l...ll'TE('ll JOI'Ri\.'tL Oh'I|i\'(;lNEt:lll\6 l,\'1) TIt('lI\'Ol-(r(;r' I(l) J00.t:61-:4
B E N C H N I A R K I N G
A N D V A L I D A T I O N O F H O T I T O I , L I N G
SI NI TII,AI'ION NIODE
I-S
N l o r g r i d g c . * A . l t . a n d O d e r v o l c , O . A .
l)cpartnrcnt ol' llechanical Lnginecring. I r n i v e r s i t v o l ' Ib a d a n . lb a d a n .
, l B S T ' R . 4 C T
trlotlrcmatical models representing the various stilgas in the hot rolling process of stcel
productiorr x,erc produccd. Simulated models us(d tttre vilidateil usiug tha I'-XCEL packoge und
tltcrt srtltjccted
lo o sensitivitl' analysis undcr idenlicul c'ottditiuns
to pruli<'t tltc oplirttur,t optriltittg
c'ottditiotts
ttndar x'hiclt thc esscrttittl
process strps (il,, ba curriul out.
'fhe
results sltox'ed tltot Jcrritc groin siit, is rrrore sclsitile to tltc ratuined stroin than to the
coolirtg rile or thc uustt,rtite
gruin size. It tt,us olso in.ferred Ji'om the xwrk thut n drop itt tlrt
austenita-lt:rrite
(y-{t ) lrunslbnnation lemperulurt: ltuds to un increose in tha tcnsila strength oJ
lha stctl. irftrs is irt tgreemct,t rtitlt ittdustrial pructic(s.
K c v l o r d s : I ) r o c c s s n r o d c l r r r u , h o l s t r r p r o l l r n g . n t e ' c h a n i c l l p r o p e r t l c s , s r r t r r r l u t r o r r * ,\utlror lo nhortr corrcspondcnce should hc acldrc'sscd.
Svnrbol I ) l),,. d,,
t '
t
\ 1 1 ; S .
( ' . o , . o , ,
d,,
o ,
o , , , o s t tl
d l t t
t €
, l r ' ,
€
t,
a r
o,t
o . Y S . L . \ ' . S . . o ,
( ' , . . f " Z
x. x,...
F.s.
x.,.
xR\
t i , , . 1 . , i . l i i r , ' . t \ r r ia
R
SR\
N o l a t i o n l l e a n i n g
Glain sizc I n i t i a l g r a i n s i z e Tcnrpe'rature -l'inrc
Ift'all llo\\' slress
Steady state stress
Saturatiorr stress
Pcak stress S t r a i n
Peak strain
Dynamrc recrystallizatron stress
Strain ratc
D;'nanric rr'crystallization strain
Critical strain
Sanlration straiu
Retained strain
Dislocation strengthe'ning
I-ouer yield stress
Tensile strength
Zener-Hollon'lon parameter
[:raction recrystal lized
Time for 500,6 recrystalhzatron
A c t l V a t r o n e n e r g y
Unir c'rsal constant
Static rec r1'stallization
[.init !l rcrons Nlicrons
"c
Scctrnd t\{t,a
Ivl Pa
T,IPA
\,tPa
t\4
Pa
sccortr'l
t\{Pa
il{Pa
\{t,a
,llorgridgc,,4.R. onil Oletvile, G..4. i L.'lltTECll Journal ol Enginutriug ond Terhnologt' l(l) 2003: 6l-'1
Qur. Q, , .'\ctivalion encru)* lirl statrc r!'crystalliratl()n KJ rnol /
t 1 . 1 1 1 . r 1 , , . . [ ) , . l) . ; . I ) . , S t a t r c r e c r t s l a l l r z a t r o n g r a l n s l z c \ l i c r o n S
S, Urarn srrrlacc to graln volunle ratur
Q.r l)eformatron activation cncrgy KJ nul
l). (.iratn size aiier uratn gr(twth N'ltcrons
i. f tnre allou'ed tor grarn gro\\ th SeconC
Q* Actlvation cnergy for grarn gros'tlr KJ nrol
t,n Inlcrpass tinre Second
'l-,,s,,, 'l"inre'lbr
95')1, or full rc-crystalllzation Sccontl
d , D Austettite grarn srzc \'licrons
Xpr. Xu,,, Dynantically' rccrystallized liactrorr
l),1,,,, t1.1,,,. l)r,rr. f)1,r Grain size atier tlynanric rccryslallrzation Microns
I),,,.1,,. d,,,,1. i|1y,,1p1. I)111y. Grarrt stze alter n'retadynanlc recrystallrzatrott i\4lcrons
I),,,,.., d,,,,,
I)n. [)r,R. I), Partiall,v recrystallized grain srze l\'licrorrs
( ' . t l .4 . 7" . ( , C o o l i n g r a t e " ( ' ' s e c o n d
,l ,,. l),, I;crrilc' grain srzc \'licrons
( ' c q C a r b o n e q u i v a l e n t W e i g l t t ( ) i ,
'f,r,rir
Tenrpcrature at shich transformation begins uC
-l
,,,r Mean transtbrnlalion lemperaturr' for ll'rrite "C
\,',. \, Volunt fraction of l'errite
S,, Pearlitc intcrlamellar spacing Nticrons
tl, Translirrmed plrase lrardncss ltrr ferrite Brinell
lln Transfornl!'d phasc lturdness lbr pearlite Brincll
\',, ; Volunr liaction lor pc:rrlite
lln -l-ranslirrnred phasc hardness firr bainrte Brinell
Vu Volume ttactron for blrnite
\h,,, EllL'ctive Niobiunr conccntralrorr Weight 9i'
Q,,nr Activation errergv lilr nretadvnanric rccrystallization KJ,nrol
L,,rrrrpr 'l'irne lbr 509i, nretadl'nanric rccrystallizatton Second
[ \ b 1 , ' F . q u i v a l e r t t N i o b i u n r c o n c c n l r a l i o n W e i g l t t ' ] i '
1,,,. I .r,\ No recrystallization temperaturr' "('
K . S r r p c r s u t u r a t i o n r a t i o
l ) , . , , , . I , , , , r p . t p . . [ t , , , , . P r c c r p i t a t i o n t i n t e S e c o n d l l s l . \ I l i g h s t r e n - u t h . l o s ' a l l o y
l('c l:uce centrr'd cubic
| \ ' t R o D t r ( ' t ' l o \
l l r s t o l r c . r l l r ' . t l t e d c v c k r p n r e n t a n i l a t l r ln c c r n c r r l o I s o c r c t r c s h a v c h c e t r ir r t r n r a t e l y t i e t l { o r r r e n r b c r s ' a l - . r l r t r t o p r u d u c e a n c l n r a n t p t t l a t e n r u t c r r r l s t t r l l l l t h e r r n c c r l s ( \ \ ' i l l i a n r . 1 9 9 7 a r r c l l ) h r r n r r a l ! ' t i l 1 . l ( ) l x ) ) I i l r l t c t v i l i z u t i o n s l r u v e b c c n t l c s r s n a t c d b v t h e l e rc l o l ' r t t a t e r i a l s ( | c ' \ ' e l o p n ) c n t , r c . . S t o r t c A g c . l l t ' o u z c A g e ( O d c r r o l c . 2 0 0 1 ) . ' l ' l r e c l c v c l o p r n e r r t o l ' r r u n v t e c h n o l o g i c s t h a t n r a k c Iruntan criste rrcc s() t:orttlirt luhle ltas br'en l n t l u l a t c l ) , i . r s s { ) c l J l c ( l i r ; l h t l ; : J c c c s ! ! t ' i l i t } , o f
r r t tl r l r ' rr L r t c l i : t l s .
