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The strain rate as a factor influencing the hot forming simulation of medium carbon microalloyed steels
MATERIALS SCIENCE & ENGINEERING ELSEVIER
Materials Science and Engineering A216 (1996) 155-I60
A
The strain rate as a factor influencing the hot forming simulation of medium carbon microalloyed steels M. Cars?, V. Ldpez a, F. Pefialba b, O.A. Ruano a aDepartment of Physical Metallurgy, CENIM, CSIC, Av. Gregorio del Amo 8, 28040 Madrid, Spain bINASMET, Camino de Portuetxe i2, 10009 San Sebastian, Spain Received 9 February 1996
Abstract
Two medium carbon microalloyed steels, one with vanadium and the other with vanadium and titanium, have been studied by means of high-temperature torsion tests. The evolution of tile austenitic grain size with defomaation has been determined together with the rheological characteristics. On the basis of these data, the apparent activation energy for deformation and the Zener-Holiomon parameter have been calculated. The dependence of the final austenitic grain size on the initial one and on the thermomechanical treatment conditions (true strain, true strain rate and temperature) have been analyzed. Two mathematical expressions are proposed to describe the evolution of the austenitic grain size due to static or dynamic recrystallization. It was found that the strain rate can be as important as the strain to influence the final microstructure and therefore the mechanical properties of the final product. Keywords: Medium carbon steels; MicroalIoys; Grain size; Torsion simulation
1. Introduction The different factors influencing the thermomechanical steel treatments have been studied for decades on low carbon steels due to their importance in the optimization of the final products. Specifically, the austenitic grain refining induced in microalloyed steels, at a determined strain and strain rate, is of great importance to obtain improved mechanical properties [1-53 On studying the thermomechanical treatments, it is usual to give a paramount importance to the strain, and only a secondary relevance to the strain rate. The laboratory simulations usually follow strictly the temperature and the amount of deformation of the thermomechanical treatments. However, these simulations have usually been conducted at strain rates lower than those used in industrial processes. The object of this work is to demonstrate the influence of the strain rate on the final results, showing the importance of carrying out the simulations at strain rates similar to those used in industry. The final austenitic grain size is related to the size before simulation as a function of strain, strain rate and treatment
temperature. The simulations have been carried out by means of torsion tests on medium carbon steels (0.300.40%C) which are used in critical automotive components (wheel hubs, crank-shafts, etc.). 2. Materials and experimental procedure
Two microalloyed steels have been studied. Their compositions are shown in Table 1. The first steel is a typical medium carbon vanadium microalloyed steel. The second steel has a higher carbon content and a small percentage of titanium is added. Hot torsion tests have been conducted on these steels. The torsion machine, describe(t elsewhere [6], has a maximum speed of 2400 rpm. The torsion samples had a gauge length of 17 mm, 6 mm in diameter in the deformed region. A non-deformed region of 12 mm diameter is present in the head of the sample. The samples are heated by a high frequency induction furnace. The temperature measurement, by means of a two-colour pyrometer, is continuous. The samples are introduced in a silica tube, with a helium inlet, to ensure protection against oxidation and to minimize adiabatic heating (about 10 K at 14 s-1 and 1398 K).
156
M, Carsi et al. / Materials Science and Engineering A216 (I996) 155-160
Table 1' ChemicaI compositions in wt. % and p,p.m.* %C
%Mn
%Si
%S
%P
%Cr
%Ni
%Mo
%V
%Ti
%Cu
%Sn
%A1
N~
O~
0.29 0.38
1.30 1.30
0.41 0.48
0,026 0,039
0.021 0.020
0,09 0.15
0.10 0,14
0,02 0.04
0.10 0.12
0,003 0.011
0.24 0.21
0,02 0.02
0,029 0.030
0,0167 0.0147
30 34
Steel I Steel 2
The strain, e, and the strain rate, ~ can be obtained by means of the following expressions [7]: G=
=
27rRN
(1)
2rcR~
(2)
where R is the sample critical radius, N the number of turns, 3? the number of turns per second and L the effective sample length. The effective stress in a torsion test can be defined, at the critical radius, as [7] o--F _~j---~ ~( 53 -
+ 3 ( 0 + m))
(3)
where F is the torque, r the sample radius, 0 the work hardening exponent in the equation 0= dlnF d in e k r
(4)
and m the strain rate sensitivity in the equation m
=dlnF dln~l~,r
3. Results and discussion
