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Hot Deformation Behavior of a Novel Ni-Cr-Mo-B Ultra-heavy Plate Steel by Hot Compression Test
JOURNALOFIRON ANDSTEELRESEARCH,INTERNATIONAL２ ０ １ ５,２ ２( ９):８ １ ８ Ｇ ８ ２ ６
Ho tDe f o rma t i onBe ha v i o ro faNo v e lNi ＧCr ＧMo ＧBUl t r a Ｇ he a v y P l a t eS t e e lbyHo tCompr e s s i onTe s t
１, ２ ３ ３ １, ４, ５ ３ Zh i Ｇ Ｇ yuGAO , TaoPAN, Zhuo WANG, Guo quanLIU , HangSU
( １．S t a t eKeyLabo r a t o r o rAdvanc ed Me t a l sand Ma t e r i a l s,Un i ve r s i t fSc i enc eandTe chno l ogyBe i i ng,Be i i ng１０００８３, yf yo j j ; , , , Ch i na ２．Co l l egeo fMa t e r i a l sSc i enc eandEng i ne e r i ng L i aon i ngTe chn i c a lUn i ve r s i t i n１２３０９９ L i aon i ng,Ch i na; y Fux , , , ; ３．Di v i s i ono fEng i ne e r i ngS t e e l 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 ４．Schoo lo fMa t e r i a l s j Sc i enc eandEng i ne e r i ng,Un i ve r s i t fSc i enc eandTe chno l ogyBe i i ng,Be i i ng１０００８３,Ch i na; ５．Co l l abo r a t i ve yo j j I nnova t i onCen t e ro fS t e e lTe chno l ogy,Un i ve r s i t fSc i enc eandTe chno l ogyBe i i ng,Be i i ng１０００８３,Ch i na) yo j j Ab s t r a c t:Ho tde f o rma t i onbehav i o ro fanove lNi ＧCr ＧMo ＧBhe avyp l a t es t e e lwa ss t ud i edbyho tc omp r e s s i ont e s t s, wh i chwe r ec onduc t edona Gl e eb l e Ｇ ３８００t he rmo Ｇme chan i c a ls imu l a t o rc o r r e spond i ngt ot het empe r a t u r er angeo f ８５０－１１５０℃ wi t ht hes t r a i nr a t e so f０ ０１－１０s－１ andt het r ues t r a i no f０ ８．Ther e su l t ssugge s tt ha tt hema o r i t j y o ff l owcu r ve sexh i b i tat i c a ldynami cr e c r s t a l l i z a t i on ( DRX)behav i o rwi t hanappa r en ts i ng l epe aks t r e s sf o l Ｇ yp y l owedbyag r adua lf a l lt owa r dsas t e ady Ｇ s t a t es t r e s s．Impo r t an tcha r a c t e r i s t i cpa r ame t e r so ff l owbehav i o ra sc r i t i c a l /s /s s t r e s s t r a i nf o ri n i t i a t i ono fDRXandpe akands t e ady Ｇ s t a t es t r e s s t r a i nwe r ede r i vedf r omcu r ve so fs t r a i nha r den Ｇ i ngr a t eve r suss t r e s sands t r e s sve r suss t r a i n,r e spe c t i ve l t e r i a lc ons t an t so ft hei nve s t i t eds t e e lwe r ede t e r Ｇ y．Ma ga mi nedba s edonAr r hen i us Ｇ t ons t i t u t i vee t i on,andt hent hepe aks t r e s swa sp r ed i c t edbyt hee t i onwi t ht he ypec qua qua /mo ho tde f o rma t i ona c t i va t i onene r f３７９１３９J l,andt hep r ed i c t edva l ue sag r e ewe l lwi t ht heexpe r imen t a lva l ue s． gyo Fu r t he rmo r e,t hee f f e c to fZene r ＧHo l l omonpa r ame t e ront hecha r a c t e r i s t i cpo i n t so ff l owcu r ve swa ss t ud i edus i ng t hepowe rl awr e l a t i on,andt her a t i oo fc r i t i c a ls t r e s sands t r a i nt ope aks t r e s sands t r a i nwe r ef oundt obe０ ９１and ０ ４６,r e spe c t i ve l y． Ke r d s:Ni ＧCr ＧMo ＧBhe avyp l a t es t e e l;ho tde f o rma t i on;c ons t i t u t i vee t i on;a c t i va t i onene r r a c t e r i s t i c qua gy;cha ywo r ame t e r pa
The deve l opmen to fh i Ｇ s t r eng t h and h i Ｇ gh gh t oughne s ss t e e l sf o r ma r i ne eng i ne e r i ng i s eve r r owi ng wi t ht heimpo r t anc eo fo f f sho r eo i landga s g [ １] r e sour c e sexp l o i t a t i onr e c ogn i z ed ．Ni ＧCr ＧMo ＧBu l Ｇ t r a Ｇhe avy p l a t es t e e li so f t en r e f e r r ed a sh i gh s t r eng t hl ow a l l oy (HSLA ) ma r i ne eng i ne e r i ng [ ２] , s t e e l andi sus edi nc r i t i c a lapp l i c a t i onssucha s r oduc t i onp l a t f o rm,sh i i l d i ngandp r e s su r eve s Ｇ p pbu s e lands oon．Ni,Cr,MoandBe t c．a r eo f t enu t i Ｇ l i z edt oimpr oveha r denab i l i t nt hes t e e lp l a t e．Re Ｇ yi s e a r che sonNi ＧCr ＧMo ＧBs t e e lmo s t l o cus edont he yf [ ３] componen top t imi z a t i on de s i her e l a t i on Ｇ gn andt sh i r o c e s s e s,mi c r o s t ruc t u r e sandp r ope r Ｇ psamongp [] t i e s４ ,wh i l ea lmo s tnoe f f o r tha sbe enpa i dt oun Ｇ de r s t andt heho tde f o rma t i onbehav i o ro ft hes t e e l,
wh i chi squ i t eimpo r t an tt oop t imi z et heho two rk i ng r oc e s spa r ame t e r sandge tan i c es t he t i cme chan Ｇ p yn i c a lp r ope r t ft hep r oduc t s． yo Thes i ne Ｇhype rbo l i cl aw i nan Ar rhen i us Ｇ t ype equa t i onha sbe ensuc c e s s f u l l edf o rcha r a c t e r i Ｇ y us [ ,] z i ngho tde f o rma t i onbehav i o r５ ６ andop t imi z i ngt he [] t he rmo Ｇme chan i c a lp r oc e s spa r ame t e r s７ o fma t e r i Ｇ [ ８] a l s．Mo r eove r,Po l i akandJona s sugge s t edt ha t ( t hei n i t i a t i on o f dynami cr e c t a l l i z a t i on DRX ) ys c anbei den t i f i edf r om change si nt hes l opeo ft he s t r a i nha rden i ngr a t eve r susf l ows t r e s scur ve s．Ac Ｇ , co rd i ng l tde f o rma t i on behav i o ro f Fe Ｇ ２５Mn Ｇ y ho [] ３S i Ｇ ３AlTWIPs t e e lwa ss t ud i edbyL ie ta l９ ．us i ng Ar rhen i us Ｇ t t i t u t i veequa t i onandt he me t hＧ ypecons [ ] odo fPo l i akandJona s．Mi r z adehe ta l．１０ de t e r Ｇ
Founda t i onI t em:I t emSpons o r edbyNa t i ona lNa t ur a lSc i enc eFounda t i ono fCh i na ( ５１０７１０１９,５１３７１０３０);Na t i ona lHi chno l ogyRe s e a r ch ghTe andDeve l opmen tPr og r am o fCh i na ( ２０１３AA０３１６０１);Na t i ona lKey Te chno l ogy Re s e a r chand Deve l opmen tPr og r am o ft he Mi n i s t r fSc i enc eandTe chno l ogyo fCh i na ( ２０１１BAE２５B０１) yo B i o r aphy: Zh i Ｇ c t o rCand i da t e; E Ｇma i l: zh i c om; Re c e i v e dDa t e:De c embe r１８,２０１４ yuGAO,Do yugao＠１２６ g Co r r e s i ngAu t ho r:Guo Ｇ c t o r,Pr o f e s s o r; E Ｇma i l:g l i u＠us t b edu cn quanLIU,Do pond
I s sue９ Ho tDe f o rma t i onBehav i o ro faNove lNi ＧCr ＧMo ＧB Ul t r a Ｇhe avyP l a t eS t e e lbyHo tComp r e s s i onTe s t
mi nedt heho t wo rk i ng c ons t an t sand de f o rma t i on a c t i va t i onene r fa med i um c a rbon mi c r oa l l oyed gyo s t e e lbyc ons t i t u t i veequa t i on,andt hes t r a i nha rd Ｇ en i ngr a t eve r suss t r e s scu r ve swe r eus edt or eve a l whe t he rDRXhado c cu r r ed．Thec r i t i c a lc ond i t i ons f o rt hei n i t i a t i ono fDRXo fbo r onmi c r oa l l oyeds t e e l we r es t ud i ed us i ngt heabove me t hod by Me í ae t j a l．,andt her e su l t sa r ei n ag r e emen t wi t ho t he r [ ] common l epo r t eds t e e l s１１ ． yr I nt h i ss t udy,ho tde f o rma t i onbehav i o ro fNi Ｇ Cr ＧMo ＧBs t e e lwa si nve s t i t edbyho tc omp r e s s i on ga t e s t s．Thecha r a c t e r i s t i cpa r ame t e r ssucha sc r i t i c a l cond i t i onf o ri n i t i a t i on o f DRX,pe ak ands t e ady Ｇ /s s t a t es t r e s s t r a i na td i f f e r en tt empe r a t u r e s and , s t r a i nr a t e so ft h i ss t e e lwe r ec a l cu l a t ed andAr rhe Ｇ n i us Ｇ t t i on wa se s t ab l i shed．Then,a c co rd Ｇ ypeequa i ngt ot heequa t i on,t hepe aks t r e s s e swe r ep r ed i c t ed andva l i da t edwi t ht heexpe r imen t a lr e su l t s．I nadd i Ｇ t i on,t her e l a t i onsh i twe en cha r a c t e r i s t i c pa Ｇ ps be r ame t e r sandZene r ＧHo l l omonpa r ame t e rwe r ebu i l t． , Cons equen t l het heo r e t i c a lba s i sf o rop t imi z i ng y t ho two rk i ngp r o c e s s e so ft heNi ＧCr ＧMo ＧBs t e e lwa s e s t ab l i shed．
１ Ma t e r i a l sandExp e r imen t a lPr o c e du r e s
The pr i nc i lchemi c a lc ompo s i t i on (ma s s％ ) pa o ft heNi ＧCr ＧMo ＧBs t e e lemp l oyedi nt h i swo rki sC ０ １２,S i０ ３０, Mn １ ２０,Ni１ ８０,Cr０ ５, Mo ０ ５,B０ ００１６,Al０ ０５,Ti０ ０１５,V ０ ０３６,Cu , ０ ３２ a nd Fe b a l a n c e． S i ng l e Ｇ a s si s o t h e rma l ho t p un i ax i a lc omp r e s s i ont e s t swe r ec ondu c t e don Gl e e b l e Ｇ ３８００ t h e rmo Ｇme c h a n i c a ls imu l a t o r． Cy l i nd r i c a lt e s t s e c ime n sw i t h８mmi nd i ame t e ra nd１５mmi nh e i t p gh we r ef a b r i c a t e dc a r e f u l l r omt h ea nn e a l e db i l l e tw i t ha yf , v e r ods u r f a c ef i n i s h． I na dd i t i on f o rmi n imi z i ngt he ygo i n f l u e n c eo ff r i c t i onont h ef l ow b e h a v i o r,at a n t a l um f o i lwi t hat h i c kn e s so f０ ０５mmwa sp l a c e db e twe e nt he anv i la ndt h es e c ime n． p Thec ompr e s s i ont e s t swe r ec a r r i edou ta c co rd Ｇ i ngt ot hepr o c e s ss chemei nF i １．Thespe c imens g we r eaus t en i t i z eda t１２００℃ f o r３００st oob t a i nun i Ｇ f o rm aus t en i t i c mi c r o s t ruc t u r e, t hen c oo l ed a t １０℃/st od i f f e r en t de s i r ed de f o rma t i on t empe r a Ｇ t ur e s( ８５０－１１５０℃ ,s t epo f１００℃ )andhe l df o r １０st oe l imi na t et he rma lg r ad i en t s,andt henspe c i Ｇ ̇ menswe r ei s o t he rma l l f o rmeda ts t r a i nr a t e s( ε) yde －１ r ang i ngf r om ０ ０１t o１０s wi t hani n t e r va lo fan o rde ro fmagn i t udewi t hat rues t r a i n( ε)o f０ ８．I n t h i sc a s e,t het rues t r e s s Ｇ s t r a i nda t a we r er e c o rded au t oma t i c a l l r i ng c omp r e s s i on． Al lt he spe c i Ｇ y du menswe r e wa t e rquenchedr ap i d l op r e s e r vet he yt
８１９
mi c r os t ruc t ur e sa te l eva t ed t empe r a t ur ea f t e rt he de f o rma t i on,andt he mi c r os t ruc t ur eo ft hespe c i Ｇ menswa sexami nedbyop t i c a lmi c r os copyo fOl m Ｇ y pus．
F i １ Pr o c e s ss ch emef o rho tc omp r e s s i on g t e s t so fNi ＧCr ＧMo ＧBs t e e l
２ Re s u l t sandDi s c u s s i on ２ １ F l owcu r v e sana l s i s y σ)cur ve sob Ｇ F i ２dep i c t st hef l ow s t r e s s( g t a i nedf r omt heho tcomp r e s s i ont e s t so ft heNi ＧCr Ｇ Mo ＧBs t e e la td i f f e r en tt empe r a t ur e sr ang i ngf r om ８５０t o１１５０℃ wi t hs t r a i nr a t e so f０ ０１,０ １,１and －１ , １０s r e spe c t i ve l e en f r om F i ２,t he y． As s g cur ve s,exc l ud i ngt hos ea tl owe rt empe r a t ur eand h i rs t r a i nr a t e,exh i b i tobv i oust i c a lDRXso f Ｇ ghe yp t en i ngbehav i o r wi t has i ng l epe aks t r e s sf o l l owed [ ] byag r adua lf a l lt owa rdsas t e adys t a t es t r e s s１２ ,