Siccl:, rre orrc 0l'the n]ost cornntonlv Used c ( i n : t l u ! [ i ( ) l l I r l i . r l c n a i s . A n e u ' c l a s s o l ' s t e c l 5 ts t h e i o ' r . r l l r r r . lr r g h s t r c r r g l h v a r i c l y . - [ ' h c r e rs r r t i l i t r ' , . r l ' s l r ' t ' l t i ; r ' ( f r r u ' l r r l l r l , r r d c o n s l r r r c l r o n ; r l : r f r r l r , : ; r l i o t t s r r ' s t \ o n ' l h c l i c t t l u t r t c l l t h t ' r ' r ' a r . l i l v s r r r n l i c d r n a
\
u rde rarrge ol' dilll'rc-nt product fornrs and rvith a rusclirl range of nraterials propertics. the use of
nrethocl shiclr imparls such in.rportant characteristics
on thenr during their production should be carelirlll'
krokecl into, artd hcncc, the choice of'thc hol rolhng
process for stecl produclion.
Rcsearch into controlled hot rclling
nrodeling arrd sinrulation has beerr going on since the
1 9 6 0 ' s (' l ' a r n u r a q t al. 1988. I-aasraoui a n d J o n a s , l 9 9 l) . l \ l a n l , r n o d c l s h a v c b e c n s u g g e s t c d o v e r lh c yr'ers. bv rcsearchers. to simulatc the lirll range of the dill'erent slascs ilt hot, controlled rollrng. A detailcrl rcvrew ol'thcsc rru.'Jcls ts avaihble rn litcraturcs (Cser et al. 1999, Phanirrj et al, 2000). These nndels have
saved stc'el industries all ovcr the rvorld millions of
dollars: lirr the 1' have considerably rccluced the
nurnbcr' ol c\pcnntcntal test runs nce dcd lirr thc
produciron ol'stccl \\rth lnrprovc,l plopcrties nec(led
tlorgridge..-1.R. anl ()dtx'ole, G..1.,'L.'lI'TECll Journal of Engiueuit,gfln.l Tuhnolog.t' l(l) 200.1:61--l
l!'\c.il Jllct's havc userj drl-lr'rcnt c\p!'nmental
lilclllods to crfr\ out such slntuttlton: ticpcllcllng trt the lrlrouul ol- total detilrnrirtrt'rn. sltalrl rates.
tenrpcraturc. and tlpes ol- sllnulation cquipment
a r r i l a b l e ( l ' u J c u s z . 1 9 q 2 . \ l e d i n a et al. 1996. Bai q! rl. l9q(r rnrl [)-1rkl el !1. 199] Phrniraj et ql. :(-r0(). elc) I-rborrtor') hot rollinr. llot conlpressron tests. hol torsl()r'l tr'sts and tensil(' tr'sls have bec'u t l t t ' t t ' t t l s l i ( ) l l l l n ( 1 1 1 .
Strtcc thc uitrntlttc tinl ot' .r rrttrtlc'ller rs trr p r c d l c t .r s . r c c t r r . r t r l r J s p o s s l b l r - l h c n r l ' c h a n r c a l p r ( ) p c r t l e s o t n u i r ( ) - J l l ( ) \ s t c c l s li r r t t t r i t z u t t o n r n dr'slgn rnd p|o.luctrrru: rehcatlns of the stecl belirrc rrrlllng nrust be accurltelt taken carr' ol so that the
.rstrnt rreld ol'tlrc steel and the proclucts clualitv
could he cllectrr r'lr optrnrrzed. Other inrportant
lictors inclutJe florr 511s55. statlc recrvstallizatron.
pt'rk strc'ss. tlr nantrc rr'cr)'stalllzatron.
llretld\ llrnlc reclr stallrzation. grain gro\\ th. rto-|ecrr sta I lrzatrrru t!'llrpcrirlure. prec ipitatroll kinetrcs.
p.rrtral rccrrstallrzltr,rn. accunrulatetl strain and
l.rntr' trlnslbrrrr;rt:ons $ hrch are
thernlr-rrrcciimic.rl propr'rllcs covering the r'ntire span of t h e h o t r o l l r n s .
l ' l r r ' p r e s e n t s o r k a i m s a t p r o r i d i n r l s a v s i.r rrhrch tlle c:rstru i'reld of the dil'ti'rent steels cirn hc !:rc.ltlv lnll-rro\cd. the developrrrent of nxrrc crtr'rr\ -cl'tlclcnl pr ocesslnS tr'clln(rlosl lor thc itr'cli and tltr' tlek'rrnrrt,rtl()r't of nr()dcls that rrill oltlnlrlc pr r)r'lu.'ts' !]tlrlll\ arr.l thc process e l l ' i c r c n c r o l l l l c h o t r o l l n r g .
} I A I ' E R I A T - S A \ D I I T . I ' H O D S
Erpclrnrcnls \\'crc carlted out to Jclernlrte lhe hr'hlvrrrtrr r)f sonrr' stc-el sallrpl!'s to Jiiertaltt tlte strarrts. stlulll rlllcs. tentl)r'rttures alld olhcr puranlelcrs Jl'l'ectlng Ihc prtttluctton antl .-JStulg rreld of stcel. -flrr.' str-'el san'tplt's Nerc-specillll brought tirrrn Finland end sonrr' of tltetr prr)pertlr's $ere .rlreadl' kno$-n and iletailed in Tahlc ll. Tests c'n these s'ere in uniarrrl tension. rorsir)n and conlpressron of axiall) s!'nurretncal or
plane sanrples. Surface treatment and pr€paration
\\ere clrned out on the specintens. These rrpr'ratror'rs prcpared the Specimens used lbr a later
nlc'tallrrgraphrc slu,jies conducted on thenr for the
Jetcmrinltrt'rrr oi the crtstal gralns. their sizes and
sraln gro\\ th $ hich occuned tlue to thc heat
treJtnreut the slrrrples \\.e[e sub-lected lo.
fhe cirrrc-r'rt concerns rrl ntaior steel
productt s rr ltrclt rrtr olvB tltr' P11rk'ction of thc c n v l r r ) l l l t l c r ) t a n . i c 0 l n P C l t l t r r n ' i o r l ) rt t r n r - t r t t l l s . u p g r a d l n g t l t e .1 r . u l t t r o f t h e p l t r t i u . r h r i n r p r o v r n g t l t e ld . t p t r r e c ( ) n i r r r l s \ s t e n t s . u i l l ( \ r i u ! n t g t o t r l s t e e l r r ) l l s t o r g d u c e r ' , r l l \ \ e a r . rc d u c t l o n r r r th e c o s t o l ' p r o d u c t r o n i r \ c i r n t r r t a t r n g l l o n - f \ s c n t i a l p r o c c s s
slcps. nun\ ol' rrhrch are cnerr.:\ lntenslve and
elrnu:ratitrn e.t- thc rc'helling ploccss rn i'rvour of . i r n l n r r c rc c r ) s t a l i l l a t l r r n h a v e b c c o n r e l n l p ! . r a t i \ e \lorc intportrnrl\'. ncrr nrc'thtrtls .rrt. beirrg tor . i : : i i t i a s t i r l ! . r n . i r o l l r r r g r r l t l t r n s t n p s .
