ISIJ I nternational , Vo l. 38 (1998) , No. 10, pp. 1093- 1099

Effect of Cooling Rate on ZST, llT and ZDT of Carbon Steels Near Melting Point

Young Mok WON , Kyung-hyun KIM ,1) Tae-jung YEO and Kyu Hwan OH

、‘y

School of Materials Science and Engineering and Research Institute of Advanced Materials, Seou l National University, San 56 -1, Shinrim-dong, Kwanak-ku, Seoul 151 -742, Korea. 1) Technology Development Group, M/U FAB. Department, Semiconductor R & D, Samsung Electronics, Yongin, Kyungi -Do 449 -900, Korea.

(Received on February 23, 1998: accepted in final form on June 3, 1998)

The effect of cooling rate on the characteristic temperatures such as liquidus temperature (Td , zero strength temperature (ZST). liquid impenetrable temperature (LlT) and zero ductility temperature (ZDT) has been investigated by calculating the non-equilibrium pseudo binary Fe-C phase diagram. The effect of cooling rate on T L was not significant. The effect of cooling rate on ZST, 니T and ZDT was significant due to segregation of solute elements at the final stage of solidification. Using the microsegregation analysis proposed by Ueshima, the calculated temperatures at the sol id fractions of 0.75 and 0.99 corresponded to the experimenta lly measured ZST and ZDT, respectively. Prediction equation on ZST, 니T and ZDT, which can take into account cooling rate and steel composition, was proposed . At given steel composit ions and cooling rates, the suggested prediction equation on ZST, LlT and ZDT could successfully describe the experimentally measured data and the calculated data from microsegregation analysis.

KEY WORDS: cooling rate; non -equilibrium pseudo binary Fe- C phase diagram; microsegregation; liquidus temperature (T L); zero strength temperature (ZST); liquid impenetrable temperature (니T); zero ductility temperature (ZDT).

1. Introduction

Continuous casting process becomes the mainstay of the modern steelmaking. The continuously cast prod-ucts have many advantages over ingot casting, such as improved productivity, reduced energy consumption, reduced cost, and high quality.1) However, at higher

solidus temperature and the di fTerence between ZST and ZDT on cooling was larger than that on heating.

) ~asti~g .. sp~eds "and lar?cr red때ons， internal and longitudinal surface cracks can easily occur. In recent years, internal and longitudinal surface cracks havε agatn become an important concern as it was twenty years ago.

HoweS) reported that the liquidus temperature calc-ulated with equivalent carbon content has been adequate for many classes of steel, but the solidus temperature calculated with equivalentcarbon content and the cooling rate, has been valid only in very dilute steel compositions. The so lidus temperature at a cooling rate of 1.00 Cjsec is 10、Ner about 20-450 C at various steel compositions than that at a cooling rate of 0.1 OCjsec. However, the effect of cooling rate on ZST, LIT and ZDT using the non-equilibrium pseudo binary Fe- C phase diagram has not been reported yet.

During continuous casting of steels, internal and longitudinal surface cracks tend to occur in a brittle temperature range by thermal and mechanical deforma-tion. 2 ) To prevent the occurrcnce of these cracks in continuous casting slabs, better understandings on the melting behavior and the mechanical properties near the melting point is essential. The mechanical properties can be characterized by four characteristic temperatures; zero strength temperature (ZST), zero ductility temperature (ZDT), liquid impenetrable temperature (LIT) and liquidus temperature (TL). 2) Melting starts on heating at a temperature lower than a fully solidifying tempera-ture on cooling and the ZST, ZDT and LJT on heating are di fTerent from those on cooling.3 ) Yu et al.4 ) reported that, in low carbon steel, ZST on heating was lower than the solidus temperature and nearly equal to ZDT, but ZST on cooling was higher than the equilibrium

1093

The objective of present study is to predict ZST, LIT and ZDT at various steel compositions and cooling rate conditions. To accomplish this, the non-equilibrium pseudo binary Fe- C phase diagram has been calculated and the fitting equation for ZST, LIT and ZDT has been proposed from experimenta l1y measured data by previous researchεrs.4• 6 - 10)

2. Analysis

2.1. Calculation of Microsegregation

The microsegregation in a continuously cast strand has been calculated using the direct di fTerence method suggested by Ueshima et al. 11 ) Kim el al. 2 • 1 2 ) have ex-plained the deformation behavior of mushy zone and

(Ç) 1998 I SIJ

ISIJ International , Vol. 38 (1998) , No. 10

Jongitudinal surfacc cracks at variolls stcel composi-tions during continllolls casting.