andt hepe aks t r e s sbe come sl e s sobv i ous l he ywhent de f o rma t i ont empe r a t ur ede c r e a s e so rt hes t r a i nr a t e i nc r e a s e s． I tc ana l sobes e ent ha tt heh i rt het empe r a Ｇ ghe , , t ur et hel owe rt hef l ows t r e s sa ch i eved wh i l et he l owe rt hes t r a i nr a t e,t hel owe rt hef l ows t r e s sob Ｇ t a i ned．Thecomb i nede f f e c to fwo rkha rden i ngand t he rma l l c t i va t edso f t en i ngr e su l t edi nt he s ephe Ｇ ya nomena．I no t he rwo rds,t hee f f e c t so ft hede f o rma Ｇ t i ont empe r a t ur eands t r a i nr a t eonf l ows t r e s scou l d beexp l a i nedi nt e rmso fd i s l oc a t i on me chan i smand dynami cr e cove r e c r t a l l i z a t i on．Hi rt empe r Ｇ y/r ys ghe a t ur e sandl owe rs t r a i nr a t e spr ov i del onge rt imef o r ene r c cumu l a t i onandh i rmob i l i t fa t omsa t gya ghe yo bounda r i e sf o rt henuc l e a t i onandg r owt ho fdynami Ｇ c a l l e c r t a l l i z ed g r a i nsandd i s l oc a t i onann i h i l a Ｇ yr ys [ １３] , t i on ．Cons equen t l l ow s t r e s si sr educ ed a t y f h i rt empe r a t ur e sandl owe rs t r a i nr a t e s．I ncon Ｇ ghe t r a s t,t he r ei snoenought imef o rt henuc l e a t i on, r owt ho fDRX g r a i nsandd i s l oc a t i onann i h i l a t i on g unde rcond i t i onso fl owe rde f o rma t i ont empe r a t ur e s [ ] andh i rs t r a i nr a t e s１４ ,andt heso f t en i nge f f e c t ghe
８２０
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
o ft he rma l l c t i va t edp r o c e s si swe ake r,andt he r e Ｇ ya f o r e,t heh i rf l ows t r e s si sa ch i eved．Mo r eove r, ghe
t hec l e a rpe aks t r e s sd i s appe a r sg r adua l l f t e ri n i Ｇ ya t i a lwo rk ha r den i ng andas t e adyl eve li se a s o yt r e a ch wi t h noappa r en ts i f DRX cha r a c t e r i s Ｇ gnso , t i c si nd i c a t i ngt ha tt heba l anc eo fwo rkha r den i ng anddynami cr e c ove r sob t a i nedandDRX mayoc Ｇ yi
curso l e l nt hel oc a la r e ao ft hes amp l e s． yi Tosumma r i z e,t hel owe rs t r a i nr a t eandh i r ghe t empe r a t ur ef a c i l i t a t edynami cr e c r s t a l l i z a t i o n． I n y add i t i on,t he s ecur ve sob t a i nedf r om t hecompr e s Ｇ s i ont e s t si np r e s en ts t udya r econs i s t en twi t ht he r a l l epo r t ed de f o rma t i on cha r a c t e r i s t i c so f gene yr [ [ １０,１５] １６] o t he ra l l oys t e e l s andc a rbons t e e l s ．
̇ ̇ ̇ ̇ ( a) ０１s－１; ( b) １s－１; ( c) d) ε ＝０ ε ＝０ ε ＝１s－１; ( ε ＝１０s－１．
F i ２ F l owc u r v e so fNi ＧCr ＧMo ＧBs t e e la tv a r i ou st emp e r a t u r e sandd i f f e r en ts t r a i nr a t e s g
２ ２ Mi c r o s t r u c t u r a le v o l u t i on DRXi sac ommonc h a r a c t e r i s t i co fme t a l l i cma t e r i Ｇ a l swi t hl owe rs t a c k i ngf a u l te n e r nho td e f o rma t i on gyi [ ] r o c e s s１７ ．Th eo c c u r r e n c eo fDRXi st r a d i t i on a l l d e n Ｇ p yi t i f i e df r om t h ep r e s e n c eo fs t r e s sp e a k si nt h ef l ow [ ] c u r v e s１８ a ss howni nF i ２,a ndc ou l db ef u r t h e rv e r i Ｇ g f i e dby mi c r o s t r u c t u r a le v o l u t i ondu r i ng ho td e f o rma Ｇ t i on．F i ３i l l u s t r a t e sop t i c a lmi c r o s t r u c t u r e so ft h ee x Ｇ g e r ime n t a ls t e e ld e f o rme da t ８５０℃ und e rc on s t an t p s t r a i nr a t e so f０ ０１s－１ a nd１０s－１,r e s e c t i v e l tc an p y．I
b es e e nt ha tt heo r i i n a lg r a i n se l ong a t e da l ongt hed e Ｇ g f o rma t i on d i r e c t i on,andt hei n i t i a lg r a i n bound a r i e s , we r ef i n e l e r r a t e d．I na dd i t i on on l ewn ew DRX ys yaf r a i n snu c l e a t e da tt hes e r r a t e dp a r to fi n i t i a lg r a i n g bound a r i e sowi ngt ot hel owe rd e f o rma t i ont emp e r a t u r e, d emon s t r a t i ngo c c u r r e n c eo fl o c a lDRX．Wi t ht hei n Ｇ c r e a s eo fs t r a i nr a t e,t hes e r r a t e ds t r u c t u r ea r oundt he i n i t i a lg r a i n bound a r i e sg r a du a l l e du c e d,andf ewe r yr numb e ro fDRXg r a i n seme r e donp r i o rg r a i nbound a Ｇ g r i e s．
F i ３ Op t i c a lmi c r o s t r u c t u r e so fs e c imen sd e f o rme da t０ ０１s－１ ( a)and１０s－１ ( b)and８５０℃ g p
Fr om F i ４,a st hede f o rma t i ont empe r a t ur e g , i nc r e a s edt o９５０℃ t hes amp l e sa td i f f e r en ts t r a i n r a t e shaveunde r i ousdynami cr e c r t a l l i z a Ｇ goneobv ys t i on,andt heo r i i na lg r a i nswe r er ep l a c eden t i r e l g y byt henew DRX g r a i nsandt hes i z eo ft he DRX r a i nsi nc r e a s edobv i ous l heo t he rhand,a s g y．Ont c anbes e enf r om F i ４( b),wi t hi n c r e a s i ngs t r a i n g
r a t eupt o１０s－１ a tac ons t an tt empe r a t u r eo f９５０℃ , t hes i z eo ft heDRXg r a i nsde c r e a s ed．Tha ti sbe c aus e t he r ei snoenought imef o rt heg r owt ho fDRXg r a i ns a tah i rs t r a i nr a t e．Thes imi l a rr u l eo fmi c r o s t r uc Ｇ ghe t u r a le vo l u t i onc ou l dbef ounda tde f o rma t i ont empe r Ｇ a t u r eo f１０５０and１１５０℃ andv a r i ouss t r a i nr a t e s, andt her e su l t sa r eno tshownhe r e．
I s sue９ Ho tDe f o rma t i onBehav i o ro faNove lNi ＧCr ＧMo ＧB Ul t r a Ｇhe avyP l a t eS t e e lbyHo tComp r e s s i onTe s t
８２１
b)and９５０℃ a)and１０s－１ ( F i ４ Op t i c a lmi c r o s t r u c t u r eo fs e c imen sd e f o rme da t０ ０１s－１ ( g p
Assugge s t edabove,t hedynami cr e c r t a l l i z a Ｇ ys t i oni sc omp l e t ea t９５０℃ andaboveunde ra l ll eve l s , o fs t r a i nr a t e．Howeve r dynami cr e c r t a l l i z a t i on ys i spa r t i a la t８５０℃ duet ot hel owe r de f o rma t i on , t empe r a t u r e．Fu r t he rmo r ei ti nd i c a t e st ha tt her e Ｇ c r t a l l i z edmi c r o s t ruc t u r edependsont hede f o rma Ｇ ys t i onc ond i t i onso ft empe r a t u r eands t r a i nr a t e．The e f f e c t so fde f o rma t i ont empe r a t u r eands t r a i nr a t e onDRX pr o c edu r ec anbes imu l t aneous l e f l e c t ed yr [ ] byZene r ＧHo l l omonpa r ame t e r( Z)１９ ．Thede c r e a s e , , o fZ va l ue i e i nc r e a s i ng de f o rma t i ont empe r a Ｇ t ur eand/o rde c r e a s i ngs t r a i nr a t e, l e adst omo r ead Ｇ equa t epr o c e ed i ngo fDRX． ２ ３ De t e rmi na t i ono fcha r a c t e r i s t i c pa r ame t e r so f ho tde f o rma t i on Cha r a c t e r i s t i c pa r ame t e r so f ho t de f o rma t i on a r eimpo r t an ti nd i c a t o r sr e f l e c t i ngt het he rma lde Ｇ f o rma t i onbehav i o ro fma t e r i a l．Fo ri ns t anc e,c r i t i Ｇ ) ( c a ls t r e s sands t r a i n σcandεc a twh i chDRXi n i t i Ｇ a t e sa r equ i t eimpo r t an twhenmode l i ngho tf o rmi ng [ ] oc e s s e sus i ngf i n i t ee l emen tme t hod２０ ,andpe ak pr ) ( s t r e s sands t r a i n σpandεp haveimpo r t an tp r a c t i Ｇ
c a ls i i f i c anc ei ni ndus t r i a lp r oduc t i on２１ ．Fr om gn , t h i spo i n to fv i ew f o ragoodde s i faho two rk Ｇ gno i ngp r o c e s s,i ti sne c e s s a r t ok n o wt h ec h a r a c t e r i s Ｇ y t i cpa r ame t e r so fho tde f o rma t i on． Theana l i sba s edons t r a i nha r den i ngr a t e( θ) ys wa spe r f o rmedt o de t e rmi net hecha r a c t e r i s t i c pa Ｇ r ame t e r so fho tde f o rma t i on．Theθva l ue swe r eob Ｇ [ ] t a i ned wi t hc en t r a ld i f f e r enc eapp r oa ch２２ ．Thee Ｇ l a s t i cpo r t i ono ff l owcu r ve swa sr emovedandf l ow da t awe r ef i t t edandsmoo t hened wi t han８ t h Ｇ o rde r l a l,s oa st oe l imi na t ei n t e r f e r enc ec aus ed po ynomi byt empe r a t u r ef l uc t ua t i ons,l ub r i c a t e ba r r i e rand non Ｇun i f o rmf l owi nt hede f o rma t i onp r o c e s sandob Ｇ t a i nabe t t e ra c cu r a c fθva l ue sf o rt heana l i s． yo ys [ ]
２ ３ １ Cr i t i ca lc ondi t i onfo ri n i t i a t i onofdynamＧ i cr e c rys t a l l i za t i on Asmen t i onedabove,t hepr e s enc eo fas t r e s s aki nrheo l og i c a lcur ve( F i ２) i so f t encons i de r ed pe g a st heso l eme chan i c a lr e l i ab l es i lo ft heons e to f gna [ ] DRX ２３ ;howeve r,i tdoe sno tpr ov i dep r e c i s ei n Ｇ f o rma t i onabou tt heons e to fDRX．Be s i de s,DRX t ake sp l a c ei nmanyma t e r i a l sevent houghnoc l e a r l y de f i neds t r e s s pe aksa r eobs e r vedi nt he i rexpe r i Ｇ [ １１] , men t a lf l ow cur ve s ．Mo r eove ri ti sd i f f i cu l tt o know t hec r i t i c a lcond i t i onf o ri n i t i a t i on o f DRX dur i ng f o rmi ng ba s ed on mi c r os t ruc t ur e obs e r va Ｇ t i on．Al t e rna t i ve l hecon t en tde s c r i bedbe l owi sa y,t r e l i ab l eme t hodo fde t e rmi n i ng DRXc r i t i c a lcond i Ｇ t i on． Thec r i t i c a ls t r e s sf o ri n i t i a t i ono fDRX cou l d bei den t i f i edbyani n f l e c t i onpo i n ti nθ－σcur vebe Ｇ ve,a c co rd i ngt o f o r et hepe akpo i n to ft heσ－εcur [] wo rko fPo l i akandJona s８ andt hec r i t i c a ls t r a i n cou l dbede f i nedby mapp i ngt heσc ba cki n t oσ－ε [ ] cur ve,a c co rd i ngt owo rko fS t ewa r t２４ ．Howeve r, aque s t i ona r i s e she r e:howt ode t e rmi net hei n f l e c Ｇ vea c cur a t e l r oc edur ef o r t i onpo i n to fθ－σcur y．A p de t e rmi n i ngt hei n f l e c t i onpo i n to fcur vei nadvanc ed ma t hema t i c swa si n t r oduc edt oso l vet h i sp r ob l emi n t h i spape r,andt h i sme t hodha sno tbe enadd r e s s ed i nt hes t ud i e so ft hepa r ame t e ri den t i f i c a t i on． F i ５showst hedependenc eo fs t r a i nha rden i ng g r a t eonf l ow s t r e s sa td i f f e r en tt empe r a t ur e sand s t r a i no f１０s－１ ．F i ６( a)and６( b)showt hede Ｇ gs ( / ) eo ff i r s tde r i va t i ve d θd σ ands e condde Ｇ pendenc r i va t i ve ( d２θ/d σ２)o fθve r susσonf l ows t r e s sco r r e Ｇ , spond i ngt ot hecond i t i onso fF i ５ r e s e c t i v e l g p y． , Ass e enf r om F i ５ t heθ－σcur ve sshowc l e a ri n Ｇ g f l e c t i on po i n t, wh i ch cou l d be de t e rmi ned f r om F i ６ba s edon ma t hema t i c a lp r i nc i l e;t ha ti st o g p , s ay t hes t r e s s e sco r r e spond i ngt ot he max imao f t hed θ/d σve r susσcur ve sandz e r opo i n t so fd２θ/d σ２
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
８２２
ve r susσcu r ve sa r ec ons i de r eda sσcf o rt heons e to f DRX．Us i ngt h i sme t hod,σcf o rt heons e to fDRX a tva r i oust empe r a t u r e sands t r a i nr a t e s we r eob Ｇ t a i nedandt her e su l t sa r eg i veni nTab l e１．I tcou l d bes e ent ha tσci nc r e a s e swi t hi nc r e a s i ngs t r a i nr a t e andde c r e a s i ngt empe r a t u r e．Fu r t he rmo r e,i ne a ch i ne a r l c r e a s e s wi t ht hef l ow cur veo fF i ５,θl y de g s t r e s s;a f t e rt ha t,t hecu r ve sg r adua l l oa ychanget l owe rs l opeandt hen d r op t owa r dθ ＝０ a t pe ak s t r e s s,andt h i sme anst ha tt hepe aks t r e s sc ou l dbe [ ] de t e rmi nedbyt h i s me t hod１８ ,anda c c o r d i ng l e Ｇ yr su l t so fpe aks t r e s sunde rva r i ousp r o c e s s e sc ond i Ｇ t i onsa r ea l s ot abu l a t edi nTab l e１． F i ６ Cu r v e so ff i r s t( a)ands e c ond ( b)d e r i v a t i v e g o fs t r a i nha r d en i ngr a t ev e r s u sf l ows t r e s s a td i f f e r en tt emp e r a t u r e sand１０s－１
F i ５ Cu r v e so fs t r a i nha r d en i ngr a t ev e r s u sf l ow g s t r e s sa td i f f e r en tt emp e r a t u r e sand１０s－１
