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Effects of tantalum on austenitic transformation kinetics of RAFM steel
J our na lo fI r onandS t e e lRe s e a r ch, I n t e r na t i ona l２４ (２０１７) ７０５－７１０
E f f e c t so ft a n t a l umonaus t en i t i ct r ans f o rma t i onk i ne t i c so fRAFMs t e e l
J i an Ｇ Ｇ changL i u, Chen Ｇ x iL i u∗ , B i Ｇ i Ｇ unL i guoChen, Yong yuYan, Hu j
S t a t eKeyLabo r a t o r fHyd r au l i cEng i ne e r i ngS imu l a t i onandSa f e t lo fMa t e r i a l sSc i enc e & Eng i ne e r i ng, Ti an i n yo y, Schoo j Un i ve r s i t an i n３００３５０, Ch i na y, Ti j ARTICLEINFO
ABSTRACT
Keywo rds: RAFMs t e e l Tan t a l umc on t en t Gr a i ng r owt h Aus t en i t i ct r ans f o rma t i on k i ne t i c s Ac t i va t i onene r gy
TheRAFM (r educ eda c t i va t i onf e r r i t i c/ma r t ens i t i c) s t ee l scont a i n i ngd i f f e r entt ant a l um cont ent s (０wt ％ , ０ ０２７wt ％ , ０ ０７３wt ％ ) we r ede s i a s t．Di f f e r en t i a ls c ann i ngc a l o r ime t r gnedandc yand op t i c a lmi c r o s c opywe r eemp l oyedt oexp l o r et hei n f l uenc eo ft an t a l umc on t en tont heaus t en i t i ct r ans Ｇ f o rma t i ono fRAFMs t e e l s．Theaus t en i t i ct r ans f o rma t i onk i ne t i c swa sde s c r i bedbyapha s e Ｇ t r ans f o r Ｇ ma t i onmode l．Themode l, i nvo l v i ngs i t es a t ur a t i onnuc l e a t i on, d i f f us i on Ｇ c on t r o l l edg r owt handimＧ i ngemen tc o r r e c t i on, wa se s t ab l i shed ba s ed on t he c l a s s i c a lJ ohns on ＧMeh l ＧAv r ami ＧKo lmogo r ov p mode l．Thepha s e Ｇ t r ans f o rma t i onk i ne t i c spa r ame t e r s, i nc l ud i ngD０ (p r e Ｇ exponen t i a lf a c t o rf o rd i f Ｇ f us i on) andQd (a c t i va t i onene r o rd i f f us i on), we r ec a l cu l a t edbyf i t t i ngt heexpe r imen t a lda t aand gyf t hek i ne t i cmode l．Ther e su l t si nd i c a t edt ha tt heave r ageg r a i ns i z ei sde c r e a s edwi t ht hei nc r e a s eo f t an t a l um．Theva l ue so fAc１andAc３ (ons e tandf i n i sht empe r a t ur eo faus t en i t i ct r ans f o rma t i on, r e Ｇ spe c t i ve l r ei nc r e a s edbyi nc r e a s i ngt het an t a l umc on t en t．Thei nc r e a s eo ft an t a l umc aus edt hede Ｇ y) a c r e a s eo fD０．Howeve r, Qdi si nc r e a s ed wi t ht hei nc r e a s eo ft an t a l um．I nadd i t i on, a sac a r b i de s f o rmi nge l emen t, t an t a l um wou l dr educ et hec a r bond i f f us i onc oe f f i c i en tands l owdownt heaus t en i t i c t r ans f o rma t i onr a t e．
１． I n t r odu c t i on I nt h ef u s i onr e a c t o r s, t h er e du c e da c t i v a t i onf e r r i t i c/ ma r t ens i t i c (RAFM ) s t e e l s we r ebe i ng c ons i de r ed a st hepr e f e r r edc and i da t ef o rt hes t ruc t u r a lma t e r i a l owi ngt ot he i rr educ eda c t i va t i onab i l i t t t e r yandbe [ , ] t he rmo Ｇ s i c a lp r op e r t i e s１ ２ ．Th ed e s i f RAFM phy gn o s t e e l swa sba s edont he mod i f i c a t i ono ft het r ad i Ｇ t i ona lhe a tr e s i s t an ts t e e l, ma i n l ep l a c i ngt he y byr l ong Ｇ l i vedt r ansmu t a t i one l emen t so f Mo, Nb, and Co wi t hr e l a t i v e l s h o r t Ｇ l i v e dt r a n s m u t a t i one l emen t s y , o fT aa nd W．Sof a r as i i f i c a n tamoun to fr e s e a r c h gn anddeve l opmen to fRAFM s t e e l sha sbe enc onduc Ｇ [ , ] t edi nma nyc oun t r i e s,s u c ha sF８２Hs t e e li nJ a a n３ ４ , p [ , ] EUROFER９７s t e e li nEu r op e４ ５ , ９Cr ２WVT as t e e li n [６,７] [ , ] USA andCLAMs t e e li nCh i na８ ９ ． Gene r a l l ak i ng, aus t en i z a t i oni st hef i r s ts t ep yspe o f he a tt r e a tmen tf o rs t e e l s．The cho i c eo f he a t t r e a tmen t pa r ame t e r s du r i ng t he aus t en i t i z i ng r oc e s si sv i t a lt ot hef i na lmi c r o s t ruc t u r eand me Ｇ p chan i c a lp r ope r t i e so ft hes t e e l．Ther e s e a r cho faus Ｇ t en i t i ct r ans f o rma t i on k i ne t i c si s bene f i c i a lt ot he [ ] cho i c eo fhe a tt r e a tmen tpa r ame t e r s１０ ．The r e f o r e, ∗ Co r r e spond i ngau t ho r．Ph． D． EＧma i laddr e s s:cxl i u t ． om (C X ． Li u) ． ju＠１６３c
ag r e a ti n t e r e s tex i s t sf o rt her e s e a r cho ft heaus t e Ｇ [ ] n i t i ct r ans f o rma t i onk i ne t i c s１１Ｇ１４ ．Thek i ne t i c smod Ｇ e li sane f f e c t i vewayt oi nve s t i t epha s et r ans f o r Ｇ ga ma t i on． I n gene r a l, a pha s et r ans f o rma t i on mode l cons i s t so ft hr e es t eps: nuc l e a t i on, g r owt handimＧ i ngemen to ft heg r owi ngnew pha s epa r t i c l e s．The p s et r ans f o rma t i onp r oc e s sc anbe mode l eds epa Ｇ pha [ ] r a t e l rdimp i ngemen ti semp l oy e d１５ ．The y whenha c l a s s i c a lJ ohn s on ＧMe h l ＧAv r ami ＧKo lmogo r ov (JMAK) mode lha sbe en wi de l d e v e l o e da n d us edt or e Ｇ y p s e a r cht he pha s et r ans f o rma t i onbehav i o ri n many [ , , ] s t ems１３ １４ １６ ．Fo raus t en i t i ct r ans f o rma t i on, i ti s ys we l la c c ep t edt ha tt henuc l e a t i onandt heg r owt ho f aus t en i t eg r a i n dur i ng t he pha s et r ans f o rma t i on r oc e s sc an bede s c r i bed by t hea t omscon t r o l l ed p d i f f us i on, s i nc et heaus t en i t i ct r ans f o rma t i ont ake s l a c ea th i empe r a t ur e．Thed i f f us i ono fc a rbon p ght ha sag r e a te f f e c tont henuc l e a t i onand g r owt ho f aus t en i t eg r a i nf o rs t e e l s．Re c en t l e s e a r che s y, somer i nd i c a t edt ha tt hea l l oy i nge l emen t sa l sohaveg r e a t i n f l uenc eont he pha s et r ans f o rma t i onf o rs t e e l s, andt hei n f l uenc eo fa l l oy i nge l emen t sont heaus t e Ｇ n i t i ct r ans f o rma t i onk i ne t i c sha sa t t r a c t edex t ens i ve
Re c e i ved５J anua r c e i vedi nr ev i s edf o rm１２ Ma r ch２０１７; Ac c ep t ed１３ Ma r ch２０１７ y２０１７; Re Ava i l ab l eon l i ne１５Ju l y２０１７ １００６ Ｇ ７０６X/Copy r i tⓒ２０１７, Th ee d i t o r i a lo f f i c eo fJ ou r n a lo fI r ona ndS t e e lRe s e a r c h, I n t e r n a t i on a l． Pub l i s h e dbyE l s e v i e rL imi t e d．Al lr i t sr e s e r v e d． gh gh
J G ． Chene ta l．/Journa lofI r onandSt e e lRe s ear ch, In t e rna t i ona l２４ (２０１７) ７０５－７１０
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a t t en t i ona r oundt hewo r l d１３ １４ １７ １８ ．Tan t a l umi san impo r t an ta l l oy i nge l emen ti n RAFM s t e e l, wh i ch [ , ] c ana f f e c tt hepr e c i i t a t i ono fc a rb i de s１９ ２０ ．The r e Ｇ p f o r e,t an t a l umha ss i i f i c an te f f e c tont heme chan i Ｇ gn c a lpr ope r t i e so ft heRAFMs t e e l． I nadd i t i on, some r epo r t si nd i c a t et ha tt an t a l um p l aysanimpo r t an t r o l ei nr e f i n i ngt hep r i o raus t en i t eg r a i no fRAFM [ , ] s t e e l２１ ２２ ．Henc e,t an t a l um wou l dbeboundt ohave s i n i f i c a n t e f f e c to na u s t e n i t i ct r a n s f o r m a t i o nk i ne t Ｇ g , i c so fRAFMs t e e l．Howeve rt hee f f e c to ft an t a l um con t en tont heaus t en i t i ct r ans f o rma t i onk i ne t i c so f RAFMs t e e lha sno tbe ens t ema t i c a l l t ud i ed． ys ys Wi t h i nt h i sc on t ex t, t h i sa r t i c l ea imst or e s e a r ch t hee f f e c to ft an t a l umc on t en tonaus t en i t i ct r ans f o r Ｇ ma t i onk i ne t i c so fRAFMs t e e l s．Themode lo faus Ｇ t en i t i ct r ans f o rma t i on k i ne t i c s ba s ed on JMAK mode lwa sdeve l oped, andt heaus t en i t i ct r ans f o r Ｇ ma t i onk i ne t i c spa r ame t e r swe r eob t a i nedbyf i t t i ng t heaus t en i t i ct r ans f o rma t i onf r a c t i onde t e rmi nedby DSC (d i f f e r en t i a ls c ann i ngc a l o r ime t r r imen t s y) expe andk i ne t i cmode l． [
