ISIJ Internationa l, Vo l. 36 (1996), No. 3, pp. 284- 289
Effect of Carbon and Sulfur in Continuously Cast Strand on Longitudinal Surface Cracks
Kyung-hyun KIM , Tae-jung YEO, Kyu Hwan OH and Dong Nyung LEE
Department of Metallurgical Engineering and Center for Advanced Material Research , Seoul Nat ional University, San
56-1 Shinrim-dong, Kwanak -ku, Seoul 151 -742, Korea.
(Received on August 10, 1995; accepted in final form on November 29,
1995、
Effects of carbon and sulfur on the longitudina l surface cracks have been investigated by calculating the
non-equ ili brium pseudo binary Fe- C phase diagram and introducing t he strain in brittle temperature range
for continuous casting of steels. The cracking tendency as a function of carbon content was well described
by the strain in brittle temperature range. The strai n in brittle temperature range was influenced by the other
solute elements as well as carbon . The carbon content at which longitudinal surface cracking is maximized
decreased with increasing sulfur content. At a given carbon conte nt, the possibility of su rface cracking
increased with increasing su lfur conten~.
KEY WORDS: carbo n; su lfur; longitudinal surface crack; microsegregation; non -equi librium pseudo binary
Fe- C phase diagram; strain in brittle temperature range.
1.
behavior arose from shrinkage of the solid shell near the
meniscus owing to the solid-state b-y transformation.
M a tsurni ya et al. 5> suggested that the carbon content a t
which the strain developed i11 a brittle temperature
ra nge of Ta - 30。C < T < Ta is maximized, beca n1e 0.14
wt0/o C, where Ta is the temperature at wl1ich the
solid fraction becomes 0.85 in the equilibrium binary
F옹C phase diagram. H owever, since they used the
equilib rium binary F e-C phase diagram in order to
de fi ne the brittle temperature range, they did not take
into accou nt the e ffect of other solute elements such as
phosphorous and sulfur etc . and the microsegregation
of solute element duri11g non-equilibrium so lidification
011 the formation of cracks. Even though many investigations of the relationship between the formation of
lo ngitudinal surface cracks and the carbon co ntent of
the steel have been conducted ,6- 10> the reported carbon
content at which lo ngitudinal cracking is ma ximized
differs each other in the range of 0 .08 wt0/ o < C < 0.25
wt0/o . This may be attributed to the differences in the
operating factors such as casting speed, mold flux, cooling
ratε, etc. and the differences in the steel con1positions
Stich as sulfur, phospho rus a nd silicon in the studies.
H owever, thε effect of the steel composition on the
form atio n of longitudin al cracks using the non-equilibrium phase diagrarn has not been repo rted yet, and
a 1nore qua ntitative and systematic study m ust be
made to interpret the surface cracking phe11omena.
The objective of present study is to predict the
possibility of longitudinal surface cracks as a function
of ca rbon content. T o accomplish this, the nonequi librium p seudo binary Fe-C phase diagram has been
calculated and the relationship between the car bon
Introduction
Co nti nuous casting has become the mainstay of most
modern steelmakers. In addition to the commo nly mentioned advantages over it1got casting, such as improved prodt1ctivity, redt1ced energy consumption and
reduced costs, co11tinuously cast products are normally
of h igher quality. 11 H owevεr, since continuously cast
strands are solidified quickly, the surface quality of the
stra nd suffers co nsiderably from the presence of
longitudina l surface c racks. 2> E ven tho ugh th e facto rs
affecting the qual ity of the strand have been known as
casting speed, mold cooling, mold flux , mo ld oscillation,
steel com positio11 a11d so on , it is very diffict1lt to analyze
qua11 titatively the effect of all the operating factors on
the quality of the st rand because of interactio ns a mopg
the parameters.