Figure I(a) shows a schematic diagram of growing dendrites in the continuously cast strand. The transverse cross section of dendrites is approximatcd by a regll lar hexagon, one sixth of which is shown in Fig. I(b). The complete mixing of so lute clements in the Jiquid phase and local eqllilibrium at liquidjð, liqllidfy and ðfy interfaces are assumed. The diffusion of solute in solid and liqllid phases along the axial direction of dendrite is assumed to be ncgligible. y-Fe phasc develops from the intcr떠ce betwecn ð- Fe and Iiquid phase. [n the solidjliquid and ðjy interfaces, the s이 ute concentrations are assumed to be in the local cquilibrium. O uring ðjy transformation , silicon, phosphorus a nd sulfur are redistributed from y- Fe to ð-Fe, because the equilibrium distribution coefficient ky/ð is Icss than 1, but carbon and manganese are redistributed from ð-Fe to y-Fe due to k1/δ > 1. Using the assumptions of the complete mixing in liquid phase, no axial diffusion and local equilibrium , the solute distributions in the three phases, ð- Fe, y-Fe and liquid, were calculated. Thc calcula tion was made

(a)

local equilibrium

complete mixing

(b)

Fig. 1. (a) Schem띠ic drawing showing the ll10rph이ogy of thc dendrite :‘ rray “nd (b) thc lransversc cross seclion assumcd in thc finite difTcrcncc sirnulation.

by dividing the triangula r transverse cross section into 100 meshes parallel to vertical lines. When the liquidus temperature, TL> and thc ðjy transformation temperature, TAr4, becomc equal to the actual temperature of one mcsh , the solidifìcation and ðJy transformation in one mcsh are assumed to be completed and thc interfaces mo얘 to the ncxt mesh. TL and TAr4 are calculatcd using thc following equations.13 , 14)

TL = 1 536 - 78(wt%C) - 7.6(wt%Si) - 4.9(wl%Mn) - 34.4(wt%P) - 38(wt%S) ............................. ( 1)

TAr4 = 1392+ 11 22(wt%C) - 60(wt%Si) + 12(wt%Mn) - 140(wt% P) - 160(wt%S) …(2)

The equilibrium distribution coefficients and diffusion coclTìcients of the solutc clements are given in Table 1. 10) The solid “aclion，강， ð-Fe fraction, ~r.， and y-Fe fraction, 있， in the solid orJand liquid phasc werε calculated as a function of temperature at various steel compositions and cooling ra tes in Table 2.

2.2. Equation for Characteristic Temperatures l애n o야r(띠der to describe tl네hπccl이ha따lπrac따t떠er‘센iκc tempe히r‘'a따tlωu따lfes su(‘c이;h 、-'/

as ZST, LIT and ZOT as a function of steel composition and cooling rate, we used the Clyn옹Kurz microse-grcgation model 15’ which takes into account the solutc diffusion in solid. Thc relation betwcen the solid fraction and the temperature can be exprcssed as follows

섹 1 -꿇)[ 1 - ( ;r펴 )(1 -2Qk)꽉

인ιv

/

j、

‘,‘ -

D

-깐

A악 ---,‘

where Tf is the melting temperature of pure iron, TL is lhc liquidus temperature, k is the eq uilibri um rcdistribu-tion coefficient of solutc clemen t, α and Q are parameters expressing the degree of back diffusion of solute element,

Tablc 1. Equilibriu ll1 distribution coefficients and diffusion coefficicnts of solute elements. ’ ”

‘ _./

Elcmcnt pπ JlC J!i'i O'(lO"xm'/s) OT( IO"xm’Is) C 0.19 0.34 1.79 0.01 27exp(-8 1 379/RT) 0.076Icxp(.143511 /RT) Si 0.77 0. 52 0.68 8.0exp( .248948/RT) 0.3exp(-25 1 458/RT) Mn 0.76 0.78 1.03 O. 76exp( .224430n‘T) 0.055exp( -249366/RT)

0.23 0.13 0.57 2.gexp(.230120IRT) O.O lexp(-1 8284 I/Rn S 0.05 0.035 0.70 4.56exp( .21 4639/RT) 2.4cxp( .223425/RT)

Tablc 2. Chcrnical compositions of carbon stccls (wt %) and cooling rates. (OC/sec) Samplc C Si Mn P S T rcf.