,
,
,
]
No １—Spe c imen１; No ２—Spe c imen２; No ３—Spe c imen３．
F i １． DSCcu r ve so fRAFMs t e e l s． g
２．Ma t e r i a l sandExp e r imen t a lMe t hod s
２ １．Ma t e r i a l spr epara t i onand di e r en t i a ls can Ｇ f f n i ngca l o r ime t ry Thed e s i e dRAFM s t e e l swe r ec a s ti n t oa ni ngo t gn wi t hwe i to f２５kgi nava cuumi nduc t i onf u rna c e． gh Subs equen t l hei ngo t swe r ef o r n t oc l i nde r y, t gedi y ba r s, wi t has i z eo f１２０mmi nhe i tand６０mmi n gh d i ame t e r．Th ed e t a i lc h emi c a lc ompo s i t i on so fRAFM s t e e l sa r eshowni nTab l e１．Thema i nd i f f e r enc ebe Ｇ twe ent hr e espe c imensi st hed i f f e r enc eo ft an t a l um con t en t．Af t e rt ha t, t hespe c imens we r e ma ch i ned i n t oc l i nd r i c a lspe c imenswi t hal eng t ho f２mmand y ad i ame t e ro f４mmus edt ot heDSCexpe r imen t．Al l DSCs amp l e s we r ehe a t edf r om r oom t empe r a t ur e upt o１０５０°Ca tahe a t i ngr a t eo f２０°C/mi nand t henc oo l edt or oom t empe r a t u r e wi t ht hec oo l i ng r a t eo f４０°C/mi n． I no r de rt oobs e r vet heva r i a t i on o fau s t e n i t i ct r a n s f o rma t i ont emp e r a t u r e(on s e tt emp e r Ｇ a t u r eAc１ a ndf i n i s ht emp e r a t u r eAc３ ) c l e a r l h eDSC y, t cur ve sc on t a i n i ngpha s et r ans f o rma t i oni n f o rma t i on we r ei n t e r c ep t eddu r i nghe a t i ngpr o c e s s, a ss e eni n F i １．Thet angen t me t hodi sus edt o me a su r et he g s et r ans f o rma t i ont empe r a t u r e, andF i ２shows pha g t hes chema t i cd i ag r am． Tab l e１ Chemi c a lc ompo s i t i onso fRAFMs t e e l s (wt ％ ) Spe c imen C
Cr
W
Mn
S i
V
Ta ０
２ ２．Mi c r o s t ruc t ura lo b s e rva t i on The mi c r os t ruc t ur e so f RAFM s t e e l we r eana Ｇ l edt hr oughop t i c a lmi c r os copy (OM) ．OMi nve s Ｇ yz t i t i onswe r ec a r r i edou tt o me a sur et hepr i o raus Ｇ ga t en i t eg r a i ns i z eo ft hes t e e l s．Thes amp l e sf o rOM exami na t i onwe r eg r oundwi t has e r i e so fS iCpape r f r om２４０t o２０００ g r i t, me chan i c a l l l i shedbya ypo d i amond pa s t e wi t hg r anu l a r i t f２ ５ μm, and yo e t chedbyanab l uen tso l u t i ono fp i c r i ca c i d (２ mL ab l uen t, １００ mL wa t e r, ２gp i c r i ca c i d) ．Thee t ch Ｇ i ngcond i t i onwa st het empe r a t ur eo f７０°Candt ime o f３ mi n．Thel i ne a ri n t e r c ep tme t hod wa sadop t ed unde rt hr e ed i f f e r en td i r e c t i onst ome a sur et hepr i o r [ ] aus t en i t eg r a i ns i z e２３ ．
３．Re s u l t sandDi s c u s s i on
３ １．Mi c r o s t ruc t ura lana l i s ys Fe
１
０ ０６ ８ ９１ １ ７３ ０ ３７ ０ ０５ ０ ２２
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０ ０４ ８ ９３ １ ７１ ０ ４４ ０ ０４ ０ ２２ ０ ０７３ Ba l anc e
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F i ２． Tangen tme t hodus edt ome a su r eaus t en i t epha s e g t r ans f o rma t i ont empe r a t u r e s．
Ba l anc e
０ ０５ ８ ９２ １ ６６ ０ ３１ ０ ０３ ０ ２３ ０ ０２７ Ba l anc e
Theo r i i na l mi c r os t ruc t ur eo ft hespe c imensi s g ma r t ens i t es t ruc t ur e, a sshowni nF i ３．The mi Ｇ g c r os t ruc t ur e so ft heRAFM s t e e l scon t a i n i ngd i f f e r Ｇ en tt an t a l um con t en t sa f t e rt he DSC me a sur emen t a r eshowni nt heOM mi c r og r aphso fF i ４． I no rde r g
G ． Chene ta l．/Journa lofI r onandSt e e lRe s ear ch, In t e rna t i ona l２４ (２０１７) ７０５－７１０ J
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(a) Spe c imen１; (b) Spe c imen２; (c) Spe c imen３．
F i ３． Or i i na lop t i c a lmi c r og r aphso fs t ud i edRAFMs t e e l s． g g
(a) Spe c imen１; (b) Spe c imen２; (c) Spe c imen３．
F i ４． Op t i c a lmi c r og r aphso fRAFMs t e e l s． g
t oi nve s t i t et heaus t en i t i ct r ans f o rma t i on behav Ｇ ga i o r, t hespe c imensf o r OM obs e r va t i oni se t ched, andt he g r a i ns i z ei s me a su r ed byt he me t hodde Ｇ s c r i bedi nSe c t i on２ ２．Th i se t ch i ng me t hodi ssu i t Ｇ ab l ef o r pr e s en t a t i on o ft he p r i o raus t en i t eg r a i ns (PAGs) r a t he rt hant hema r t ens i t es t ruc t u r e． I tc an bef oundt ha tt he p r i o raus t en i t eg r a i ns i z ei sde Ｇ c r e a s edwi t ht hei nc r e a s eo ft an t a l um c on t en t．Th i s [ ] sc on s i s t e n tw i t ht h ep r e v i ou swo r k s１９ ． phenomenoni Theva l ue so ft heave r ageg r a i ns i z ea r e (５２ ７４± ), ( ) ( ) ６ ３ ３４ ３３±３ ８ and ２２ ４２±２ ４ μm, r e spe c Ｇ t i ve l i sc anbeexp l a i nedt ha tt henumbe ro fun Ｇ y．Th d i s so l vedc a rb i de si nc r e a s e swi t ht hei nc r e a s eo ft an Ｇ t a l umc on t en t．Theund i s s o l vedc a rb i de sa r eve r f Ｇ ye f e c t i vei nc on t r o l l i ngt heaus t en i t eg r a i ng r owt hby [ , ] i nn i ng t he g r a i n bounda r i e s２１ ２２ ．Ot he rc a rb i de p f o rmi nge l emen tha st heana l ogousr epo r t．Tic anr e Ｇ t a rdt heaus t en i t eg r a i nowi ngt ot heex i s t enc eo fun Ｇ [ ] d i s so l vedTi(C,N) i nh i a rbons t e e l s２４ ．Nband ghc Vc anf o rm Nb(C,N) and V(C,N), h i nde r i ngt he [ ] aus t en i t eg r a i ng r owt ho fNb ＧVs t e e l s２５ ．
３ ２．Au s t en i t et ran s o rmed f rac t i on and au s t en i t e f t ran s o rma t i onra t e f
I no r de rt oi nve s t i t et hee f f e c to ft an t a l umcon Ｇ ga t en tont heaus t en i t i ct r ans f o rma t i onbehav i o r, as e Ｇ r i e so fDSC me a su r emen t swe r ec a r r i edou twi t ha l l spe c imens．F i １showst heDSCcu r ve sc on t a i n i ng g s et r ans f o rma t i oni n f o rma t i ono ft hespe c imens pha dur i ngt heaus t en i z a t i onp r o c e s s． I tc anbef oundt ha t t he r ea r etwoendo t he rmi cpe aks: t hef i r s toneex i s Ｇ t eda r oundt het empe r a t u r eo f７５０°C, wh i chi st he
Cur i et empe r a t ur e; t hes e cond oneex i s t edi nt he r angeo f８６０－９２０°C, wh i chi nd i c a t edt heaus t en i t i c t r ans f o rma t i on．The Ac１ and Ac３ we r e ob t a i ned t hr ought he me t hodde s c r i bedi n Se c t i on２ １．The Ac１andAc３i nc r e a s ef r om ８６１t o８６９°Cand８９９t o ９１９°C, r e spe c t i ve l ss howni nT ab l e２． I tc anb e y, a e xp l a i n e dt ha tt heaus t en i t i ct r ans f o rma t i oni sd i f f i Ｇ cu l tt ot ake p l a c eowi ngt ot hei nc r e a s eo fund i s Ｇ so l vedc a rb i de sc aus edbyadd i ngt an t a l um, andt he aus t en i t i ct r ans f o rma t i oni sr e t a rdedt ot heh i r ghe t empe r a t ur e． Tab l e２ faus t en i t i ct r ans f o rma t i onf o rRAFMs t e e l s Ac１ andAc３ o Tan t a l umc on t en t/wt ％
Ac１/°C Ac３/°C
