ISIJ International, Vol. 39 (1999), No. 1, pp. 91-98

High Temperature DeformationAustenite and 6-Ferrite Regions

Behavior of Carbon Steel in the

DongJin SEOL.YoungMokWON.Tae-jung YEO.Kyu HwanOH.Joong Kil PARK1)andChangHeeYIM1)

Division of Materials Science and Engineering and Research Institute of AdvancedMaterials. Seoul National University. San56-1, Shinrim-dong, Kwanak-ku, Seoul 151 -742, Korea. 1) iron &Steel Making Research Team,Technical ResearchLaboratories, POSCO,Pohang. P.O,Box 36, 1, Koedong-dong, Kyungbuk, 790-785, Korea.

(Received on July 16. 1998.• accepted in final form on October 6. l998)

Stress-strain relations of carbon steels in the */ Phaseand ~phase regions have been analyzed throughthe high temperature tensile tests at various temperatures from 11OOto 1450'C and strain rates from I0-4to I0-2/s using Gleeble system. During hot tensile test. a ceramic fiber tube wasused to reduce the radial

temperature gradient in the heated specimen. The flow stresses of carbon steels varied not only with thetest temperatures and strain rates, but also with the process condition of cooling rate, The measuredflowstress of ~phase was lower than that of yphase. The deg~eeof strain hardening of ~phase wasnegligible

comparedwith that of yphase. Asimple constitutive equation, which takes into account temperature, strain

and strain rate, could successfully describe the measuredflow stress of carbon steel by hot tensile test. Thecaiculated flow stress was in good agreementwith experimentally measureddata.

KEYWORDS:ceramic fiber tube; cooling rate; hot tensile test; constitutive equation,

l. Introduction

In recent years, continuous casting process of steel

slabs has been developed toward higher casting sppedand thinner strand thickness to increase productivity.

These changes toward severe process conditions in-

creased the possibility of cracking in the cast strand.

To prevent the occurrence of crack in the cast strand,the better understanding on the high temperaturedeformation behavior of carbon steel is fundamentallyimportant in achieving good quality cast products,becausemanyof the cracks observed in the cast strand

are knownto be formed in the high temperature rangeof low ductility. Thus, to analyze and control the crack-ing in the cast strand, the accurate quantification of the

high temperature material properties, such as strength

and ductility, has been required.Wrayl~3) investigated the deformation behavior of

y phase and ~ phase with various steel grades, ana-lyzing stress-strain relations at the strain rate rangeof 6.7x lO4-6.7x l0~2/s and temperature range of

900l 500'C in furnace. Suzuki et al.4'5) and Revauxeta/.6) carried out remelt-type tensile tests, in which thetested specimen was deformed during cooling from the

liquidus temperature. Nakagawaet al.7) jnvestigated the

Table l.

deformation behavior of plain carbon steels in the mushyzone with the remelt type tensile testing machine. Yuetal.8) investigated the tensile behavior of the solldifyingshell subjecting to temperature gradients similar to thosein continuous casting mold. But the changes of hightemperature mechanical properties according to the

process condition like a coollng rate in continuous cast-ing have not been well described.

In this study, the high temperature deformation be-haviors of y phase and 8 phase were investigated

through the tensile tests using Gleeble 1500 system, andthen the obtained stress-strain relations were analyzedwith a simple constitutive equation. In measuringstress-strain relations of y phase, two different coolingrates were taken into account to investigate its effects onthe high temperature mechanical properties of carbonsteels.

2. Experimental Procedure

Thechemica] compositions of the speclmensAand Bused for cylindrical tensile tests are listed in Table 1. Themechanical properties of y phase and ~ phase weremeasuredwith samplesAand B, respectively. The lengthof a cylindrical specimen was 110mmand the diameter

Chemic'al composition of the specimens. (wto/.)

C Mn sl P sSampleASampleB

0.137

0.0026l 28

O,12

0.403

0,006o020

0,013

0.006

oolO

91 C 1999 ISIJ

ISIJ International. Vol. 39

was lOmm.The growth direction of solidified structure

can be assumedas samecondition in each specimen,becausethe specimensweremachinedfrom the columnardendrite region in the narrow side of as-cast slab andthe longitudinal direction, i.e., the tensile axis, of spec-imen was parallel to the casting direction.

