ;   ( d)1200 ℃.

F i 􀆰4 Compa r i s onb e twe ene xp e r imen t a landp r e d i c t e df l ows t r e s s e sbyd e v e l op e dc on s t i t u t i v emod e l sa t g d i f f e r en td e f o rma t i ont emp e r a t u r e s

i nve s t i t i on,a imi ngt ova l i da t et hea c cu r a c ft he ga yo e s t ab l i shed c ons t i t u t i ve mode l i ng.The p r ed i c t ed aks t r e s sands t e ady G s t a t es t r e s si nc r e a s ewi t hi n G pe c r e a s i ngt hes t r a i nr a t eandde c r e a s i ngt hede f o rma G t i ont empe r a t u r e.Th i si sc ons i s t en twi t ht heexpe r i G men t a lr e su l t s.Thegoodag r e emen tbe twe ent heex G r imen t a land p r ed i c t edbehav i o r so fS32654s t e e l pe i l l us t r a t e st ha tt he p r opo s ed c ons t i t u t i ve equa t i on ha sh i c cu r a c nde s c r i b i ngt hede f o rma t i onbe G gha yi hav i o ro ft h i sma t e r i a l.   I no rde rt of u r t he reva l ua t et hep r ed i c t ab i l i t f yo t hec ons t i t u t i veequa t i onsf o rS32654s t e e l,t hec o r G R2 )andt heave r ageabs o l u t e r e l a t i oncoe f f i c i en t( ( ) r e l a t i vee r r o r AARE a r ec a l cu l a t edbyt hef o l l owG i ngequa t i ons:

P .TheR2i semp l oyedt oshowt hel i ne a rr e l a t i on G sh i twe ent hep r ed i c t edandexpe r imen t a lva l ue s pbe o ft hemode l.AAREi sanunb i a s e ds t a t i s t i cp a r ame t e r f o re v a l u a t i ngt hep r e d i c t ab i l i t famode l.The r e f o r e, yo

h i rva l ueo fR2 andl owe rva l ueo f AARE c an ghe r an t e eabe t t e rp r ed i c t ab i l i t ft hecons t i t u t i ve gua yo mode lf o rS32654s t e e l.Asshowni nF i 􀆰5,mos to f g t heda t apo i n t sl i ef a i r l l os et ot hebe s tr eg r e s s i on yc l i neandt heva l ueo fco r r e l a t i oncoe f f i c i en tf o rt he deve l opedcons t i t u t i vemode li sc a l cu l a t eda s0 􀆰988, i nd i c a t i ngagoodag r e emen tb e twe e np r e d i c t e dande x G

N

  R2 =

∑( Ei -E )( Pi -P )

i=1

N

N

i=1

i=1

2 2 ∑( Ei -E ) ∑( Pi -P )

( 14)

1 N Ei -Pi (   AARE= ∑ ×100% 15) Ni=1 Ei whe r e,E i st heexpe r imen t a lva l ue o ft hes t r e s s f r omt heho tc ompr e s s i ont e s t;P i st hec a l cu l a t ed va l ueo ft hes t r e s sf r omt hec ons t i t u t i ve mode l i ng;

Ei st heme anva l ueo fE andPi st heme anva l ueo f

F i 􀆰5 Co r r e l a t i onb e twe ene xp e r imen t a land g r e d i c t e df l ows t r e s sda t a p

184

    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 􀆰23 

r imen t a lf l ows t r e s sva l ue s.The AAREi sde t e r G pe mi nedt obe5 􀆰2% byEq 􀆰( 15).     Ther e l a t i ve l i o r r e l a t i onc oe f f i c i en tand yh ghc l ow ave r ageabs o l u t er e l a t i vee r r o rr eve a lt ha tt he r e d i c t i o nr e s u l t s c a n f i t f o r t h ee x e r i m e n t a l r e s u l t s p p andsugge s tt hei s suet ha tt hee s t ab l i shedc ons t i t u G t i vemode l sc anbeus edsuc c e s s f u l l nt henume r i c a l yi s imu l a t i ono fho t wo rk i ng andop t imi z a t i on o ft he ho tde f o rma t i onpa r ame t e r sf o rt h i ss t e e l.

3 Conc l u s i on s

   ( 1)Att h et emp e r a t u r eh i e rt h a n1150 ℃ a nd gh s t r a i nr a t el owe rt han0 􀆰1s-1 ,t hef l owcu r ve sex G h i b i ta lmos ts t e ady G s t a t e behav i o ra f t e rr e a ch t he ak,wh i l ea th i rs t r a i nr a t e,c on t i nuousf l ow pe ghe s o f t en i ngoc cu r s. ( )    2 Th ec on s t i t u t i v ee a t i on swh i c hr e l a t ebo t h qu t h epe aks t r e s sandpe aks t r a i nt ode f o rma t i ont emG r a t ur eands t r a i nr a t ea r ep r opo s edf o rho tde f o rmG pe , a t i ono ft hes t e e l andt heappa r en ta c t i va t i onene r gy /mo a tpe aks t r a i ni sde t e rmi nedt obe486kJ l.    ( 3)Th ec on s t i t u t i v e mod e l i ngc on s i d e r i nge f f e c t o fs t r a i ni sd e v e l op e dt op r e d i c tt h ef l ows t r e s so fs t ud i e d a l l oydur i ng ho tde f o rma t i on.I ti sf oundt ha tt he ma t e r i a lcons t an t sα,n,Q andl nA a r ef unc t i onso f t hes t r a i nandc an be we l lf i t t ed by emp l oy i ng an e i t h G o rde rpo l a l.Thedeve l opedc ons t i t u t i ve gh ynomi mode lc anbeus edf o rde s c r i b i ngt hede f o rma t i onbe G hav i o ro fsupe r aus t en i t i cs t a i n l e s ss t e e lS32654. Re f e r enc e s:

[ 1]  J.Ol s s on,W.Wa s i e l ews k a,Ma t e r.Co r r o s. 48 ( 1997)791 G 798. [ 2]  Y. L i u,R.Hu,J 􀆰S. L i,H􀆰C.Kou,H􀆰G. L i,Ma t e r. Sc i. Eng. A508 ( 2009)141 G 147. [ 3]  S.He i no,M.Knu t s on Gwede l,B.Ka r l s s on,Ma t e r. Sc i. Fo r um 318 G 320( 1999)143 G 150. [ 4]  G.Mo r i,D.Baue r n f e i nd,Ma t e r.Co r r o s. 55 ( 2004)164 G 173.

[ 5]  E 􀆰X.Pu,W􀆰J. Zheng,J 􀆰Z.Xi ang,Z 􀆰G.Song,J.L i,Ma t e r. Sc i.Eng.A598 ( 2014)174 G 182. [ 6]  E 􀆰X.Pu,W􀆰J.Zh e ng,J 􀆰Z.X i a ng,Z 􀆰G.Song,H.Fe ng,Y 􀆰L. )27 ( Zhu,Ac t aMe t a l l. S i n.( Eng l.Le t t. 2014)313 G 323. [ 7]  Y 􀆰H.X i a o,C.Guo,X 􀆰Y.Guo,Ma t e r.S c i.Eng.A528 ( 2011) 6510 G 6518. [ 8]  F.Y i n,L.Hu a,H􀆰J.Ma o,X 􀆰H.Ha n,Ma t e r.De s. 43 ( 2013) 393 G 401. [ 9]  H.Mi r z adeh,J 􀆰M.Cabr e r a,A.Na a f i z adeh,Ac t a Ma t e r.59 j ( 2011)6441 G 6448. [ 10]  Z 􀆰J.Pu,K􀆰H.Wu,J. Sh i,D. Zou,Ma t e r. Sc i.Eng.A192/ 193 ( 1995)780 G 787. [ 11]  Y􀆰C.L i n,D 􀆰X.Wen,J.Deng,G. L i u,J. Chen,Ma t e r.De s. 59 ( 2014)115 G 123. [ 12]  Q􀆰C.Fan,X 􀆰Q. J i ang,Z 􀆰H.Zhou,W. J i,H􀆰Q.Cao,Ma G t e r.De s. 65 ( 2015)193 G 203. [ 13]  Y.Han,G􀆰J.Qi ao,Y.Sun,D 􀆰N.Zou,Ma t e r.Sc i.Eng.A 539 ( 2012)61 G 67. [ 􀆰P.We i,J. 􀆰Z.Xi ang,X 􀆰G. Song,J 14]  E 􀆰X.Pu,W􀆰J. Zheng,Z I r onS t e e lRe s. I n t21 ( 2014)975 G 982. [ l,A􀆰K.Bhadur i,Ma t e r.De s.31 15]  D.Saman t a r ay,S.Manda ( 2010)981 G 984. [ 16]  F.Chen,F 􀆰C.Ren,Z 􀆰S.Cu i,X 􀆰M.La i,J. I r onS t e e lRe s. I n t. 21 ( 2014)521 G 526. [ t e r.Sc i.Eng.A528 17]  C 􀆰L.Gan,Y􀆰D.Xue,M􀆰J.Wang,Ma ( 2011)4199 G 4203. [ 18]  F 􀆰C.Ren,J.Chen,J. I r onS t e e lRe s. I n t. 20 ( 2013)No 􀆰11, 118 G 124. [ G 􀆰M. Zhang,Ma Shao,L. Zhen,L.Yang,X 19]  Y.Wang,W􀆰Z. t e r. Sc i.Eng.A497 ( 2008)479 G 486. [ 20]  E 􀆰I.Po l i ak,J 􀆰J. J ona s,I S I J. I n t. 43 ( 2003)684 G 691. [ 21]  C 􀆰M. S e l l a r s,W􀆰J.MeG.T e a r t,I n t.Me t a l l.Re v. 17 ( 1972)1 G g 24. [ 􀆰Y.L i u,Ma t e r.Sc i. 􀆰G.L i,S 􀆰Y.Wang,C 22]   M􀆰J.Zhang,F Eng.A527 ( 2010)6771 G 6779. [ 23]  Q􀆰L.Yong,Se c onda r s e si nS t e e l s,Me t a l l ur i c a lI ndus G yPha g t r e s s,Be i i ng,2006. yPr j [ 24]   W􀆰F.Smi t h,J.Ha shemi,Founda t i onso f Ma t e r i a l sSc i enc e i na Ma ch i nePr e s s,Be i i ng,2011. andEng i ne e r i ng,Ch j [ Zuo,C 􀆰F.Chen,J.Al l oys i u,J 􀆰J.Cheng,Q. 25]  L.Wang,F.L Comp. 623 ( 2015)69 G 78. [ 26]  M.EIWahab i,J 􀆰M.Cabr e r a,J 􀆰M.Pr ado,Ma t e r.Sc i.Eng. A343 ( 2003)116 G 125. [ 27]  H􀆰J.McQue en,Ma t e r. Sc i.Eng.A101 ( 1988)149 G 160.