M a ny studies3 - 1 이 showed that the effect of carbon
content is most cri tical at the beginning of longitudinal
surface crack due to the enhanced shrinkage of steels
undergoi11g the b-y tra nsforn1ation during casting. The
first com prehensive investigation of the relationhsip
between the mold heal flu x a.nd tl1e carbon content was
conducted by Singh and Blazek. 3> According to their
ex perimental resul ts, the value of the mo ld 11eat flux
has a m inimum at 0. 1 w t 0/o carbon steel, whereas for
t he ca rbo n co nten t hi gher than about 0.25 wt0/o, the
niold heat flux is nea rly constant. They also have shown
that the shell of a low-carbon steel has a distinctly
wavy appearancε at surface and large fluctuations in
thickness, \vhereas the shell of a higher carbon grade
has t he smoother surface a nd the lower fluctuation in
th ic kness. Grill a nd Brimacombe4> sugges ted that this
ψ
1996 ISIJ
284
ISIJ International, Vol. 36 (1996), No. 3
content a nd the possibility of cracking has been investigated and quantified using the concept of a strain
in brittle temperature range.
and TAr4 are calculated using the following equa tions.
TL = I 536.0-78(wt0/oC) - 7.6(wto/oSi)
- 4.9(wt0/oMn) - 34.4(wto/o P) - 38(wt 0/oS) …… (I)
2.
Calculation Procedures
TAr4 = 1392.0 + l l 22(wt0/oC) -60(wt 0/oSi)
+ 12(wt0/oMn)- 140(wt0/o P) - I 60(wt0/oS) ·… (2)
2.1. Calculation of M icrosegregation
The microsegregation in a continuously cast strand
has been calculated using the direct difference method
suggested by Ueshi1na. 11 > Figure l(a) shows growing
dendrites in the continuously cast strand. The transverse
cross section of tl1em is approximated by a regttlar
hexagon, one sixth of which is shown in Fig. l(b). The
completε mixing in the liquid phase is assumed to give
rise to the tiniform solute concentrations in the transverse section of the dendrite. The diffusion in solid and
liquid in the axial direction of dendrite is assumed to be
negligible. y-Fe develops from the interfa9e between bFe and liquid phase. In the solid- liquid and 6/y interfaces, the solute concentrations a re assumed to be in the
local equilib rium . Let kYIδ be the equilibrium distribution coefficien between y-Fe and <5-Fe, then during the
b/y transformation, silicon, pl1osphorus and sulfur, for
홀 which k rfli < l , a re redistributed from y-Fe to b-Fe, but
carbon and 111anganese, for which k Yl0 > 1, are redistribu ted from b- Fe to y-Fε. On the assumptions of
the complete mixing in liqt1id, no axial diffusion and local
equilibrium, the solu te distributions in the three phases,
fJ , y and liqt1id, were calculated. The calculation was
made by dividing the triangular transverse cross section
into 50 parts paral lel to ver tical lines in Fig. l (b). When
the liquidus temperature, 12> TL, and the b/y transforma tion temperature, 13> TAr4, become equal to the
actual temperature of the sample, the solidification and
b/y transformation in one pa rt are assumed to be completed and the interfaces move to the next part. TL
The solute concentrations in Eqs. ( I) and (2) represent
those in the y/ L and b/y interfaces, respectively. The
coefficients in Eq. (2) were determined fro1n the respective
equilibrium Fe- X (X = C, Si, Mn, P, S) bi11ary phase
diagra1ns.