Thes t r e s s e si den t i f i eda tt hec r i t i c a landpe ak i n t scou l dbeus edt ode t e rmi net hec r i t i c a land po ak s t r a i n us i ng t he above Ｇmen t i oned mapp i ng pe me t hod,andt hec r i t i c a landpe aks t r a i nsands t r e s Ｇ s e scou l dbef oundi nF i ２a sc i r c u l a randt r i angu l a r g
Tab l e１ Cha r a c t e r i s t i cpa r ame t e r so fho td e f o rma t i onb eha v i o rund e rv a r i ou sc ond i t i on si nv e s t i a t e df o rNi ＧCr ＧMo ＧBs t e e l g ̇ ε/s－１
０ ０１
T/℃
１１３ ５８
１０５０
０ ２０
０ １３
０ ２８
７６ ２４
０ １１
６０ ８７
０ ５８
２２０ ５３
１０５０
０ ３２
１１４ ５５
９５０
０ ４９ ０ ２１
１５６ ９０
０ ４１
１５４ ７９
８５０ ９５０
１０５０ １１５０
０ ４３ ０ ３３ ０ ５３ ０ ５１ ０ ４６ ０ ４１
０ ５８
０ ２９
２０９ ９７
０ ７３
２１８ ４６
０ １５
１０２ ３４
０ ７０
９６ １４
０ １８
０ １９
１０５０
１１３ ０１ ２８５ ５０ ２２６ ４８ １９１ ４８ １４１ ６８
ma rked,r e spe c t i ve l omF i ２, i ti sev i den tt ha t y．Fr g h i rt empe r a t u r eo rl owe rs t r a i nr a t ec ons i de r ab l ghe y de c r e a s e st hec r i t i c a lpo i n to fDRX,a swe l la st he akpo i n to ft hef l owcu r ve． pe ２ ３ ２ St eady Ｇ s t a t es t r e s sands t ra i n Thes t e ady Ｇ s t a t es t r e s sands t r a i n( σs andεs)
cou l dbede t e c t edf r om t heaboveθ－σ cu r ve sand
σs/MPa
６９ ６９
０ ０６
１８３ ７７
２５６ ５５
εs ０ ６８
０ ０７
０ ７３
σc/MPa １６４ ２２
０ １６
８１ ３８
８５０
９５０
εc
１７５ ２６
８５０
１１５０ １０
０ ３０
０ ５４
９５０
１１５０
１
σp/MPa
８５０
１１５０
０ １
εp
１０５ ００ ５６ ８４
１３９ １５
０ ５４
０ ７２
０ ３０
２４３ ３８
０ ５５ —
０ １６
１３５ ３８
０ ７１
０ １３
６３ ７７
０ ６５
１６９ ７０
６４ ８４ ４８ ８１
１５６ １２ ６８ １７ —
１８２ ７７
９７ ３１
０ ６８
１０４ ４７
２０２ ２２
０ ７６
２７６ ７６
０ ２０
１７５ ４８
０ １７
９９ ７５
０ ７３
０ ３１ ０ ２３
１７３ ０９
１２７ ７４
０ ７９ ０ ７３ ０ ６９
１４９ ０１ ２８２ ２４ ２２１ ３３ １８６ ９９ １３６ ９１
σ－ε cur ve s,r e spe c t i ve l e en f r om F i ５, y． As s g , DRXc aus e sadownwa rdi n f l e c t i oni nt hep l o tl e ad Ｇ i ngt oz e r o,nega t i ves t r a i nha rden i ngr a t e sandz e r o aga i n．I nt h i sc a s e,po i n t s whe r et he p l o tc r os s e s z e r of r om abover epr e s en tt he pe aks t r e s s e s,and i n t swhe r ei tc r os s e sz e r of r om be l ow r epr e s en t po , s t e ady Ｇ s t a t es t r e s s e s．Ac co rd i ng l heexa c tva l ue s yt
I s sue９ Ho tDe f o rma t i onBehav i o ro faNove lNi ＧCr ＧMo ＧB Ul t r a Ｇhe avyP l a t eS t e e lbyHo tComp r e s s i onTe s t
o fs t e ady Ｇ s t a t es t r e s swe r ede t e rmi neda tt hes e cond oc cur r enc eo fθ＝０i nt heθ－σcu r ve sandt hent he s t e ady Ｇ s t a t es t r a i nsc ou l dbede t e rmi nedbyt hes imi Ｇ l a rmapp i ng me t hoda ss o l v i ngt hec r i t i c a ls t r a i ns． Thes t e ady Ｇ s t a t es t r e s s e sands t r a i nsa ch i eveda r e a l sol i s t edi nTab l e１． ２ ４ Con s t i t u t i v ee t i on sf o rpe aks t r e s spr e d i c t i on qua Thec omb i nede f f e c t so fde f o rma t i ont empe r a Ｇ t ur eand s t r a i nr a t e on t he de f o rma t i on behav i o r cou l dber epr e s en t edbyZene r ＧHo l l omonpa r ame t e r [ ] ( Z)i nanexponen t i a lf o rm ２５ a sf o l l ows: Q ( Z＝εexp( ) １) RT st h ea c t i v a t i o ne n e r fho td e f o rma t i on, wh e r e,Q i g yo /mo /( J l;Ri sun i v e r s a lg a sc o n s t a n t,８ ３ １ ４５J mo lK); a ndTi st h ea b s o l u t et emp e r a t u r e,K．
r i ng ho t Ther e l a t i onsh i twe enσ and Z du p be de f o rma t i on,e spe c i a l l th i empe r a t u r e,c anbe ya ght de s c r i bedbyanequa t i onknowna st he Ar rhen i us Ｇ [ ] t t i on２６ ,wh i chha sbe ensuc c e s s f u l l ed ypeequa yus f o rf l ow s t r e s s pr ed i c t i oni n ho tde f o rma t i on do Ｇ ma i nsandc anbeg i venby: ( Z ＝ A１σn１ ασ＜０ ８ ２) ( ) ( Z ＝ A２expβσ ασ＞１ ２ ３)
( Z ＝ A [s i nh( ασ)] n Fo ra l lσ ４) whe r e,A１ ,A２ ,A,n１ ,n, αandβa r eappa r en tma Ｇ an bec a l cu l a t ed t e r i a lc ons t an t s．Theva l ueo fα c rl aw ( Eq ( ２))i ssu i t ab l e wi t hα＝β/ n１ ．Thepowe , f o rr e l a t i ve l ow s t r e s s e s．Conve r s e l heexpo Ｇ yl y t nen t i a ll aw de s c r i t i ono fs t r e s s( Eq ( ３))i son l p y r e f e r r edf o rh i t r e s s e s．Howeve r,t hehype rbo l Ｇ p ghs i cs i nel aw ( Eq ( ４))c ou l dde s c r i bet het empe r a t ur e ands t r a i nr a t edependenc eo ft hes t r e s st hr oughou t [ ] t heen t i r er angeo fho two rk i ng２７ ． I ti sc l e a rt ha tt hec ons t i t u t i veequa t i ons,i e Eq s ( ２),( ３)and ( ４),r e f l e c tt her e l a t i onsh i b e p Ｇ twe ent hef l ows t r e s s,de f o rma t i ont empe r a t u r eand , s t r a i nr a t e andc ou l dbeus edt oc a l cu l a t et heho t de f o rma t i onc ons t an t sanda c t i va t i onene r ft he gyo ma t e r i a l us i ng t e s t da t a by r eg r e s s i on ana l i s． ys Howeve r,t heequa t i onsabovedono tc on t a i nt he e f f e c to fs t r a i nonf l ows t r e s sandnos t r a i nf o rde Ｇ t e rmi na t i ono ff l ows t r e s si sspe c i f i ed．Thus,cha r Ｇ a c t e r i s t i cs t r e s s e ssucha ss t e adys t a t e,pe ak,o rt he oneco r r e spond i ngt oaspe c i f i cs t r a i n may beus ed [ ] f o rt h i s pu rpo s e１８ ．S i nc et hes t e ady Ｇ s t a t es t r e s s mayno tbep r e c i s e l t t a i nedo rt he r emaybesome ya [ ] so f t en i ng duet o mo r l og i c a levo l u t i on２８ ,pe ak pho
８２３
s t r e s swa semp l oyedt oc a l cu l a t et hecons t an t si nt he Eqs ( ２),( ３)and ( ４)i nt h i sr e s e a r ch． ２ ４ １ De t e rmi na t i onof ma t e r i a lc on s t an t s Bys ub s t i t u t i ng Eq ( １)t oEq s ( ２) － ( ４)and t ak i ngn a t u r a ll og a r i t hmf r ome a c hs i d eo fr e s u l t i nge Ｇ , : a t i on st hef o l l owi nge xp r e s s i on sc ou l db eob t a i n e d qu Q ( n l n ５) ε ＝ n１l σ＋l nA１ － RT Q ( l n ε ＝βσ ＋l nA２ － ６) RT Q ( ε ＝ nl n[ s i nh( ασ)] ＋l nA － ７) l n RT Fo rs i t u a t i onwhe r et emp e r a t u r ei sf i x e d,byd i f f e r Ｇ e n t i a t i ngEq s ( ５),( ６)and ( ７),r e s e c t i v e l hee x Ｇ p y,t , : r e s s i ono fn１ βandnc anb ee xp r e s s e da s p n１ ＝
∂ l n ε σ ∂ l n
∂ l n ε β ＝ ∂ σ
T
( ８)
T
( ９)
∂ l n ε ( １０) ∂ l n[ s i nh( ασ)] T Thu s,t hev a l u e so fn１,βandn c anb eob t a i n e d , εv e r s u sl nσ l εv e r s u sσand f r omt hes l op ei np l o t so fl n n l n e r s u sl n[ s i nh( α σ)] emp l oy i ngt hev a l u e so fp e ak εv s t r e s sandc o r r e s i ng s t r a i nr a t eandt emp e r a t u r e pond , f r omt hec omp r e s s i ont e s t sr e s e c t i v e l e e nf r om p y．Ass F i ７,t hel i n e a rr e r e s s i ono ft he s ed a t ag i v e st hea v e r Ｇ g g a ev a l u e so f９ ８３２２３,０ ０６６９４MPa－１ and７ １３３７０ g f o rn１,β andn,r e s e c t i v e l i ou s l he s ep l o t s p y．Obv y,t ha v eagoodl i n e a rr e l a t i on s h i hea v e r a ev a l u eo f p,andt g t hec o r r e l a t i onc o e f f i c i e n t s( Rc)a r e０ ９９０５６,０ ９９６８８ and０ ９９５３２,r e s e c t i v e l r t he r,t hev a l u eo fα＝β/ p y．Fu －１ n１c anb ed e t e rmi n e da s０ ００６８１MPa ,andt hev a l u e RT)a nA－Q/( tc on s t an tt emp e r a t u r ef o rv a r i Ｇ o fbT ＝l ou ss i t u a t i on su s e dt od e t e rm i n et h eme a nv a l u eo fAl a t e r ] ε－l n[ s i nh( α σ) ． c a nb eob t a i n e df r omt h ei n t e r c e t so fl n p ２ ４ ２ Ca l cu l a t i onof Q Thea c t i va t i onene r ep r e s en t st hel eve lo fan gyr ene r b a r r i e rt ob es u r m o u n t e di ns o m ea t o m i s t i c gy [ ２９] ; me chan i sms t husge t t i ngandana l z i ngt hea c t i Ｇ y va t i onene r so fg r e a ts i i f i c anc ef o rac l e a run Ｇ gyi gn de r s t and i ngont heho tde f o rma t i onbehav i o randt he [ ] co r r e spond i ng r a t e Ｇ con t r o l l i ng me chan i sms３０ ． Cons i de r i ngt ha ts t r a i nr a t ei sacons t an t,byt ak i ng r t i a lde r i va t i veo fe a chs i deo fEq．( ７)t oT－１ ,t he pa : exp r e s s i ono fQ c anbeg i vena s ∂ l n[ s i nh( α σ)] ( Q ＝ nR １１) ̇ ∂T－１ ε I ti sobv i ous l ha tt heva l ueo fQ c anbede t e r Ｇ yt mi nedf r om t he me ans l opeo fl i ne si nt hep l o to f l n[ s i nh( ασ)] －T－１ , a sshowni nF i ８andt heva l ue g n ＝
８２４
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 ７ Re l a t i on so fl nε－l nσ ( a),l nε－σ ( b)andl nε－l n[ s i nh ( c) ασ)] ( g a td i f f e r en td e f o rma t i ont emp e r a t u r e sc a l c u l a t e dba s e donp e aks t r e s s
i sde t e rmi neda s３７９１３９Jmo l－１ ．Theave r ageco r Ｇ r e l a t i on c oe f f i c i en t f o r r eg r e s s i on ana l i s i s ys ０ ９９５５１,wh i chsugge s t st heapp r op r i a t ene s so fhy Ｇ rbo l i cs i nel awt oc a l cu l a t et hea c t i va t i onene r pe gy． / ( ) , Subs t i t u t i ngQ andT i n t obT ＝l nA －Q RT t he a v e r a eo fA a tv a r i ou sl e v e l so fd e f o rma t i ont emp e r a Ｇ g t u r ec ou l db ee a s i l v a l u a t e da s２ ５０４７９×１０１４ ． ye
n i t i ono fhype rbo l i cs i ne,t hepe aks t r e s scou l dbe : de s c r i beda sf o l l ows １/７ １３３７０ ïì ïìï Z ï ) ＋ ４６ ８４ l níï ( p ＝１ １４ ïσ ５０４７９×１０ î ２ ï ï / ２/７ １３３７０ é ù １ ２ üïï ï Z ê ú ) ( ê ( íï １２) ＋１úú ýï １４ êë û ２ ５０４７９×１０ þ ï ï ï ３７９１３９) ï Z ＝ε exp( ï RT î F i ９showscompa r i sonso ft heexpe r imen t a l g andp r ed i c t edpe aks t r e s s e sby Eq ( １２)f o ra l lde Ｇ f o rma t i oncond i t i ons．AsshownF i ９,mos to ft he g da 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 onl i ne yc andt heag r e emen tbe twe ent heexpe r imen t a land r ed i c t edva l ue si ss a t i s f a c t o r p y．
F i ８ Re l a t i ono fl n[ s i nh ( td i f f e r en t ασ)] －T－１ a g s t r a i nr a t e sob t a i n e dba s e donp e aks t r e s s
I ti swo r t hmen t i on i ngt ha tt heva l ueo fQ dev i Ｇ a t e sl a r l r om t he s e l f Ｇ d i f f us i on i n aus t en i t e, ge yf [ ] wh i chi sr epo r t eda s２７００００Jmo l－１ ３１ ．Al t hough t heho t wo rk i ng a c t i va t i onene r he gy dependsont ma t e r i a lbe i ngc ons i de r ed, i ti susua l l r e f e r r e d t oa s y , appa r en t va l ue be c aus e no a c c oun ti s gene r a l l y t akeno ft hei n t e rna lmi c r o s t ruc t u r a ls t a t eandi ti s on l r i vedf r om an Ar rhen i usp l o t wi t hal i ne a r yde r angeandt hea s sump t i ont ha tt he mi c r o s t ruc t ur e r ema i nsc ons t an t．Theho two rk i nga c t i va t i onene r Ｇ l ue sa r eo f t en muchl a r rt hananyimag i ned gyva ge a t omi cme chan i sm．Th i sc anbea s c r i bedt ot hef a c t t ha ti nho two rk i ng,t he mi c r o s t ruc t u r e s mayi n i Ｇ t i a l l i f f e rt os ome deg r e ef o rd i f f e r en tp r ehe a t s yd and evo l ve r ap i d l td i f f e r en tr a t e s du r i ng t e s Ｇ ya [ ] t i ng２８ ．Mo r eove r,f o rmi c r oa l l oyeds t e e l s,t heso l Ｇ u t ed r age f f e c to f mi c r oa l l oy i nge l emen t sp r oh i b i t s t hemovemen to fbounda r i e sandr e su l t si nah i r ghe [ １１] a c t i va t i onene r gy ． ２ ４ ３ Pr edi c t i onofpeaks t r e s sanda s s e s smen ton edi c t ab i l i t pr y Ac c o r d i ngt oEq．( ７),andc ons i de r i ngt hede f i Ｇ