Figure I showsa schematic diagram of high tempera-ture tensile tests using the computer-controlled servo-hydraulic Gleeble 1500 system. The specimenwasheat-ed by electrica] current along the axial direction. Vacu-

umatmosphere of about 5x 104torr was maintainedin the chamber to prevent oxidation of the specimenand minimize the heat convection which can cause aradial thermal gradient due to surface cooling.

Figure 2 shows a schematic diagram of the coveredspecimen with a cerarnic fiber tube. To control the

temperature of specimen, a R-type (Pt-Ptl30/0Rh) ther-

mocouplewas welded to the midspan surface of speci-

menas shown in Fig. 2. Workzone was taken as 10

mmand testing was performed up to a strain of 0.1.

The tensile strain of O.1 is sufficient to simulate the hightemperature deformation behavior of strand in contin-

uous casting process of steel slabs. Ferguson9) reportedthat the thermal gradients in the axial and radial

directions of the cy]indrical specimencause the strengthgradient in both directions andcould not give the strengthof corresponding temperature. Therefore, a precise

temperature control within the work zone is neededto get the pertinent stress-strain relationships at thecorresponding temperatures. To reduce the radlal tem-perature gradient of the tensile specimen, the specimenwascovered with a center-drilled ceramic fiber tube. Theceramic fiber tube is weak enough not to change the

measuredstrength. To investigate the reduction of radial

temperature gradient due to covering specimen with the

VacuumChamber

4=Tension

Thermocouple

Movingiaw Fixed Jaw

CopperGrip Specimen

Fig. l. Schematic diagram ofthe Gleeble tensile testing system.

(1999), No. 1

ceramic fiber tube, the temperature difference betweenthe surface and center axis of specimen was measuredwith the covered and uncovered specimen, respectively.In order to measure the temperature of center axis, ahole of 2.5 mmdiameter wasdrilled parallel to the tensileaxis of the specimen with a thermocouple placed at thebottom of the hole as shownin Fig. 2.

Figure 3 shows a schematic representation of twodifferent thermal histories. Patterns I and 2, which wasapplied to the tensile test of sample A. The specimenwas rapidly heated up to 1400'C, and then held beforecooling to the test temperature. Pattern I has shorterholding time at 1400'C and faster cooling rate froml 400'C to the test temperature, than those of Pattern 2.

Tensile tests of sample A in the austenite region wereperformed at the temperature range of 1100-1 300'C andstrain rate range of 10~4-lO~2/s.

Tensile tests of sample B in ~ phase region wereperformed in the ternperature range of 1400l 450'C andstrain rate range of l0~4-l0~2/s, because the 8phaseappears during continuous casting of ultra low carbonsteel and low carbon steel at the initial stage ofsolidification. Thermal analysis with sample B by theheat-flux DSCwasconducted to confirm that the sam-ple B is ~ phase in the test temperature range of

l 400-1 450'C. The specimen was heated up to 1500'Cwith the heating rate of l'C/s, and then maintainedlOmin before cooling with the cooling rate of 1'C/s.

The 8/y transformation temperature during heating wasabout 1390'C, and that during cooling was aboutl 372'C. In tensile testing, sample Bwas heated up to

l 450'C for full transformation into 8phase, then tested

at the temperature of 1450, or 1400'C after cooling withthe cooling rate of 5'C/s.

3. Constitutive Equation for Deformation

Anumberof studies have beenconducted by previousworkerslo- 13) to develop constltutive equations descri-

bing high temperature deformation behavior of metals.With relation to the continuous casting of carbon steels,

Kozlowski et al. 14) developed various unified constitutiveequations defining inelastic strain rate as functions ofseveral variables such as stress, temperature, plastic strain

and time in order to model the mechanical behavior ofcarbon steel in yphase region as follows.

~p=~p(a, T)........

.,,,......(1)

JawArea

lOWork Zone Meehanical

Restraint

L_~~_]r,E'~~1S~!~~pan

110

O1999 ISIJ

Fig. 2.

SpecimenLength

Schematic diagram of the specimen.

92

unit : m:n

ISIJ International, Vol. 39 (1999). No. 1

i400 'C

Fig. 3.