ßI 0.0-0.8 0‘ 34 1.52 0.01 2 0.015 10 6) CI 0.0-0.8 0.015 1.05 0.0009 0.0008 0.1 7 A 0.001-0.83 0.01-0.26 0.03-1.33 0.007.0. 11 0.001.0.018 4 4) B 0.015- 1.0 0.2 1-0.42 0.56-1.66 0.008-0.014 0.01 1-0.02 10 6) C 0.06-0.6 0.005.0.015 1.03-1.06 0.0005-0.0009 0.0005-0 0008 0.17 7) D 0. 13-0.82 0.005-0.24 0.78-1.08 0.0005-0.11 0.0006-0.062 0.17 8) E 0.003-1 .6 0.01 -0.23 0.01.0.5 0.0006-0.004 0.0003-0.004 20 9)

0.04-0.67 0.01-0.24 0.28-0.81 0.001-0.085 0.00 1-0.008 20 10)

(Q 1998 ISIJ 1094

ISIJ I nternational, Vol. 38 (1998) , No. 10

".(1 0)

where superscrip t i denotes solute elemen t. However, Eq. ( 10) is not suitable to describe characteristic temperatllrc, becausc various parameters such as k.‘, D~， αI and Q ‘ a re very complex coefficient of sol ute elemen t. T herefo rc, characteristic tcmperature mllst bc casily described to carbon equivalcnt, Lf'(C;), which is taken in to account etfect o f various pa~ameters such as k i, D~， αI and Q ’· Thus, cha racteristic temperature can be expressed as l‘ü llows.

T = 1 536 -ε u’ (Cj )' [ 1- 2Q ik’Jk‘ - 1)/( 1 -2Sl써} o 17)

"l 19)

• 21) ‘ 23) • 25)

~

• 。--&청

。"" . 0Oδ

v ?

? • 。 Q

ref 。 16)

6 18) 。 20)

• 22)

... 24)

1000

E ~ 그 800 。1

c

g 600 a. (/)

훌 400 @

걷 200

검

T= 1536- [ ~f'(C;)l [ 1 -λ( 1 _ 2Qk)](k - l) /(I - W

0 1 10 100 Cooling Rate , oC/sec

Fig. 2. Comparison of thc calculatcd and mcasured dendrite arm spacings 16- 2S) as a function of cooling ratc.

‘ .:.!!ILJ 1000 0.1

--

Q = cx( l - exp( - 1 /α)) -한xp( - 1 /2α)， α=A.r’”

where f '(C;) is a function of the solute concentrations. The relation between the solid fraction and temperature can be dctcrmined from Eq. ( 11 ) a t the given stcel composition and cooling ratc.

Ds is the solute ditfusion coefficient in the solid , fr is the local solidificatio n time, ì.. is the dendrite arm spacing.

T he dendrite arm spacing has been modeled as a function of cooling rate. Using the measllred dendrite a rm spacings a t the various cooling rates/ 6- 25) it has

} / been determined that t |1e rc|ationship between the . dendrite a rm spacing and cooling rate, T, has been expresscd as follows.

1n order to determine the solid fraction in mushy zone as a function of temperature, the microsegregatio n of solute elements has been assessed. Many studies showed that ZST and ZDT correspond to the tempcra-ture at which the solid fractio n bccomcs about 0.6491 -0.826 - 28) and 0 .98_ 1.0,8.26.28) rcspectively. Moitra ef al.2 7 ) considered ZST as the temperature at the solid fraction o f 0.7. Kobayashi26) proposed that ZST and ZDT corrcspond to the tempera ture at which the solid fract ion bccomes 0.8 and 0.99, respectively. From thc high tempcrature tensile test of carbon steels, Nakagawa el al. 8) a lso proposed that ZDT corresponds to the temperature at which the solid fraction reaches 0.98 through the high temperature tensile test of carbon steel, and Kim28) suggested that ZST and ZDT correspond to the temperatures at which the solid fraction becomes 0.6491 and 1.0 from the mi띠'osegregation analysis of various carbon compositions, respectively.