\ l r t h e n u t r c a l n l r t l c l l r n s a n d s r n r u l a t r o n o l t h e
propertlcs of hot rolled products are being usccl so
that the ntotleis constructed coulcl be r'asrlv
nunipulated to yieltl a nution picture ol'reality. For
t l t i s n o r k . t h c s r . ' r r r l d d i t i o n t o t h e u s e o f t h e I : X C l l l packagc g!'l.rr't'atr'd rlata rvhich sere latcl conrbirred s i t h t h c e a r l r c r o h t c r n e d c r p e r i n r e n t a l r r ' s u l ( s a n d rtieqrrrtc "ad;trstnrcrrts" \\ cre nlade bct\\ ccll lh!.s!' r uiucs lntl lll()s!' rvarlahlc li'onr rndustrrc-s untl turlls. Nlth thr' rcsult tlrirt bettel opelaling contlrlions \\'erc pr()posc(l Ior tirc' hot rolling pl'ocess uscd ill n r o l l u c t l ( ) n ( l l s l f L'1.
'fhc'rc
ilrt several ptrssrble oblcctrr c's that
rnar' _lustriv tlre nrathenratrcal modelling of the hot
rollrng prt)s1'55. fhese include' the analysis ol' nretal tlou and or thc nrctallur-glcal e'r'ents during and alier
the pass. thc ott-line scheduhng of the tlrati. the
on-Irnc' adatr'rtnc control of the process or the dcsign ol' the nrill: thr' rolls. the tiarrre. the drire spindle. thc bclr rngs. or thc scre\\'do\\'n system.
I T T - S T : I - ' I ' S A N D D I S C I ' S S I O N S
.\ppcndices I and 2 give the values of thc
paranrcters usc'd in the validation of the sinrulated
nnrlcls. The resrrlts obtaincd fi'ont the validation ol'
thc rrro.L'ls in llre process stc'ps are as prr'sented lrl l'.rhle ll .,\ conrplrison ol'thesc results \\'ith thosc ot' t h c ( ' u r b o n - \ l a n g a n e s e 1 C - \ l n ) s t e c - l s i s c a r n c d o r r t ln
lahlc IIL .fhc corrrparison ntade lrere arr those
o h t a r n c ' d f l t - r n r t h e a v e r a s i r t g o u t o l ' t h e r c s u l t s s r t l t srrrrrlrr averagc'tl values lirr thc ( -\ln stc'cl lirr tlte lrot. c o r r t r o l l c - d r o l l i n g p r o c e s s . ' [ ' h r s r e v e a l s a p o s s i [ ) l c
lnlluencc of both the nricro-allo1 s arrtl thc
su'hstrtulronal e lenlents orl the properties ol' the
dr l'ierc-nt sleel protltrced.
The nujor microstructural changes that
t'rccurleti due to the addition o1'both micro-alloys artd
substrtutional elements ate grain retinenrenl due tcr
recrlstallization and strain - induced precipitation ol'
the crrbo-nitrides. The strengthening of the steel
oblarned are lluough precipitation hardenin-u and thc
refinenlent of the ferrite grains through reduction ol' t h e a u s t e n i t e - f e r r i t e ( / - a \ t r a n s l b r n r a t i r r n tr'lllpera ttlre.
-l'hc'
percentage cortrpt-rsitious of additires
used tor the ralidation of thr' sintulated nrodels arc'
l l o r g r i d g t . . - l . R ' a n d ( h l e v o l t , ( i . 1 . I t l l l . ( l l . l o r t r t r , t l r t l l i n g i n c c r i n g u u l I t , t l t n o l o g t , l ( t r 2 0 0 l : 6 J - - J
l l S O s a n d 0 5 l t o . l - 1 ) s r ( ' . . 1 \ r ' . t r \ r l \ ) u l L ( , l t ) l ) J i l \ o n \ \ l l h l h c ( ' - \ l n ' t r ' i : i
I h c r e t l r r e t r o n u t \ l J l r c J r t r i r r 1 , , 1 . , , 1 , ' r , " , ' a ! r r a i l l s i z e s ( h o r n - l . i t o 3 0 . - s ln t c r ( ) l l \ . iu t d i r ( ) t n - 1 2 l o l ( ) t ) n l i c l ( ) l t s t c \ p c ! : t l \ c l \ ' ) . r r r i l r r h r r t r t l t ( ) I l , r . i r r c i ; r u s l r c l \ \ t t i r . ' t l l . u t u l ( ) n l t l c r r t t c g r a r r r s \ \ l l t r ' i l t u l p f ( ) r c r l i t c n t u " i r a n t c a i t) r {) l ) c r l t c s o i t h e p r ( ) d r r c l s . . \ r r o l l r r ' r a ( ) n t n h u t i n u l i c t ( ) l r s r c d u c c d
I a b l e l : l ) r r c e n l l ( ' o
l i o n o f A d d i t i r e s I s r : r l
- C o n s t
Percentaqe C
M n
g l a r r ) g r o n l i l . t l l r ' f r r r e l . r t l r r L r r r - r r c r c c r v s t a l l t z u l r 0 n t l r o r n 5 . 1 . 6 0 t o - 1 - l i t r n l r \ t( ) l t \ t I h e s e o c c u l a s a r c s r r l t o i t l r c S t c a l l ) r u l i r r t ' , i r l u ! r ( ) . t t u t l u r e i b n l t u ( l .
- l h c
! f ( l i l ! ll { ) l ) \ l t i l t l f c l l n e n t c n t O h t l t n t ' t l l l r r o t t s l t f ' h c . l r . r r r ' : t ' r ll r l l o . . : r r n c d a b r t v e l e t l t o a l r r s l t c ' r t t i t r r n . r l r ' l c n : t l c \ t r e n S t h 1 a c h a n u e li o n r i l i ( ) . _ i t o 7 9 6 \ l l ' . r r
t l t - - l . l n t ' ' \ ' i A 3 6
l-i5iav
tl'i.rl ruo
0 . 1 5
0 ? 1 | 0 2 2
r, e.r-l-,r-iTlllsr
0 0J r ijliS
i - - i
, -
i - .