０
０ ０２７
０ ０７３
８９９
９０５
９１９
８６１
８６４
８６９
Theaus t en i t ef r a c t i on, fγ, c anbeob t a i nedf r om [ ] t heDSCcur ve s２６ : æ １ ö÷ T ( ) (１) fγ(t) ＝ ç Ftd t èΔH ø ０ whe r e, ΔH i st het o t a len t ha l faus t en i t e pychangeo s et r ans f o rma t i on; F (t)i st hehe a tf l ux; andti s pha t ime． fγa saf unc t i ono ft empe r a t ur e (T ) f o ra l lspe c i Ｇ mensi sshowni nF i ５．F i ６and７i l l us t r a t et he g gs aus t en i t et r ans f o rma t i onr a t e (dfγ/d t) a saf unc t i on o ft empe r a t ur e (T ) andaus t en i t ef r a c t i on (fγ), r e Ｇ spe c t i ve l t en i t et r an s f o rma t i ono fs e c ime n s y．Theaus p c on t a i n i ngd i f f e r e n tt an t a l umc on t e n t sexh i b i t st hef o l l Ｇ
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G ． Chene ta l．/Journa lofI r onandSt e e lRe s ear ch, In t e rna t i ona l２４ (２０１７) ７０５－７１０ J
becon f i rmedbyt heva l ue s (t hed i f f e r enc ebe twe en da t ao fAc３ and Ac１ i n Tab l e２), s i nc et hehe a t i ng r a t ei ss amef o ra l ls amp l e s． (i i i) Theaus t en i t i ct r ans f o rma t i onp r oc e s so fa l l spe c imensshowson l t en i t et r ans f o rma t i on yoneaus r a t emax imum (s e eF i ６and７), demons t r a t i nga gs [ ] no rma laus t en i t et r ans f o rma t i oncha r a c t e r i s t i c１１ ． (i v) The max imum va l ueo faus t en i t i ct r ans f o r Ｇ ma t i onr a t ei sde c r e a s ed wi t ht hei nc r e a s eo ft an t a Ｇ l umcon t en t (s e eF i ６and７) ． gs
３ ３．Ki ne t i c sana l i sofau s t en i t i ct ran s o rma t i on ys f o c e s s pr No １—Spe c imen１; No ２—Spe c imen２; No ３—Spe c imen３．
F i ５． Aus t en i t ef r a c t i ona saf unc t i ono ft empe r a t u r ef o r g RAFMs t e e l s．
I ngene r a l, JMAK mode lde s c r i be st heso l i d Ｇ s t a t e s et r ans f o rma t i on a st hr e es t eps: nuc l e a t i on, pha r owt h, andimp i ngemen t．Themode lo fnuc l e a t i on g andg r owt hs t age sa s sume st ha ta l lnewg r a i nsneve r s t opnuc l e a t i ngandg r owi ng, i r i ngt hei n t e r r e l a Ｇ gno t i onsh i fnew g r a i nsi nt hepha s et r ans f o rma t i on po , ha r oc e s s, i e． rdimp i ngemen ti si r edi nt he p gno aus t en i t i cnuc l e a t i onand g r owt h pr oc e s s．TheimＧ i ngemen t mode li sco r r e c t edi nt heimp i ngemen t p , , r o c e s s i e ． h a r di m i n e m e n to f r o w i n r a i n s p p g g gg i sr andoml i s t r i bu t ed． yd Theex t endedvo l ume, Ve, andt hepha s et r ans Ｇ , , f o rmedf r a c t i on f c anbede t e rmi nedt hr ought h i s [ ] me t hod２７ a sf o l l ows:
∫V N (T (τ))Y(t,τ)dτ
Ve＝
No １—Spe c imen１; No ２—Spe c imen２; No ３—Spe c imen３．
F i ６． Au s t e n i t et r a n s f o rma t i onr a t ea saf unc t i ono ft empe r a Ｇ g t u r ef o rRAFMs t e e l s．
No １—Spe c imen１; No ２—Spe c imen２; No ３—Spe c imen３．
F i ７． Au s t e n i t et r a n s f o rma t i onr a t ea saf unc t i ono faus t en i t e g f r a c t i onf o rRAFMs t e e l s．
owi ngk i ne t i cf e a t u r e s: (i) Ac１andAc３a r ebo t hi nc r e a s edbyt hei nc r e a s e o ft an t a l umc on t en t (s e eTab l e２andF i ５) ． g (i i) Theove r a l laus t en i t i ct r ans f o rma t i ont imei s i nc r e a s eds l i t l hei nc r e a s eo ft an t a l um con Ｇ gh y byt t en t (s e eTab l e２, F i ５and６) ．Espe c i a l l tc an gs y, i
t
０
(２)
æ V ö (３) f＝１－expç － ÷ è Vø whe r e, N i st henuc l e a t i onr a t e; V i st hes amp l e ; st hevo l umeo fas i ng l epa r t i c l ea t vo l ume andY i t imet, wh i chnuc l e a t eda tt imeτ． I nt henuc l e a t i onpr oc e s s, t hes i t es a t ur a t i onnu Ｇ [ , ] c l e a t i onmode li semp l oyed．L i ue ta l ２８ ２９ ha si nd i Ｇ c a t edt ha tt hes i t es a t ur a t i onnuc l e a t i onmode li sap Ｇ ,t l i c ab l ef o raus t en i t i ct r ans f o rma t i on, i e． henu Ｇ p c l e a t i ono faus t en i t ewa sa s sumedt ohavebe encomＧ l e t eda tt hes t a r ts t ageo fg r owt h, andt hust he p numbe ro f nuc l e a t i on r ema i ned unchangedi nt he subs equen tg r owt hpr oc e s s．Thes i t es a t ur a t i onnu Ｇ [ ] c l e a t i onr a t ec anbeexpr e s s eda s２８ : æT (t) －T０ ö (４) ÷ N (T ) ＝N ∗δç è ø φ æT(t)－T０ ö æT(t)－T０ ö ÷i ÷＝ wh e r e,δç saD i r a cf un c t i o n:δç è ø è ø φ φ T (t) ( ) , ( ) T t － T æ ö ０ T t ≠T０ ; ０ ÷ ＝１; N ∗ i δç st he ∞ , T (t) ＝T０ T０ è ø φ numb e ro fp r e Ｇ e x i s t i ngnu c l e ip e run i tvo l umea tt＝０; st hehe a t i ngr a t e; andT (t) ＝T０ ＋φ t．Fo rt hes i t e φi ∗ s a t ur a t i onnuc l e a t i on mode l, N ＝N ．Thenumbe r o fpr e Ｇ ex i s t i ngnuc l e ipe run i tvo l ume (N ∗ ) c anbe de t e rmi nedbyt hef o rmu l a: N ∗ ＝１/d３ he r edr r, w r e s en t st heave r ageg r a i ns i z e．Theco r r e spond i ng p
{
e
∫
J G ． Chene ta l．/Journa lofI r onandSt e e lRe s ear ch, In t e rna t i ona l２４ (２０１７) ７０５－７１０
va l ue so ft henuc l e a t i ondens i t r el i s t edi nTab l e３． ya Tab l e３ Av e r a ea u s t e n i t eg r a i ns i z ea nda u s t e n i t ep r e Ｇ ex i s t i ngnuc l eus g dens i t fRAFMs t e e l s yo Tan t a l umc on t en t/wt ％
dr/μm
N ∗ /m－３
０
５２ ７４
６ ８２×１０１２
０ ０２７
３４ ３３
２ ４７×１０１３
０ ０７３
２２ ４２
８ ８７×１０１３
I nt heg r owt hp r o c e s s, t hed i s s o l u t i onandd i f f u Ｇ s i ono fa l l oy i nge l emen ti nt hev i c i n i t ft hei n t e r Ｇ yo f a c eha sag r e a ti n f l uenc eont hewho l eaus t en i z a t i on r oc e s s．The r e f o r e, t hed i f f us i on Ｇ c on t r o l l edg r owt h p mode li sadop t edi nt heg r owt hp r o c e s so faus t en i t e t r ans f o rma t i on．Thevo l umeo fag r owi ngpa r t i c l e, [ ] anbeexpr e s s eda s２３ : Y, c
∫D (T (t))dt)
Y ＝g(
t
(５)
d/m
τ
whe r e, gi sapa r t i c l e Ｇ t r a c t o r (g＝１f o rcu Ｇ geome yf ; / b i cg r owt h g＝４π ３f o rsphe r i c a lg r owt h); di st he d imens i ona l i t ft h eg r owt h (d＝３), s i n c et h eg r owt h yo o fpa r t i c l ei st hr e ed imens i ona l i t st heg r owt h y; m i modepa r ame t e r (１f o ri n t e r f a c e Ｇ c on t r o l l edg r owt h, ２f o rvo l umed i f f u s i on Ｇ c on t r o l l e dg r owt h); D (T(t))i s [ ] t hed i f f us i onc oe f f i c i en t, andc anbeg i vena s１６ : æ Qd ö (６) ÷ D (T (t)) ＝D０expç － è RT ø whe r e, D０ i st he p r e Ｇ exponen t i a lf a c t o rf o rd i f f uＧ ; st hea c t i va t i onene r o rd i f f us i on; andR s i on Qdi gyf i st hega sc ons t an t． Subs t i t u t i ngEqs (４), (５) and (６) i n t oEq (２), : t heex t endedvo l umec anbeexp r e s s eda s T (t) T (t) æT (t) －T０ ö e ∗ ÷g[ V ＝ VN δç D０ T０ T (τ) è ø φ æ Qd ö æçT ö÷ ３/２ æçT (τ) ö÷ ] d (７) ÷d expç － è φ ø è RT ø èφ ø T(t) æ Qd ö ÷d h et emp e r a t u r ei n t e r a l Howe v e r,t e x T g pç － T(τ) è RT ø c anno tbea c cu r a t e l r e s s ed．Byt heapp r ox ima Ｇ yexp t i on me t hodo fexpans i on, t het empe r a t u r ei n t eg r a l [ ] c anbeexp r e s s eda s３０ : T (t) Qd ö æ Qd ö æ ÷d ÷ expç － T ≈expç － ( ) Tτ è RT ø è RT (t) ø T (t) æQd(T －T (t)) ö ÷d expç T＝ T (τ) è R (T (t))２ ø ２ Qd öR (T (t)) æ ÷ expç － Qd è RT (t) ø æ æQd(T (τ) －T (t)) ö ö (８) ÷÷ ç１－expç RT (t)２ è è øø Subs t i t u t i ngEq (８) i n t oEq (７), Ve c anbeex Ｇ : r e s s e da s p / Qd öR(T(t))２ æD０ ö ３ ２ æ ÷ xpç － Ve＝VN ∗g ç ÷ {e Qd èφ ø è RT(t) ø æQ (T －T (t)) ö ３/２ [１－expç d ０ (９) ÷ ]} è R (T (t))２ ø