Calculation of Non-equilibrium Pseudo Binary Fe-C
Phase Diagram
The non-equilibrium pseudo binary Fe-C phase
diagram was calculated using the microsegregation a11alysis in the previous section. Equilibrium distribt1tion
coefficien ts and diffusion coefficients of the solute
elements a re given in Table I . The weight solid fraction
자 in the solid plus liquid phase, and <5-Fe fraction 잇
and y-Fe fraction 'fs in the solid phase were ca lculated
as a function of temperature for various carbon contents
at a cooling rate of 0.17 K/sec and dendrite arn1 spacing
of 1 000 µm. Schmidtman 14>and Shi111 5l 1neasured ZDT
(zero ductility te1nperature) and ZST (zero strength
te1nperat11 re) of two carbon steels of Al and A2 in Table
2 as a. fu nction of carbon content, which are co1npared
with the calculated non-eq uilibrium phase diagrams in
Figs. 2(a) and 2(b), respectively. Here the thick solid li11es
represent the non-equilibrium phase diagram and the
thin lines represent the equilibrium binary Fe- C phase
diagram. The complete solidifica tion tempera ture, i.e. the
temperat ure at which the solid fraction, fs becomes 1, is
about 50-- 100 K lower than the equilibrium solidus
temperature. At low carbon concentrations (C< O. I
wt% ) in specimen A I, b- y transformation ta kes place
after steel fully solidifies, whereas a.t ca rbon concentrations (0.1wt0/o < C<0.42 wto/o) at which the peritectic
reaction occurs, b- y transformatio11 takes place d11ring
solidificatio11. The calculated complete solidification
temperatures are in good agreen1ent with the ZDTs
111casu rcd by Schmidtman, which can lead to the
conclusion that l1ot tears mainly depend on the presence
of the i11terdendritic liquid films dtie to the n1icrosegrega tion of solute elements. The measured ZSTs agree
with the temperatt1 re at which the solid fraction beco1nes
the critical solid fraction of about 0. 7 .1 5- 17l If thc solid
fraction decreases below the critical solid fraction with
increasing temperature, the steel does not have the
strength. As can be seen in Fig. 2(b), the same discussion
11olds in specimen A2. That is, the complete solidifica2.2.
‘ //
8
solute diffusion
calculation with FDM
';. \'.;.-γ
ν7 、
t
(a)
l
/
비
mixing
c。mplete
\
Fig. l. (a) Schematic drawing showing the morphology of the
dendrite array and (b) the transverse cross section
assumed in the numerical simulation.
Table l. Equili briun1 distribution coefficienls and diffusion coefficients of solute elen1ents.11l
Element
c
Si
Mn
p
s
k ~IL
k YIL
k ilfy
D6 (10- 4 × 1112/s)
D' (10 - 4 x m2/s)
0.19
0.77
0.76
0.23
0.05
0.34
0.52
0.78
0.13
0.035
1.79
0.68
1.03
0.57
0.70
0.0 127 exp( - 81 379/ RT)
8.0 exp( - 248 948/ RT)
0. 76 exp( - 224 430/ RT)
2.9 exp(- 230 120/RT)
4.56 exp( - 214 639/ RT)
0.0761 exp( - 143 511/ R T)
0.30 exp( - 25 1458/RT)
0.055 exp( - 249 366/ RT)
O.OIOexp(- 182 841 / R T)
2.4exp(- 223 425/ R T)
285
© 1996 ISIJ
ISIJ International, Vol. 36 (1996), No. 3
Table 2. Chen1ical co1npositions of carbon steels. (\vt%)
시
1.60
1.00
1.20
0.36
0.36
0.36
0.01
0.00
0.017
0.016
0.016
0.016
wm
R
mm
%
0.015
0.00
0.02
0.013
0.039
0.078
14)
15)
24)
25)
'
ro
<l.l
‘(1J
z'
--§ 100
,
‘
η
그
-0
φ
‘(
s、
•
•
ZST (a)
ZDT
--‘ ductilitv
Zer。
temo
Liquid
impenetrable
temp. Zero
strength
temp
ν
‘
」
@
m
u。-@」
긍@QE뉴
y
、
、
0.6
0.8
、
wt0/o
/
L
、
U
、‘l
t
/’
-
」@gE@LF
υ。 ω」긍m
1450
y
ZST
ZDT
0.2
0.4
、--、
、
ZDT
ZST
Temperature
LIT
자。l
끼,q
and consequently reduces the zero ductility temperature
of steel. A tensile strain applied to the mushy zone causes
the separation of dendrites. Thus, the solid fraction at
which cracks form, should be defined to investigate this .~
phenomenon in the range of 0 <자 < 1.