F i ９ Re l a t i onb e twe enp r e d i c t e dande xp e r imen t a lp e ak g s t r e s s e sa t８５０－１１５０℃ and０ ０１－１０s－１
I no rde rt o eva l ua t et he p r ed i c t ab i l i t ft he yo , cons t i t u t i veequa t i onquan t i t a t i ve l s t a n d a r ds t a t i s Ｇ y t i c a l pa r ame t e r si nc l ud i ng co r r e l a t i on coe f f i c i en t ( r ageabso l u t er e l a t i vee r r o r( AARE)and Rc),ave r e l a t i vee r r o rbe twe ent heexpe r imen t a lr e su l t sand r ed i c t edr e su l t s we r ec a l cu l a t ed．Rc i scommon l p y us edi ns t a t i s t i c s wh i chr ep r e s en t ss t r eng t ho ft he l i ne a rr e l a t i onsh i twe en t he expe r imen t a l and p be r ed i c t edva l ue s,andAAREi sa l soun i ve r s a ls t a t i s Ｇ p t i c a lpa r ame t e r sf o rme a sur i ngt hep r ed i c t ab i l i t fa yo nume r i c a l mode l． AARE i s compu t ed t hr ough a t e rm byt e rm compa r i sono ft her e l a t i vee r r o rand cons equen t l sunb i a s eds t a t i s t i c a lpa r ame t e r sf o r yi [ ３２] me a sur i ng t he pr ed i c t ab i l i t f a mode l ． The yo sma l l e rt heva l ueo fAAREi s,t hebe t t e rt her e su l t
I s sue９ Ho tDe f o rma t i onBehav i o ro faNove lNi ＧCr ＧMo ＧB Ul t r a Ｇhe avyP l a t eS t e e lbyHo tComp r e s s i onTe s t
８２５
i s．Theya r ede f i nedr e spe c t i ve l s: ya N
Rc＝
σiE －σE)( σiP－σP) ∑ (
i＝１ N
N
i＝１
i＝１
２ ２ ∑( ∑( σiE －σE) σiP－σP)
i i １ N σE －σP ×１００％ AARE＝ ∑ i Ni＝１ σE
( １３) ( １４)
σiE －σiP ( Re l a t i vee r r o r＝ i ×１００％ １５) σE st heexpe r imen t a lf l ows t r e s s;σiPi st he whe r e,σiEi r e d i c t e df l o w s t r e s so b t a i n e df r o m s t r a i n Ｇ c o m e Ｇ p pn s a t ed Ar rhen i us Ｇ t ons t i t u t i veequa t i on;σE and ypec r et heme anva l ue so fexpe r imen t a landp r ed i c t ed σP a f l ows t r e s s e s,r e spe c t i ve l st het o t a lnumＧ y;andNi be ro fda t as e t semp l oyedi nt hei nve s t i t i on． ga Theva l ueo fRc be twe ent heexpe r imen t a land ed i c t ed da t af r om t he c ons t i t u t i ve equa t i on i s pr ０ ９９４６０．Th i ssugge s t st ha tt hec ons t i t u t i veequa Ｇ t i ona ch i evedha sbe t t e rl i ne a rr e l a t i onsh i twe en pbe t heexpe r imen t a landp r ed i c t edr e su l t s．TheAARE o ft hec ons t i t u t i veequa t i oni s４ ２９％ ,andt her e l a Ｇ , t i vee r r o ri s －１４ ５７％ t o３ ４７％ wh i chi nd i c a t e s t ha tt hedeve l opedc ons t i t u t i ve mode lha sexc e l l en t ed i c t ab i l i t fpe aks t r e s sunde rt heexpe r imen t a l pr yo cond i t i onso ft hei nve s t i t eds t e e l．F i １０shows ga g t hes t a t i s t i c a lana l i so ft her e su l t so fc ons t i t u t i ve ys equa t i on,wh i chi sdep i c t eda st hes amp l enumbe r f r equenc r susr e l a t i vee r r o rp l o t．I tc anbes e en yve t ha tt her e l a t i vee r r o r swi t h i n ±１０％ ob t a i nedf r om t hecons t i t u t i veequa t i onsi sshownf o r mo r et han ９３％ o ft het e s tda t as e t s,wh i chr eve a l st heh i r ghe a c cur a c ft hec ons t i t u t i veequa t i onandi tc anme e t yo t her equ i r emen t sf o reng i ne e r i ngc a l cu l a t i ons．
F i １０ S t a t i s t i c a lana l s i so fr e l a t i v ee r r o rb e twe en g y e xp e r imen t a landp r e d i c t e dp e aks t r e s s e sby Ar rh en i u s Ｇ t ec on s t i t u t i v eequa t i on yp
２ ５ Re l a t i on s h i twe encha r a c t e r i s t i cpa r ame t e r s pbe andZene r ＧHo l l omonpa r ame t e r Fo racons t an ti n i t i a lg r a i ns i z e,t her e l a t i on Ｇ sh i twe en cha r a c t e r i s t i c pa r ame t e r so ff l ow p be cur ve sandZene r ＧHo l l omonpa r ame t e rcou l dbeex Ｇ [] r e s s eda sf o l l ows９ : p ( C ＝ KZm １６) whe r e,C i s a cha r a c t e r i s t i c pa r ame t e ro ff l ow cur ve,andK andm a r ema t e r i a lcons t an t sdepend Ｇ
en tont hea l l oycompos i t i on．Ther e l a t i onsbe twe en r amＧ t hep r ev i ouscha r a c t e r i s t i cpa r ame t e r sandZ pa e t e rwe r ep l o t t edi nF i １１onal oga r i t hmi cs c a l e, g andt henr eg r e s s i onana l i so ft he s ep l o t sr e su l t ed ys i nt hef o l l owi ngequa t i ons: ( ８２３９７Z０１０４２３ σp ＝３ １７) εp ＝０ ０１３２９Z００９５７４ σc ＝２ ８００００Z
０ １１０３３
εc ＝０ ００４５７Z０１０３４２ σs ＝２ ００６２４Z
０ １２０８１
２８４４５Z００２５１０ εs ＝０
( １８) ( １９) ( ２０) ( ２１) ( ２２)
F i １１ Cha r a c t e r i s t i cpa r ame t e r so ff l owc u r v e sa sf unc t i on so fZ g
I tc ou l dbef oundt ha tt he r ei sagoodl i ne a rr e Ｇ l a t i onbe twe enl n σp,l n σc,l n σsandl nZ wi t ht hel i ne Ｇ , a rco r r e l a t i onc oe f f i c i en to f０ ９８４８４ ０ ９８５７４and ０ ９７５４１,r e spe c t i ve l heo t he rhand,poo r y．Ont co r r e l a t i ons we r e f ound be twe en cha r a c t e r i s t i c
s t r a i nsandZ onl oga r i t hmi cs c a l e,andt h i smaybe c aus edbyal imi t a t i ono ft hepowe rl aw ( Eq ( １６)) wh i chi smo r esu i t ab l ef o rt hede s c r i t i ono ft her e Ｇ p l a t i onsh i twe ens t r e s sand Z．Fur t he rmo r e,a l l pbe o ft hecha r a c t e r i s t i c pa r ame t e r si nc r e a s e wi t hi nＧ
８２６
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
c r e a s i ngZ va l ue ( i nc r e a s i ngs t r a i nr a t eo rde c r e a Ｇ s i ngt empe r a t u r e),wh i chi sc ons i s t en twi t ht hep r e Ｇ v i ousana l i s．Thec r i t i c a lr a t i o so fbo t hσc/ σp and ys / ema i nf a i r l ons t an t．Theme anc r i t i c a ls t r e s s εc εpr yc r a t i oi s０ ９１,r ang i ngf r om ０ ７８t o０ ９７,wi t ha s t anda r ddev i a t i ono f０ ０４,whe r e a st heme anc r i t i Ｇ , c a ls t r a i nr a t i oi s０ ４６ r ang i ngf r om０ ３０t o０ ６０, wi t has t anda r d dev i a t i on o f０ ０８． The c r i t i c a l , / , s t r e s sr a t i o σc σp de t e rmi nedf o rt hep r e s en t Ni Ｇ Cr ＧMo ＧBs t e e li sc ons i s t en twi t ht heva l uegene r a l l y r epo r t edo f０ ９０f o rl owc a rbonNb ＧTimi c r oa l l oyed [ ３３] , , s t e e l ．I nadd i t i on t hec r i t i c a ls t r a i nr a t i o εc/εp, ob t a i nedhe r ei si nag r e emen twi t ht ha tr epo r t edf o r [ ] bo r on mi c r oa l l oyeds t e e l１１ ,wh i chr ange sbe twe en ０ ３５ and ０ ７３, wi t h a me an va l ue o f０ ５３．I t shou l dbeno t edt ha tf o rs omes t e e lg r ade ssucha s med i um c a rbon mi c r oa l l oyeds t e e l,t he h i ghεc/εp [ １０] va l ueo f０ ６２ha sa l s obe enr epo r t ed ．
３ Conc l u s i on s
( １)DRXi st he ma i nr e a s onf o rdynami cf l ow so f t en i ngo ft hei nve s t i t eds t e e l．DRXi sope r a t i ve ga evena t８５０℃ and１０s－１ ．Thede c r e a s eo fZ va l ue l e adst omo r eex t ens i veo fDRX． ( ２)Theimpo r t an tcha r a c t e r i s t i cpa r ame t e r so f DRXi nc l ud i ngt hec r i t i c a lc ond i t i onf o ri n i t i a t i ono f , , DRX t he pe aks t r e s sands t r a i n andt hes t e ady s t a t es t r e s sands t r a i nwe r ede t e rmi nedf r omt heda Ｇ t ao ft rues t r e s s Ｇ s t r a i nands t r a i nha r den i ngr a t e． ( ３)Thecha r a c t e r i s t i c pa r ame t e r st endt oi n Ｇ c r e a s ea ss t r a i nr a t ei nc r e a s e sandt empe r a t u r ede Ｇ c r e a s e s,wh i chi nd i c a t et ha tt hepa r ame t e r so fho t wo rk i ngdependont het empe r a t u r eands t r a i nr a t e． ( ４)Thea c t i va t i onene r fho tde f o rma t i ono f gyo t hes t e e l wa sc a l cu l a t ed wi t h a mo r eexa c tva l ue us i ngt heAr rhen i us Ｇ t rbo l i cs i nel awt ha ti s ypehype /mo equa lt o３７９１３９J l． ( ５)Thec ons t i t u t i veequa t i oni sob t a i nedt oex Ｇ e s sho two rk i ngcha r a c t e r i s t i c so ft hei nve s t i t ed pr ga s t e e lwi t hah i r ed i c t ab i l i t ghp y． ( ) ６ Bo t hpe aks t r e s sands t r a i nc anbep r ed i c t ed byt heZ pa r ame t e ri npowe r Ｇ l awequa t i onsandt he r a t i oso fc r i t i c a ls t r e s sands t r a i nt ope aks t r e s sand s t r a i na r eabou t０ ９１and０ ４６,r e spe c t i ve l y． Re f e r enc e s:
[ １] T．L．Fu,Z．D．Wang,Y．L i,J．D．L i,G．D．Wang,App l． The rm． Eng． ７０ ( ２０１４)８００ Ｇ ８０７．
[ ２] X． Y．Wang,T． Pan,H．Wang,H． Su,X． Y． L i,X． Z． Cao,Ac Ｇ t a Me t a l l． S i n． ４８ ( ２０１２)４０１ Ｇ ４０６． [ ３] T． Pan,X．Y．Wang,H．Wang,Y． L i,H． Su,C． F．Yang,J． I r onS t e e lRe s． I n t． １８ ( ２０１１)２４２ Ｇ ２４５． [ Su,C． F．Yang,Ac t a Me t a l l． S i n． ５０ ４] T． Pan,X．Y．Wang,H． ( ２０１４)４３１ Ｇ ４３８． [ L i u,L． Zhou,Q．Han,B． J i ang,Z．L i,J． I r on ５] D． Zhang,Y． S t e e lRe s． I n t． ２１ ( ２０１４)１０４２ Ｇ １０４８． [ S． Chen,J． Deng,Ma t e r． De s． ５２ ( ２０１３) ６] Y． C． L i n,Y． Di ng,M．
１１８ Ｇ １２７． [ l,A．K． Bhadur i,Ma t e r． Sc i． Eng．A ７] D． Saman t a r ay,S．Manda ５２８ ( ２０１１)５２０４ Ｇ ５２１１． [ ８] E． I． Po l i ak,J． J． J ona s,Ac t a Ma t e r． ４４ ( １９９６)１２７ Ｇ １３６． [ F． Yi n,F． S． Shangguan,K．Wang,Q． ９] D． J． L i,Y． R． Feng,Z． L i u,F． Hu,Ma t e r． Sc i． Eng． A５２８ ( ２０１１)８０８４ Ｇ ８０８９． [ １０] H．Mi r z adeh,J．M． Cabr e r a,J．M． Pr ado,A． Na a f i z adeh,Ma Ｇ j t e r． Sc i． Eng． A５２８ ( ２０１１)３８７６ Ｇ ３８８２． [ １１] I．Me í a,A． Bedo l l a Ｇ J a cu i nde,C．Ma l donado,J．M．Cabr e r a, j Ma t e r． Sc i． Eng． A５２８ ( ２０１１)４１３３ Ｇ ４１４０． [ Tao,J． １２] K．Wu,G． Q． L i u,B． F．Hu,F． L i,Y．W． Zhang,Y． T． L i u,Ma t e r． De s． ３２ ( ２０１１)１８７２ Ｇ １８７９． [ J． １３] X．Xi ao,G．Q． L i u,B． F．Hu,X． Zheng,L．N．Wang,S． Chen,A． Ul l ah,Compu t．Ma t e r． Sc i． ６２ ( ２０１２)２２７ Ｇ ２３４． [ １４] Y． H． Xi ao,C． Guo,X． Y． Guo,Ma t e r． Sc i． Eng． A５２８ ( ２０１１)
６５１０ Ｇ ６５１８． [ １５] H． Y． L i,Y． H． L i,X． F．Wang,J． J． L i u,Y．Wu,Ma t e r． De s． ４９ ( ２０１３)４９３ Ｇ ５０１． [ １６] D． L． Ba r aga r,J．Me ch．Wo rk． Te chno l． １４ ( １９８７)２９５ Ｇ ３０７． [ １７] A． Dehghan ＧManshad i,M． R． Ba r ne t t,P． D．Hodgs on,Ma t e r． Sc i． Eng． A４８５ ( ２００８)６６４ Ｇ ６７２． [ １８] H．Mi r z a d e h,A． Na a f i z a d e h,M．Mo a z e ny,Me t a l l．Ma t e r． T r a n s． j A４０ ( ２００９)２９５０ Ｇ ２９５８． [ １９] C． Zene r,J． H． Ho l l omon,J． App l． Phys． １５ ( １９４４)２２ Ｇ ３２． [ ２０] E． I． Po l i ak,J． J． J ona s,I S I JI n t． ４３ ( ２００３)６８４ Ｇ ６９１． [ ２１] H． L．We i,G．Q． L i u,X． Xi ao,H． T． Zhao,H． Di ng,R．M． Kang,Ma t e r． Sc i． Eng． A５６４ ( ２０１３)１４０ Ｇ １４６． [ ２２] H．Mi r z adeh,A． Na a f i z adeh,Ma t e r． Chem． Phys． １１６ ( ２００９) j １１９ Ｇ １２４． [ ２３] R． Di ng,Z． X． Guo,Ac t a Ma t e r． ４９ ( ２００１)３１６３ Ｇ ３１７５． [ ２４] G． R． S t ewa r t,A．M． Elwa z r i,S． Yue,J． J． J ona s,Ma t e r． Sc i． Te ch． Lond． ２２ ( ２００６)５１９ Ｇ ５２４． [ ２５] L．Ma,L．Wang,Z． L i u,G．Yang,L． Lu,M． Peng,J． I r on S t e e lRe s． I n t． ２１ ( ２０１４)１０３５ Ｇ １０４１． [ ２６] C．M． Se l l a r s,W． J．McTega r t,Ac t a Me t a l l． １４ ( １９６６)１１３６ Ｇ
１１３８． [ ２７] Z． Y． Chen,S． Q． Xu,X． H． Dong,Ac t aMe t a l l． S i n． ２１ ( ２００８) ４５１ Ｇ ４５８． [ ２８] H． J．McQue en,N．D．Ryan,Ma t e r． Sc i． Eng．A ３２２ ( ２００２) ４３ Ｇ ６３． [ ２９] H． J．McQu e e n,S．Yu e,N． D． Ry a n,E． Fr t e r． Pr o c e s s． y,J．Ma T e c hno l． ５３ ( １９９５)２９３ Ｇ ３１０． [ ３０] H． T． Zhao,G． Q． L i u,L． Xu,Ma t e r． Sc i． Eng． A５５９ ( ２０１３) ２６２ Ｇ ２６７． [ ３１] J．M． Cabr e r a,A．AlOma r,J．M． Pr ado,J． J． J ona s,Me t a l l． Ma t e r． Tr ans． A２８ ( １９９７)２２３３ Ｇ ２２４４． [ ３２] D． S ama n t a r a nd a l,A． K． Bh a du r i,Ma t e r． De s． ３２ ( ２０１１) y,S．Ma