∫
∫
∫
∫
∫
７０９
Subs t i t u t i ngEq (９) i n t oEq (３), f c anbeex Ｇ r e s s eda s: p / Qd öR(T(t))２ æD０ ö ３ ２ æ ÷ xpç － xp{－N ∗g ç ÷ [e f＝１－e Qd èφ ø è RT(t) ø æQ (T －T (t)) ö ３/２ (１－expç d ０ } (１０) ÷ )] è R (T (t))２ ø Upt onow, t hedeve l opedJMAK mode lha sbe en e s t ab l i shed． I nEq s (９) and (１０), t heva l ue so fN ∗ c anbee s t ima t ed by t he me a sur ed p r i o raus t en i t e r a i ns i z e, a ss e eni nTab l e３．Twoo t he ri ndepend Ｇ g en tpa r ame t e r so faus t en i t i ct r ans f o rma t i on, p r e Ｇ e x Ｇ o n e n t i a l f a c t o rf o rd i f f u s i o na n dt h ea c t i v a t i o ne n e r p gy f o rd i f f u s i on,c anb ec a l c u l a t e dou tbyf i t t i ngt heexpe r Ｇ imen t a lda t aandt hedeve l opedJMAK mode l． I tc an beobs e r vedt ha tt hef i t t edcur ve sa r ei ngoodag r e e Ｇ men twi t ht heexpe r imen t a lva l ue s, a ss e eni nF i ８． g TheQdi sr a i s ed, wh i l et heD０i sl owe r edbyi nc r e a s Ｇ i ngt an t a l umcon t en t, andt heva l ue so ft hema r el i s Ｇ t edi nTab l e４．
No １—Spe c imen１; No ２—Spe c imen２; No ３—Spe c imen３．
F i ８． Comp a r i s onb e twe e naus t en i t ef r a c t i onme a su r edand g f i t t edbyk i ne t i c smode lo fRAFMs t e e l s． Tab l e４ Ki ne t i cpa r ame t e r s, a c t i va t i onene r o rd i f f us i onandp r e Ｇ gyf e xpon e n t i a lf a c t o rd e t e rmi n e dbypha s e Ｇ t r ans f o rma t i onmode l o fRAFMs t e e l s Tan t a l umc on t en t/wt． ％
Qd/(kJmo l－１) D０/(m２s－１) Er r o r/ ％
０
９４ ６
２ ８×１０－５ ２ ８
０ ０２７ ９８ ５
０ ０７３
１０５ ０
１ ８×１０－５ １ ３６×１０－５ ３ ０
３ ０
The me c han i sm o fau s t e n i t i ct r an s f o rma t i on ma i n l y d e e nd sont henu c l e a t i onandt hed i f f u s i on Ｇ c on t r o l l e d p r owt hi nt hemode l．Espe c i a l l a rbond i f f us i oni s g y, c t hema s t e rf a c t o rt ocon t r o lt heaus t en i t eg r owt hi n [ , ] c a rbons t e e l３１ ３２ ． I tc anbef oundf r om Tab l e４t ha t Qdi si nc r e a s edbyt hei nc r e a s eo ft an t a l um．Theva l Ｇ ue so fQd f o rt hes amp l e s wi t hd i f f e r en tt an t a l um con t en t so f０ wt ％ , ０ ０２７ wt． ％ and０ ０７３ wt． ％ a r e９４ ６, ９８ ５and１０５ ０kJ/mo l, r e spe c t i ve l y．The va l ue so fc a l cu l a t edd i f f us i ona c t i va t i ona r es imi l a rt o
７１０
J G ． Chene ta l．/Journa lofI r onandSt e e lRe s ear ch, In t e rna t i ona l２４ (２０１７) ７０５－７１０
t heva l ue so ft hea c t i va t i onene r o rd i f f us i ono f gyf [ ] c a rboni nf e r r i t e (８０ kJ/mo l) ３３ ; howeve r, t he r e a r esomedev i a t i ons．Th i sc an beexp l a i nedbyt he f a c tt ha tt hei nc r e a s eo ft an t a l ume l emen twou l dr e Ｇ t a rdt hed i f f us i ono fc a rbondu r i ngaus t en i t i ct r ans Ｇ f o rma t i on．Henc e, t he me chan i sm o fd i f f us i on Ｇ con Ｇ t r o l l edi sno ton l t h ec a r b o nd i f f u s i o n． I n R A FM y s t e e l s, t an t a l umi sac a rb i de sf o rmi nge l emen t．The numbe ro fund i s s o l vedc a rb i de si nc r e a s e swi t ht an t a Ｇ [２１] , l um wh i chl e adst oa mo r ec onsump t i ono fc a r Ｇ boni n ma t r i x．The r e f o r e, t hec onc en t r a t i ond i f f e r Ｇ enc eo fc a rbon be twe en und i s s o l ved c a rb i de s and ma t r i xi sl a r i chi sf avo r ab l et ot henuc l e a t i on ge, wh o faus t en i t e．Howeve r, t heund i s s o l vedc a rb i dep r e Ｇ c i i t a t e shavet hemax imumt he rmodynami cs t ab i l i Ｇ p t i ch wou l dr educ et hec a rbond i f f us i onc oe f f i Ｇ y, wh c i en tands l ow downt heaus t en i t i ct r ans f o rma t i on r a t e．Att hes amet ime, t hes t ab l ec a rb i de shavean e f f e c t i vep i nn i nge f f e c tont heaus t en i t eg r a i nbound Ｇ a r i e s．Th e r e f o r e, t h ei n c r e a s eo ft a n t a l uml e adst ot he de c r e a s eo faus t en i t eg r a i ns i z e．
４．Conc l u s i on s
(１) Th ep r i o ra u s t e n i t eg r a i ns i z ei sd e c r e a s e dwi t h t hei nc r e a s eo ft an t a l umc on t en ti nRAFMs t e e l． (２) Theaus t en i t i ct r ans f o rma t i ont empe r a t ur e s, Ac１ and Ac３ , a r ea l li nc r e a s ed wi t ht hei nc r e a s eo f , t an t a l umc on t en t． I nadd i t i on t heaus t en i t i ct r ans Ｇ f o rma t i ont imei si nc r e a s eds l i t l t ht hei nc r e a s e gh ywi o ft an t a l um． (３) Th emod e lo fa u s t e n i t i ct r a n s f o rma t i onk i n e t i c s b a s e donJMAK mode lwa se s t ab l i shed, andt hep r e Ｇ exponen t i a lf a c t o rf o rd i f f us i on (D０) andt hea c t i va Ｇ ( t i onene r o rd i f f us i on Qd) we r ec a l cu l a t edou t． gyf (４) Thei nc r e a s eo ft an t a l umc ane l eva t et hea c t i Ｇ va t i on ene r o rd i f f us i on o fc a rbon i n RAFM gy f s t e e l, wh i chi nd i c a t e st hemo r ed i f f i cu l td i f f us i ono f c a rbondu r i ngaus t en i t i ct r ans f o rma t i on．Tan t a l um, a sana l l oy i nge l emen tf o rc a rb i de sf o rmi ng, r educ e s t hec a rbond i f f us i onc oe f f i c i en tands l owsdownt he aus t en i t i ct r ans f o rma t i onr a t e．
Acknowl e dgmen t
The wo rki sf i nanc i a l l o r edbyt he Ch i na yspons Na t i ona lFundsf o r Di s t i ngu i shed Young Sc i en t i s t s (Gr an t edNo． ５１３２５４０１), t heNa t i ona lNa t u r a lSc i Ｇ enc eFounda t i ono fCh i na (Gr an t edNo． ５１５０１１２６), andt h eNa t i on a lMa e t i cCon f i n eme n tFu s i onEn e r gn gy ( ) Re s e a r c hP r og r am Gr a n t e dNo． ２０１５GB１１９００１ ．
Re f e r enc e s
[１] J．Kna s t e r, A．Moe s l ang, T．Mur oga, Na t ur ePhys． １２ (２０１６)
４２４ Ｇ ４３４． [２] S oga, H．Tan i l． J．Z i nk l e, A．Moe s l ang, T．Mur gawa, Nuc Fus i on． ５３ (２０１３) １ Ｇ １３． [３] P．Ma M．Ol i ve r, J．Nuc l．Ma t e r． ３１８ (２００３) １３２ Ｇ １４２． rmy, B [４] K．Ehr l i ch, Fus i onEng．De s． ５６ (２００１) ７１ Ｇ ８２． [５] E．Luc on, W．Vande rmeu l en, J．Nuc l．Ma t e r． ３８６ (２００９) ２５４ Ｇ ２５６． [６] MA．Soko l o v a, H．T a n i awa b, G R．Od e t t e c, K．Sh i b a, R L． g Kl ueh, J．Nuc l．Ma t e r． ３６７ (２００７) ６８ Ｇ ７３． [７] R L．Kl ueh, D J．Al exande r, M．Ri e t h, J．Nuc l．Ma t e r．２７３ (１９９９) １４６ Ｇ １５４． [８] Q．Hu Ba l u c, Y． Da i, S． J i t s uk awa, A．Kimu r a, J．Kony s, a ng, N． E． R J．Ku r t z, R．L i nd a u, T．Mu r o a, G R．Od e t t e, B．Ra g j, R S t o l l e r, L．T a n, H．T a n i awa, AAF．Tava s s o l i, T．Yamamo Ｇ g t o, F．Wan, Y．Wu, J．Nuc l．Ma t e r． ４４２ (２０１３) S２ ＧS８． [９] Q．Hu Pe ng, S． Zh e ng, i u, C． L i, B．Hu a ng, L． a ng, Q．Wu, S．L Q．Ha n, Y．Wu, Fu s i onEng．De s． ８６ (２０１１) ２６１１ Ｇ ２６１５． [１０] K． J a a s on, P．Pe e t s a l u, M．Sa a r na, Es t．J．Eng．１８ (２０１２) ２２１ Ｇ ２３１． [１１] Y C．L i u, F． Somme r, E J．Mi t t eme i e r, Ac t aMa t e r． ５１ (２００３) j ５０７ Ｇ ５１９． [１２] D．L i, YA．Mi n, X C．Wu, J． I r onS t e e lRe s． I n t． １７ (２０１０) No １１, ６２ Ｇ ６６． [１３] L G．Kong, YH． L i u, J A． L i u, YL． Song, S S． L i, R H． Zhang, T J．L i, Y．L i ang, J．Al l oy．Compd． ６４８ (２０１５) ４９４ Ｇ ４９９． [１４] C X．L i u, YC．L i u, D T． Zhang, Z S．Yan, App l．Phys．A １０５ (２０１１) ９４９ Ｇ ９５７． [１５] AT W．Kempen, F．Somme r, E J．Mi t t eme i e r, J．Ma t e r． j Sc i． ３７ (２００２) １３２１ Ｇ １３３２． [１６] H．