Clyne et αI. 21l proposed the CSC (crack susceptibility coe삐cient) to estimate the cracking tendency in
continuously cast steel. They divided the mushy zone
into the mass and liquid feeding zone and the cracking
zone. Cracks formed in the mass and liquid feeding zone
are refilled with the surrounding liquid, whereas cracks
formed in the cracking zone can not be refilled with the
liquid because the dendrite arms are compacted enot1gh
to resist feeding of the liquid. They proposed thε solid
fraction in the boundary between the two zones to be
0.9. Davies and Shin22l also used the same value.
Matsumiva et al. 5> used 0.85 as the solid fraction in the
boundary.
We adopt this concept for cracking zones. Let thε solid
fraction at the boundary between the two zones bε 많
and the temeprature at which the solid fraction reaches
많 be the liquid impenetrable temperature (LIT). We also
used 자 = 많 = 0.9 as Clyne and other suggested. When 감
the steel is fully solidified, i.e. λ = 1, the interdendritic 」/
liquid film is removed and hence the possibility of
cracking is reduced. Accordingly ZDT can be defined as
the temperature at which the solid fraction reaches unity
(ζ= 1). Therefore the brittle tεmperature range T8 may
be defined as ZDT < T8 <LIT.
I .0
l
•
Q
Fig. 3. Mechanical properties in the high temperature zone of
reduced ductility and corresponding presentation of
solid/liquid interface during casting (after Brin1acombe 18l).
Carb。n c。ntent,
•
Solidus Liquidus
temp temp
\
0
?’
ιJ
m
、
. 1350 Non-equilibrium PseudoFe-C Phase Diagram
0.2
steel
\
1450
1400
m。lten
-‘--?
그。
1550
SU「r。unding
「~
,
,
Duct씨ty
*‘
()
---Q
.0.6
0.용
f .0
wt%
Fig. 2. Non-equilibrium pseudo binary Fe- C phase diagram
of (a) 0.32Si- l .6M n-0.0 IP-0.0 l 5S carbon steel and (b)
1.0 Mn carbon steel.
Carb。n c。ntent,
tion temperatures agree with the measured ZDTs and
ZSTs agree with the temperature at which the solid
fraction is 0.7. It follows from the above results that
the nlicrosegregation analysis througl1 the direct difference method well simulates the solidification phenomena during the continuous casting.
3. Results and Discussion
3.2. Strain in Brittle Temperature Range, s~H
The total strain of steel may be expressed as
TH +ι EXT
B= ε
3.1. Determination of Brittle Temperature Range
Figure 3 shows the schematic presentation of mechanical properties of steel at high temperature. 18l
The strength and ductility of steel have a small value
below the solidus temperature because of thε existence
of interdendritic liquid film. All cracks observed in
continuously cast steel originate and propagate along the
interdendrites in mushy zone except transverse crack.
The ductility loss of the mushy zone is associated with
the microsegregation of solute elements at solidifying
dendrite interfaces.19·20l This solute enrichment locally
lowers the solidus temperature of interdendritic liquid
© 1996 ISIJ
‘‘
。
>
“-r
1350
ι
---,、 .、ι
、m
0.32
0.00
.0.10
0.14
0.14
0.14
Ref.
一「m그 ‘그(르ω
건)
M
s
、、때
Mn
Sample
(
、앉
Si
p
...... (3)
where εTI-t is the strain induced by variation of
temperature and sExT is the strain induced by external
operating factors such as 1nold flux, mold taper and
curvature of mold. In order to investigate only the effect
of steel composition on the formation of longitudinal
s11rface cracks, εTH must be investigated. BTH is generally
expressed as the sum of the strain caused by cooling and
the strain caused by phase transformation as follows:
286
ISIJ International, Vol. 36 (1996), No. 3
tha.11 that of B2. SulfL1r h<:1s the very s1nall eqt1ilibrium
distribution coefficient between solid a nd liquid pl1ases,
the complete solidification tempera ture drasticall y decreases with increasing sulfur co11tent from 0.01 3 ~1t0/o
(B2) to 0.078 \vt0/o (B4) as shown in Figs. 4(b), (c) and
4(d).