２７９７ Ｇ ２８０２． [ ３３] M． Shaban,B． Eghba l i,Ma t e r． Sc i． Eng．A５２７ ( ２０１０)４３２０ Ｇ ４３２５．
JOURNALOFIRON ANDSTEELRESEARCH,INTERNATIONAL２ ０ １ ５,２ ２( ９):８ １ ８ Ｇ ８ ２ ６
Ho tDe f o rma t i onBe ha v i o ro faNo v e lNi ＧCr ＧMo ＧBUl t r a Ｇ he a v y P l a t eS t e e lbyHo tCompr e s s i onTe s t
１, ２ ３ ３ １, ４, ５ ３ Zh i Ｇ Ｇ yuGAO , TaoPAN, Zhuo WANG, Guo quanLIU , HangSU
( １．S t a t eKeyLabo r a t o r o rAdvanc ed Me t a l sand Ma t e r i a l s,Un i ve r s i t fSc i enc eandTe chno l ogyBe i i ng,Be i i ng１０００８３, yf yo j j ; , , , Ch i na ２．Co l l egeo fMa t e r i a l sSc i enc eandEng i ne e r i ng L i aon i ngTe chn i c a lUn i ve r s i t i n１２３０９９ L i aon i ng,Ch i na; y Fux , , , ; ３．Di v i s i ono fEng i ne e r i ngS t e e l 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 ４．Schoo lo fMa t e r i a l s j Sc i enc eandEng i ne e r i ng,Un i ve r s i t fSc i enc eandTe chno l ogyBe i i ng,Be i i ng１０００８３,Ch i na; ５．Co l l abo r a t i ve yo j j I nnova t i onCen t e ro fS t e e lTe chno l ogy,Un i ve r s i t fSc i enc eandTe chno l ogyBe i i ng,Be i i ng１０００８３,Ch i na) yo j j Ab s t r a c t:Ho tde f o rma t i onbehav i o ro fanove lNi ＧCr ＧMo ＧBhe avyp l a t es t e e lwa ss t ud i edbyho tc omp r e s s i ont e s t s, wh i chwe r ec onduc t edona Gl e eb l e Ｇ ３８００t he rmo Ｇme chan i c a ls imu l a t o rc o r r e spond i ngt ot het empe r a t u r er angeo f ８５０－１１５０℃ wi t ht hes t r a i nr a t e so f０ ０１－１０s－１ andt het r ues t r a i no f０ ８．Ther e su l t ssugge s tt ha tt hema o r i t j y o ff l owcu r ve sexh i b i tat i c a ldynami cr e c r s t a l l i z a t i on ( DRX)behav i o rwi t hanappa r en ts i ng l epe aks t r e s sf o l Ｇ yp y l owedbyag r adua lf a l lt owa r dsas t e ady Ｇ s t a t es t r e s s．Impo r t an tcha r a c t e r i s t i cpa r ame t e r so ff l owbehav i o ra sc r i t i c a l /s /s s t r e s s t r a i nf o ri n i t i a t i ono fDRXandpe akands t e ady Ｇ s t a t es t r e s s t r a i nwe r ede r i vedf r omcu r ve so fs t r a i nha r den Ｇ i ngr a t eve r suss t r e s sands t r e s sve r suss t r a i n,r e spe c t i ve l t e r i a lc ons t an t so ft hei nve s t i t eds t e e lwe r ede t e r Ｇ y．Ma ga mi nedba s edonAr r hen i us Ｇ t ons t i t u t i vee t i on,andt hent hepe aks t r e s swa sp r ed i c t edbyt hee t i onwi t ht he ypec qua qua /mo ho tde f o rma t i ona c t i va t i onene r f３７９１３９J l,andt hep r ed i c t edva l ue sag r e ewe l lwi t ht heexpe r imen t a lva l ue s． gyo Fu r t he rmo r e,t hee f f e c to fZene r ＧHo l l omonpa r ame t e ront hecha r a c t e r i s t i cpo i n t so ff l owcu r ve swa ss t ud i edus i ng t hepowe rl awr e l a t i on,andt her a t i oo fc r i t i c a ls t r e s sands t r a i nt ope aks t r e s sands t r a i nwe r ef oundt obe０ ９１and ０ ４６,r e spe c t i ve l y． Ke r d s:Ni ＧCr ＧMo ＧBhe avyp l a t es t e e l;ho tde f o rma t i on;c ons t i t u t i vee t i on;a c t i va t i onene r r a c t e r i s t i c qua gy;cha ywo r ame t e r pa
The deve l opmen to fh i Ｇ s t r eng t h and h i Ｇ gh gh t oughne s ss t e e l sf o r ma r i ne eng i ne e r i ng i s eve r r owi ng wi t ht heimpo r t anc eo fo f f sho r eo i landga s g [ １] r e sour c e sexp l o i t a t i onr e c ogn i z ed ．Ni ＧCr ＧMo ＧBu l Ｇ t r a Ｇhe avy p l a t es t e e li so f t en r e f e r r ed a sh i gh s t r eng t hl ow a l l oy (HSLA ) ma r i ne eng i ne e r i ng [ ２] , s t e e l andi sus edi nc r i t i c a lapp l i c a t i onssucha s r oduc t i onp l a t f o rm,sh i i l d i ngandp r e s su r eve s Ｇ p pbu s e lands oon．Ni,Cr,MoandBe t c．a r eo f t enu t i Ｇ l i z edt oimpr oveha r denab i l i t nt hes t e e lp l a t e．Re Ｇ yi s e a r che sonNi ＧCr ＧMo ＧBs t e e lmo s t l o cus edont he yf [ ３] componen top t imi z a t i on de s i her e l a t i on Ｇ gn andt sh i r o c e s s e s,mi c r o s t ruc t u r e sandp r ope r Ｇ psamongp [] t i e s４ ,wh i l ea lmo s tnoe f f o r tha sbe enpa i dt oun Ｇ de r s t andt heho tde f o rma t i onbehav i o ro ft hes t e e l,
wh i chi squ i t eimpo r t an tt oop t imi z et heho two rk i ng r oc e s spa r ame t e r sandge tan i c es t he t i cme chan Ｇ p yn i c a lp r ope r t ft hep r oduc t s． yo Thes i ne Ｇhype rbo l i cl aw i nan Ar rhen i us Ｇ t ype equa t i onha sbe ensuc c e s s f u l l edf o rcha r a c t e r i Ｇ y us [ ,] z i ngho tde f o rma t i onbehav i o r５ ６ andop t imi z i ngt he [] t he rmo Ｇme chan i c a lp r oc e s spa r ame t e r s７ o fma t e r i Ｇ [ ８] a l s．Mo r eove r,Po l i akandJona s sugge s t edt ha t ( t hei n i t i a t i on o f dynami cr e c t a l l i z a t i on DRX ) ys c anbei den t i f i edf r om change si nt hes l opeo ft he s t r a i nha rden i ngr a t eve r susf l ows t r e s scur ve s．Ac Ｇ , co rd i ng l tde f o rma t i on behav i o ro f Fe Ｇ ２５Mn Ｇ y ho [] ３S i Ｇ ３AlTWIPs t e e lwa ss t ud i edbyL ie ta l９ ．us i ng Ar rhen i us Ｇ t t i t u t i veequa t i onandt he me t hＧ ypecons [ ] odo fPo l i akandJona s．Mi r z adehe ta l．１０ de t e r Ｇ
Founda t i onI t em:I t emSpons o r edbyNa t i ona lNa t ur a lSc i enc eFounda t i ono fCh i na ( ５１０７１０１９,５１３７１０３０);Na t i ona lHi chno l ogyRe s e a r ch ghTe andDeve l opmen tPr og r am o fCh i na ( ２０１３AA０３１６０１);Na t i ona lKey Te chno l ogy Re s e a r chand Deve l opmen tPr og r am o ft he Mi n i s t r fSc i enc eandTe chno l ogyo fCh i na ( ２０１１BAE２５B０１) yo B i o r aphy: Zh i Ｇ c t o rCand i da t e; E Ｇma i l: zh i c om; Re c e i v e dDa t e:De c embe r１８,２０１４ yuGAO,Do yugao＠１２６ g Co r r e s i ngAu t ho r:Guo Ｇ c t o r,Pr o f e s s o r; E Ｇma i l:g l i u＠us t b edu cn quanLIU,Do pond
I s sue９ Ho tDe f o rma t i onBehav i o ro faNove lNi ＧCr ＧMo ＧB Ul t r a Ｇhe avyP l a t eS t e e lbyHo tComp r e s s i onTe s t
mi nedt heho t wo rk i ng c ons t an t sand de f o rma t i on a c t i va t i onene r fa med i um c a rbon mi c r oa l l oyed gyo s t e e lbyc ons t i t u t i veequa t i on,andt hes t r a i nha rd Ｇ en i ngr a t eve r suss t r e s scu r ve swe r eus edt or eve a l whe t he rDRXhado c cu r r ed．Thec r i t i c a lc ond i t i ons f o rt hei n i t i a t i ono fDRXo fbo r onmi c r oa l l oyeds t e e l we r es t ud i ed us i ngt heabove me t hod by Me í ae t j a l．,andt her e su l t sa r ei n ag r e emen t wi t ho t he r [ ] common l epo r t eds t e e l s１１ ． yr I nt h i ss t udy,ho tde f o rma t i onbehav i o ro fNi Ｇ Cr ＧMo ＧBs t e e lwa si nve s t i t edbyho tc omp r e s s i on ga t e s t s．Thecha r a c t e r i s t i cpa r ame t e r ssucha sc r i t i c a l cond i t i onf o ri n i t i a t i on o f DRX,pe ak ands t e ady Ｇ /s s t a t es t r e s s t r a i na td i f f e r en tt empe r a t u r e s and , s t r a i nr a t e so ft h i ss t e e lwe r ec a l cu l a t ed andAr rhe Ｇ n i us Ｇ t t i on wa se s t ab l i shed．Then,a c co rd Ｇ ypeequa i ngt ot heequa t i on,t hepe aks t r e s s e swe r ep r ed i c t ed andva l i da t edwi t ht heexpe r imen t a lr e su l t s．I nadd i Ｇ t i on,t her e l a t i onsh i twe en cha r a c t e r i s t i c pa Ｇ ps be r ame t e r sandZene r ＧHo l l omonpa r ame t e rwe r ebu i l t． , Cons equen t l het heo r e t i c a lba s i sf o rop t imi z i ng y t ho two rk i ngp r o c e s s e so ft heNi ＧCr ＧMo ＧBs t e e lwa s e s t ab l i shed．
１ Ma t e r i a l sandExp e r imen t a lPr o c e du r e s
The pr i nc i lchemi c a lc ompo s i t i on (ma s s％ ) pa o ft heNi ＧCr ＧMo ＧBs t e e lemp l oyedi nt h i swo rki sC ０ １２,S i０ ３０, Mn １ ２０,Ni１ ８０,Cr０ ５, Mo ０ ５,B０ ００１６,Al０ ０５,Ti０ ０１５,V ０ ０３６,Cu , ０ ３２ a nd Fe b a l a n c e． S i ng l e Ｇ a s si s o t h e rma l ho t p un i ax i a lc omp r e s s i ont e s t swe r ec ondu c t e don Gl e e b l e Ｇ ３８００ t h e rmo Ｇme c h a n i c a ls imu l a t o r． Cy l i nd r i c a lt e s t s e c ime n sw i t h８mmi nd i ame t e ra nd１５mmi nh e i t p gh we r ef a b r i c a t e dc a r e f u l l r omt h ea nn e a l e db i l l e tw i t ha yf , v e r ods u r f a c ef i n i s h． I na dd i t i on f o rmi n imi z i ngt he ygo i n f l u e n c eo ff r i c t i onont h ef l ow b e h a v i o r,at a n t a l um f o i lwi t hat h i c kn e s so f０ ０５mmwa sp l a c e db e twe e nt he anv i la ndt h es e c ime n． p Thec ompr e s s i ont e s t swe r ec a r r i edou ta c co rd Ｇ i ngt ot hepr o c e s ss chemei nF i １．Thespe c imens g we r eaus t en i t i z eda t１２００℃ f o r３００st oob t a i nun i Ｇ f o rm aus t en i t i c mi c r o s t ruc t u r e, t hen c oo l ed a t １０℃/st od i f f e r en t de s i r ed de f o rma t i on t empe r a Ｇ t ur e s( ８５０－１１５０℃ ,s t epo f１００℃ )andhe l df o r １０st oe l imi na t et he rma lg r ad i en t s,andt henspe c i Ｇ ̇ menswe r ei s o t he rma l l f o rmeda ts t r a i nr a t e s( ε) yde －１ r ang i ngf r om ０ ０１t o１０s wi t hani n t e r va lo fan o rde ro fmagn i t udewi t hat rues t r a i n( ε)o f０ ８．I n t h i sc a s e,t het rues t r e s s Ｇ s t r a i nda t a we r er e c o rded au t oma t i c a l l r i ng c omp r e s s i on． Al lt he spe c i Ｇ y du menswe r e wa t e rquenchedr ap i d l op r e s e r vet he yt
８１９
mi c r os t ruc t ur e sa te l eva t ed t empe r a t ur ea f t e rt he de f o rma t i on,andt he mi c r os t ruc t ur eo ft hespe c i Ｇ menswa sexami nedbyop t i c a lmi c r os copyo fOl m Ｇ y pus．
F i １ Pr o c e s ss ch emef o rho tc omp r e s s i on g t e s t so fNi ＧCr ＧMo ＧBs t e e l
２ Re s u l t sandDi s c u s s i on ２ １ F l owcu r v e sana l s i s y σ)cur ve sob Ｇ F i ２dep i c t st hef l ow s t r e s s( g t a i nedf r omt heho tcomp r e s s i ont e s t so ft heNi ＧCr Ｇ Mo ＧBs t e e la td i f f e r en tt empe r a t ur e sr ang i ngf r om ８５０t o１１５０℃ wi t hs t r a i nr a t e so f０ ０１,０ １,１and －１ , １０s r e spe c t i ve l e en f r om F i ２,t he y． As s g cur ve s,exc l ud i ngt hos ea tl owe rt empe r a t ur eand h i rs t r a i nr a t e,exh i b i tobv i oust i c a lDRXso f Ｇ ghe yp t en i ngbehav i o r wi t has i ng l epe aks t r e s sf o l l owed [ ] byag r adua lf a l lt owa rdsas t e adys t a t es t r e s s１２ ,