Fig. 1 shows an example of torque-strain curves for steel 1 obtained directly from torsion tests at 1423 K. These curves can be transformed into stress-strain curves by means of Eqs. (3), (4) and (5). Fig. 2 shows these curves for the same steel in a plot cr versus e. The curves clearly show a decrease in stress, after reaching a maximum, until a constant value is obtained. The start of this regime, considered as the steady state, is obtained at increasing strains with increasing strain rates. However, the steady state is present in all curves at a strain of 1.5. The stress corresponding to this value of strain has been used for calculation of the Zener-Hollomon equations. The parameters given in Eq. (6) (Q, A, ~ and n) can be obtained from stress-strain curves in the steady state at different temperatures and strain rates by means of an algorithm [8,9]. Specifically, values of o', and T correspond to data given in Fig. 3 for steel 1 and in Fig. 4 for steel 2. The Zener-Hollomon equations particularized for both steels are the following: Steel 1:
(5)
exp(252 kJ/mol per RT) = 1.015 x 1011(Sinh 0.0064e) 5'21
Torsion tests to determine 0 and m were conducted to failure. The Zener-Hollomon equation, used to relate the temperature, strain rate and steady state stress, o-, is given as follows: exp(Qder/RT ) = A (Sinh c~¢)"
(6)
where (2a~ris the apparent activation energy, R = 8.314 J/mol the gas constant and A, ~ and n are material constants. The term ~ e x p ( 0 d d R T ) = Z is the ZenerHollomon parameter. The values of Qd~r, A, c
(7)
Correlation r = 0.997 Steel 2: exp(301 kJ/mol per RT)
(8)
= 4.360 x 1014(Sinh 0.0039~) 5'3° 4 14 s "1
3
F, Nm
i
2 s °1 t
t
0
0,5
I
1,5
2
2,5
3
Numberof turns Fig.' 1. Torque versus number of turns for Steel 1.
157
3I. Carsi et al./ Materials Science and Eugineering A216 (199.6) I55-I60 140
. . . .
1206080
~
. . . .
~
. . . .
,
. . . .
,
. . . .
10 tlS~ [
J ~
Z
..... l
o, MPa
,,~x, I oo,',~,,
',Y,I~ : {
........
E,s "1
40
~ o • C • © •
20
0.5
1
1.5
2
2.5
K K K K K
i
60
Fig. 2. Stress vs. strain at various temperaturesand strain rates.
1323 1353 1393 1423 1453 1473
10.0 c~,MPa
Correlation r = 0.996 The Zener-Hollomon approach is usually used to describe the creep behavior in a wide range of strain rates and temperatures. From a more basic approach, it is usual to analyze the data by means of a power law equation of the form: i = K exp(Qa~f/RT)crn'
(9)
where K is a material constant and n', the stress exponent, shofild be equal to n when the Sinh is equivalent to the arc. Independently of n', the Qdefvalue should be the same as that obtained from the Zener-Hollomon equation. Figs. 3 and 4 show strain rate versus stress curves for steels 1 and 2, respectively. The figures show that the experimental data obtained at six different temperatures can be accurately described by Eq. (9). The n values at the different temperatures are close to 6. The difference between this value and that obtained from the Zener-Hollomon equation can be attributed to the c~G producthaving a valffe higher than 0.8 and therefore to the Sinh(c~o-) being higher than c~a. The activation energy for deformation of both steel's can be obtained from Figs. 3 and 4 by plotting the strain rate at a given stress as a function of the inverse of the absolute temperature. The results are presented in Figs. 5 and 6 at a stress of 90 and 80 MPa for steels 1 and 2, respectively. The Qdefvalues are 255 and 295 k J/tool for steels 1 and 2, respectively. These values coincide with those obtained using the Zener-Hollomon equation (252 and 301 kJ/mol). It is known that the final austenitic grain size under static recrystallization conditions can be related to the Zener-Hollomon parameter, Z, by the equation [1114]: Drec = ]':D0~ ; Z q
Fig. 3. Strain rate vs. stress for Steel 1. The study of these steels under static recrystallization conditions was carried out considering deformations lower than 0.8 times the cteformation at the peak stress. Figs. 7 and 8 show thefinal austenitic grain size under static recrysiatliz.atiori, conditions as a function of deformation at various strain rates for initial austenitic grain sizes of 1t0 and 70 ~m for steels 1 and 2, respectively. The data from Figs. 7 arid'8 can be used to obtain the parameters k, p, and q of Eq. (10). This has been done using the regression plane derived from Eq. (10). Its general expressionis logDr~o=logk+logDo+p(lbge)+q(logZ)
(11)
The activation energies used, included in Z, are those obtained by the mathematical algorithm of the ZenerHollomon equations. Initial austenitic grain sizes in the range 125-55 pm were considered. The following relations were obtained: Steel 1:
D r e o = 2 1 . 2 D o e - ° ' 4 2 Z -°'I8°
(12)
Steel 2:
Drec= 317.3Doe-°'21Z -°''-35
(13)
. . . .
i
•
10
~, S-1
///
/
~
~
•
1353 K ,~73 K
--x--- 1398 K
(1 O)
where k is a material constant, D~o the recrystallized austenitic grain diameter, Do the initial austenitic grain size, and p and q are parameters describing the static recrystallization process.
t
),~ 1423 K ,
60
,
,
~, MPa
1
r
I00
Fig. 4. Strain rate vs. stress for SteeI 2.