To investigate the effect of sulfur content on the brittle
1·
α *dT + /J.ε<5 -
ε TH =
}' ............... (4)
To
+A
o·
C
”
I
Z M
- c* + A
j
c” C ”y
en
1500
.... ( 5)
where 양 and A샌-;’ may be interpreted as the thermal
strain and the strain induced by b-y tra nsformation in
the brittle temperature range, respectively. The strai11,
사H, can be simply expressed as a function of density as
follows:
F
6
TH
C
‘
-
f5=0.0
1400
y
1350
f5=0.9
f5= 1.0
0.
·J
p(Tfs=o.9)
l
0.4
0.
1.0
0.8
Carbon content, wt0/o
............. (6)
1550
j
~
+ Yf:
--
.
p(T)
.......... (7)
·-4 × Io - 6 (wt1Yo C) ψ(T)
Y
~
l
JS
-
s
@
@」
gm」@gEF
0/s
Q。
{) p(T)
ι
10 -6 (wt0/oC)0p(T)
with
ll
f5=0.0
1450
、、、“
1400
、 f5=0 .7
y
1350
f5=0.9
f5=1.0
p(T) = 7875.96-0.297T - 5.62 × Io - 5T 2 (kg/m3)
(Ref. 23))
)' p(T) = 8099.79 - 0.506T (kg/m3)
/
、
Liquid
where
p(T ) =
l
이
ρ(T1. = 1 。)
(a)
Liquid
-
ιc
4
ρ6
TH -_
1550
」@QE@lF
Q。 @」긍m
LIT
α
”
셉
where T is the temperatu re, T。 is the refere nee
temperature, α * is the thermal expa.nsion coefficient
defined as α * = d.εTH/dT ar1ci Aε'5 - y is the strl:tin due to
b-y transformation. In th ε brittle tem perature range
(ZDT < TB< LIT), sTH becomes the strain in brittle
tempera.ture range, e ~H, which may be ex pressed as
0.2
δ;·
σE
1.0
0.8
Carbon content. wt0/o
(Ref. 23))
1550
Here p(T1s =T.rs) is the density when the solid fractio n
is T자, p(T1. = 1) is the density when the solid fraction is
I, and left superscripts b a nd y indicate b-Fe and y-Fe,
respectively. Since 댄 and Yf~ in Eq. (7) have been
computed as a function of temperature for va rious carbon
contents th rough the calculation of microsegregation, 17)
the var ti or1 of
using Eq. (6) .
(c)
Liquid
-
@
Q。 m」긍m」@gE뉴
3.3. Effect of Solute Element on Formation of Cracks
The strains in brittle temperature range have been
computed to investigate the effect of solute elements on
the forn1a tion of cracks fo r steel compositions of Bl ,
B2, B3 and 84 in Table 2. The Bl and 8 2 are the steel
compositions at which the effect of carbon content on
the formation of cracks has been measured by Blazek24>
and Saeki et c1!., 25> respectively. The B3 and 8 4 are the
steel compositions which i11clude the sulfur content as
much as 3 and 6 times higher than B2, to investigate the
effect of sulfur content on the formation of longitudina l
surface cracks and the carbon content at which
longitudinal cracking is maximized.
Figures 4(a), 4(b), 4(c) and 4(d) show the non-equilibrit1m pseudo binary Fe-C phase diagran1s for steel compositions of B1, B2, B3 a nd B4, respectively. Since the
manganese conten t of B I is higher than that of B2, the
complete solidification temperature (ZDT) of B 1 is lower
f5=0.0
1450
f5=0.7
1400
f5=0.9
y
1350
0.4
1.0
Q.8
Carbon content, wt0/o
1550
(d)
Liquid
1500
-
\
f
1400
ls
캐
」@gE
Q。 @」긍m
←m
f5=0.0
7
8+y
1350
.--- f5=1.0
0.2
0.4
πE
f5=0.9
σg
1.0
Carbon content, wt0/o
Fig. 4. Non-equilibri um pseudo binary Fc-C phase diagran1
of (a) BI , (b) 82, (c) B3 and (d) 84.