andt hepe aks t r e s sbe come sl e s sobv i ous l he ywhent de f o rma t i ont empe r a t ur ede c r e a s e so rt hes t r a i nr a t e i nc r e a s e s． I tc ana l sobes e ent ha tt heh i rt het empe r a Ｇ ghe , , t ur et hel owe rt hef l ows t r e s sa ch i eved wh i l et he l owe rt hes t r a i nr a t e,t hel owe rt hef l ows t r e s sob Ｇ t a i ned．Thecomb i nede f f e c to fwo rkha rden i ngand t he rma l l c t i va t edso f t en i ngr e su l t edi nt he s ephe Ｇ ya nomena．I no t he rwo rds,t hee f f e c t so ft hede f o rma Ｇ t i ont empe r a t ur eands t r a i nr a t eonf l ows t r e s scou l d beexp l a i nedi nt e rmso fd i s l oc a t i on me chan i smand dynami cr e cove r e c r t a l l i z a t i on．Hi rt empe r Ｇ y/r ys ghe a t ur e sandl owe rs t r a i nr a t e spr ov i del onge rt imef o r ene r c cumu l a t i onandh i rmob i l i t fa t omsa t gya ghe yo bounda r i e sf o rt henuc l e a t i onandg r owt ho fdynami Ｇ c a l l e c r t a l l i z ed g r a i nsandd i s l oc a t i onann i h i l a Ｇ yr ys [ １３] , t i on ．Cons equen t l l ow s t r e s si sr educ ed a t y f h i rt empe r a t ur e sandl owe rs t r a i nr a t e s．I ncon Ｇ ghe t r a s t,t he r ei snoenought imef o rt henuc l e a t i on, r owt ho fDRX g r a i nsandd i s l oc a t i onann i h i l a t i on g unde rcond i t i onso fl owe rde f o rma t i ont empe r a t ur e s [ ] andh i rs t r a i nr a t e s１４ ,andt heso f t en i nge f f e c t ghe
８２０
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
o ft he rma l l c t i va t edp r o c e s si swe ake r,andt he r e Ｇ ya f o r e,t heh i rf l ows t r e s si sa ch i eved．Mo r eove r, ghe
t hec l e a rpe aks t r e s sd i s appe a r sg r adua l l f t e ri n i Ｇ ya t i a lwo rk ha r den i ng andas t e adyl eve li se a s o yt r e a ch wi t h noappa r en ts i f DRX cha r a c t e r i s Ｇ gnso , t i c si nd i c a t i ngt ha tt heba l anc eo fwo rkha r den i ng anddynami cr e c ove r sob t a i nedandDRX mayoc Ｇ yi
curso l e l nt hel oc a la r e ao ft hes amp l e s． yi Tosumma r i z e,t hel owe rs t r a i nr a t eandh i r ghe t empe r a t ur ef a c i l i t a t edynami cr e c r s t a l l i z a t i o n． I n y add i t i on,t he s ecur ve sob t a i nedf r om t hecompr e s Ｇ s i ont e s t si np r e s en ts t udya r econs i s t en twi t ht he r a l l epo r t ed de f o rma t i on cha r a c t e r i s t i c so f gene yr [ [ １０,１５] １６] o t he ra l l oys t e e l s andc a rbons t e e l s ．
̇ ̇ ̇ ̇ ( a) ０１s－１; ( b) １s－１; ( c) d) ε ＝０ ε ＝０ ε ＝１s－１; ( ε ＝１０s－１．
F i ２ F l owc u r v e so fNi ＧCr ＧMo ＧBs t e e la tv a r i ou st emp e r a t u r e sandd i f f e r en ts t r a i nr a t e s g
２ ２ Mi c r o s t r u c t u r a le v o l u t i on DRXi sac ommonc h a r a c t e r i s t i co fme t a l l i cma t e r i Ｇ a l swi t hl owe rs t a c k i ngf a u l te n e r nho td e f o rma t i on gyi [ ] r o c e s s１７ ．Th eo c c u r r e n c eo fDRXi st r a d i t i on a l l d e n Ｇ p yi t i f i e df r om t h ep r e s e n c eo fs t r e s sp e a k si nt h ef l ow [ ] c u r v e s１８ a ss howni nF i ２,a ndc ou l db ef u r t h e rv e r i Ｇ g f i e dby mi c r o s t r u c t u r a le v o l u t i ondu r i ng ho td e f o rma Ｇ t i on．F i ３i l l u s t r a t e sop t i c a lmi c r o s t r u c t u r e so ft h ee x Ｇ g e r ime n t a ls t e e ld e f o rme da t ８５０℃ und e rc on s t an t p s t r a i nr a t e so f０ ０１s－１ a nd１０s－１,r e s e c t i v e l tc an p y．I
b es e e nt ha tt heo r i i n a lg r a i n se l ong a t e da l ongt hed e Ｇ g f o rma t i on d i r e c t i on,andt hei n i t i a lg r a i n bound a r i e s , we r ef i n e l e r r a t e d．I na dd i t i on on l ewn ew DRX ys yaf r a i n snu c l e a t e da tt hes e r r a t e dp a r to fi n i t i a lg r a i n g bound a r i e sowi ngt ot hel owe rd e f o rma t i ont emp e r a t u r e, d emon s t r a t i ngo c c u r r e n c eo fl o c a lDRX．Wi t ht hei n Ｇ c r e a s eo fs t r a i nr a t e,t hes e r r a t e ds t r u c t u r ea r oundt he i n i t i a lg r a i n bound a r i e sg r a du a l l e du c e d,andf ewe r yr numb e ro fDRXg r a i n seme r e donp r i o rg r a i nbound a Ｇ g r i e s．
F i ３ Op t i c a lmi c r o s t r u c t u r e so fs e c imen sd e f o rme da t０ ０１s－１ ( a)and１０s－１ ( b)and８５０℃ g p
Fr om F i ４,a st hede f o rma t i ont empe r a t ur e g , i nc r e a s edt o９５０℃ t hes amp l e sa td i f f e r en ts t r a i n r a t e shaveunde r i ousdynami cr e c r t a l l i z a Ｇ goneobv ys t i on,andt heo r i i na lg r a i nswe r er ep l a c eden t i r e l g y byt henew DRX g r a i nsandt hes i z eo ft he DRX r a i nsi nc r e a s edobv i ous l heo t he rhand,a s g y．Ont c anbes e enf r om F i ４( b),wi t hi n c r e a s i ngs t r a i n g
r a t eupt o１０s－１ a tac ons t an tt empe r a t u r eo f９５０℃ , t hes i z eo ft heDRXg r a i nsde c r e a s ed．Tha ti sbe c aus e t he r ei snoenought imef o rt heg r owt ho fDRXg r a i ns a tah i rs t r a i nr a t e．Thes imi l a rr u l eo fmi c r o s t r uc Ｇ ghe t u r a le vo l u t i onc ou l dbef ounda tde f o rma t i ont empe r Ｇ a t u r eo f１０５０and１１５０℃ andv a r i ouss t r a i nr a t e s, andt her e su l t sa r eno tshownhe r e．
I s sue９ Ho tDe f o rma t i onBehav i o ro faNove lNi ＧCr ＧMo ＧB Ul t r a Ｇhe avyP l a t eS t e e lbyHo tComp r e s s i onTe s t
８２１
b)and９５０℃ a)and１０s－１ ( F i ４ Op t i c a lmi c r o s t r u c t u r eo fs e c imen sd e f o rme da t０ ０１s－１ ( g p
Assugge s t edabove,t hedynami cr e c r t a l l i z a Ｇ ys t i oni sc omp l e t ea t９５０℃ andaboveunde ra l ll eve l s , o fs t r a i nr a t e．Howeve r dynami cr e c r t a l l i z a t i on ys i spa r t i a la t８５０℃ duet ot hel owe r de f o rma t i on , t empe r a t u r e．Fu r t he rmo r ei ti nd i c a t e st ha tt her e Ｇ c r t a l l i z edmi c r o s t ruc t u r edependsont hede f o rma Ｇ ys t i onc ond i t i onso ft empe r a t u r eands t r a i nr a t e．The e f f e c t so fde f o rma t i ont empe r a t u r eands t r a i nr a t e onDRX pr o c edu r ec anbes imu l t aneous l e f l e c t ed yr [ ] byZene r ＧHo l l omonpa r ame t e r( Z)１９ ．Thede c r e a s e , , o fZ va l ue i e i nc r e a s i ng de f o rma t i ont empe r a Ｇ t ur eand/o rde c r e a s i ngs t r a i nr a t e, l e adst omo r ead Ｇ equa t epr o c e ed i ngo fDRX． ２ ３ De t e rmi na t i ono fcha r a c t e r i s t i c pa r ame t e r so f ho tde f o rma t i on Cha r a c t e r i s t i c pa r ame t e r so f ho t de f o rma t i on a r eimpo r t an ti nd i c a t o r sr e f l e c t i ngt het he rma lde Ｇ f o rma t i onbehav i o ro fma t e r i a l．Fo ri ns t anc e,c r i t i Ｇ ) ( c a ls t r e s sands t r a i n σcandεc a twh i chDRXi n i t i Ｇ a t e sa r equ i t eimpo r t an twhenmode l i ngho tf o rmi ng [ ] oc e s s e sus i ngf i n i t ee l emen tme t hod２０ ,andpe ak pr ) ( s t r e s sands t r a i n σpandεp haveimpo r t an tp r a c t i Ｇ
c a ls i i f i c anc ei ni ndus t r i a lp r oduc t i on２１ ．Fr om gn , t h i spo i n to fv i ew f o ragoodde s i faho two rk Ｇ gno i ngp r o c e s s,i ti sne c e s s a r t ok n o wt h ec h a r a c t e r i s Ｇ y t i cpa r ame t e r so fho tde f o rma t i on． Theana l i sba s edons t r a i nha r den i ngr a t e( θ) ys wa spe r f o rmedt o de t e rmi net hecha r a c t e r i s t i c pa Ｇ r ame t e r so fho tde f o rma t i on．Theθva l ue swe r eob Ｇ [ ] t a i ned wi t hc en t r a ld i f f e r enc eapp r oa ch２２ ．Thee Ｇ l a s t i cpo r t i ono ff l owcu r ve swa sr emovedandf l ow da t awe r ef i t t edandsmoo t hened wi t han８ t h Ｇ o rde r l a l,s oa st oe l imi na t ei n t e r f e r enc ec aus ed po ynomi byt empe r a t u r ef l uc t ua t i ons,l ub r i c a t e ba r r i e rand non Ｇun i f o rmf l owi nt hede f o rma t i onp r o c e s sandob Ｇ t a i nabe t t e ra c cu r a c fθva l ue sf o rt heana l i s． yo ys [ ]
２ ３ １ Cr i t i ca lc ondi t i onfo ri n i t i a t i onofdynamＧ i cr e c rys t a l l i za t i on Asmen t i onedabove,t hepr e s enc eo fas t r e s s aki nrheo l og i c a lcur ve( F i ２) i so f t encons i de r ed pe g a st heso l eme chan i c a lr e l i ab l es i lo ft heons e to f gna [ ] DRX ２３ ;howeve r,i tdoe sno tpr ov i dep r e c i s ei n Ｇ f o rma t i onabou tt heons e to fDRX．Be s i de s,DRX t ake sp l a c ei nmanyma t e r i a l sevent houghnoc l e a r l y de f i neds t r e s s pe aksa r eobs e r vedi nt he i rexpe r i Ｇ [ １１] , men t a lf l ow cur ve s ．Mo r eove ri ti sd i f f i cu l tt o know t hec r i t i c a lcond i t i onf o ri n i t i a t i on o f DRX dur i ng f o rmi ng ba s ed on mi c r os t ruc t ur e obs e r va Ｇ t i on．Al t e rna t i ve l hecon t en tde s c r i bedbe l owi sa y,t r e l i ab l eme t hodo fde t e rmi n i ng DRXc r i t i c a lcond i Ｇ t i on． Thec r i t i c a ls t r e s sf o ri n i t i a t i ono fDRX cou l d bei den t i f i edbyani n f l e c t i onpo i n ti nθ－σcur vebe Ｇ ve,a c co rd i ngt o f o r et hepe akpo i n to ft heσ－εcur [] wo rko fPo l i akandJona s８ andt hec r i t i c a ls t r a i n cou l dbede f i nedby mapp i ngt heσc ba cki n t oσ－ε [ ] cur ve,a c co rd i ngt owo rko fS t ewa r t２４ ．Howeve r, aque s t i ona r i s e she r e:howt ode t e rmi net hei n f l e c Ｇ vea c cur a t e l r oc edur ef o r t i onpo i n to fθ－σcur y．A p de t e rmi n i ngt hei n f l e c t i onpo i n to fcur vei nadvanc ed ma t hema t i c swa si n t r oduc edt oso l vet h i sp r ob l emi n t h i spape r,andt h i sme t hodha sno tbe enadd r e s s ed i nt hes t ud i e so ft hepa r ame t e ri den t i f i c a t i on． F i ５showst hedependenc eo fs t r a i nha rden i ng g r a t eonf l ow s t r e s sa td i f f e r en tt empe r a t ur e sand s t r a i no f１０s－１ ．F i ６( a)and６( b)showt hede Ｇ gs ( / ) eo ff i r s tde r i va t i ve d θd σ ands e condde Ｇ pendenc r i va t i ve ( d２θ/d σ２)o fθve r susσonf l ows t r e s sco r r e Ｇ , spond i ngt ot hecond i t i onso fF i ５ r e s e c t i v e l g p y． , Ass e enf r om F i ５ t heθ－σcur ve sshowc l e a ri n Ｇ g f l e c t i on po i n t, wh i ch cou l d be de t e rmi ned f r om F i ６ba s edon ma t hema t i c a lp r i nc i l e;t ha ti st o g p , s ay t hes t r e s s e sco r r e spond i ngt ot he max imao f t hed θ/d σve r susσcur ve sandz e r opo i n t so fd２θ/d σ２
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
８２２
ve r susσcu r ve sa r ec ons i de r eda sσcf o rt heons e to f DRX．Us i ngt h i sme t hod,σcf o rt heons e to fDRX a tva r i oust empe r a t u r e sands t r a i nr a t e s we r eob Ｇ t a i nedandt her e su l t sa r eg i veni nTab l e１．I tcou l d bes e ent ha tσci nc r e a s e swi t hi nc r e a s i ngs t r a i nr a t e andde c r e a s i ngt empe r a t u r e．Fu r t he rmo r e,i ne a ch i ne a r l c r e a s e s wi t ht hef l ow cur veo fF i ５,θl y de g s t r e s s;a f t e rt ha t,t hecu r ve sg r adua l l oa ychanget l owe rs l opeandt hen d r op t owa r dθ ＝０ a t pe ak s t r e s s,andt h i sme anst ha tt hepe aks t r e s sc ou l dbe [ ] de t e rmi nedbyt h i s me t hod１８ ,anda c c o r d i ng l e Ｇ yr su l t so fpe aks t r e s sunde rva r i ousp r o c e s s e sc ond i Ｇ t i onsa r ea l s ot abu l a t edi nTab l e１． F i ６ Cu r v e so ff i r s t( a)ands e c ond ( b)d e r i v a t i v e g o fs t r a i nha r d en i ngr a t ev e r s u sf l ows t r e s s a td i f f e r en tt emp e r a t u r e sand１０s－１