Pattern 1SchematicPatterns l

representation

and 2.

1400'C

Pattern 2of thermal histories of

~p=~p((T, T, t)..........

..........(2)

ip=~p(a, T, 8p).........

..........(3)

~p=~p(a, T, t, ep)......

..........(4)

Ueharaet al. I s) usedHollomon's equation in modelingcontinuous casting of low carbon steels as follows.

a=K8" ............(5)

Strain hardening exponent, n, assumedto be dependent

on the strain rate, wasdetermined from the experimen-tally obtained curve, as a function of the Zene~Hollomonparameter, Z.

Garofalo suggested the relation between effective

plastic strain rate, ~p, and flow stress, (T.16) Flow stressis determined by a balance between the accumulation ofdislocations due to strain hardening and eliminatlon ofdislocations due to recovery.

ip =Aexp( - Q/RT)[sinh(c((T)] 1/"'..

.........,(6)

Hanet al,17) proposed the following relation in order

to obtain an expression for the flow curves at various

temperatures and strain rates,

~p=Aexp( - Q/RT)[sinh( pK)] 1/"'

.. . . ... . .

.(7)

(T=K8'p'

whereAandPare constants, Qand Rare the activation

energy for deformation and the gas constant, mis thestrain rate sensitivity, Kand n are the strength coefficient

and the strain hardening exponent, respectively. Theparticuiar case of Eq. (7) for 11=0, corresponds to the

form of Eq. (6).

Assuming the negligible elastic strain at high tem-perature range, the parameters in Eq. (7) can be de-

termined by a non-linear curve fitting of all the exper-imentally measuredstress-strain curves. The high tem-perature deformation behavior of continuous castingsteels can be quantitatively described as a function ofthe process variables such as strain, strain rate andtemperature using the Eq. (7).

4. Results and Discussions

Figure 4shows the measuredtemperature difference,

AT, between the surface temperature, T~, and center axis

temperature, T., of the covered sampleAspecimenwiththe ceramic fiber tube and the uncovered specimen. In

93

O

HF~

Fig. 4.

70

60

50

40

3a

20

10

o

o-- uncovered oe- covered

olololo ll o

ol o ee-eellel

2a

800 900 1Oao I i OO 1200 1300 140aSurface Temperature, oC

Comparison of the measured radial temperaturedifference of sampleAbetweencovered and uncoveredspecimen as a function of surface temperature.

16

~:~ 12

(D

8~s(D

Fig.

4

o

uncovered

-Ocovered

1200"c

-C]- -1- 13000c _e-e-e-eo-O-~e-e o-O-~6L~~(';~(':~~(';:dll:~ioe-O-O-

/8//&/~' _I-1-1-Iel& -I-I-l-I-I~Il~// ~o/ Cl- Cl

= ~1 ~D~I~1 1 C]~C]~. •--C]~'/1-~ Cl~~l~il~ c]'-~C]

C]*-~_l

0.00 0.02 O.04 O06 O08 O10

Strain

5. Comparisonof the me'asured flow stress of sample Abetweencovered anduncovered specimenas a functionof strain at the strain rate of l0~3/s.

the uncovered specimen, the temperature difference

betweensurface and center axis increases with increasingsurface temperature. This temperature difference is dueto the heat loss at specimensurface mainly by radiation.

Heat loss by convection in vacuumis reported as about0.1 o/o of total heat loss,18) With ceramic fiber tube, the

temperature difference decreases and becomealmostuniform as about 17'C avove the surface temperature of

l OOO'C,becausethe ceramic fiber tube prevents the heatloss by radiation at the specimen surface. Suzuki et al.4)

measuredthe temperature difference betweensurface andcenter axis of 0.1 o/o Csteel specimen without coveringand reported that the ternperature difference is about50'C. Therefore, the high temperature tensile tests withceramic fiber tube can provide the precise mechanicalbehavior of carbon steel at the given test temperature.In this study, the surface temperature was used as the

test temperature.Figure 5showsthe effect of covering on the flow stress

of sampleAat the strain rate of 10~3/s. Theflow stresses

of the covered and uncovered specimens decrease withincreasing test temperature. At the given test tempera-tures, the fiow stress of the covered specimen is about

l2 MPahlgher than that of the uncovered specimen. Atthe same test temperature, the surface temperature of

(c) 1999 ISIJ

IS]J International, Vol.

test specimen is the same, but the temperature at the

center axis of the covered specimen is lower than that ofthe uncovered specimen, due to the temperature dif-

ference along radial direction as shownin Fig. 4.