'
r-lb1El-'--:
ozAl
n2t 1
0 0 1 5
0 0 9 5
0 J 5 I
i o r , U 1 5
1 1 2 1 2 6
i 0 1 0 5
0 3 0 i 0 1 s
, . 0 . i ; U O a I 0 0 0 30 1 8
| . 0 2 9
0 0 2 t
i 0 1 i O C a r . 0 0 5
0 . 4 6 i 0 { r 7
l l o r g r i l g t , l . R . a n d O l t t t o l t , G . . - 1 . ' l , l l I L ( ' l t , l o u r n u l o | l i n g i n e a r i n g n n d I ' e c h n o l o g . t . lt I t ) l t t t ; 6 1 . - 1
T a b l e ll : V a l i d a t e d
M o d e l s fo r Other Types of Steels
I
4
!_esPol
t (Q,l?_:
t-
eglVl
Lcl)l
Ve|trc("c)
I
1 2 1 3
6 1
. . i
r
1 3 2 9
6 8
+
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_ s 2 9 5
4 6 5 0
N O
i C O N S T
9rql _9toqt! i q [e[eqti n g
M O D E L
l s o t h e r m a l G r a i n G r o w t h M o d e l
5_
I
Sljr4l
d -Qo_*f
rt e_xp([;/T)
!
' '---r--- - - -- - -- -'r--crain Size in Continous lg.hggling llodel
rqOq,[ 9. rlow_
S_!rsss_
wl
9_q9!s
' I
l _ _ _
-, lyQ. ry
e,_i__iq9l!9l__j
__
M O D E L
Vatue
(MPal
7 1
4 3
g
I
"
o = o t ( o r l : 9 r J ( 1 ; e x p ( - F , r , r ( e e 0 1 " 1 1
1 0
1 C r - l r r t o ,
t r r t F S ' ; ,
1 , 1 n = ( M F S , , , * , , r , , ( 0 . 8 3 5 + 0 . 5 1 N b + 0
0 9 8 M n
i ____ i__,___
L_ to.l?8cg"110,1{aVp,'1fQ.!Z_5v+o.g1ryrlfl
Is,ol1!(9scX:rr!
? Q n , 1
_
4 1 7 0 B
4 0 2 1 1
I
T a b l e ll C : S t a t i c R e c r y s t a l l i z a t i o n
, _ -___
!(i!,-e_t
i9-s
9! s t a tlg !9_c1y9tq!l
f z a t 19
ry M o { el9
----.----.l-MD NO i
.CONST i
[\,4ODEL
I Value(s.1
r _ 1 1__ - !4q-T_r_-_l.lb
L
__ _- t. r:Ae
oe
pDoexp(Q/RTJ
_ j
OaqA j
-
12- i-- y- _-'_--
- --,Ii'i=A'exp(QllRl)
- - - 1 2 ss
,
i
1 3
i
"
i _ ____-.
_,+-*,_
_tl_r_Ar9sg
rE' .'exp(Qr/RT,-)-
_ _, _
*_ _
q,3_Z
t __ 1! _ _i r'ro-e f_
_ _____,_ to
s=2,4{1g_llq_l
' 'l_I_e}pglgggqBL _ ___ i 101 Z-8 l
. 1 ! _ _ i _ " _ t t q 5 : l . O . q ] 0 t 1 i " l e 5 p ( s 5 ! Q 0 Q l { T L
-, -,_. -1e_
___1,___lLo.tr
I
_ to
s=3
677'10'2oDftqlg;ryerpQlgggAllD
| _ _0
q1__
l
r--'t=--\!-
-i-- -:- -;-=-
br|Ql-1-9-1-rl-g:!gilelp€9998q8ll-- -- . 2?7J
10 ,:,
;_ _ Ls_____L
Nq-_Ti:IIo_
i _____
_
to
r=a41
'9p(a/RT)
_
'
81 71
I
: - _ + _ _ _ _ _ _ _ _ ' r , J " - : ; - ; - . j . = - j j . J . - _ _ _ - _ _ l
r _ 1 9 _ t
V _
,
_ _ _ L u _ s _ = _ 1 0 3 3 ' 1 0 ' 0 e ' ' 0 o o e
2 6 D e x p ( 1 5 8 0 0 0 / R T 1
;
_1.04_-t i
r-- ?9-- J---
r- --
-I-ur:ql1-00.19
'€-1{'Dsp(aqqqq0l8ll--f-!lo
---t
;-zr
i crrilq-vlQ l=-
. --.-
Tos=1.57*10'1ae'?sdlp(zzrooo{UL
--+
-15-,_4i--l
r
22
i
Nb-Tl i_ ____=b,:3.677'10'20D2(e -0.08)2e
'0 '76exp(:q!qg0ET)
_l_:oU
j
;_L3*__ _J__
tul_o_-_Tr
_t
_ , T,r_i,_=_1q:ot'e-t
tte't'to't tt
rlqoE-Tl __)__?_e]1
-t:
i -J-q---l---
. l - _ _ , - - - _ 1 _ _ . - ' - _ - f f i | - _ ^ ' . .
r-r-v
t, ^'=5't0.'8(e-0
085)'3
5D2exp[280000/RT]
; -2,-51 - ,
L -- 25 .-. j-gupeqo
a6- i-v:J-
,
!s.=e,3'10lrlo!1fiagoogo,n1-
---
i oot ,
' t,rgriilKc, ,1. R. unil Oiltx'olc, G..4. / L.4l'TECMournol of Engineering aud Tedtnolog)' I ( I ) 2003: 61-74
Table ll C Contd.
Io::llz11q|iqlj'"xp(271_000/Rr)
| s5 44 _
t 6 5=8.31 - 1 0 ' ' ' d t o t - t r r ' f - u " ' e x p ( 2 6 3 0 0 0 r
\ l ^
c o N s i
32 -- * Ir-V .:
__*oro::qfc_o_"gl{9lp$!qge0/Ell
d,""=Ado t 3e-Pexp(-Qo,/RT )
.___3,1_l _U-I!!!-_j.
D,",'=B*CDo'e-tlexp(Q50000/Rf
)l'
I _ _ _ $ , _ ,
N b - v _ _ _ ]
Qr"]=-
1 2 s +24.4
(v* N b )o'N'
ooDoo
tsLlfu4GfqqO/El
? A T i - \ /
v v I r - v I
D , = 4 . 3 ' 1
9 5 . 7 D 0 ' s t ' o
t t e x p [ - 3 5 0 0 0 0 / R
3 7
| E u t e c t o i d l
D,=9.91
D0
54t4
65
et-o
texpl-1
7540/RTJ
44.46
38
i
V-T
__g:1
S.tDt
ttr" tt
st"
terpf-15000/RTl
r 3 9
Austenitic
=2.24e4 sDZ-o 06i + o
=83.9e-0 537D0 3552-0 0655' 4 1
Cr-Mo
0.678-0 67I
A36
0 36€-0 368-28060/RT
i
4120
d,., n = V 3 " d oe
u
r'e_t
e.Ip hL2/ BI)
3 7 . 8 9
_____
Table ll C: Static Recrystallization
I
Grain Growth After Static Recrvstallisa
r
N O .
i C O N S T
Growth During 1st Second Model
!!- ,:t Cr-Mo I
-
dt=d2s^^*4.0"10t(t,o-4.32t0
s)exp(-1
1lqqqiBl
Growth After lst Second Model
i--;5 T
I
d ' = d ' s n x + 1 . 5 ' 1 0 ' ' ( l o - 4 . 3 2 t 0
s ) e x p ( - 4 0 0 Q ! 0 / R T )
Table ll D: Dynamic Recrystallization
C r i t i c a l a n d P e a k S t r a i n s M o d e l s
M D . N O . i
' , O O N S T .