Using the microsegregatio n ana lysis, ZST and ZDT were calculatcd at vario us steel compositions and cooling rates in Table 2. Figure 3(a) shows the calcu1atcd ZST correspond to the temperatures at the solid fraction of 0.649 1, 0.7, 0.75 and 0.8, a long with the experimentally measured ZST by previous workers. 4 ,6- 10) A t the low carbon stcel, the calcu1ated ZST is much alike at the solid fraction of 0.649 1- 0.8, but, at the high carbo n steel, the calc ulated ZST is ditferent from the experimentally measured ZST at various solid fractions. Figure 3(b) shows thc calculated ZDT corrcspond to the tempera ture

! at the solid fraction o f 0 .98, 0.99 and 1.0, alo ng with the experimentally measured ZDT by previous work-ers.4 •6- 10) At the solid fract ion of 1.0, the calculated ZDT deviate from the experimentally meaured ZDT. T he solid fraction of 0.98 and 0.99, the calculated ZDT is m uch alike to the experimentally measllred ZST. Thc extremes, means and standa rd dcviations of the dif-

Rcsults and Discussions 3. Æ=B'T- II ................................. (6)

where B and n are experimcnlal constant paramelers. The valuc o f B and n a l‘e obtai ncd to be 3 19.4 and 0.378 by the bCSl fittin g of the mcasured dendrite arm spacings, respcctively. Figure 2 shows thc calculated a nd measured dendrite arm spacings as a function of cooling rate at the various steel compositions. The dendrite arm spacing is seen to bc well described by Eq. (6) in the given cooling rate.

T hc local so lidification timc, μ ， can be given as fol-lows.

.. .. (7)

where 6. T,., is the solidification temperature ra nge. From Eqs. (5), (6) and (7), α can be given as follows.

6.Ts r - T

4D .. 6.T. _. ’ “ α=펴삼 T- 1 + Z닐 T- n’ (8)

.....

whcre A is an experimental consta nt parameter indicating the relation betw야n the solute d itfusion coefficient and solidification temperature range, and the va lue of m is obtained to bc 0.244.

Above Eqs. (3), (4) and (8) reduce to the Scheil equation as α and Q approaches zero (no back ditfusio n in the solid), i.e. cooling rate becomes il얘nity， and to the lever rule as α approaches infinity and Q approaches 0.5, i.e. cooling rate becomcs zcro.

To describe characteristic temperature, Eq. (3) can be expressed as fo llows.

(Ç) 1998 ISIJ 1095

T= Tr- (자- η.)[ 1 -자( 1 - 2Qk)J

ISIJ International , Vo l. 38 (1998) , No. 10

ferences between the measured and calculated tempera-tures, are presented in Table 3. Within the population of 45 carbon steels, ZST and ZDT at which the solid fraction becomes 0.75 and 0.99, respectively, show the minimum mean value and standard deviation. At the solid fraction of 0.75 and 0.99, the calculated ZST and ZDT by microsegregation analysis in the given condi-tion of steel compositions and cooling rates are in rea-sonable agreement with the experimentally measured ZST and ZDT, as shown in Figs. 3(a) and 3(b). In this study, authors determined ZST and ZDT as the tem-peratures where the solid fraction is 0.75 and 0.99, respectively.

The prediction equations for ZST, LIT and ZDT de-pend on cooling rate and steel composition are derived from the experimentally measured data of previous

1600

1550 + Is=0.6491 x Is=0.70 。 IS=0.75

lIE Is=0.80 잉 1500 1-(/) F、J

정 1450 m 그

읍 1400 Q

**Q4

엽 1350 ’‘

1300 1300 1350

(a)