Chen, YC．L i u, Z S．Yan, YL．L i, L F． Zhang, App l． Phys．A９８ (２０１０) ２１１ Ｇ ２１７． [１７] Y． Xi a, M． Enomo t o, Z G．Yang, Z D． L i, C． Zhang, Ph i l o s． Mag． ９３ (２０１３) １０９５ Ｇ １１０９． [１８] QJ．Ma, Y．Shao, YC．L i u, Z M．Gao, L M．Yu, I n t． J． Ma t e r．Re s． １０４ (２０１３) ９３５ Ｇ ９４０． [１９] J G．Chen, C X．L i u, YC．L i u, B Y．Yan, HJ．L i, J．Nu Ｇ c l．Ma t e r． ４７９ (２０１６) ２９５ Ｇ ３０１． [２０] Z X．Xi a, C．Zhang, NQ．Fan, YF．Zhao, F．Xue, S J． L i u, Ma t e r． Sc i．Eng．A５４５ (２０１２) ９１ Ｇ ９６． [２１] Rav i k i r ana, R．My t h i l i, S．Ra u, S． Sa r o a, T． J ayakuma r, E． j j Ra end r akuma r, Ma t e r．Cha r a c t． ８４ (２０１３) １９６ Ｇ ２０４． j [２２] Z X．Xi a, C． Zhang, QY．Huang, S J．L i u, Z D．L i, Z G． Yang, J． I r onS t e e lRe s． I n t． １８ (２０１１) No ９, ４７ Ｇ ５２． [２３] F．L i u, F．Somme r, C．Bo s, E J．Mi t t eme i e r, I n t．Ma t e r． j Rev． ５２ (２００７) １９３ Ｇ ２１２． [２４] H．Ma, S L．L i ao, S F．Wang, J．I r onS t e e lRe s．I n t．２１ (２０１４) ７０２ Ｇ ７０９． [２５] A．Ka rmaka r, S．Kundu, S．Roy, S．Neogy, D．Sr i va s t ava, D．Chakr aba r t i, Ma t e r． Sc i．Te chno l． ３０ (２０１４) ６５３ Ｇ ６６４． [２６] N．Zo t ov, V．Ma r z i t s ch, E J．Mi t t eme i e r, J．Al l oy． ynkev j Compd． ６１６ (２０１４) ３８５ Ｇ ３９３． [２７] D J．Wang, YC． L i u, C． Bao, WX．Tan, Z M．Gao, App l． Phys．A９６ (２００９) ７２１ Ｇ ７２９． [２８] YC．L i u, D J．Wang, F．Somme r, E J．Mi t t eme i e r, Ac t a j Ma t e r． ５６ (２００８) ３８３３ Ｇ ３８４２． [２９] Y C．L i u, F． Somme r, E J．Mi t t eme i e r, Ac t aMa t e r． ５８ (２０１０) j ７５３ Ｇ ７６３． [３０] D J．Wang, YC． L i u, YH． Zhang, J．Ma t e r． Sc i． ４３ (２００８) ４８７６ Ｇ ４８８５． [３１] R．Th i e s s en, I．Ri cha r ds on, J．S i e t sma, Ma t e r．Sc i．Eng．A ４２７ (２００６) ２２３ Ｇ ２３１． [３２] E．Hawbo l t, B．Chau, J．Br ima c ombe, Me t a l l．Ma t e r．Tr ans． A１６ (１９８５) ５６５ Ｇ ５７８． [３３] E , Bu A． Br a nd e s, Smi t h e l l sMe t a l sRe f e r e n c eBo ok, ６ t he d． t t e r Ｇ wo r t h s, London, １９８３．
E f f e c t so ft a n t a l umonaus t en i t i ct r ans f o rma t i onk i ne t i c so fRAFMs t e e l
J i an Ｇ Ｇ changL i u, Chen Ｇ x iL i u∗ , B i Ｇ i Ｇ unL i guoChen, Yong yuYan, Hu j
S t a t eKeyLabo r a t o r fHyd r au l i cEng i ne e r i ngS imu l a t i onandSa f e t lo fMa t e r i a l sSc i enc e & Eng i ne e r i ng, Ti an i n yo y, Schoo j Un i ve r s i t an i n３００３５０, Ch i na y, Ti j ARTICLEINFO
ABSTRACT
Keywo rds: RAFMs t e e l Tan t a l umc on t en t Gr a i ng r owt h Aus t en i t i ct r ans f o rma t i on k i ne t i c s Ac t i va t i onene r gy
TheRAFM (r educ eda c t i va t i onf e r r i t i c/ma r t ens i t i c) s t ee l scont a i n i ngd i f f e r entt ant a l um cont ent s (０wt ％ , ０ ０２７wt ％ , ０ ０７３wt ％ ) we r ede s i a s t．Di f f e r en t i a ls c ann i ngc a l o r ime t r gnedandc yand op t i c a lmi c r o s c opywe r eemp l oyedt oexp l o r et hei n f l uenc eo ft an t a l umc on t en tont heaus t en i t i ct r ans Ｇ f o rma t i ono fRAFMs t e e l s．Theaus t en i t i ct r ans f o rma t i onk i ne t i c swa sde s c r i bedbyapha s e Ｇ t r ans f o r Ｇ ma t i onmode l．Themode l, i nvo l v i ngs i t es a t ur a t i onnuc l e a t i on, d i f f us i on Ｇ c on t r o l l edg r owt handimＧ i ngemen tc o r r e c t i on, wa se s t ab l i shed ba s ed on t he c l a s s i c a lJ ohns on ＧMeh l ＧAv r ami ＧKo lmogo r ov p mode l．Thepha s e Ｇ t r ans f o rma t i onk i ne t i c spa r ame t e r s, i nc l ud i ngD０ (p r e Ｇ exponen t i a lf a c t o rf o rd i f Ｇ f us i on) andQd (a c t i va t i onene r o rd i f f us i on), we r ec a l cu l a t edbyf i t t i ngt heexpe r imen t a lda t aand gyf t hek i ne t i cmode l．Ther e su l t si nd i c a t edt ha tt heave r ageg r a i ns i z ei sde c r e a s edwi t ht hei nc r e a s eo f t an t a l um．Theva l ue so fAc１andAc３ (ons e tandf i n i sht empe r a t ur eo faus t en i t i ct r ans f o rma t i on, r e Ｇ spe c t i ve l r ei nc r e a s edbyi nc r e a s i ngt het an t a l umc on t en t．Thei nc r e a s eo ft an t a l umc aus edt hede Ｇ y) a c r e a s eo fD０．Howeve r, Qdi si nc r e a s ed wi t ht hei nc r e a s eo ft an t a l um．I nadd i t i on, a sac a r b i de s f o rmi nge l emen t, t an t a l um wou l dr educ et hec a r bond i f f us i onc oe f f i c i en tands l owdownt heaus t en i t i c t r ans f o rma t i onr a t e．
１． I n t r odu c t i on I nt h ef u s i onr e a c t o r s, t h er e du c e da c t i v a t i onf e r r i t i c/ ma r t ens i t i c (RAFM ) s t e e l s we r ebe i ng c ons i de r ed a st hepr e f e r r edc and i da t ef o rt hes t ruc t u r a lma t e r i a l owi ngt ot he i rr educ eda c t i va t i onab i l i t t t e r yandbe [ , ] t he rmo Ｇ s i c a lp r op e r t i e s１ ２ ．Th ed e s i f RAFM phy gn o s t e e l swa sba s edont he mod i f i c a t i ono ft het r ad i Ｇ t i ona lhe a tr e s i s t an ts t e e l, ma i n l ep l a c i ngt he y byr l ong Ｇ l i vedt r ansmu t a t i one l emen t so f Mo, Nb, and Co wi t hr e l a t i v e l s h o r t Ｇ l i v e dt r a n s m u t a t i one l emen t s y , o fT aa nd W．Sof a r as i i f i c a n tamoun to fr e s e a r c h gn anddeve l opmen to fRAFM s t e e l sha sbe enc onduc Ｇ [ , ] t edi nma nyc oun t r i e s,s u c ha sF８２Hs t e e li nJ a a n３ ４ , p [ , ] EUROFER９７s t e e li nEu r op e４ ５ , ９Cr ２WVT as t e e li n [６,７] [ , ] USA andCLAMs t e e li nCh i na８ ９ ． Gene r a l l ak i ng, aus t en i z a t i oni st hef i r s ts t ep yspe o f he a tt r e a tmen tf o rs t e e l s．The cho i c eo f he a t t r e a tmen t pa r ame t e r s du r i ng t he aus t en i t i z i ng r oc e s si sv i t a lt ot hef i na lmi c r o s t ruc t u r eand me Ｇ p chan i c a lp r ope r t i e so ft hes t e e l．Ther e s e a r cho faus Ｇ t en i t i ct r ans f o rma t i on k i ne t i c si s bene f i c i a lt ot he [ ] cho i c eo fhe a tt r e a tmen tpa r ame t e r s１０ ．The r e f o r e, ∗ Co r r e spond i ngau t ho r．Ph． D． EＧma i laddr e s s:cxl i u t ． om (C X ． Li u) ． ju＠１６３c
ag r e a ti n t e r e s tex i s t sf o rt her e s e a r cho ft heaus t e Ｇ [ ] n i t i ct r ans f o rma t i onk i ne t i c s１１Ｇ１４ ．Thek i ne t i c smod Ｇ e li sane f f e c t i vewayt oi nve s t i t epha s et r ans f o r Ｇ ga ma t i on． I n gene r a l, a pha s et r ans f o rma t i on mode l cons i s t so ft hr e es t eps: nuc l e a t i on, g r owt handimＧ i ngemen to ft heg r owi ngnew pha s epa r t i c l e s．The p s et r ans f o rma t i onp r oc e s sc anbe mode l eds epa Ｇ pha [ ] r a t e l rdimp i ngemen ti semp l oy e d１５ ．The y whenha c l a s s i c a lJ ohn s on ＧMe h l ＧAv r ami ＧKo lmogo r ov (JMAK) mode lha sbe en wi de l d e v e l o e da n d us edt or e Ｇ y p s e a r cht he pha s et r ans f o rma t i onbehav i o ri n many [ , , ] s t ems１３ １４ １６ ．Fo raus t en i t i ct r ans f o rma t i on, i ti s ys we l la c c ep t edt ha tt henuc l e a t i onandt heg r owt ho f aus t en i t eg r a i n dur i ng t he pha s et r ans f o rma t i on r oc e s sc an bede s c r i bed by t hea t omscon t r o l l ed p d i f f us i on, s i nc et heaus t en i t i ct r ans f o rma t i ont ake s l a c ea th i empe r a t ur e．Thed i f f us i ono fc a rbon p ght ha sag r e a te f f e c tont henuc l e a t i onand g r owt ho f aus t en i t eg r a i nf o rs t e e l s．Re c en t l e s e a r che s y, somer i nd i c a t edt ha tt hea l l oy i nge l emen t sa l sohaveg r e a t i n f l uenc eont he pha s et r ans f o rma t i onf o rs t e e l s, andt hei n f l uenc eo fa l l oy i nge l emen t sont heaus t e Ｇ n i t i ct r ans f o rma t i onk i ne t i c sha sa t t r a c t edex t ens i ve