I
a s _ i _ a 1 6 _ _ ;
_ _
|
412A
,
'ud'"-'uj.'lo_lg"p!2q{0_91RT)
I
2.05 ,
i
t t . o q
4 1 . 6 5
1 1 . 2 0
4 3 . 0 1
= 1
. 1
4 9
, , 1Mo
Mo-Ti
i
4120
M O D E L
=0.0040d0
sole'
41000/RT
0 . 8 4 E
4.3'10-3Do 2ozo 174
= 5 . 9 " 1 0 - 3 D 0 m z o 1 7 4
5.24',1
0 szo 18= 7 .07'1o4dzo
1 5
tn=A'1 *d.b' tbzexp(P 1 /RT
50
Ye!-!e--__,
1 . 3 6 I
1 . 1 4
1 . 3 1
1 . 7 9
0 . 6 1
2.49
0 . 5 0
0 . 4 2
5 2
i 1 s 3 B V
i , ,
- - ---+---'-
-.-54
i
436
I
=l-i
edQ&--30_
_ r 1Q3e/
_+ __
_!q9_=J2'_4n'd"otlelp(jlRL
i o ro i
3 1
I
c r
,
1 o s = 2 7 s ' 1 0 - "
d - 0 1 2 s r ' 2 4 s d 1 0 6 e x p ( 1 8 4 0 0 0 / R T )
I
g . z o
i
T a b l e ll D Contd.
illorgridgt:, A.R. anl Olcx,olc, G..'1. / L.4I'TECII Journal ol Engineering and Technology lf t I )00.1: 6J-74
4 1 Z V :
1538V I
56
i z o
|
7 1
7-i
0 2 2
57
C r
i--:_-
^-' ry-BegytEljlqliel-Uoq4s'
(vglrrne_Ereclio_1Lx)
_ _1=_ _ I
I ruo i corusr. I
rrloDEL
i varue
i _ _ . _ : : i t l
i 5 8 i C r - B i X ^ o ( E l = 1 - e , x o [ - ? 9 9 6 t ( r - r ^ ) / ( r . - r ]l ' ' ] i o t s i
;
58
I
cr-B *1---
xaeG):=-1:qlpL?ggtlle-_ed1le,-e,ll''J
_ ,r_ _Q_35_
I
i t r r l l { i - , ^ \ - . ^ - - - i ^ n n ^ r - , - r t l l
_ _Ipdq= 1-efpta,9i€(s4il
0 27
60
I
e ) = 1
3lq4,(L,r)l:"
)
0 2t
6 1
'-o\l(o
0 1 3
K i n e t i c s o f
i z a t i o n M o d e l s
'CONST
M O D E L
Velqe(s,I
=6.66"10-6e
'-o
stexo(
1 36000/RT
2 . 5 4
t o
s = 6 . 6 6 - 1 0 - 6 e
' - 0
t ' e x p ( 1
1 0 0 0 0 / R T
i r - ^ ^ = 6 6 6 * 1 o - 6 r ' - 0 6 1 e x n / 1 2 3 o o o / R T ) i t i ^
i t50'l- ; 6 . 6 6 1 0 - 6 e ' 0 6 1 e x p ( 1 2 3 0 0 0 / R T ) _ _ - 1 _ _ _ , j j _ y y _
l8l
_
V-Ti
.,."=
1.g,'1
0-6do0
?4€'o
tue"p11!921/T)
il+[vl+2.8)"10-82-06q[p(38QlED
___ __
] _ 1?g
?ryAi{elp0z-q41f)
, - -a}8
=?_13:10
f TepLllz
aQo/BI)
6 0 0
4120
1
538V
' - - - - ' - - 12 5 3
_?_,91,
_ .
5,5Q ,
3._6q .
Cr-Mo !
N O .
I C O N S T . I
M O D E L
V a l u e
L__
|
t-
04rcro!91
r - _ .
T
i 7 4
I
zs
I trroJl_f_
__ _ pupru119
roj.al,''
,_
__- i 12
1 2 . 7
5
L_ z0
I q-Mo _L
d-I1pe.ellZglql
',elp-t1qolq/!1lL
20 41
r----l-i l 4 1 2 0 l
l l i - c , i
t,_ tt
t tt3_s!__l_
_ ____{'o,iv_q12.-:'
_
j
tnn
i t53_s!_j_
_____{'o,iv_q:4:'_
i 3_1,07
,
Gr_ain
Growth{_telq9Qgynern'cfggry_s-EllLzatlqq
_ __ i_.
___
l
M O D E L
i vatue
; (lvtcrons)
-
cr.*th o,rri"iljls"9;lq nrg@l _
_-_
--__-
i
'
qruq-i-
d2=d2r,,,ronx+1.2'107(!e?!g!qrle-Ip(:ll!90-Q/tsIt-
+ - _ - - - ' - - . - 'i 5s.79
,
Growth After 1st Seco_nd
Models
_ ___
I
I 3 2 . 5 0
6 5
66
M o
A36
69
2 5 0
2 7 0
I
-tqr=V4.2.%xpGg-/8l)--
- - ----i
*&r:l ry:F_e_xp(3!_Q!0!1nT)l_lllep€2490/Rr)
i
L-*73
i
cr
i ---!es-?,Q11!i,o'*qu,C-+o,eQ8-r)
I
M e t a d v n a m i c
R e c r v s t a l l i z a t i o n
G r a i n S i z e M o d e l s
- - - - -T
T a b l e ll E : M e t a d y n a m i c
R e c r y s t a l l i z a t i o n
Cr-Mo I
ll orgrilgt, ..1. R. un il Oilctrolt. G...1. / L..l l'T EC H Journol o.f Engineering and Technologl I ( I ) 2003: 64-:1
T a b l e ll F : N o n - R e c
l l i z a t i o n
T e m
a t u r e M o d e l s
I H.ro
no _LqgNgf I
_
__ MopEL
i
e r
T^.=AE-0 128,-o o1t-o 1i a z r N b - B i
T " , = ( A ' L o g [ C l [ N b ] + g ' 1 s c 1 2 8 ' - 0 0 1 t 0 0 4 ie45.63 I
815.20
T a b l e ll G : K i n e t i c s o f P r e c i p i t a t i o n
M o d e l s
M O D E L
Vrf
r"f .l I
r M D N O I . C O N S T . '
R o o s = 0 . 3 3 * 1 0 - ' n d . t E ' t e x p ( 3 6 0 0 0 0 / R T ) 2 . B g I
84
Roos=2.89*10-"d"'q'efp(l!QQ998TL
-l-qif-j
T a b l e ll H : F e r r i t e
G r a i n S i z e M o d e l s
I v a t u e
l_rile*\o'..l
.corusr
lqqa_El
I
, i
- r
I o c \ / T ; i n = ? 7 t r + A i e n + 1 A ? . - 0 5
i
8 5
V - T i
1
D " = 3 . 7 5 + 0
1 8 D + 1
. 4 C i " "
i
8 6
i
i
D , ,
= t l - - _ Q
4 q e
, - l)l {3+1 4Cr
t ' 2 + 1 4 1 - e x p ( - 1
. 5 ' 1 0 2 D
|-'-_---i_-_-t--_-L_ 87
i
V-T
_
D,,
=(D/(1+(0.036+0.0233Cr0
s)D))
I
I
i
Du/D,,
=1+(0
0026+0.053%C+0.006%Mn+0.009%Nb+4.23%V.N-L- g!-=1fu1
%Ti).(1
.5+0
1'2)"Du
- l a t w s t o l u c i t l l F l € e r d t l l t l l r 9 l l l l e _
M i c r o n s
1 3 . 2 7 |
1 e
0 8 I
1 2 . 0 e I
T a b l e ll l : L o w e r Y i e l d S t r e s s M o d e l s
MD NO | .CONST.