287
© 1996 ISIJ
ISIJ International, Vol. 36 (1996), No. 3
carbon content from C2 to C3, e~H is also only a function
of thermal contraction because 8-y transformation is
co1npleted before the solid fraction reaches T.fs· Therefore, the effect of b- y transfo rmation on the strain in
brittle temperature range becomes dominant between
C1 and C2, becomes maximum at Cmax' becat1se all b- y
tra11sformation occurs in the brittle temperature range.
Since Z DT, LIT and 8- y transfo rmation are influenced
by solute elements such as carbon and sulfur, C 1, C2 a11d
cn1ax also vary witl1 steel composition.
,Figures 7(a) a11d 7(b) show the strai11 in brittle
te1nperature ran ge as a function of carbon content ir1 the
case of Bl and B2, respectively. In the case of 81 , a
maximum strain appears at a carbon content of 0.11
wt0/o, whereas a maximum strain appears at 0.1 3-0. 14
wt0/o C in the case of B2, because the brittle temperature range and b-y transformation range vary with
tl1e conce11tration of solt1te elements. Whe11 the large
volume contraction due to b- y transformation occurs at
the final stage of solidification, the possibility of cracking increases. Therefore cracking tendency cah be
predicted using the analysis of microsegregation and the
calculation of strain in brittle temperature range. As
shown in Fig. 7(a), the strain in brittle temperature
ra 11ge is in good agreement with the longitudina l cracking freq uency. The longi tudinal cracking frequency was
measured at a commercial plant as a function of the
carbon content of line pipe steel. 24> The carbon conte11t
temperature ran ge of 0. 3 wt0/o carbon steel, tl1e ZST, LIT
and ZDT were obtained fro1n data fs=0.7 , f~ =0.9 and
λ = 1.0, respectively, in Figs. 4(b), (c) and 4(d). The rest1lts
are plotted in Fig. 5. Tl1e effect of sulfur content on ZST
and LIT is not significant, whereas the effect of sulfur
content on ZDT is significant, because sulfur is segregated at the final stage of solidification. Thus the brittle
temperature range extends to the lower temperature, and
the possibility of cracking is expected to increa.se with
increasing sulfur content.
Figures 6(a) a11d 6(b) show tl1e typical non-equilibrium
pset1do binary Fe-C phase diagram of carbon steel, and
E망I ' ε얀 and ~e~-y as a function of carbo11 content,
respectively. In the carbon content from zero to C 1, 상H
is only a function of thermal contraction because fJ-y
tra nsformation occurs after steel is fully solidified. In the
1500
•
상 1450
’
@
•
‘-----∼‘
E
--
u
e ””--’
m e o nu %
’
‘
l
@
1350
0.00
0.02
때야
s
때
•
a. 1400
끼
@
‘-
kU
‘
LIT
”미
n3
야
.--
때
•
‘그
•
ZST
-
ZDT
0.10
2.5x l0-3
Fig. 5. The ZST, LIT and ZDT of 0.3 wto/o carbon steel (B2,
B3, B4) as a function of sulfur content.
(a)
0.10Si- l .2Mn-O.O 17P-0.02S
2.0x1o·3
。3
1520
l .5xl0-3
(a)
工
뉴-
I.Ox 10·3
1480
0
-
5.0x l0-4
LTI(f.,.=O.
/
B「ittle
temperaturi
range
1440
1400
0.0
C1 Cmax
c2
0·8.oo
ZDT(f5=1 .
πi
ITT
0.4
01
55
‘
.15 0.20
σ~5
0.30
이
I.5x10·3
20 응
ro
(.)