F i ５ Cu r v e so fs t r a i nha r d en i ngr a t ev e r s u sf l ow g s t r e s sa td i f f e r en tt emp e r a t u r e sand１０s－１
Thes t r e s s e si den t i f i eda tt hec r i t i c a landpe ak i n t scou l dbeus edt ode t e rmi net hec r i t i c a land po ak s t r a i n us i ng t he above Ｇmen t i oned mapp i ng pe me t hod,andt hec r i t i c a landpe aks t r a i nsands t r e s Ｇ s e scou l dbef oundi nF i ２a sc i r c u l a randt r i angu l a r g
Tab l e１ Cha r a c t e r i s t i cpa r ame t e r so fho td e f o rma t i onb eha v i o rund e rv a r i ou sc ond i t i on si nv e s t i a t e df o rNi ＧCr ＧMo ＧBs t e e l g ̇ ε/s－１
０ ０１
T/℃
１１３ ５８
１０５０
０ ２０
０ １３
０ ２８
７６ ２４
０ １１
６０ ８７
０ ５８
２２０ ５３
１０５０
０ ３２
１１４ ５５
９５０
０ ４９ ０ ２１
１５６ ９０
０ ４１
１５４ ７９
８５０ ９５０
１０５０ １１５０
０ ４３ ０ ３３ ０ ５３ ０ ５１ ０ ４６ ０ ４１
０ ５８
０ ２９
２０９ ９７
０ ７３
２１８ ４６
０ １５
１０２ ３４
０ ７０
９６ １４
０ １８
０ １９
１０５０
１１３ ０１ ２８５ ５０ ２２６ ４８ １９１ ４８ １４１ ６８
ma rked,r e spe c t i ve l omF i ２, i ti sev i den tt ha t y．Fr g h i rt empe r a t u r eo rl owe rs t r a i nr a t ec ons i de r ab l ghe y de c r e a s e st hec r i t i c a lpo i n to fDRX,a swe l la st he akpo i n to ft hef l owcu r ve． pe ２ ３ ２ St eady Ｇ s t a t es t r e s sands t ra i n Thes t e ady Ｇ s t a t es t r e s sands t r a i n( σs andεs)
cou l dbede t e c t edf r om t heaboveθ－σ cu r ve sand
σs/MPa
６９ ６９
０ ０６
１８３ ７７
２５６ ５５
εs ０ ６８
０ ０７
０ ７３
σc/MPa １６４ ２２
０ １６
８１ ３８
８５０
９５０
εc
１７５ ２６
８５０
１１５０ １０
０ ３０
０ ５４
９５０
１１５０
１
σp/MPa
８５０
１１５０
０ １
εp
１０５ ００ ５６ ８４
１３９ １５
０ ５４
０ ７２
０ ３０
２４３ ３８
０ ５５ —
０ １６
１３５ ３８
０ ７１
０ １３
６３ ７７
０ ６５
１６９ ７０
６４ ８４ ４８ ８１
１５６ １２ ６８ １７ —
１８２ ７７
９７ ３１
０ ６８
１０４ ４７
２０２ ２２
０ ７６
２７６ ７６
０ ２０
１７５ ４８
０ １７
９９ ７５
０ ７３
０ ３１ ０ ２３
１７３ ０９
１２７ ７４
０ ７９ ０ ７３ ０ ６９
１４９ ０１ ２８２ ２４ ２２１ ３３ １８６ ９９ １３６ ９１
σ－ε cur ve s,r e spe c t i ve l e en f r om F i ５, y． As s g , DRXc aus e sadownwa rdi n f l e c t i oni nt hep l o tl e ad Ｇ i ngt oz e r o,nega t i ves t r a i nha rden i ngr a t e sandz e r o aga i n．I nt h i sc a s e,po i n t s whe r et he p l o tc r os s e s z e r of r om abover epr e s en tt he pe aks t r e s s e s,and i n t swhe r ei tc r os s e sz e r of r om be l ow r epr e s en t po , s t e ady Ｇ s t a t es t r e s s e s．Ac co rd i ng l heexa c tva l ue s yt
I s sue９ Ho tDe f o rma t i onBehav i o ro faNove lNi ＧCr ＧMo ＧB Ul t r a Ｇhe avyP l a t eS t e e lbyHo tComp r e s s i onTe s t
o fs t e ady Ｇ s t a t es t r e s swe r ede t e rmi neda tt hes e cond oc cur r enc eo fθ＝０i nt heθ－σcu r ve sandt hent he s t e ady Ｇ s t a t es t r a i nsc ou l dbede t e rmi nedbyt hes imi Ｇ l a rmapp i ng me t hoda ss o l v i ngt hec r i t i c a ls t r a i ns． Thes t e ady Ｇ s t a t es t r e s s e sands t r a i nsa ch i eveda r e a l sol i s t edi nTab l e１． ２ ４ Con s t i t u t i v ee t i on sf o rpe aks t r e s spr e d i c t i on qua Thec omb i nede f f e c t so fde f o rma t i ont empe r a Ｇ t ur eand s t r a i nr a t e on t he de f o rma t i on behav i o r cou l dber epr e s en t edbyZene r ＧHo l l omonpa r ame t e r [ ] ( Z)i nanexponen t i a lf o rm ２５ a sf o l l ows: Q ( Z＝εexp( ) １) RT st h ea c t i v a t i o ne n e r fho td e f o rma t i on, wh e r e,Q i g yo /mo /( J l;Ri sun i v e r s a lg a sc o n s t a n t,８ ３ １ ４５J mo lK); a ndTi st h ea b s o l u t et emp e r a t u r e,K．
r i ng ho t Ther e l a t i onsh i twe enσ and Z du p be de f o rma t i on,e spe c i a l l th i empe r a t u r e,c anbe ya ght de s c r i bedbyanequa t i onknowna st he Ar rhen i us Ｇ [ ] t t i on２６ ,wh i chha sbe ensuc c e s s f u l l ed ypeequa yus f o rf l ow s t r e s s pr ed i c t i oni n ho tde f o rma t i on do Ｇ ma i nsandc anbeg i venby: ( Z ＝ A１σn１ ασ＜０ ８ ２) ( ) ( Z ＝ A２expβσ ασ＞１ ２ ３)
( Z ＝ A [s i nh( ασ)] n Fo ra l lσ ４) whe r e,A１ ,A２ ,A,n１ ,n, αandβa r eappa r en tma Ｇ an bec a l cu l a t ed t e r i a lc ons t an t s．Theva l ueo fα c rl aw ( Eq ( ２))i ssu i t ab l e wi t hα＝β/ n１ ．Thepowe , f o rr e l a t i ve l ow s t r e s s e s．Conve r s e l heexpo Ｇ yl y t nen t i a ll aw de s c r i t i ono fs t r e s s( Eq ( ３))i son l p y r e f e r r edf o rh i t r e s s e s．Howeve r,t hehype rbo l Ｇ p ghs i cs i nel aw ( Eq ( ４))c ou l dde s c r i bet het empe r a t ur e ands t r a i nr a t edependenc eo ft hes t r e s st hr oughou t [ ] t heen t i r er angeo fho two rk i ng２７ ． I ti sc l e a rt ha tt hec ons t i t u t i veequa t i ons,i e Eq s ( ２),( ３)and ( ４),r e f l e c tt her e l a t i onsh i b e p Ｇ twe ent hef l ows t r e s s,de f o rma t i ont empe r a t u r eand , s t r a i nr a t e andc ou l dbeus edt oc a l cu l a t et heho t de f o rma t i onc ons t an t sanda c t i va t i onene r ft he gyo ma t e r i a l us i ng t e s t da t a by r eg r e s s i on ana l i s． ys Howeve r,t heequa t i onsabovedono tc on t a i nt he e f f e c to fs t r a i nonf l ows t r e s sandnos t r a i nf o rde Ｇ t e rmi na t i ono ff l ows t r e s si sspe c i f i ed．Thus,cha r Ｇ a c t e r i s t i cs t r e s s e ssucha ss t e adys t a t e,pe ak,o rt he oneco r r e spond i ngt oaspe c i f i cs t r a i n may beus ed [ ] f o rt h i s pu rpo s e１８ ．S i nc et hes t e ady Ｇ s t a t es t r e s s mayno tbep r e c i s e l t t a i nedo rt he r emaybesome ya [ ] so f t en i ng duet o mo r l og i c a levo l u t i on２８ ,pe ak pho
８２３
s t r e s swa semp l oyedt oc a l cu l a t et hecons t an t si nt he Eqs ( ２),( ３)and ( ４)i nt h i sr e s e a r ch． ２ ４ １ De t e rmi na t i onof ma t e r i a lc on s t an t s Bys ub s t i t u t i ng Eq ( １)t oEq s ( ２) － ( ４)and t ak i ngn a t u r a ll og a r i t hmf r ome a c hs i d eo fr e s u l t i nge Ｇ , : a t i on st hef o l l owi nge xp r e s s i on sc ou l db eob t a i n e d qu Q ( n l n ５) ε ＝ n１l σ＋l nA１ － RT Q ( l n ε ＝βσ ＋l nA２ － ６) RT Q ( ε ＝ nl n[ s i nh( ασ)] ＋l nA － ７) l n RT Fo rs i t u a t i onwhe r et emp e r a t u r ei sf i x e d,byd i f f e r Ｇ e n t i a t i ngEq s ( ５),( ６)and ( ７),r e s e c t i v e l hee x Ｇ p y,t , : r e s s i ono fn１ βandnc anb ee xp r e s s e da s p n１ ＝
∂ l n ε σ ∂ l n
∂ l n ε β ＝ ∂ σ
T
( ８)
T
( ９)
∂ l n ε ( １０) ∂ l n[ s i nh( ασ)] T Thu s,t hev a l u e so fn１,βandn c anb eob t a i n e d , εv e r s u sl nσ l εv e r s u sσand f r omt hes l op ei np l o t so fl n n l n e r s u sl n[ s i nh( α σ)] emp l oy i ngt hev a l u e so fp e ak εv s t r e s sandc o r r e s i ng s t r a i nr a t eandt emp e r a t u r e pond , f r omt hec omp r e s s i ont e s t sr e s e c t i v e l e e nf r om p y．Ass F i ７,t hel i n e a rr e r e s s i ono ft he s ed a t ag i v e st hea v e r Ｇ g g a ev a l u e so f９ ８３２２３,０ ０６６９４MPa－１ and７ １３３７０ g f o rn１,β andn,r e s e c t i v e l i ou s l he s ep l o t s p y．Obv y,t ha v eagoodl i n e a rr e l a t i on s h i hea v e r a ev a l u eo f p,andt g t hec o r r e l a t i onc o e f f i c i e n t s( Rc)a r e０ ９９０５６,０ ９９６８８ and０ ９９５３２,r e s e c t i v e l r t he r,t hev a l u eo fα＝β/ p y．Fu －１ n１c anb ed e t e rmi n e da s０ ００６８１MPa ,andt hev a l u e RT)a nA－Q/( tc on s t an tt emp e r a t u r ef o rv a r i Ｇ o fbT ＝l ou ss i t u a t i on su s e dt od e t e rm i n et h eme a nv a l u eo fAl a t e r ] ε－l n[ s i nh( α σ) ． c a nb eob t a i n e df r omt h ei n t e r c e t so fl n p ２ ４ ２ Ca l cu l a t i onof Q Thea c t i va t i onene r ep r e s en t st hel eve lo fan gyr ene r b a r r i e rt ob es u r m o u n t e di ns o m ea t o m i s t i c gy [ ２９] ; me chan i sms t husge t t i ngandana l z i ngt hea c t i Ｇ y va t i onene r so fg r e a ts i i f i c anc ef o rac l e a run Ｇ gyi gn de r s t and i ngont heho tde f o rma t i onbehav i o randt he [ ] co r r e spond i ng r a t e Ｇ con t r o l l i ng me chan i sms３０ ． Cons i de r i ngt ha ts t r a i nr a t ei sacons t an t,byt ak i ng r t i a lde r i va t i veo fe a chs i deo fEq．( ７)t oT－１ ,t he pa : exp r e s s i ono fQ c anbeg i vena s ∂ l n[ s i nh( α σ)] ( Q ＝ nR １１) ̇ ∂T－１ ε I ti sobv i ous l ha tt heva l ueo fQ c anbede t e r Ｇ yt mi nedf r om t he me ans l opeo fl i ne si nt hep l o to f l n[ s i nh( ασ)] －T－１ , a sshowni nF i ８andt heva l ue g n ＝
８２４
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 ７ Re l a t i on so fl nε－l nσ ( a),l nε－σ ( b)andl nε－l n[ s i nh ( c) ασ)] ( g a td i f f e r en td e f o rma t i ont emp e r a t u r e sc a l c u l a t e dba s e donp e aks t r e s s
i sde t e rmi neda s３７９１３９Jmo l－１ ．Theave r ageco r Ｇ r e l a t i on c oe f f i c i en t f o r r eg r e s s i on ana l i s i s ys ０ ９９５５１,wh i chsugge s t st heapp r op r i a t ene s so fhy Ｇ rbo l i cs i nel awt oc a l cu l a t et hea c t i va t i onene r pe gy． / ( ) , Subs t i t u t i ngQ andT i n t obT ＝l nA －Q RT t he a v e r a eo fA a tv a r i ou sl e v e l so fd e f o rma t i ont emp e r a Ｇ g t u r ec ou l db ee a s i l v a l u a t e da s２ ５０４７９×１０１４ ． ye
n i t i ono fhype rbo l i cs i ne,t hepe aks t r e s scou l dbe : de s c r i beda sf o l l ows １/７ １３３７０ ïì ïìï Z ï ) ＋ ４６ ８４ l níï ( p ＝１ １４ ïσ ５０４７９×１０ î ２ ï ï / ２/７ １３３７０ é ù １ ２ üïï ï Z ê ú ) ( ê ( íï １２) ＋１úú ýï １４ êë û ２ ５０４７９×１０ þ ï ï ï ３７９１３９) ï Z ＝ε exp( ï RT î F i ９showscompa r i sonso ft heexpe r imen t a l g andp r ed i c t edpe aks t r e s s e sby Eq ( １２)f o ra l lde Ｇ f o rma t i oncond i t i ons．AsshownF i ９,mos to ft he g da 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 onl i ne yc andt heag r e emen tbe twe ent heexpe r imen t a land r ed i c t edva l ue si ss a t i s f a c t o r p y．
F i ８ Re l a t i ono fl n[ s i nh ( td i f f e r en t ασ)] －T－１ a g s t r a i nr a t e sob t a i n e dba s e donp e aks t r e s s
I ti swo r t hmen t i on i ngt ha tt heva l ueo fQ dev i Ｇ a t e sl a r l r om t he s e l f Ｇ d i f f us i on i n aus t en i t e, ge yf [ ] wh i chi sr epo r t eda s２７００００Jmo l－１ ３１ ．Al t hough t heho t wo rk i ng a c t i va t i onene r he gy dependsont ma t e r i a lbe i ngc ons i de r ed, i ti susua l l r e f e r r e d t oa s y , appa r en t va l ue be c aus e no a c c oun ti s gene r a l l y t akeno ft hei n t e rna lmi c r o s t ruc t u r a ls t a t eandi ti s on l r i vedf r om an Ar rhen i usp l o t wi t hal i ne a r yde r angeandt hea s sump t i ont ha tt he mi c r o s t ruc t ur e r ema i nsc ons t an t．Theho two rk i nga c t i va t i onene r Ｇ l ue sa r eo f t en muchl a r rt hananyimag i ned gyva ge a t omi cme chan i sm．Th i sc anbea s c r i bedt ot hef a c t t ha ti nho two rk i ng,t he mi c r o s t ruc t u r e s mayi n i Ｇ t i a l l i f f e rt os ome deg r e ef o rd i f f e r en tp r ehe a t s yd and evo l ve r ap i d l td i f f e r en tr a t e s du r i ng t e s Ｇ ya [ ] t i ng２８ ．Mo r eove r,f o rmi c r oa l l oyeds t e e l s,t heso l Ｇ u t ed r age f f e c to f mi c r oa l l oy i nge l emen t sp r oh i b i t s t hemovemen to fbounda r i e sandr e su l t si nah i r ghe [ １１] a c t i va t i onene r gy ． ２ ４ ３ Pr edi c t i onofpeaks t r e s sanda s s e s smen ton edi c t ab i l i t pr y Ac c o r d i ngt oEq．( ７),andc ons i de r i ngt hede f i Ｇ