i
tvlODEL
Value
' _----
--1- - -''-'
. T H , I F a ) I
- _ _ _ _
I
I - B-9_ ] -
v- --i LYq-9?:-6-+26.1[Mn]+60
2[Sil+759[P]+212
9[Cq]*1l86.qu1qn*t!,7d-,1-l
'---
n
soa0L]
I
Models
Relate
Lower
Yield
Stress
to Mean
Free
Path in Ferrite
l
t-
----T-I
9 0
l E u l
i-
^:
-T:
, . :f---.:-
-
I
3 0 8 2 3
I
9 0
| E u t e c t o i d
I
o " = 3 0 8 + 0
0 Z ( 1 7 P 1 ;
i - - r
T a b l e ll J : M o d e l s Qg_lqrfprng
C o n t r i b u t i o n
o
c i p i t a t i o n to S t r e n g t h e n i n g ( L . Y . S )
_
i M-o
ryq r ^cq.'Wf-,
__
fugAql
__
_
i varue i
r ( M P a t i
, L - - - i - : - r - - . ' '
I
g g
I
- _ - - - t - - _ _ - T
V
i
o o = 5 7 L o g C r + 7 0 0 [ V ] + 7 8 0 0 [ N l + 1 9
]
1 6 2 0
|
I a t I ' , i ^ - r o o l ' r " l r A A t Q r r - l z t A ' o n f \ / l r Q A A . A t t r l l + 1 O O l n / 1 ' r \ i 1 A ' A " I
i ,_g+ _j
--_L
___o,:1e-9{cb!!?
ilqll!5pq!i$qlq$]1te ern(cr)
I 15 82 _l
i _ ,u -- j- *p.Ii L -q'7-500([N!11qlllr1-
*,j- so oo---j
T a b l e ll K : T e n s i l e
t h M o d e l s
:
i
i
_ _ _ - _ r - - l
i ( M P a ) i
. t
l - ^ - r F A A , ^ ^ a 1 r ^ 1 , r a ^ r i r - ! r n n r r - i r , ^ t 4 n r n l r r T a a r N t i r r a o c n / f a l t r - r I T n a r n i
. _e_q_*l__U__ | IS=164
e.634
rlcl+53'6[Mn]+99llQiLqq].9lPl+472
6[Nil+333e
4[rylf_e*llzgryg ]
i
i
r l d r r . o s
I
i
l ;
r
-
-
: :
-9 8
i
" __ | ___
o , = 7 7 3 + 0 . 0 s 8 ( 1 / M ) + 1 2 2 [ S i l
- ] * q q q . o s :
lllotgridgo. .4-R. and odet'ole. G..4. / LAT\TECII Journal of Engineering and Technolog.t I ( t ) 200.1: hJ--J
Ilodels * ( l - N l n
fq!!rl!y-tll
(rrarn Growth rn Reheat ( M rcrons )
120-1
F l o n ' S t r e s s i \ { P a i
i Slatrc Recrlslalhzation. t511 lSecond) , !trlL.' Rr..f'rt"l l,roti
Static Recrystallization Grairr (irou,th ( \'licrons \lctadvnamic Recrvstallization. li,, ( Second )
, \'lelatlwanric Recr (.irain Srze (Mrcronsi
i \ l
mic Recr Grain Grouth (MicronsI-'crrrle Grarn Size (Microns)
r 0 . 8
l ' a b l e I I I : C risons Betrveen C-Ntn and Other'I'
Lorver Yie.ld Stress. [..\'.S ( MPa) L l t r n r a t e ' [ ' e n s i l e S t r e n g t h . L : I . S ( M P a )
coN('l-r'stoN
Ihe lilllouing conclusions can be draun:
l. l:crrite grain size is nnre sensitive to the
retained strain than to the coohng rate or
thc austetrite grarn size. llosever. there is
a linut to the size of thc lbrritc -urain that
can be obtained by increasing the retarned
strain or the cooling rate.
2 A drop in the austenite-ferrite (y-al
translbrnration te r.nperature leads lo an
increase in the tensile strength ofthe stecl.
3. The use of the computer in the validation of the simulated models reduces the '
nunrber of experimental test runs needed for the lbrmulation and determination of prr)ccss parameters required in steel pr(xluctrtrn.
R } : } E R ] - \ ( ' E S
Ilar. l).. \'ut'. S.. \laccaqno. I-. and Jonas, J. ( 1 9 ( ) 6 1 . " S l a l r c Recrl'stallization o f N b a n d N b - l ]
Steels llnder ('orrlrrrous Cooling Conditions. lSlJ
lnternational, Vol. -16. No.8. pp. 1084 - I093. ( 'scr. L.. l-errard, J. and Pietrzyk. N,l. ( 1999). lathenratical and Physical
Sirrrulation of the Properties of Hot Rolled Prtr'ducts. I st Edrtron, Elsevier Science Ltd., Uxlbrd, United Kingdom.
Djaka, T.. Chandra. T.. Dunne, D., Yu. D., Killmore, C. and hngley, D. (1997). "Effect of Molybdenum on the Austenite Recrystallization Br'haviour of Nb-Ti Steel". The ]'hird lnlernational
*: Phoniraj ct g!,2000.
Conlbrence on Recrvstallization and Rclatctl
Phenonrerta. \'tonterey'. t'SA. pp. 397 404.