Figure 6shows a schematic diagram of temperatureprofile in the specimenat the sametest temperature. Thecenter temperature of specimen decreases from T.,2 toT*,1 whenthe specimen is covered. Thus, the apparentmechanical properties of the covered specimen is higherthan that of the uncovered specimen. An uncoveredspecimen partially melted in the center axis at the test

temperature of 1400'C, because of higher temperatureof center axis than surface temperature due to large radi-

al thermal gradient.

To calculate the flow curves of y phase, the ex-perimentally measureddata of Patterns I and 2 werebest fitted to Eq. (7) by a non-linear fitting method toobtain parameters in Table 2. The evaluated activationenergies for the deformation of y phase, which can beassumedto be constant for homologous temperature(TIT*) greater than O5,12) were found to be 373.4 and422.9kJlmol in Patterns I and 2, respectively. Previousreports on the activation energy for deformation of p]ain

carbon steels in y phase region are listed In Table 3.

As-cast specimenshave larger initial grain size than hotworked specimens, and the activation energies for de-

formation of the as-cast specirnens are higher than

ro

r

Thermocouple

Specimen rz I

l

WorkZone

-\ r:~\

radial direction

\ \ z: axial direction

\l COVered uncovered ro: specimenradiL

l \ Ts : surface temp.i Tc : center axis ter

specimenradius

O T* Tc.1center axrs temp.

T, 2Temperature

Fig. 6. Schematic diagram showing the radial temperatureprofiles from the center axis to surface.

39 (1999), NO, 1

those of the hot workedspecimens, as shownin Tab]e 3.

Figure 7showsthe austenite grain size of sampleAas

a function of test temperatures in each pattern. Theaustenite grain size was measuredby intercept methodusing the quenchedspecimenafter loading thermal cyclescorresponding to each pattern before tension. Thegrainsize of Pattern 2at various test temperatures are abouttwice as that of Pattern I .

Larger yaustenite grain slze

of Pattern 2before tensile deformation is related withthe longer holding time of Pattern 2than that of Patternl. The change of yaustenite grain size according to thetest ternperature in each pattern is small, as shown in

Fig. 7, which meansthat the grain growth of sample Aduring cooling to the test temperature from 1400'C is

small. Maeharaet al.22) resported that the rapid graingrowth of austenite occurs after austenitizing tempera-ture during cooling and the change of grain size before

or after occurrence of the rapid grain growth is quitesmall.

Figure 8showsthe measuredand calculated flow curvesof y phase (sample A) at various strain rates andtemperatures with both cases of Patterns I and 2. Thesymbols indicate the measuredstress of yphaseand lines

indicate the calculated stress of y phase by the Eq. (7)

with the obtained parameters in Table 2. At a given strain

rate, the flow stress of yphasedecreases with increasingthe test temperature. As the strain rate increases from10~4 to l0~2/s, the flow stresses of y phase in-

30

EEa)

N~5

c~~

*O(D

ce)

co:::

25

20

15

10

05

I

,

l

o-

I

o...

lr• • Pattern 1• Pattern 2

o

Table 2. Parameters in Eq.

Fig.

i050 1100 il50 1200 1250 i300 1350 1400 1450

Temperature, oC7. The austenite grain size of sample A as a function of

test temperatures in each pattern,

(7) of yphase in two patterns.

AT(S'I) Q,(k J/mol) PT(MPa~1) m7 nT

Pattem I I 192 x 1010 373.4

Pattem2 1. 192 x lOro 42290.0381

0.0715

0.2363

0.2038

0.210

0.1544

Table 3. Reported activation energies for deformation in ~' phase region.