158
M. Carsl et al./ Materials Science and Engineer#zg A216 (1996) 155-160 .
10
40
.
2/;:
.
.
.
i
~,s-1 ~=90 MPa < ' ~ Q=255 kJ/Mol
2 r
i
6.6 10.4
r
I
I
r
t
7.0
'
i
,
i
I
1 0 .4
i
r
r
7.4
I
,
I
20
'
i
h
i
l/T, K"~
i
1
1.00
0,30
1 0 "4
Fig. 7. Static recrystallization behavior. Final austenitic grdn size vs. strain at different strain rates for Steel 1.
Fig. 5. Strain rate vs. 1/T at ~r = 90 MPa for Steel 1.
Eqs. 12 and 13 clearly shows the similar values of the exponents p and q, within th~ same order of magnitude, for the case of static recfystallization conditions. This means that the strain rate carl be as important as the strain to influence the final microstructure and therefore the mechanical properties of the final product. Therefore, it is important to simulate the industrial process at strain rates similar to those used in production. The study of these steels under dynamic recrystallization conditions was carried out considering deformations higher than e = 2. The final austenitic grain size under dynamic recrystallization conditions can be related to the Zener-Hollomon parameter by the equation [11-14]:
D~o = k'Zq'
r
(14)
where k' is a material constant and q' is a parameter describing the dynamic recrystallization process. Fig. 9 and Table 2 shows the final austenitic grain size under dynamic recrystallization conditions as a function of deformation for both steels at different austenitizing
temperatures. The data were related by means of the regression line corresponding to the equation log Dre c = log K' + q' log Z
(15)
using various initial austenitic grain sizes in the range 150-60/Lm. The final austenitic grain size was found to be independent of the initial grain size for both steels. The following relations were obtained fl'om the experimental data: Steel 1:
D = 2 6 1 5 Z -°'2°°
(16)
Steel 2:
D = 42 446Z-°'266
(17)
It is inferred by comparison of Eqs. (12), (13), (16) and (17) that q and q' have values less than zero and that are lower for steel 2 than for steel 1 ( - 0.23 < 0.18 and - 0.27 < - 0.20). Assuming q and q' less than zero, it can be demonstrated that the grain size increment diminishes with increasing values of Qdef with the condition Qa~r> - RT/q (or Qdot"> -- RT/q'). The maximum value of the activation energy is 72 kJ/mol
10 -.--o.--14
•
s"l
.=
S'1
or= 8 0 Q= 295 kJ/Mol
3
30
.i,I.ll,Frl,rl.rrll,r,,tr.I,Fr,,rPrll
7.0 10.4
7.2 10.4
7.4 10.4
~ ,3
,
r
e
l/T, K" Fig. 6. Strain rate vs. 1/T at o-= 80 beiPa for Steel 2.
Fig. 8. Static recrystallization behavior. Final austenRic grain size vs. strain at different strain rates for Steel 2,
M. Carsi et al. / Materials Science and Engineering A216 (I996) i55-I60 40
159
80 Static rec. Dynamictee.
6 0
"/0
zx A
60 /x
._= 50
g
AZ~ &
..= 20
.=
× •
Steel I (I353 K)
•
Steel 1 (1398 K)
X
Steel 2 (1353K)
•
Steel 2 (1398 KI
A&
40
•
A ;
30
rn~
×
Z~ A &
rT~ A []
20 12
I ,
10
t
i
10
20
10
20
Fig. 9. D y n a m i c recrystaliization behavior. Final austenitic grain size vs. strain rate for the two steels.