I - a a s r a o u i , A . a n d J o n a s . J . ( 1 9 9 l ) . " R e e r v s t a l l r z a t r o n o f A u s t e n i t c A t i c r [ ) c l o r n t a t r o r r a t I l r g h Temperatures. Strain Rates Arralvsis arrd \'lotlcllrng". ) \ ' l e t a l l u r g r c a l - l ' r a r t s a c l r o n s . \ ' o l l 2 A . p p . l - r l- 1 6 0 M e d i n a . S . a n d M a n c i l l a . J . ( 1 9 9 6 1 . " l n l l u c r r c c o l ' ; \ l l o y r n g l l l c n r e n t s l n S o l u t i o n o n S t a t r c Recrystallrzation Kinetics ol' llot [)clirrnrcd Steels". I S I J In t e r n a t i o r r a l . V o l . - 1 6 . N o . f i . p p . 1 0 6 - l l 0 6 q O d e u ' o l e . G . A . ( 2 0 0 3 ) . B e n c h n r a r k i n g a n d V a l r d a t r o n o f l l o t R o l l i n g S i m u l a t i o n M o d e l s l ' n p u b l r s h e d M.Sc. Prolect Report. Departnrent of Mechanical
Engineering. Univcrsity of lbadan. Nigcrra.
P h a r r r r a j . M . . S h a n r a s u n d a r . S . a n r l l. a h r l r . A ( 2 ( X ) ( ) ) . "Benchmarking and Validation of Motle ls ['sc,l lirr
Hot Strip Mill Simulation". 42nd l't\VSP ('onlcrencc
Proceedings. Vol. XXXVII. pp. ti2-s tii"l.
I'adeusz. S. (1992). "Modelling of Microstructure Evolution I)urrns ll.c'crvstallization Controlled R o l h n - e " . l S l J l n t c ' r n a t r o n a l . \ ' o l . - 1 2 . N o . l , p p . 3 6 8 - 1 7 6 .
l ' a n r u r a . 1 . . . S c k i n e . l[ . , l ' a n a k a , l . a r r d O u c h r . C .
( 1988). "Thermo-lVlechanical I)nrcessrns ot' lligh
Strength. [-ow' Alloy Stecls". l]ulterw'orths
Publication, London. pp. 148 149.
Willianl D. {19971. Mate rials Scrcnc_c:. 4nti
Engineering: An Introduction. Fourth Edition. .lohn
t!tr!:rilgt, .'1.R. tui Odcrolt, (;. l. .' L..ll'f h.('ll Jourunl ol'Ilnginttri,,t! i,tl I'tthnolog-t' l( I ) 200.1: 6-l-'t
AJrpertdir I
V l t u c r t s c r l il r t h c V a l i r l a t i o l l o l t h c S i n t u l a t c d J f t r d c l s
I t t l e s s o l l l c r r r i s c s t . r t c , l . l i t t ! c r r e r a l \ . J i u r i s ( ] l t i r c p a r l r r r e l u s u t r i r z c < l r r r la l r t l l t t r r u t l r c s r n r u l a l e t l m o i l c l s a r c a s i l l l o t ' , r :
t Beheclisg Eefore_Ro_lllug
( t ) l r r t " , , . \ 0 . { ) l r r r " , , .
I l + . ' N .
l ) , l i r r r r i r , ' r t s . I l J - l K t I l:krrr Slt'ns
. \ t tl u lt t i t t . i , l l , t t ir ' l. t
\ ' ( , O ( ) i r 1 " , , . . , \ l t ) . 0 1 5 r r r " , , . D . ' , - 1 0 n r i c r o n s .
I
( i n t t n ( ' i t t n t t h in R t h c o t u r g . l i ) r r r r u s . l t S I i 2 K J r r i o l
S t r r r n l { u t c I r . l ( S i l l K . l n r o l . I i l - - l K . i ( ' l ( , . ( , - i \ r t " , , . l\ l r r l 0 . 1 7 s t " i , . X . 1 , . , , O . f i . S t r a r n . 0 . 1 . ( J , , \ -i(XXXX, J r r r o l . Q , ' l - r ( l ( X i O . l r r r o l . I t e a k S t r i t i n . { : r , , O . - l - 5 .
,r. Kittel ies ol' Sl :rt ic llccrlst :rllizll ion
R t i . l l : K J r u o l . I l l r . l K . l ) o 5 ( ) rr t r c r o r r s . Q l - i - l ( X X X ) J n x r l .
Q , " . l \ ( ) { ) ( } 0 . 1 r r r o l . \ . ( t . - { . S t r a l l t r a l c I s . . S t r t r r r , ( l 2. l}lrrl .. l..l ul'1.i,. S t a t r c l l c c r t s t : r l l r z l r t r t r r r ( i r a i r r S r z c
l ) i u r r r r c r o r r s . S t r a r n O 2 . R . . t i - ' l l 2 K . f n n l . I l l 7 . t 5 . Q . r . - i - l 0 i X X l J n n l . ( ir.rrn ( irorrtlr a l l c r S t a t r c R c c r v s t a l l r z a t r , r r r
t . l():. l, l,r, l(l\. d,... .t1; tlllcrotls. t,,r",. l(ls. lt ' l{ .lll KJ nml. I l:7-l K.
J l)rnanric ltccrriGflization '
t t + ' ( rrtr.ul ;rrrtl I t e a k S t r u i n
Qr,, .l I l(xx) KJ rrxrl. Qa -'ll(XX)0 J nml. [),, -. 50 rnicrons. T : 1273 K
5. ltirrcties of Nelrdrnenric llccrrsllllization
l ) ' . . | ( i l l l i c r o n s . S 1 r a i n R a t e = . l s . K l 7 . R - 8 . 3 l 2 K J , m o l . I . = | 2 7 . 1 K . \ | ctltlrrranuc Rccl$stalhzatiorr ( ira rn S rze
? - r
Q . r - 1 . l ( l ( t ( X I K J n x r l . S t r a i n R a t c I s . ' l ' . . 1 2 7 - 1 K . R . - t { . 3 1 2 K J ' n n l . ( rrlrn (irorrth alicr \{ctarlvtranltc l ( c e r v s t a l l r z a t r o n
r,, J(fs. -l I J7,1 R. p,,*;. lJ nricrons. R S.-l l:KJ ntrl. &, .- ls i', r..o Rccrlsaullisation'JcntIrcral urc.'l'n r
t l : s . l ' I l 2 - 3 K . l. l'crritc Grain Size
C . u - 0 1 - l s t ' l r , . D - , 2 2 n r i c r o n s . a . 3 " ( ' i s . 1 ' = l 2 T l K . R c t a i n e d S t r a r n - 0 . l . X r = 0 . 9 . D . 4 0 n r i c r o n s s l.ontt I'ickl Strcss
S r 0 . - 1 - 1 u t ' t ' i , . \ = 0 . 0 2 u r ' l t , . M n l . J r r ' t ' ) i , . X , . t ) . 9 . D l 0 n r i c r o n s . C = 0 . l 8 w t % r , 6 r = 3 " ( ' , ' s . D . -l()rnrcrorts, -[' I J7-1 6. 6'u 0.fi)9 $,t '),o, [P]= 0.009 wl 'i6.
9 ('ontribulion of Precinitrtion to l.oner Yicld Stress (l,.Y.S)
i\ I 0 (x).
[Nl 0.02.
{(:] -=
0. t. c.R. = 3"c,.s.
[Til = 0.m].
It; l'crrrilc Strcrrplh.