Investigator Year QT(kJ/mol ) Specunen Initial grain size('Jwl)

Sakui et al.21) 1977

Sakai et a!. 19] 1981

Kozlowski ela!.14) 1992

Kime! a!.20) 1996

This study 1998

288

286

373~69

326

373~423

O16'/oC steel 40-50(hot rolled and heat treated)

O.160/eC steel 40-60(hot forged and rolled)

various carbon steels 50-500(vacuummelted)

O10'/,C steel

(hot rolled)

O. 1370/,C steel I130-2070(as-cast)

C 1999 ISIJ 94

ISIJ International. Vol. 39 (1999), No. 1

a5o_~co(oo

(,)

COCL~u,co(D

(/)

35

30

25

20

15

10

5

o

(a) ~=10~4/s

0,00

35

30

25

20

15

10

5

o

~L,

I lC]

o

Cl

o

Cl

o

i IOO

Cl

1200

A1300'c

Odh-A• -e-

Pattern 1Pattern 2

c]c]~loJ:lc] c:lJ:lo

A A AA, ~ A A=

O o O. O, o O O O_ O.

Line calculated by Eq (7)

o02 0,04

(b) ~=10~3ls

A~~~~ e

o o (yc,o

ooo

35

30

25

c!,

O_ 20~

coco

15oU) 10

Fig.

5

o

o02

(c) ~=10~2/s

O

~

~eo

Cl

~e

Straino06

11OO

D

t~200

A=h

0,08

1300'c

o~r

o lo

Pattern 1Pattern 2

[]

II Ill~~~2~~~

e e• oeo O OO

o04

Cl

I

o

I

o

Line calculated by Eq (7)

Strain

OC]

b ~5 'O

Line calculated by Eq (7)

o06

[:]

I

D

O08 o lo

CIC],

l I

AJL

C]

~A

1100 ~200 1300*C

C] A O-1- ~=Ih

C]

A,A

Pattern 1Pattern 2

0.00 O02 O100.04 0.06 0.08

Strain

8. The measured (symbols) and calculated (lines) flow

curves of ~/ Phase(sample A) in two patterns at various

temperatures and strain rates of (a) I0~4/s, (b) lO3/sand (c) lO2/s, respectively.

crease as shown in Fig. 7. At a given strain rate andtest temperature, the difference of flow stress betweenPatterns I and 2 is observed in all the flow curves of yphase. The fitted flow curves by Eq. (7) are in goodagreementwith the experimentally measuredflow curves.The high temperature deformation behavior of carbonsteel in yphase region can be well described by Eq. (7).

Theflow stresses of Pattern I increase morerapidly thanthose of Pattern 2with the increase of strain, as shownin Fig. 7. Smaller initial grain size in case of Pattern l

95

54 -I -1 1OO'C

3 --A--12000c

2 ---e -- 13000c

1a;O_ O~t~ -1

-2 'I

_3 A-4

-5

~I

I_//~~/

// JL

l~ eA ~""~~~e___/

1O~' I0~3 10~2

Strain Rate, S~1

Fig. 9. The difference between the fiow stress of sample A in

Patterns I and 2as a function ofstrain rate at a givenstrain of 0.05.

leads to more rapid dislocation accumulation and sopromotes an increased strain hardening,23) which is

shownas the nv of Pattern l. 0.210, comparedwith thatof Pattern 2, 0.1544, in Table 2.

Figure 9showsthe differences between the fiow stress

of sample A in Patterns I and 2as a function of strain

rate at a given strain of 0.05. ACFin the figure meansthedifference between the stress of Patterns I and 2 i.e.

crl

-cr2 where the superscript indicates each pattern. At

a given strain rate of l0~4/s, the flow stresses of Pattern

2 are 2-3 MPahigher than those of Pattern I,which

shows the negative value of Acr. But the flow stressesof Pattern I becomelarger than those of Pattern 2with increaslng strain rate. The trend of increasing A(T

with the increase of strain rate is more distinguished atlower temperature. In case of lower temperature andhigher strain rate, the flow stress of Pattern I showshigher value than that of Pattern 2. In case of highertemperature and lower strain rate, the flow stress ofPattern 2has higher value than that of Pattern I .