1400 1450 1500 1550 1600 Measured ZST, oC

1600

1550 + Is=0.98 。 Is=0.99

X Is=I.00 앙 1500 1-임 1450 검 잭 1400 긍 (1) U 1350

N ” /

/ ‘ . 、

1300

1250 1250 1300 1350 1400 1450 1500 1550 1600

Measured ZDT, oC I'ig. 3, The calculated (a) ZST and (b) ZDT using thc mi-

croscgrcgation analysis along with the experiment-ally I11casurcd data of ZST and ZDT by previous workers,4 ,6 - 'O) respectivcly.

workers4,6 - 1이 as shown in Figs , 3(a) and 3(b). The corresponding solid fractions for ZST, LIT and ZDT were 0.75, 0.9 and 0.99, respective1y. And, k and A are assumed as a constant parameter. The experimentally measured ZST and ZDT data were best fitted by Eq , (11) to obtain parameters as follows.

T=늬1536 -←-[탠함F?f (κC갇J} [1-λ(1 -2갱짧찌Qα찌째k셔씨)J

ISIJ International, Vol. 38 (1998) , No. 10

250 C-K , Fitting Eq.

200 ~ U T, 。ð.Tc 디

늘 100 ~ ð.Ts ..... , X

0.0 0.6 1.0 0.8 0 ‘ 2 0.4 Solid Fraction

Fig. 4. Comparison of thc calc lIlatcd ð. Ti of variOllS solutc elelllents by lhe Clync Kurz Illodcl and prcdiction cqllat lOn

1550 (a)

믿 1450 그

i m 」

요 1400 ι E @ 1-

1350 • ZST • ‘、‘

fs=0.9

1300 0.0

• ψT , 、、믿0.99 0.2 0.4 0.6 0.8 1.0

Carbon Content, wt%

1550 、‘ , /

L U

/ , . ‘ 1500

g f,,'10.0 s 、잉 1450

그

띤 ~ 1400 E m 누-

1350 • ZST • ZDT

fs=0.99 1300

0.0 0.2 0.4 0.6 0.8 1.0 Carbon Content. wt%

Fig. 5. Non-cquil ibrilllll pscudo binary Fe C phasc diagralll of (a) 0.34Si- 1.52Mn 0.012P 0.015S carbon sleeJ and (b) 0.015Si 1.05Mn 0.0009P 0.0008S carbon steel. along with the I11casurcd ZST “nd ZDT‘ 6.7)

ysis. Schmidtmann el al.6 ) and Shin et al.7 ) measured ZDT and ZST of two carbon steels B 1 and C I in Table 2 as a function of carbon content. Figures 5(a) and 5(b) show the calculatcd non-cquilibrillm phase diagram comparcd with the measurcd data. The thick solid lines rcpresent the non-eq llilibrillm pselldo Fe‘ C phase diagram and the thin lines represent the equilibrium binary Fe- C phase diagram ‘ The complete solidifìcation tem perature, i.e. the tempcrature at which the solid fraction, λ becomcs 1, is abollt 50-100oC lower than the equil ibri1l111 solidlls templ따lI rc . 1n sample B 1 at carbon concentra tions lower than about 0.05 wt% C, ð/y transforma tion takes place after solidification, whereas at carbO I1 concentrations higher than about

1550

Ü 1500 。

Liquid

@

늠 1450 i m ‘-m 틀 1400 m 1- 1.0 Kls

-- 10 Kls 1350

1300 0.0

- - 10? Kls """、‘、~， fs=0.990.2 0.4 0.6 0.8 • O

Carbon Conte nt, wt% Fig. 6. EfTect ofco이ing rate on thecharacteristic tClllperaLures

such as 7',. (.(, =0.0), ZST (ι =0.75), LlT (/, =0.9) and ZDT (λ = 0.99) of BI ncar thcir mclting point

0.05 wt % C, ðfy transformation la kes place during so-lidification. The calculatcd complete solidifì cation tem-peratures are in good agreement with ZOT measured by Schmidtmann.6 ) In the temperature range between ZOT and L1T , which is known as brittle temperature range, thc steel shows ho t tea r undcr applied tensile slrcss state by thcrmal and mechanical deformation. In the bri ttle temperature range, the solidi fyi ng steel begins to behave like solid susceptible to crack due to no Iiquid feeding bctween dend rite arms. As shown in Fig. 5, above ZDT, the steel is not fully solidi fìed due lo microseg-regation. Thus, hot tears mainly depend on the prescnce of the interdendritic liquid fì lms due to the microseg-regation of solute elemen ts. But, hot tears formed between LIT and ZST can be rcfìlled with the surrounding liquid . The measured ZST agrees with lhe tcmperaturc at which the solid fraction becomcs about 0. 75 as shown in Fig. 5, At the temperature between ZOT and ZST, the steel has no ductility due to interdendritic liquid fì lm, but strength dlle to mechanical network belween dendri tes. Above ZST, thc steel has no slrength and no ductil ity, and behave as a liquid