I ( | ( ) . l r r 1 " . . . [ \ l n l = l . 3 3 s t ' Z o , [ S i ] : 0 . 2 5 w t " / o , [ P l : 0 . 0 0 9 r v t ' ) i , . [ N i l = 0 . 0 0 9 w t ' 7 o . D = l 0 r n i c r o n s . X , ( , ( ) .
Appcndix
2
'l
hc parlrnctcrs listcd bclos'arc specific and have been used to vahdate the simulated modcls listcd abovc cithcr
rrhollv br thcrusclvcs or rn c s'ith the listed in
\\'lrcn thc s{rakrng tcntpcrature is lower than I I
k r r n - 0 S . 1 1
, 3O7..t0{[. Kr=8.74*104,
K r : 4 . 2 6 4 ' 1 0 ' '
\\'hcn the xiakrn.g
temperature
is in the range I150 - 1250"C
- i.2l.l + t1406/T.
Kl = 1.29*10-tn.
K2 = 1.94t105'
t =
SPECIFIC
PARAN,IETERS.
VALI.JES
AND REMARKS
I
s
().606(rld,cxp(5(lns)'i
2). A", = 0.4861d'cxp
(4(lns)')
c \ p ( t n (
I J J l l : , , ,
A u , ) ) r r
) . d u ,
= d*exp((lns)'12).
d * - M e d i a n
g r a i n
d i a m e t e r
Appendlr I ('ontti
llorgridge,
"1.R. and Olet'ole, G..4. / L..lI'TECtt Journu! of'Eugitrt,t,rin:: uttl Tt,t'hnolo.:;1 t( t t )u0l: hJ--l
K - 5 6 6 M P a . e , r = ' - 0 . 0 1 . 1 . n { ) . 2 1 9 , p = - 0 . 0 0 1 2 . n r - - 0 . 0 1 8 . e ' r , - 0 . g 2 s . 1 , , l ( ) t t K ) Q1:296kJrmol. cn 2.84* l0-rl),, . 0 , J , , , - JSc''"Iexp(-J106() I t | )
n 0 . 2 . 1 e ' ( ' r r e x p ( l 8 ( ) 0 0 R I ) . o . . ' / . 1 2 . " u ' "
\/alid for 0.-i2 0.66ni'Mn. 0-0.89i, Nb. 0 E] l .3|i,]i, ('r. 0-0.46,)6Ni. 0. l5-0.97,11, N{o. and 0-0.27ui, \.'
o , , l . l 8 l e ' e x p ( l - I O O ( X ) R l ) 1 " r t
Q' 1247 | 4 + 282tt.s.68[ l\,ln l-647 | (r 68[Sr ] . 72 775 .10[ \1o | + ]63_11; -1 -, 1 l 2 l 1 0 0 . 3 7 [ N b ] u ' , A - - 3 . 8 t r 9 . 1 O ' r e x p ( - 7 . 9 2 1 . l 0 " e ] . s . . t . q . . - 0 . 5 . r . n . - i
A - 2 - 5 . 3 3 1 8 e x p ( - 1 . 0 1 . 1 7
l 0 ' ' g * r .
Q * = e e x p l l t
t { {
I t - t S R ( ' - t ) l
H = 4 0 0 0 0 0 J m o l - ' . S R C T { K ) \ - T ' . - l 0 5 . l 0 r l ) ' t " , ; " ' "
A . - 5 . 1 5 . 1 0 - ' t
s . B = 2.0.
Q . - 2 6 2 k J
r r m l
A = 1 . 8 * 1 0 ' ' " , y = - . 1 . 6 , S t r a i r t -0 5 r ) T > 9 1 5 " C , Z : e ' e x p ( 2 4 8 { ) 0 0 R T T > g l 5 " c
Steel 0.06%C, 1.2%Mn, 0.22'76Si, (). l8'%\ftr. 0.()l',,, I i. () 029o,i,A1. 0.(X)27,,,,,N Stecl 0. 1 -l'Zo C, 1 .4 Mn.0.0 l '2, 'l'i. 0.0{" ,, V. 0.01 ?oN
S t e e l 0 . 7 2 % C , l . 2 V u M n . 0 . 2 8 o , i , S i . ( , ( X ) 2 ' l o A l . 0 . 2 l c r l , ( - r .
S t e e l 0 . 2 ' b C , l . 3 6 0 l ' \ 1 n , 0 . 2 6 ' i i , S i . 0 . ( ) ( ) 4 ; , \ / . 0 0 0 1 , , i , A l . 0 . ( ) f i r , ' , , \ B - l . l . C : 1 7 0 . x 0 l - i . r , 0 5 7 . z , ( ) l l t b r 0 . ( ) l ' l ' r - ( 0 . O t J - 0 1 . 1 \ ' ) - o ( ) l . t \
\-8 9 |$rgrr1: r. 1'1 (' l()i\ l S . l k . l rn t r l B " 1 . 0 8 , C : 1 7 6 . 2 . r ( ) 0 2 . 1' - 0.t,6. t 0 . O 9
l.or 0.01 Ti-0.04V-0.025Nb-0.008N
0. 0,1 -0. | --1')1,\'. 0 - ( ). 0 2 5 ",, N b. 0. 00ll -0. 0 2 J,l,,N Steel 0. l 3')i, C. 1 .4')irMn. 0.01 96Ti. 0.04" ,, \'. 0 1 " ,,\ S t c e I 0 . 7 2 ' i z , r ( ' . l.2,li Mn.0.280,r, S r . 0 . ( x ) 1 , , , . . \ 1 . 0 . 2 1 9 6 c r
S r c c l 0 . 2 ' l i , ( ' , L369a N{n,0.269ir S i . 0 . 0 9 " , , \ ' . u . 0 0 l u , , A l , 0 . 0 0 6 o 1 , N
= - 1 5 | 2 - e " r e -84.7kJ nrol Rl t ( ) . \ 0 . . T < l
1. ' 6-l .5
$l9i), 12.5
ss r
! lI 000>T>g90uc
S t e c l 0 . 2 % C . 1 3 6 % M n . 0 . 2 6 % S i
0.09%
V. 0.001%
Al. 0.00(r",,\
l). D,, - Grain rellnement ratio
.. 127 kJ/nrol
r u 1 1 l . i ' , B = 1 1 5 6 = N b + 0 . 3 1 I ' r . 0
, r n , , , 5 7 k r g T ' + 7 0 0 [ V ] + 7 9 { ) 0 [ \ ] + 1 o
\ I i \ ' l c a n l i e e p a t h fo r s l r p . \ { . l S , , ( l- 0 . 1 _ s [ ( ' l ) S , , . 0 . l5 p n r
S,,.: 0. L5lrm
i
I i I
I
1
- t
on- Prcc rpitation strcss
S r c e l t t 7 2 ' l ; , C ' . 1 . 2 " i , \ { r r . 0 2 S ' , S,,_-0 l-5trrnr
S , , < 0 . l51rnr. s , , i l 1 9 . - i - a - l
\\rhere !l
2 S , , (
l - 0
r 5 [ (
\ 1 n
l - " 1 .
( ' r l - 1 7 . - 5S r_+ I
I
I
I