0.14Si-0.36Mn-O.OI6P-0 . 이 is ‘15 잉
(13
't
그
10 응
,、
.。
C
”·
ν
ν
”‘
+A
커
·
재
”
ι
”‘
*,
/
、
l
j
C
’
비
2.0x Io·.)
t/
0.0020
-
πTO
Carbon content, wt0/o
Carbon content wt0/o
0.001 5
0.05
=
폰 0 I .Ox I 0·3
:0
5
μ〉
드 m」
i
0.0010
Ec
--
3-
.
u。@」긍m」@
뉴(나E@
w~
-a。H
I
QI
」Q
@@〉@그σ@」·iQ
드를
-mm
애
%야
0.08
0.04
0.06
Sulfur c。ntent, wt0/o
*
그
.---
。)
드
。
5.0xl0-4
m
0
c
。
x
φ
0.0005
ooooi.o
0.05
0.15
ι20
0.25
σ'.fO
o.3-S
c
Carbon content, wto/o
6 ‘3
.4
0.5
Fig. 7. Measured longitudinal cracking frequency24·251 and
calculated strain in the brittle te1nperature range as a
function of carbon content in (a) BI and (b) B2.
Symbols and lines indicate the measured and calculated
va Iues. res peeti vel y.
Carbon content, wt0/o
Fig. 6. (a) Typical non-equilibrium pseudo binary Fc-C phase
diagram of carbon steel and (b) 갑II‘ Ct and 6c~-y as
a function of carbon content.
© 1996 ISIJ
π 1-0
"O
288
ISIJ International, Vol. 36 (1996), No. 3
/
2x I 0-3
A
O
B
O
C
O
$쩌않
3x I 0-3
A
-
-
-
I」「
C
’
at which the solid fraction becomes a critical solid
fraction of about 0. 7 corresponded to ZST.
(2) The effect of carbon content and other sol utε
element on the formation of longitudi11al surface cracks
could be successfully explained by introducing the strai11
in the brittle temperature range.
(3) The possibility of cracking increased witl1 i11creasing sulfur content and the carbon content at which
longittidinal surface cracking freq uency is maxin1ized
decreased because brittle temperature range extended to
the lower temperatures.
Q
Ix I 0-3
0
0.0
B
L0.1
0.2
Carbon content, wt0/o
c
0..1
Fig. 8. Effect of sulfur content on strain in brittle temperature
range.
I)
2)
3)
4)
at which longitudinal cracking frequency becomes
maximum is about 0.1 wt0/o. Figure 7(b) shows the index
of longitudi nal surface cracks25> and calculated strain
in brittle temperature range as a function of carbon
content. The index of longitudinal surface cracks shown
in Saeki et al. ’s paper is a valt1e εxpressing the longitudinal surface cracking frequency. The carbon con、- tent at which the maximum number of longitudinal
cracks form is about 0.14 wt0/o, which agrees well with
the experimental observations. According to thesε
results, the strain in brittle temperature range well describεs the tendency of longitudinal surface cracking
during continuous casting.
Figure 8 sl1ows the variation of strain in brittle te1nperature range \vith the sulft1r content from 0.01 3 wt0/o
(82) to 0.078 wt0/o (B4). The strain in brittle temperature
range increases with increasing sulfur content. Even
though the effect of sulfur content on 6- y transforma.tion is not significant, the strain in brittle temperature
range increased wi th increasing the sulfur content, because ZDT drastically decreases \vith increasing sulfur
content due to the microsegregation as shown in Figs.
4(b)- 4(d) and Fig. 5. This gives rise to increase in the
thermal strain ( = 간다 α *dT) regardless of f>- y transformation, which in turn increases a~H. This result is in
agreement with the observations26 - 28> that the pos_ sibility of cracking increases with incrεasing sulfur
content. The carbon content at which longitudinal
surface cracking frequency becomes maximum decreases
from 0.1 4 to 0.1 wt0/o with increasing sulfur content,
because the brittle temperature range extends to lower
temperatures due’ to segregation of sulfur at the lower
carbon concentrations.
4.
5)
6)
7)
8)
9)
IO)
11 )
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
Conclusion
(1) Non-equilibrium pseudo-binary Fe- C phase
diagrams were calculated using the microsegregation
analysis which took 6-y transformation into account.
From the phase diagrams, the complete solidification
temperature corresponded to ZDT and the temperature
26)
27)
28)
289
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