Using lhe microsegregation analysis, ZST, LIT a nd ZOT have been computed to investigate the εffect of cooling rate for steel compositions of B 1 in Table 2. Figure 6 shows the non-equilibrium pseudo binary Fe- C phase diagrams for steel cornpositions of B 1 at various cooling rates of O. J, 1, 10 and 100oCfsec. The ι of 0.0, 0.75, 0.9 and 0.99 are corresponded to the characteristic tcmperature of TL, ZST, L1T and ZDT, rcspectively. The complete solidifìcalion tempcrature decreases and the mushy zone of ð+y + L extends with increasing cooJing rate from 0 , 1 to 100oCfsec. The effect of cooling rate onTL is not significant, whereas the elTect of the cooling rate on ZST, LIT and ZOT is signifìcant due lo lhe segregation of solute elernents ncar the fì nal stage of solidification with increasing cooling rate. Thus, ZST, L1T and ZOT with increasing cooling rate extend to lower ternperature with increasing carbon content as shown in F ig. 6.

Figures 7(a) and 7(b) show the prediclcd ZST and ZOT by Eq. (12) in thc given condition of steel compositions and cooling rates, along with the experimentaJ1y measured data,4.6 - 10) respectively. At the given condi tion of steel compositi ons and cooling rates, lhe predicted

1097 @ 1998 IS IJ

ISIJ International, Vol. 38 (1998) , No. 10

(a)

1350 1400 1450 1500 1550 1600 Predicted ZST(fs=O.75) , oC

1600

g iíì 1550 r--o

11 .... '" 1500 I 。

m 암 1450 』

cn % g 140O E

t:; 1350 N

1300 1300

ZST a nd ZOT a re in reasonable agreement with the ex-

pe rime nta lly m easurcd data. Figures 8(a), 8(b) a nd 8(c) show the calculated ZST,

LIT and ZDT by microsegregation analysis in the given

condi tio n o f steel compositions a nd ∞이ing rates, a long w ith the predicted ZST, LTT a nd ZOT by E q . ( 12), re-spcctively. A good correlation o n ZST, L1T and ZOT be tween the microsegregation a n a lysis and the pred ic tion

equation a re shown a t various steel compositio n s a nd

cooling ra tes. The predictio n equa tion s of the characteristic tem-

pe ratures s uch as ZST a nd ZDT has b een s uggested by previous research ers.4. 13.39) Table 4 s hows the coef-ficient o f s이 u te elem en t estimated fr om E q. ( 12), com-paring w ith others. Yu et a/.4 ) a nd Kawawa13) p ro-posed that predic tio n equa tio n s for ZST and ZDT, re-

、-

1600

g • 1550 o 。〉

o ’l ‘ "'1500 I 。

정 1450

앙 ~ 1400 S E 느 1350 ...J

Predicted by Eq. (12)

。r

。

。

1600

패 뼈 때 때 때

Q@·(mh.。”낭)뉴띠N깅핑잉킹@』α

a

베{때

1

”ι

M

뼈

뼈 M

s 때 때

때

P

~

1300 1300 서

… / / l l 、

。

。

、

(c) 1250 IL I

1250 1300 1350 1400 1450 1500 1550 1600 Predicted ZDT(fs=O.99). oC

The calculaled (a) ZST, (b) LlT and (c) ZOT by microscgregalion analysis in Ihc givcn condition of sleel compositions “nd cooling rates, along wilh Ihe predicted ZST, L1T and ZOTby Eq. (12), respeclively.