Re c e i ved５J anua r c e i vedi nr ev i s edf o rm１２ Ma r ch２０１７; Ac c ep t ed１３ Ma r ch２０１７ y２０１７; Re Ava i l ab l eon l i ne１５Ju l y２０１７ １００６ Ｇ ７０６X/Copy r i tⓒ２０１７, Th ee d i t o r i a lo f f i c eo fJ ou r n a lo fI r ona ndS t e e lRe s e a r c h, I n t e r n a t i on a l． Pub l i s h e dbyE l s e v i e rL imi t e d．Al lr i t sr e s e r v e d． gh gh
J G ． Chene ta l．/Journa lofI r onandSt e e lRe s ear ch, In t e rna t i ona l２４ (２０１７) ７０５－７１０
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a t t en t i ona r oundt hewo r l d１３ １４ １７ １８ ．Tan t a l umi san impo r t an ta l l oy i nge l emen ti n RAFM s t e e l, wh i ch [ , ] c ana f f e c tt hepr e c i i t a t i ono fc a rb i de s１９ ２０ ．The r e Ｇ p f o r e,t an t a l umha ss i i f i c an te f f e c tont heme chan i Ｇ gn c a lpr ope r t i e so ft heRAFMs t e e l． I nadd i t i on, some r epo r t si nd i c a t et ha tt an t a l um p l aysanimpo r t an t r o l ei nr e f i n i ngt hep r i o raus t en i t eg r a i no fRAFM [ , ] s t e e l２１ ２２ ．Henc e,t an t a l um wou l dbeboundt ohave s i n i f i c a n t e f f e c to na u s t e n i t i ct r a n s f o r m a t i o nk i ne t Ｇ g , i c so fRAFMs t e e l．Howeve rt hee f f e c to ft an t a l um con t en tont heaus t en i t i ct r ans f o rma t i onk i ne t i c so f RAFMs t e e lha sno tbe ens t ema t i c a l l t ud i ed． ys ys Wi t h i nt h i sc on t ex t, t h i sa r t i c l ea imst or e s e a r ch t hee f f e c to ft an t a l umc on t en tonaus t en i t i ct r ans f o r Ｇ ma t i onk i ne t i c so fRAFMs t e e l s．Themode lo faus Ｇ t en i t i ct r ans f o rma t i on k i ne t i c s ba s ed on JMAK mode lwa sdeve l oped, andt heaus t en i t i ct r ans f o r Ｇ ma t i onk i ne t i c spa r ame t e r swe r eob t a i nedbyf i t t i ng t heaus t en i t i ct r ans f o rma t i onf r a c t i onde t e rmi nedby DSC (d i f f e r en t i a ls c ann i ngc a l o r ime t r r imen t s y) expe andk i ne t i cmode l． [
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]
No １—Spe c imen１; No ２—Spe c imen２; No ３—Spe c imen３．
F i １． DSCcu r ve so fRAFMs t e e l s． g
２．Ma t e r i a l sandExp e r imen t a lMe t hod s
２ １．Ma t e r i a l spr epara t i onand di e r en t i a ls can Ｇ f f n i ngca l o r ime t ry Thed e s i e dRAFM s t e e l swe r ec a s ti n t oa ni ngo t gn wi t hwe i to f２５kgi nava cuumi nduc t i onf u rna c e． gh Subs equen t l hei ngo t swe r ef o r n t oc l i nde r y, t gedi y ba r s, wi t has i z eo f１２０mmi nhe i tand６０mmi n gh d i ame t e r．Th ed e t a i lc h emi c a lc ompo s i t i on so fRAFM s t e e l sa r eshowni nTab l e１．Thema i nd i f f e r enc ebe Ｇ twe ent hr e espe c imensi st hed i f f e r enc eo ft an t a l um con t en t．Af t e rt ha t, t hespe c imens we r e ma ch i ned i n t oc l i nd r i c a lspe c imenswi t hal eng t ho f２mmand y ad i ame t e ro f４mmus edt ot heDSCexpe r imen t．Al l DSCs amp l e s we r ehe a t edf r om r oom t empe r a t ur e upt o１０５０°Ca tahe a t i ngr a t eo f２０°C/mi nand t henc oo l edt or oom t empe r a t u r e wi t ht hec oo l i ng r a t eo f４０°C/mi n． I no r de rt oobs e r vet heva r i a t i on o fau s t e n i t i ct r a n s f o rma t i ont emp e r a t u r e(on s e tt emp e r Ｇ a t u r eAc１ a ndf i n i s ht emp e r a t u r eAc３ ) c l e a r l h eDSC y, t cur ve sc on t a i n i ngpha s et r ans f o rma t i oni n f o rma t i on we r ei n t e r c ep t eddu r i nghe a t i ngpr o c e s s, a ss e eni n F i １．Thet angen t me t hodi sus edt o me a su r et he g s et r ans f o rma t i ont empe r a t u r e, andF i ２shows pha g t hes chema t i cd i ag r am． Tab l e１ Chemi c a lc ompo s i t i onso fRAFMs t e e l s (wt ％ ) Spe c imen C
Cr
W
Mn
S i
V
Ta ０
２ ２．Mi c r o s t ruc t ura lo b s e rva t i on The mi c r os t ruc t ur e so f RAFM s t e e l we r eana Ｇ l edt hr oughop t i c a lmi c r os copy (OM) ．OMi nve s Ｇ yz t i t i onswe r ec a r r i edou tt o me a sur et hepr i o raus Ｇ ga t en i t eg r a i ns i z eo ft hes t e e l s．Thes amp l e sf o rOM exami na t i onwe r eg r oundwi t has e r i e so fS iCpape r f r om２４０t o２０００ g r i t, me chan i c a l l l i shedbya ypo d i amond pa s t e wi t hg r anu l a r i t f２ ５ μm, and yo e t chedbyanab l uen tso l u t i ono fp i c r i ca c i d (２ mL ab l uen t, １００ mL wa t e r, ２gp i c r i ca c i d) ．Thee t ch Ｇ i ngcond i t i onwa st het empe r a t ur eo f７０°Candt ime o f３ mi n．Thel i ne a ri n t e r c ep tme t hod wa sadop t ed unde rt hr e ed i f f e r en td i r e c t i onst ome a sur et hepr i o r [ ] aus t en i t eg r a i ns i z e２３ ．
３．Re s u l t sandDi s c u s s i on
３ １．Mi c r o s t ruc t ura lana l i s ys Fe
１
０ ０６ ８ ９１ １ ７３ ０ ３７ ０ ０５ ０ ２２
３
０ ０４ ８ ９３ １ ７１ ０ ４４ ０ ０４ ０ ２２ ０ ０７３ Ba l anc e
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F i ２． Tangen tme t hodus edt ome a su r eaus t en i t epha s e g t r ans f o rma t i ont empe r a t u r e s．
Ba l anc e
０ ０５ ８ ９２ １ ６６ ０ ３１ ０ ０３ ０ ２３ ０ ０２７ Ba l anc e
Theo r i i na l mi c r os t ruc t ur eo ft hespe c imensi s g ma r t ens i t es t ruc t ur e, a sshowni nF i ３．The mi Ｇ g c r os t ruc t ur e so ft heRAFM s t e e l scon t a i n i ngd i f f e r Ｇ en tt an t a l um con t en t sa f t e rt he DSC me a sur emen t a r eshowni nt heOM mi c r og r aphso fF i ４． I no rde r g
G ． Chene ta l．/Journa lofI r onandSt e e lRe s ear ch, In t e rna t i ona l２４ (２０１７) ７０５－７１０ J
７０７
(a) Spe c imen１; (b) Spe c imen２; (c) Spe c imen３．
F i ３． Or i i na lop t i c a lmi c r og r aphso fs t ud i edRAFMs t e e l s． g g
(a) Spe c imen１; (b) Spe c imen２; (c) Spe c imen３．
F i ４． Op t i c a lmi c r og r aphso fRAFMs t e e l s． g
t oi nve s t i t et heaus t en i t i ct r ans f o rma t i on behav Ｇ ga i o r, t hespe c imensf o r OM obs e r va t i oni se t ched, andt he g r a i ns i z ei s me a su r ed byt he me t hodde Ｇ s c r i bedi nSe c t i on２ ２．Th i se t ch i ng me t hodi ssu i t Ｇ ab l ef o r pr e s en t a t i on o ft he p r i o raus t en i t eg r a i ns (PAGs) r a t he rt hant hema r t ens i t es t ruc t u r e． I tc an bef oundt ha tt he p r i o raus t en i t eg r a i ns i z ei sde Ｇ c r e a s edwi t ht hei nc r e a s eo ft an t a l um c on t en t．Th i s [ ] sc on s i s t e n tw i t ht h ep r e v i ou swo r k s１９ ． phenomenoni Theva l ue so ft heave r ageg r a i ns i z ea r e (５２ ７４± ), ( ) ( ) ６ ３ ３４ ３３±３ ８ and ２２ ４２±２ ４ μm, r e spe c Ｇ t i ve l i sc anbeexp l a i nedt ha tt henumbe ro fun Ｇ y．Th d i s so l vedc a rb i de si nc r e a s e swi t ht hei nc r e a s eo ft an Ｇ t a l umc on t en t．Theund i s s o l vedc a rb i de sa r eve r f Ｇ ye f e c t i vei nc on t r o l l i ngt heaus t en i t eg r a i ng r owt hby [ , ] i nn i ng t he g r a i n bounda r i e s２１ ２２ ．Ot he rc a rb i de p f o rmi nge l emen tha st heana l ogousr epo r t．Tic anr e Ｇ t a rdt heaus t en i t eg r a i nowi ngt ot heex i s t enc eo fun Ｇ [ ] d i s so l vedTi(C,N) i nh i a rbons t e e l s２４ ．Nband ghc Vc anf o rm Nb(C,N) and V(C,N), h i nde r i ngt he [ ] aus t en i t eg r a i ng r owt ho fNb ＧVs t e e l s２５ ．