Thedeformation of carbon steel within the experimental

ranges of the strain rates and temperatures is proceededwith diffusion and dislocation glide.24) The contribu-tion of diffusion to plastic flow increases with highertemperature and lower strain rate. As the large grain size

increases the distance of lattice diffusion, the strengthincreases with the grain size increasing at high tem-perature deformation.25) The higher stress of Pattern

2at higher temperature and lower strain rate is due tothe larger austenitic grain size of Pattern 2, as shownin

Fig. 7. However, in case of lower temperature and higherstrain rate, the flow stress of Pattern I becomelarger

than that of Pattern 2. The strengthening of grainrefinement is due to the fact that the dlslocation glideis more dominant mechanismthan diffusion at lowertemperature and higher strain rate. At the test tem-perature of 940'C and the strain rate of 2x 10~3/s,

Sakui et al.21) reported that the flow stress of 0,16 o/o Csteel with the initial grain size of 31.5ktm was about4-5 MPahigher than that with the grain size of 68.6 pmin the initial stage of deformation up to astrain of O. 15.

Figure 10 shows the flow stresses of sample A in

C 1999 ISIJ

ISIJ International. Vol. 39 (1999). No. 1

~~Uf lo

(D

8=0 05

O '

O pattern 1O~l

AO

Line calculated by Eq

I

Paftern 2l 1100'C

A 1200'C

e 1300"C

(7)

108 109 1Olo IO11 1013 10141012

ZFig. lO. The flow stress of sampleA in each pattern at a given

strain of O05 as a function of Zener-Hollornonparameter, Z.

85

8,0

~~ 75eoL

cC'~5 7o"h~~

65

60

(a)

Pattern I Pattern 2cl l 8=0 O1

A A 8=0 05

o e 8=0 i

~I

~=i0~4/s

Line calculated by Eq (9)

~

Patterns I and 2 at a given strain of 0.05 as a func-tion of Zener-Hollomon parameter, Z, where Z=~exp(Q/RT). The symbols indicate the measuredstress

of yphaseat the given strain of 0.05 and the lines indicatethe calculated stress of y phase by the Eq. (7). Themeasuredflow stresses of each pattern at various strain

rates and temperatures can be described by the Eq. (7)

in an experimental accuracy. The slope of each curve at

a given strain, alog cr/a log Z s' can be expressed by direct

differentiation of Eq. (7) as follows.

alog (T

alog ~ =f(a)je"II,

where ,f(a)=tanh(pK) K=..........(8)

(T

pK ' e"

The slope of each curve is a function of strain ratesensitivity, m. The flow stress of Pattern I at the givenstrain increases morerapidly than that of Pattern 2withthe increase of Zdue to the larger mof Pattern I ,

O.2363,than that of Pattern 2, 0.2038, as shownin Table 2. TheZener-Hollomon parameter, Z, is a function of theactivation energy for deformation, Q, at a given strain

rate and temperature. The larger activation energy for

deformation of Pattern 2, 422.9kJ/mol, than that ofPattern 1, 373.4kJ/mol, gives the larger value of Z at agiven stress and shifts the curve of Pattern 2 in thedirection of Z increasing.

To see the effect of temperature, the fol]owing relation

can be obtained by taking the natural logarithm of Eq.(7).

In[r~Isinh(pK)] mQYI where rm

,

()= =8

R )~7 A.

(9)

Figure 11 shows the measured and calculatedIn[i•1 sinh(pK)] of sample A in each pattern at givenstrains and strain rates as a function of the inverse oftemperature, l/T. The symbols indicate the measuredIn[r~1 sinh(pK)] and the lines indicate the calculatedvalues by the Eq. (9) wlth the obtained parameters in

Table 2. The measuredvalues are in good agreement

o62 o68 o70 0.72 o74o64 o66

10001T K~1

85

80

~: 7.5

c~/:'~co 70

65

60

(b)

Pattern I Pattern 2C]

'

I 8=I0~2/s

A dL ~=IO'3ls

o e ~=I0~4/s

~Q

8=0 05

f:l

JL

Line calcuiated by Eq (9)

o62 O68 O70 o,72 o74o64 O66

1000/T, K~1

Fig. Il. Plots ofln[,•~1 sinh(fik)] ofsample A in each patternat given strains andstrain rates as a function of (IIT).

with those calculated within the experimental ranges ofstrain, strain rate and temperature. The slope of eachline was referred to as the temperature sensitivity pa-rameter,26) which means the strain rate compensatedactivation energy for deformation. The temperaturesensitivity parameter of each pattern does not changewith the variation of strain, as shown in Fig, I l(a),

because the strength coefficient, K, is constant along aflow curve. The lines in Fig. I I are almost parallel,

which meansthat the temperature sensitivity parameterof each pattern is almost the samevalue in spite of thedifferent cooling rate and holding time before tension.