1600

g _..::, 1550 。‘。，

암 1500 ” ‘-

I

응 1450 m g> 합 1400

” 。‘ 을 1350 f-딩 1300

1600

-뼈

이←

」패

+

때 ”%

+

뼈 따

」뼈 뼈

{

때

M

B/

디 수 때

ι 때

때

1550 1400 1450 1500 Measured ZST, oC

Predicted by Eq. (12)

1350

D

1300 1300

1600

1550 g ã> 1500 。i

o ’l ‘'" 1450 ’-。N 1400 정 6 'ë 1350 Q) 』

ι

1300

Fig.8. The prcdicled (a) ZST and (b) ZOT by Eq. (12) along with thc expcrimentally measured dala of ZST and ZOT by previous workers，ι6- 1 0’ respeclively.

Fig. 7.

LS'J‘, L1Tand ZDT Thiswork

67.51 3.292 9.741 82.18 155.8 YES

Comparison ofcoemcienl in the equalion for characleristic temperatures.

Characle찌ic Tempe띠lure ZS"l‘ I ZDT Z • Elemenl Yu ') i Kawawa IJ’ Nagala 19) i

C 447.2 I 41 5.5 51'3.9* Mn 14.8 i 6.8 6.5 Si I 12.3 20.5 P 658.8 i 124.5 1163 S 1553.6 I 183.9 211 1

CöiïsidëraÚon o{cöûïing ;äïc .... 'NÓ T " ï\iö" N6'" ; • This cocfficien‘ is applied bclow 0.1 wl%C sleel

1098

TabJe 4.

(þ 1998 IS IJ

ISIJ International, Vol. 38 (1998) , No. 10

1600 • Predicted by Eq. (12) 디 Kawawa’s equation (ref. 13)

1500 L A Nagata et 81. equation (ref. 28)

녕

5F4 14OO A

1200

/，~ 디

。

1100 1100 1200 1300 1400 1500 1600

Measured ZDT, oC Fig. 9. Comparison of thc prcdicted ZDT by ’ prevlOus

workers. 13 ,29)

spectively, depend on only steel compositions, without ‘“ taking into account the effect of cooling rate. The co-

efficient for solute element shows the degree of micro-segregation i.ι.; the larger value of coefficient means the larger segregation and lower solidifìcation tempera ture.

Nagata et al. 29) suggested that the coefficient for C is given as a function of carbon concentration. The co-eflìcients for solute elements in Eq. (1 2) are smaller than those in the previous prediction eq uations, but this does not mean that Eq. (12) underestimate the degree of microsegregation because Eq. (12) takes into account cooling rate. The degree of the microsegregation o f sulfur a t Iiq uid lìlm is the largest among other solute elements, and the characteristic temperaturcs are sensitive to the concentration of sulfur, phosphorous and carbon in order.

Figure 9 shows the calculated ZDT from Eq. (12) and that from Kawawa 13) and Nagata et al. 29 ) in the given condition of steel compositions, along with the ex-perimentally measured data of ZDT.4，6-1이 At the low carbon concentration (high ZDT), the calcula ted ZDT

‘ ,/ from Eq. (12), Kawawa and Nagata are in good agree-ment with experimentally measured data. At the high carbon concentration (Iow ZDT), the calculated ZDT from Eq. (1 2) predicted well comparing with that from others. With increasing carbon concentration, the effect of solute microsegregation on the solidification behav-ior increases. 2) Thus Eq. (12), which can take into ac-count the cooling rate, could be useful to describe solid-ifìcation behavior of high carbon steel.

4. Conclusions

An equation for ZST, LlT and ZDT was proposed, which can take into account the steel composition and cooling rate. From the microsegregation analysis, in comparison with experimentally measured data of ZST and ZDT , the tem pera ture at which the solid fraction becomes 0.75, 0.9 and 0.99 corresponded to ZST, LlT

and ZDT, respectively. The effect of cooling rate on TL was not signifìcant,

whcrcas the effect of cooling rate on ZST, LIT and ZDT were significant due to the severe of segregation of solute elements at the final stage of solidification which is influenced by the cooling rate. The degree of the microsegregation of sulfur at liquid fi lm is the l argεst among other solute elements, and the characteristic temperatures are sensitive to the concentration of sulfur, phosphorus and carbon in order. The ZST, L1 T and ZDT can be successfully described by the suggested pre-diction equation in the given range of steel compo-sitions especially at the high carbon concentration and cooling rates.

1099

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