F i ９ Re l a t i onb e twe enp r e d i c t e dande xp e r imen t a lp e ak g s t r e s s e sa t８５０－１１５０℃ and０ ０１－１０s－１
I no rde rt o eva l ua t et he p r ed i c t ab i l i t ft he yo , cons t i t u t i veequa t i onquan t i t a t i ve l s t a n d a r ds t a t i s Ｇ y t i c a l pa r ame t e r si nc l ud i ng co r r e l a t i on coe f f i c i en t ( r ageabso l u t er e l a t i vee r r o r( AARE)and Rc),ave r e l a t i vee r r o rbe twe ent heexpe r imen t a lr e su l t sand r ed i c t edr e su l t s we r ec a l cu l a t ed．Rc i scommon l p y us edi ns t a t i s t i c s wh i chr ep r e s en t ss t r eng t ho ft he l i ne a rr e l a t i onsh i twe en t he expe r imen t a l and p be r ed i c t edva l ue s,andAAREi sa l soun i ve r s a ls t a t i s Ｇ p t i c a lpa r ame t e r sf o rme a sur i ngt hep r ed i c t ab i l i t fa yo nume r i c a l mode l． AARE i s compu t ed t hr ough a t e rm byt e rm compa r i sono ft her e l a t i vee r r o rand cons equen t l sunb i a s eds t a t i s t i c a lpa r ame t e r sf o r yi [ ３２] me a sur i ng t he pr ed i c t ab i l i t f a mode l ． The yo sma l l e rt heva l ueo fAAREi s,t hebe t t e rt her e su l t
I s sue９ Ho tDe f o rma t i onBehav i o ro faNove lNi ＧCr ＧMo ＧB Ul t r a Ｇhe avyP l a t eS t e e lbyHo tComp r e s s i onTe s t
８２５
i s．Theya r ede f i nedr e spe c t i ve l s: ya N
Rc＝
σiE －σE)( σiP－σP) ∑ (
i＝１ N
N
i＝１
i＝１
２ ２ ∑( ∑( σiE －σE) σiP－σP)
i i １ N σE －σP ×１００％ AARE＝ ∑ i Ni＝１ σE
( １３) ( １４)
σiE －σiP ( Re l a t i vee r r o r＝ i ×１００％ １５) σE st heexpe r imen t a lf l ows t r e s s;σiPi st he whe r e,σiEi r e d i c t e df l o w s t r e s so b t a i n e df r o m s t r a i n Ｇ c o m e Ｇ p pn s a t ed Ar rhen i us Ｇ t ons t i t u t i veequa t i on;σE and ypec r et heme anva l ue so fexpe r imen t a landp r ed i c t ed σP a f l ows t r e s s e s,r e spe c t i ve l st het o t a lnumＧ y;andNi be ro fda t as e t semp l oyedi nt hei nve s t i t i on． ga Theva l ueo fRc be twe ent heexpe r imen t a land ed i c t ed da t af r om t he c ons t i t u t i ve equa t i on i s pr ０ ９９４６０．Th i ssugge s t st ha tt hec ons t i t u t i veequa Ｇ t i ona ch i evedha sbe t t e rl i ne a rr e l a t i onsh i twe en pbe t heexpe r imen t a landp r ed i c t edr e su l t s．TheAARE o ft hec ons t i t u t i veequa t i oni s４ ２９％ ,andt her e l a Ｇ , t i vee r r o ri s －１４ ５７％ t o３ ４７％ wh i chi nd i c a t e s t ha tt hedeve l opedc ons t i t u t i ve mode lha sexc e l l en t ed i c t ab i l i t fpe aks t r e s sunde rt heexpe r imen t a l pr yo cond i t i onso ft hei nve s t i t eds t e e l．F i １０shows ga g t hes t a t i s t i c a lana l i so ft her e su l t so fc ons t i t u t i ve ys equa t i on,wh i chi sdep i c t eda st hes amp l enumbe r f r equenc r susr e l a t i vee r r o rp l o t．I tc anbes e en yve t ha tt her e l a t i vee r r o r swi t h i n ±１０％ ob t a i nedf r om t hecons t i t u t i veequa t i onsi sshownf o r mo r et han ９３％ o ft het e s tda t as e t s,wh i chr eve a l st heh i r ghe a c cur a c ft hec ons t i t u t i veequa t i onandi tc anme e t yo t her equ i r emen t sf o reng i ne e r i ngc a l cu l a t i ons．
F i １０ S t a t i s t i c a lana l s i so fr e l a t i v ee r r o rb e twe en g y e xp e r imen t a landp r e d i c t e dp e aks t r e s s e sby Ar rh en i u s Ｇ t ec on s t i t u t i v eequa t i on yp
２ ５ Re l a t i on s h i twe encha r a c t e r i s t i cpa r ame t e r s pbe andZene r ＧHo l l omonpa r ame t e r Fo racons t an ti n i t i a lg r a i ns i z e,t her e l a t i on Ｇ sh i twe en cha r a c t e r i s t i c pa r ame t e r so ff l ow p be cur ve sandZene r ＧHo l l omonpa r ame t e rcou l dbeex Ｇ [] r e s s eda sf o l l ows９ : p ( C ＝ KZm １６) whe r e,C i s a cha r a c t e r i s t i c pa r ame t e ro ff l ow cur ve,andK andm a r ema t e r i a lcons t an t sdepend Ｇ
en tont hea l l oycompos i t i on．Ther e l a t i onsbe twe en r amＧ t hep r ev i ouscha r a c t e r i s t i cpa r ame t e r sandZ pa e t e rwe r ep l o t t edi nF i １１onal oga r i t hmi cs c a l e, g andt henr eg r e s s i onana l i so ft he s ep l o t sr e su l t ed ys i nt hef o l l owi ngequa t i ons: ( ８２３９７Z０１０４２３ σp ＝３ １７) εp ＝０ ０１３２９Z００９５７４ σc ＝２ ８００００Z
０ １１０３３
εc ＝０ ００４５７Z０１０３４２ σs ＝２ ００６２４Z
０ １２０８１
２８４４５Z００２５１０ εs ＝０
( １８) ( １９) ( ２０) ( ２１) ( ２２)
F i １１ Cha r a c t e r i s t i cpa r ame t e r so ff l owc u r v e sa sf unc t i on so fZ g
I tc ou l dbef oundt ha tt he r ei sagoodl i ne a rr e Ｇ l a t i onbe twe enl n σp,l n σc,l n σsandl nZ wi t ht hel i ne Ｇ , a rco r r e l a t i onc oe f f i c i en to f０ ９８４８４ ０ ９８５７４and ０ ９７５４１,r e spe c t i ve l heo t he rhand,poo r y．Ont co r r e l a t i ons we r e f ound be twe en cha r a c t e r i s t i c
s t r a i nsandZ onl oga r i t hmi cs c a l e,andt h i smaybe c aus edbyal imi t a t i ono ft hepowe rl aw ( Eq ( １６)) wh i chi smo r esu i t ab l ef o rt hede s c r i t i ono ft her e Ｇ p l a t i onsh i twe ens t r e s sand Z．Fur t he rmo r e,a l l pbe o ft hecha r a c t e r i s t i c pa r ame t e r si nc r e a s e wi t hi nＧ
８２６
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
c r e a s i ngZ va l ue ( i nc r e a s i ngs t r a i nr a t eo rde c r e a Ｇ s i ngt empe r a t u r e),wh i chi sc ons i s t en twi t ht hep r e Ｇ v i ousana l i s．Thec r i t i c a lr a t i o so fbo t hσc/ σp and ys / ema i nf a i r l ons t an t．Theme anc r i t i c a ls t r e s s εc εpr yc r a t i oi s０ ９１,r ang i ngf r om ０ ７８t o０ ９７,wi t ha s t anda r ddev i a t i ono f０ ０４,whe r e a st heme anc r i t i Ｇ , c a ls t r a i nr a t i oi s０ ４６ r ang i ngf r om０ ３０t o０ ６０, wi t has t anda r d dev i a t i on o f０ ０８． The c r i t i c a l , / , s t r e s sr a t i o σc σp de t e rmi nedf o rt hep r e s en t Ni Ｇ Cr ＧMo ＧBs t e e li sc ons i s t en twi t ht heva l uegene r a l l y r epo r t edo f０ ９０f o rl owc a rbonNb ＧTimi c r oa l l oyed [ ３３] , , s t e e l ．I nadd i t i on t hec r i t i c a ls t r a i nr a t i o εc/εp, ob t a i nedhe r ei si nag r e emen twi t ht ha tr epo r t edf o r [ ] bo r on mi c r oa l l oyeds t e e l１１ ,wh i chr ange sbe twe en ０ ３５ and ０ ７３, wi t h a me an va l ue o f０ ５３．I t shou l dbeno t edt ha tf o rs omes t e e lg r ade ssucha s med i um c a rbon mi c r oa l l oyeds t e e l,t he h i ghεc/εp [ １０] va l ueo f０ ６２ha sa l s obe enr epo r t ed ．
３ Conc l u s i on s
( １)DRXi st he ma i nr e a s onf o rdynami cf l ow so f t en i ngo ft hei nve s t i t eds t e e l．DRXi sope r a t i ve ga evena t８５０℃ and１０s－１ ．Thede c r e a s eo fZ va l ue l e adst omo r eex t ens i veo fDRX． ( ２)Theimpo r t an tcha r a c t e r i s t i cpa r ame t e r so f DRXi nc l ud i ngt hec r i t i c a lc ond i t i onf o ri n i t i a t i ono f , , DRX t he pe aks t r e s sands t r a i n andt hes t e ady s t a t es t r e s sands t r a i nwe r ede t e rmi nedf r omt heda Ｇ t ao ft rues t r e s s Ｇ s t r a i nands t r a i nha r den i ngr a t e． ( ３)Thecha r a c t e r i s t i c pa r ame t e r st endt oi n Ｇ c r e a s ea ss t r a i nr a t ei nc r e a s e sandt empe r a t u r ede Ｇ c r e a s e s,wh i chi nd i c a t et ha tt hepa r ame t e r so fho t wo rk i ngdependont het empe r a t u r eands t r a i nr a t e． ( ４)Thea c t i va t i onene r fho tde f o rma t i ono f gyo t hes t e e l wa sc a l cu l a t ed wi t h a mo r eexa c tva l ue us i ngt heAr rhen i us Ｇ t rbo l i cs i nel awt ha ti s ypehype /mo equa lt o３７９１３９J l． ( ５)Thec ons t i t u t i veequa t i oni sob t a i nedt oex Ｇ e s sho two rk i ngcha r a c t e r i s t i c so ft hei nve s t i t ed pr ga s t e e lwi t hah i r ed i c t ab i l i t ghp y． ( ) ６ Bo t hpe aks t r e s sands t r a i nc anbep r ed i c t ed byt heZ pa r ame t e ri npowe r Ｇ l awequa t i onsandt he r a t i oso fc r i t i c a ls t r e s sands t r a i nt ope aks t r e s sand s t r a i na r eabou t０ ９１and０ ４６,r e spe c t i ve l y． Re f e r enc e s:
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１１８ Ｇ １２７． [ l,A．K． Bhadur i,Ma t e r． Sc i． Eng．A ７] D． Saman t a r ay,S．Manda ５２８ ( ２０１１)５２０４ Ｇ ５２１１． [ ８] E． I． Po l i ak,J． J． J ona s,Ac t a Ma t e r． ４４ ( １９９６)１２７ Ｇ １３６． [ F． Yi n,F． S． Shangguan,K．Wang,Q． ９] D． J． L i,Y． R． Feng,Z． L i u,F． Hu,Ma t e r． Sc i． Eng． A５２８ ( ２０１１)８０８４ Ｇ ８０８９． [ １０] H．Mi r z adeh,J．M． Cabr e r a,J．M． Pr ado,A． Na a f i z adeh,Ma Ｇ j t e r． Sc i． Eng． A５２８ ( ２０１１)３８７６ Ｇ ３８８２． [ １１] I．Me í a,A． Bedo l l a Ｇ J a cu i nde,C．Ma l donado,J．M．Cabr e r a, j Ma t e r． Sc i． Eng． A５２８ ( ２０１１)４１３３ Ｇ ４１４０． [ Tao,J． １２] K．Wu,G． Q． L i u,B． F．Hu,F． L i,Y．W． Zhang,Y． T． L i u,Ma t e r． De s． ３２ ( ２０１１)１８７２ Ｇ １８７９． [ J． １３] X．Xi ao,G．Q． L i u,B． F．Hu,X． Zheng,L．N．Wang,S． Chen,A． Ul l ah,Compu t．Ma t e r． Sc i． ６２ ( ２０１２)２２７ Ｇ ２３４． [ １４] Y． H． Xi ao,C． Guo,X． Y． Guo,Ma t e r． Sc i． Eng． A５２８ ( ２０１１)
６５１０ Ｇ ６５１８． [ １５] H． Y． L i,Y． H． L i,X． F．Wang,J． J． L i u,Y．Wu,Ma t e r． De s． ４９ ( ２０１３)４９３ Ｇ ５０１． [ １６] D． L． Ba r aga r,J．Me ch．Wo rk． Te chno l． １４ ( １９８７)２９５ Ｇ ３０７． [ １７] A． Dehghan ＧManshad i,M． R． Ba r ne t t,P． D．Hodgs on,Ma t e r． Sc i． Eng． A４８５ ( ２００８)６６４ Ｇ ６７２． [ １８] H．Mi r z a d e h,A． Na a f i z a d e h,M．Mo a z e ny,Me t a l l．Ma t e r． T r a n s． j A４０ ( ２００９)２９５０ Ｇ ２９５８． [ １９] C． Zene r,J． H． Ho l l omon,J． App l． Phys． １５ ( １９４４)２２ Ｇ ３２． [ ２０] E． I． Po l i ak,J． J． J ona s,I S I JI n t． ４３ ( ２００３)６８４ Ｇ ６９１． [ ２１] H． L．We i,G．Q． L i u,X． Xi ao,H． T． Zhao,H． Di ng,R．M． Kang,Ma t e r． Sc i． Eng． A５６４ ( ２０１３)１４０ Ｇ １４６． [ ２２] H．Mi r z adeh,A． Na a f i z adeh,Ma t e r． Chem． Phys． １１６ ( ２００９) j １１９ Ｇ １２４． [ ２３] R． Di ng,Z． X． Guo,Ac t a Ma t e r． ４９ ( ２００１)３１６３ Ｇ ３１７５． [ ２４] G． R． S t ewa r t,A．M． Elwa z r i,S． Yue,J． J． J ona s,Ma t e r． Sc i． Te ch． Lond． ２２ ( ２００６)５１９ Ｇ ５２４． [ ２５] L．Ma,L．Wang,Z． L i u,G．Yang,L． Lu,M． Peng,J． I r on S t e e lRe s． I n t． ２１ ( ２０１４)１０３５ Ｇ １０４１． [ ２６] C．M． Se l l a r s,W． J．McTega r t,Ac t a Me t a l l． １４ ( １９６６)１１３６ Ｇ
１１３８． [ ２７] Z． Y． Chen,S． Q． Xu,X． H． Dong,Ac t aMe t a l l． S i n． ２１ ( ２００８) ４５１ Ｇ ４５８． [ ２８] H． J．McQue en,N．D．Ryan,Ma t e r． Sc i． Eng．A ３２２ ( ２００２) ４３ Ｇ ６３． [ ２９] H． J．McQu e e n,S．Yu e,N． D． Ry a n,E． Fr t e r． Pr o c e s s． y,J．Ma T e c hno l． ５３ ( １９９５)２９３ Ｇ ３１０． [ ３０] H． T． Zhao,G． Q． L i u,L． Xu,Ma t e r． Sc i． Eng． A５５９ ( ２０１３) ２６２ Ｇ ２６７． [ ３１] J．M． Cabr e r a,A．AlOma r,J．M． Pr ado,J． J． J ona s,Me t a l l． Ma t e r． Tr ans． A２８ ( １９９７)２２３３ Ｇ ２２４４． [ ３２] D． S ama n t a r a nd a l,A． K． Bh a du r i,Ma t e r． De s． ３２ ( ２０１１) y,S．Ma
２７９７ Ｇ ２８０２． [ ３３] M． Shaban,B． Eghba l i,Ma t e r． Sc i． Eng．A５２７ ( ２０１０)４３２０ Ｇ ４３２５．