３ ２．Au s t en i t et ran s o rmed f rac t i on and au s t en i t e f t ran s o rma t i onra t e f
I no r de rt oi nve s t i t et hee f f e c to ft an t a l umcon Ｇ ga t en tont heaus t en i t i ct r ans f o rma t i onbehav i o r, as e Ｇ r i e so fDSC me a su r emen t swe r ec a r r i edou twi t ha l l spe c imens．F i １showst heDSCcu r ve sc on t a i n i ng g s et r ans f o rma t i oni n f o rma t i ono ft hespe c imens pha dur i ngt heaus t en i z a t i onp r o c e s s． I tc anbef oundt ha t t he r ea r etwoendo t he rmi cpe aks: t hef i r s toneex i s Ｇ t eda r oundt het empe r a t u r eo f７５０°C, wh i chi st he
Cur i et empe r a t ur e; t hes e cond oneex i s t edi nt he r angeo f８６０－９２０°C, wh i chi nd i c a t edt heaus t en i t i c t r ans f o rma t i on．The Ac１ and Ac３ we r e ob t a i ned t hr ought he me t hodde s c r i bedi n Se c t i on２ １．The Ac１andAc３i nc r e a s ef r om ８６１t o８６９°Cand８９９t o ９１９°C, r e spe c t i ve l ss howni nT ab l e２． I tc anb e y, a e xp l a i n e dt ha tt heaus t en i t i ct r ans f o rma t i oni sd i f f i Ｇ cu l tt ot ake p l a c eowi ngt ot hei nc r e a s eo fund i s Ｇ so l vedc a rb i de sc aus edbyadd i ngt an t a l um, andt he aus t en i t i ct r ans f o rma t i oni sr e t a rdedt ot heh i r ghe t empe r a t ur e． Tab l e２ faus t en i t i ct r ans f o rma t i onf o rRAFMs t e e l s Ac１ andAc３ o Tan t a l umc on t en t/wt ％
Ac１/°C Ac３/°C
０
０ ０２７
０ ０７３
８９９
９０５
９１９
８６１
８６４
８６９
Theaus t en i t ef r a c t i on, fγ, c anbeob t a i nedf r om [ ] t heDSCcur ve s２６ : æ １ ö÷ T ( ) (１) fγ(t) ＝ ç Ftd t èΔH ø ０ whe r e, ΔH i st het o t a len t ha l faus t en i t e pychangeo s et r ans f o rma t i on; F (t)i st hehe a tf l ux; andti s pha t ime． fγa saf unc t i ono ft empe r a t ur e (T ) f o ra l lspe c i Ｇ mensi sshowni nF i ５．F i ６and７i l l us t r a t et he g gs aus t en i t et r ans f o rma t i onr a t e (dfγ/d t) a saf unc t i on o ft empe r a t ur e (T ) andaus t en i t ef r a c t i on (fγ), r e Ｇ spe c t i ve l t en i t et r an s f o rma t i ono fs e c ime n s y．Theaus p c on t a i n i ngd i f f e r e n tt an t a l umc on t e n t sexh i b i t st hef o l l Ｇ
∫
７０８
G ． Chene ta l．/Journa lofI r onandSt e e lRe s ear ch, In t e rna t i ona l２４ (２０１７) ７０５－７１０ J
becon f i rmedbyt heva l ue s (t hed i f f e r enc ebe twe en da t ao fAc３ and Ac１ i n Tab l e２), s i nc et hehe a t i ng r a t ei ss amef o ra l ls amp l e s． (i i i) Theaus t en i t i ct r ans f o rma t i onp r oc e s so fa l l spe c imensshowson l t en i t et r ans f o rma t i on yoneaus r a t emax imum (s e eF i ６and７), demons t r a t i nga gs [ ] no rma laus t en i t et r ans f o rma t i oncha r a c t e r i s t i c１１ ． (i v) The max imum va l ueo faus t en i t i ct r ans f o r Ｇ ma t i onr a t ei sde c r e a s ed wi t ht hei nc r e a s eo ft an t a Ｇ l umcon t en t (s e eF i ６and７) ． gs
３ ３．Ki ne t i c sana l i sofau s t en i t i ct ran s o rma t i on ys f o c e s s pr No １—Spe c imen１; No ２—Spe c imen２; No ３—Spe c imen３．
F i ５． Aus t en i t ef r a c t i ona saf unc t i ono ft empe r a t u r ef o r g RAFMs t e e l s．
I ngene r a l, JMAK mode lde s c r i be st heso l i d Ｇ s t a t e s et r ans f o rma t i on a st hr e es t eps: nuc l e a t i on, pha r owt h, andimp i ngemen t．Themode lo fnuc l e a t i on g andg r owt hs t age sa s sume st ha ta l lnewg r a i nsneve r s t opnuc l e a t i ngandg r owi ng, i r i ngt hei n t e r r e l a Ｇ gno t i onsh i fnew g r a i nsi nt hepha s et r ans f o rma t i on po , ha r oc e s s, i e． rdimp i ngemen ti si r edi nt he p gno aus t en i t i cnuc l e a t i onand g r owt h pr oc e s s．TheimＧ i ngemen t mode li sco r r e c t edi nt heimp i ngemen t p , , r o c e s s i e ． h a r di m i n e m e n to f r o w i n r a i n s p p g g gg i sr andoml i s t r i bu t ed． yd Theex t endedvo l ume, Ve, andt hepha s et r ans Ｇ , , f o rmedf r a c t i on f c anbede t e rmi nedt hr ought h i s [ ] me t hod２７ a sf o l l ows:
∫V N (T (τ))Y(t,τ)dτ
Ve＝
No １—Spe c imen１; No ２—Spe c imen２; No ３—Spe c imen３．
F i ６． Au s t e n i t et r a n s f o rma t i onr a t ea saf unc t i ono ft empe r a Ｇ g t u r ef o rRAFMs t e e l s．
No １—Spe c imen１; No ２—Spe c imen２; No ３—Spe c imen３．
F i ７． Au s t e n i t et r a n s f o rma t i onr a t ea saf unc t i ono faus t en i t e g f r a c t i onf o rRAFMs t e e l s．
owi ngk i ne t i cf e a t u r e s: (i) Ac１andAc３a r ebo t hi nc r e a s edbyt hei nc r e a s e o ft an t a l umc on t en t (s e eTab l e２andF i ５) ． g (i i) Theove r a l laus t en i t i ct r ans f o rma t i ont imei s i nc r e a s eds l i t l hei nc r e a s eo ft an t a l um con Ｇ gh y byt t en t (s e eTab l e２, F i ５and６) ．Espe c i a l l tc an gs y, i
t
０
(２)
æ V ö (３) f＝１－expç － ÷ è Vø whe r e, N i st henuc l e a t i onr a t e; V i st hes amp l e ; st hevo l umeo fas i ng l epa r t i c l ea t vo l ume andY i t imet, wh i chnuc l e a t eda tt imeτ． I nt henuc l e a t i onpr oc e s s, t hes i t es a t ur a t i onnu Ｇ [ , ] c l e a t i onmode li semp l oyed．L i ue ta l ２８ ２９ ha si nd i Ｇ c a t edt ha tt hes i t es a t ur a t i onnuc l e a t i onmode li sap Ｇ ,t l i c ab l ef o raus t en i t i ct r ans f o rma t i on, i e． henu Ｇ p c l e a t i ono faus t en i t ewa sa s sumedt ohavebe encomＧ l e t eda tt hes t a r ts t ageo fg r owt h, andt hust he p numbe ro f nuc l e a t i on r ema i ned unchangedi nt he subs equen tg r owt hpr oc e s s．Thes i t es a t ur a t i onnu Ｇ [ ] c l e a t i onr a t ec anbeexpr e s s eda s２８ : æT (t) －T０ ö (４) ÷ N (T ) ＝N ∗δç è ø φ æT(t)－T０ ö æT(t)－T０ ö ÷i ÷＝ wh e r e,δç saD i r a cf un c t i o n:δç è ø è ø φ φ T (t) ( ) , ( ) T t － T æ ö ０ T t ≠T０ ; ０ ÷ ＝１; N ∗ i δç st he ∞ , T (t) ＝T０ T０ è ø φ numb e ro fp r e Ｇ e x i s t i ngnu c l e ip e run i tvo l umea tt＝０; st hehe a t i ngr a t e; andT (t) ＝T０ ＋φ t．Fo rt hes i t e φi ∗ s a t ur a t i onnuc l e a t i on mode l, N ＝N ．Thenumbe r o fpr e Ｇ ex i s t i ngnuc l e ipe run i tvo l ume (N ∗ ) c anbe de t e rmi nedbyt hef o rmu l a: N ∗ ＝１/d３ he r edr r, w r e s en t st heave r ageg r a i ns i z e．Theco r r e spond i ng p
{
e
∫
J G ． Chene ta l．/Journa lofI r onandSt e e lRe s ear ch, In t e rna t i ona l２４ (２０１７) ７０５－７１０
va l ue so ft henuc l e a t i ondens i t r el i s t edi nTab l e３． ya Tab l e３ Av e r a ea u s t e n i t eg r a i ns i z ea nda u s t e n i t ep r e Ｇ ex i s t i ngnuc l eus g dens i t fRAFMs t e e l s yo Tan t a l umc on t en t/wt ％
dr/μm
N ∗ /m－３
０
５２ ７４
６ ８２×１０１２
０ ０２７
３４ ３３
２ ４７×１０１３
０ ０７３
２２ ４２
８ ８７×１０１３
I nt heg r owt hp r o c e s s, t hed i s s o l u t i onandd i f f u Ｇ s i ono fa l l oy i nge l emen ti nt hev i c i n i t ft hei n t e r Ｇ yo f a c eha sag r e a ti n f l uenc eont hewho l eaus t en i z a t i on r oc e s s．The r e f o r e, t hed i f f us i on Ｇ c on t r o l l edg r owt h p mode li sadop t edi nt heg r owt hp r o c e s so faus t en i t e t r ans f o rma t i on．Thevo l umeo fag r owi ngpa r t i c l e, [ ] anbeexpr e s s eda s２３ : Y, c