The respective values of ,n and Qof each pattern, Iisted

in Table 2, are different each other, but the product mQare almost the samevalues.

To calculate the flow curves of ~ phase, the ex-perimentally measureddata were best fitted to Eq. (7)

by a non-linear fitting method to obtain parameters in

Table 4. Theevaluated activation energy for deformationof 8phase, Q6, wasobtained as 216.9 kJ/mol, similar tothe activation energy for lattice self diffusion in ~phaseof 251 kJ/mol.24) Strain hardening exponent of 8phase,

n~, was obtained as 0.0378, representing the negligible

hardening in comparison with that of yphase.Figure 12 shows the measuredand calculated fiow

curves of sample B in 8phase region at various strain

rates and temperatures as a function of strain. The

C 1999 ISIJ 96

ISIJ lnternational, Vol. 39 (1999), No. 1

Table 4. Parameters in Eq, (7) of 6phase.

A6(S'I) Qs(kJ/mole) Ps(MPa~1) ms ns

6754 > 108 216.9 0,0933 O1028 0,0379

5

4

CU

C~3~~

~2(1)

1

o

~=I0'2/s

O O O• O, O. O

~=10~3ls

Measured Calcuiated

i4000cO

. - 14500c

~=10'4/s

OOO O02 O04 O06 O.08 0.1 OStrain

Fig. 12. The measured(symbols) and calculated (lines) flow

curves of sample B in 6 phase region at various

temperatures and strain rates.

of ~phase showssteady-state stress development com-pared with the strain hardening of vphase, because thestrain hardening exponent of ~phase is close to zero.

coCL:~

ufu)q)

(/)

10

8

6

4

2

o

-o- YPhase

e- 6phase

l01010-0-0-0 OO-O-O-O-O-OO O

010/Oe-e-e e e e o e e e e e e o e e e

e

OOO o02 0,04 o06 O08 O10

St ra inFig. 13. Comparisonofthe measuredflow stress of sample B

wrth that of sample A at 1400 Cand ~= l0~3/s.

symbols indicate the measuredstress of 6phase and thelines indicate the calculated stress of 6phase by the Eq.(7) with the obtained parameters in Table 4. At variousstrain rates and test temperatures, the calculated fiow

curves of ~phase by Eq. (7) are in goodagreementwiththe experimentally measured flow curves. The hightemperature deformation behavior of carbon steel in ~phase region can be well described by Eq. (7) as well asin yphase region.

Figure 13 shows the measuredflow curves of sampleBin 8phase region and sample A in yphase region, atthe given strain rate of 10~3/s and test temperature of

l 400'C. At the initial stage of deformation, the flowstress of y phase is twice as high as that of ~phase,and as deformation proceeds, the difference of flow stress

between two phases becomelarger at the given strain

rate of l0~3/s and test temperature of 1400'C becauseof the larger strain hardening of y phase, as shown in

Tables 2and 4. Lower Q, mand n of ~phase results in

lower flow stress than that of y phase. The flow stress

5. Concluslon

High temperature tensile tests were carried out on the

as-cast carbon steels at various strain rates from l0~4to 10- 2/s and temperatures from I 100 to 1450'C in orderto describe the flow stress with respect to process variablessuch as strain, strain rate and temperature, in the yphaseand 8phase region. Covering tensile specimen with theceramic fiber tube reduced the temperature difference

between the center axis and surface of specimen due tothe heat loss at specimen surface. Measuredflow stress

of y phase varied not only with the change of test

temperature and strain rate, but also with the changeofthe holding time and cooling rate due to the change ofgrain size. The temperature sensitivity parameters of the

two different thermal patterns were the same. The fiowstress of ~phase wasmuchlower than that of yphaseand the degree of strain hardening wassmall comparedwith that of y phase. The simple constitutive equation,in which the parameters weredetermined from non-linearfitting of experimentally measuredflow curves, quantita-tively described the stress-strain relations of yphaseand~phase.

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