Effects of tantalum on austenitic transformation kinetics of RAFM steel

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...

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         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

706

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



0 􀆰06 8 􀆰91 1 􀆰73 0 􀆰37 0 􀆰05 0 􀆰22



0 􀆰04 8 􀆰93 1 􀆰71 0 􀆰44 0 􀆰04 0 􀆰22 0 􀆰073 Ba l anc e



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 􀆰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

􀅰



(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



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/(kJ􀅰mo l-1) D0/(m2􀅰s-1) Er r o r/ %



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 .

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