∫D (T (t))dt)
Y ＝g(
t
(５)
d/m
τ
whe r e, gi sapa r t i c l e Ｇ t r a c t o r (g＝１f o rcu Ｇ geome yf ; / b i cg r owt h g＝４π ３f o rsphe r i c a lg r owt h); di st he d imens i ona l i t ft h eg r owt h (d＝３), s i n c et h eg r owt h yo o fpa r t i c l ei st hr e ed imens i ona l i t st heg r owt h y; m i modepa r ame t e r (１f o ri n t e r f a c e Ｇ c on t r o l l edg r owt h, ２f o rvo l umed i f f u s i on Ｇ c on t r o l l e dg r owt h); D (T(t))i s [ ] t hed i f f us i onc oe f f i c i en t, andc anbeg i vena s１６ : æ Qd ö (６) ÷ D (T (t)) ＝D０expç － è RT ø whe r e, D０ i st he p r e Ｇ exponen t i a lf a c t o rf o rd i f f uＧ ; st hea c t i va t i onene r o rd i f f us i on; andR s i on Qdi gyf i st hega sc ons t an t． Subs t i t u t i ngEqs (４), (５) and (６) i n t oEq (２), : t heex t endedvo l umec anbeexp r e s s eda s T (t) T (t) æT (t) －T０ ö e ∗ ÷g[ V ＝ VN δç D０ T０ T (τ) è ø φ æ Qd ö æçT ö÷ ３/２ æçT (τ) ö÷ ] d (７) ÷d expç － è φ ø è RT ø èφ ø T(t) æ Qd ö ÷d h et emp e r a t u r ei n t e r a l Howe v e r,t e x T g pç － T(τ) è RT ø c anno tbea c cu r a t e l r e s s ed．Byt heapp r ox ima Ｇ yexp t i on me t hodo fexpans i on, t het empe r a t u r ei n t eg r a l [ ] c anbeexp r e s s eda s３０ : T (t) Qd ö æ Qd ö æ ÷d ÷ expç － T ≈expç － ( ) Tτ è RT ø è RT (t) ø T (t) æQd(T －T (t)) ö ÷d expç T＝ T (τ) è R (T (t))２ ø ２ Qd öR (T (t)) æ ÷ expç － Qd è RT (t) ø æ æQd(T (τ) －T (t)) ö ö (８) ÷÷ ç１－expç RT (t)２ è è øø Subs t i t u t i ngEq (８) i n t oEq (７), Ve c anbeex Ｇ : r e s s e da s p / Qd öR(T(t))２ æD０ ö ３ ２ æ ÷ xpç － Ve＝VN ∗g ç ÷ {e Qd èφ ø è RT(t) ø æQ (T －T (t)) ö ３/２ [１－expç d ０ (９) ÷ ]} è R (T (t))２ ø
∫
∫
∫
∫
∫
７０９
Subs t i t u t i ngEq (９) i n t oEq (３), f c anbeex Ｇ r e s s eda s: p / Qd öR(T(t))２ æD０ ö ３ ２ æ ÷ xpç － xp{－N ∗g ç ÷ [e f＝１－e Qd èφ ø è RT(t) ø æQ (T －T (t)) ö ３/２ (１－expç d ０ } (１０) ÷ )] è R (T (t))２ ø Upt onow, t hedeve l opedJMAK mode lha sbe en e s t ab l i shed． I nEq s (９) and (１０), t heva l ue so fN ∗ c anbee s t ima t ed by t he me a sur ed p r i o raus t en i t e r a i ns i z e, a ss e eni nTab l e３．Twoo t he ri ndepend Ｇ g en tpa r ame t e r so faus t en i t i ct r ans f o rma t i on, p r e Ｇ e x Ｇ o n e n t i a l f a c t o rf o rd i f f u s i o na n dt h ea c t i v a t i o ne n e r p gy f o rd i f f u s i on,c anb ec a l c u l a t e dou tbyf i t t i ngt heexpe r Ｇ imen t a lda t aandt hedeve l opedJMAK mode l． I tc an beobs e r vedt ha tt hef i t t edcur ve sa r ei ngoodag r e e Ｇ men twi t ht heexpe r imen t a lva l ue s, a ss e eni nF i ８． g TheQdi sr a i s ed, wh i l et heD０i sl owe r edbyi nc r e a s Ｇ i ngt an t a l umcon t en t, andt heva l ue so ft hema r el i s Ｇ t edi nTab l e４．
No １—Spe c imen１; No ２—Spe c imen２; No ３—Spe c imen３．
F i ８． Comp a r i s onb e twe e naus t en i t ef r a c t i onme a su r edand g f i t t edbyk i ne t i c smode lo fRAFMs t e e l s． Tab l e４ Ki ne t i cpa r ame t e r s, a c t i va t i onene r o rd i f f us i onandp r e Ｇ gyf e xpon e n t i a lf a c t o rd e t e rmi n e dbypha s e Ｇ t r ans f o rma t i onmode l o fRAFMs t e e l s Tan t a l umc on t en t/wt． ％
Qd/(kJmo l－１) D０/(m２s－１) Er r o r/ ％
０
９４ ６
２ ８×１０－５ ２ ８
０ ０２７ ９８ ５
０ ０７３
１０５ ０
１ ８×１０－５ １ ３６×１０－５ ３ ０
３ ０
The me c han i sm o fau s t e n i t i ct r an s f o rma t i on ma i n l y d e e nd sont henu c l e a t i onandt hed i f f u s i on Ｇ c on t r o l l e d p r owt hi nt hemode l．Espe c i a l l a rbond i f f us i oni s g y, c t hema s t e rf a c t o rt ocon t r o lt heaus t en i t eg r owt hi n [ , ] c a rbons t e e l３１ ３２ ． I tc anbef oundf r om Tab l e４t ha t Qdi si nc r e a s edbyt hei nc r e a s eo ft an t a l um．Theva l Ｇ ue so fQd f o rt hes amp l e s wi t hd i f f e r en tt an t a l um con t en t so f０ wt ％ , ０ ０２７ wt． ％ and０ ０７３ wt． ％ a r e９４ ６, ９８ ５and１０５ ０kJ/mo l, r e spe c t i ve l y．The va l ue so fc a l cu l a t edd i f f us i ona c t i va t i ona r es imi l a rt o
７１０
J G ． Chene ta l．/Journa lofI r onandSt e e lRe s ear ch, In t e rna t i ona l２４ (２０１７) ７０５－７１０
t heva l ue so ft hea c t i va t i onene r o rd i f f us i ono f gyf [ ] c a rboni nf e r r i t e (８０ kJ/mo l) ３３ ; howeve r, t he r e a r esomedev i a t i ons．Th i sc an beexp l a i nedbyt he f a c tt ha tt hei nc r e a s eo ft an t a l ume l emen twou l dr e Ｇ t a rdt hed i f f us i ono fc a rbondu r i ngaus t en i t i ct r ans Ｇ f o rma t i on．Henc e, t he me chan i sm o fd i f f us i on Ｇ con Ｇ t r o l l edi sno ton l t h ec a r b o nd i f f u s i o n． I n R A FM y s t e e l s, t an t a l umi sac a rb i de sf o rmi nge l emen t．The numbe ro fund i s s o l vedc a rb i de si nc r e a s e swi t ht an t a Ｇ [２１] , l um wh i chl e adst oa mo r ec onsump t i ono fc a r Ｇ boni n ma t r i x．The r e f o r e, t hec onc en t r a t i ond i f f e r Ｇ enc eo fc a rbon be twe en und i s s o l ved c a rb i de s and ma t r i xi sl a r i chi sf avo r ab l et ot henuc l e a t i on ge, wh o faus t en i t e．Howeve r, t heund i s s o l vedc a rb i dep r e Ｇ c i i t a t e shavet hemax imumt he rmodynami cs t ab i l i Ｇ p t i ch wou l dr educ et hec a rbond i f f us i onc oe f f i Ｇ y, wh c i en tands l ow downt heaus t en i t i ct r ans f o rma t i on r a t e．Att hes amet ime, t hes t ab l ec a rb i de shavean e f f e c t i vep i nn i nge f f e c tont heaus t en i t eg r a i nbound Ｇ a r i e s．Th e r e f o r e, t h ei n c r e a s eo ft a n t a l uml e adst ot he de c r e a s eo faus t en i t eg r a i ns i z e．
４．Conc l u s i on s
(１) Th ep r i o ra u s t e n i t eg r a i ns i z ei sd e c r e a s e dwi t h t hei nc r e a s eo ft an t a l umc on t en ti nRAFMs t e e l． (２) Theaus t en i t i ct r ans f o rma t i ont empe r a t ur e s, Ac１ and Ac３ , a r ea l li nc r e a s ed wi t ht hei nc r e a s eo f , t an t a l umc on t en t． I nadd i t i on t heaus t en i t i ct r ans Ｇ f o rma t i ont imei si nc r e a s eds l i t l t ht hei nc r e a s e gh ywi o ft an t a l um． (３) Th emod e lo fa u s t e n i t i ct r a n s f o rma t i onk i n e t i c s b a s e donJMAK mode lwa se s t ab l i shed, andt hep r e Ｇ exponen t i a lf a c t o rf o rd i f f us i on (D０) andt hea c t i va Ｇ ( t i onene r o rd i f f us i on Qd) we r ec a l cu l a t edou t． gyf (４) Thei nc r e a s eo ft an t a l umc ane l eva t et hea c t i Ｇ va t i on ene r o rd i f f us i on o fc a rbon i n RAFM gy f s t e e l, wh i chi nd i c a t e st hemo r ed i f f i cu l td i f f us i ono f c a rbondu r i ngaus t en i t i ct r ans f o rma t i on．Tan t a l um, a sana l l oy i nge l emen tf o rc a rb i de sf o rmi ng, r educ e s t hec a rbond i f f us i onc oe f f i c i en tands l owsdownt he aus t en i t i ct r ans f o rma t i onr a t e．
Acknowl e dgmen t
The wo rki sf i nanc i a l l o r edbyt he Ch i na yspons Na t i ona lFundsf o r Di s t i ngu i shed Young Sc i en t i s t s (Gr an t edNo． ５１３２５４０１), t heNa t i ona lNa t u r a lSc i Ｇ enc eFounda t i ono fCh i na (Gr an t edNo． ５１５０１１２６), andt h eNa t i on a lMa e t i cCon f i n eme n tFu s i onEn e r gn gy ( ) Re s e a r c hP r og r am Gr a n t e dNo． ２０１５GB１１９００１ ．
Re f e r enc e s
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