(for q = -0.18 and T = 1573 K). This value is much lower than the Qdefvalue of any steel. This implies that the grain size increment of steel 2 should be lower than that of steel 1 since the activation energy is higher in steel 2 than in steel 1. This is in agreement with the experimental observations and also in agreement with the role of titanium as grain growth inhibitor [11,15,16]. The recrystallized grain size for both steels are of the same order of magnitude. However, the solutions obtained from Eqs. 10 and 14 give different orders of magnitude for lc and k'. This is because the term Z is an order of magnitude lower in steel 2 than in steel 1 (Q~ef and q' are higher in steel 2 than in steel 1). Therefore, k and k' have to be an order of magnitude higher in steel 2. The values of the Z exponent are similar to, those found in the literature and close to those obtained by Yoshimura et al. [13]. A good concordance also exists between the predicted values of Q from the algorithm method and the experimental data. The mathematical solution for the Zener-Hollomon equation provides a Qdof value that is probably more accurate ( + 5 kJ/mol) than that obtained from Figs. 5 and 6. According to Tamura et al. [11] the grain size depends exclusively on the Zener-Hollomon parameter if dynamic recrystallization processes occur. This is in agreement with observations of the grain size for steel 1 at different strain rates and initial austenitic grain sizes (Fig. 9 and Table 2). For e/> 2 the final austenitic grain size is independent of the initial one. It can be observed that for 110 Izm or 65/~m initial austenitic grain sizes, the final austenitic grain size is about 18 /zm. The constancy of the final austenitic grain size means that the steady state stress has been reached. Therefore, only dynamic recrystallization mechanisms may operate in this region. Steel 2 has a similar behavior but the steady state starts at e = 1.6.
30 40 50 60 70 Experimenial grain size, ; m
80
Fig. 10
Finally, Fig. 10 gives the caIculated final austenitic grain size by means of Eqs. (12) and (16) as a function of the experimental one for steel 1. Similarly, Fig. 11 gives the calculated final austenitic grain size by means of Eqs. (13) and (17) as a function of the experimental one for steel 2. A good concordance between the predicted and experimental values is observed in both steels. This confirms the important role of the strain rate as a factor influencing the hot forming simulation of medium carbon microalloyed steels.
4. Conclusions
(1) The behavior of the two medium carbon~microal= loyed steels investigated is similar to that observed for low carbon microalloyed steels. (2) Two equations describing the evolution of grain size for both cases, static and dynamic recrystallization, have been obtained. These equations are similar to
60
50
0
Static rec.
a
Dynamicrec.
©
'Pa
©
40
~o $
30
©
O~
J ©,x
20 A
r
10 10
t
r
,
I
i
,
I
23 36 49 Experimental grain size,gm Fig. 11.
62
dV[. Ca~'sl er ~a[./ Materials Science and Engifwering A216 (I996) 155-160
160 Table 2 Experimental results for high strain
Steel 1
SteeI 2
Acknowledgements
e
~ (s -1)
T (K)
DO (~m)
D~¢o (,urn)
2 2 2 2 2 4 4 2 " 2
2 2 7 7 2 2 7 7 14 14
1398 I398 1423 1323 1398 1398 1398 1398 1398 1398
110 150 125 125 65 65 65 65 65 i10
28 30 25 18 30 30 30 22 19 I8
50 50 50 50 70 70 70
28 22 19 15 37 29 19
4 ~ 2 4 7 4 14 4 2I 4 2 4 7 4 21
1353 , 1353 I35~ 1353 1398 1398 1398
those describing the evolution of grain size of low carbon microalloyed steels. (3) In the case of static recrystallization, the exponent q of the Zener-Hollomon parameter is of the same order of magnitude of that corresponding to the strain, p. This implies that the contributiOri of the strain rate, included in the Zener-Hollomon parameter, is important and has to be taken into consideration in the simulation of industrial processes. This contribution is important even at low deformation. (4) In the case of dynamic recrystallization, the importance of the strain rate contribution js even more obvious since the final grain size is exclusively a function of Z.
This research was carried out under the sponsorship of Comisidn Interministerial de Ciencia y Tecnologia (C.I.C.Y.T.), Program MAT 95-0186.
References
Materials Science and Engineering A216 (1996) 155-I60
A
The strain rate as a factor influencing the hot forming simulation of medium carbon microalloyed steels M. Cars?, V. Ldpez a, F. Pefialba b, O.A. Ruano a aDepartment of Physical Metallurgy, CENIM, CSIC, Av. Gregorio del Amo 8, 28040 Madrid, Spain bINASMET, Camino de Portuetxe i2, 10009 San Sebastian, Spain Received 9 February 1996
Abstract
Two medium carbon microalloyed steels, one with vanadium and the other with vanadium and titanium, have been studied by means of high-temperature torsion tests. The evolution of tile austenitic grain size with defomaation has been determined together with the rheological characteristics. On the basis of these data, the apparent activation energy for deformation and the Zener-Holiomon parameter have been calculated. The dependence of the final austenitic grain size on the initial one and on the thermomechanical treatment conditions (true strain, true strain rate and temperature) have been analyzed. Two mathematical expressions are proposed to describe the evolution of the austenitic grain size due to static or dynamic recrystallization. It was found that the strain rate can be as important as the strain to influence the final microstructure and therefore the mechanical properties of the final product. Keywords: Medium carbon steels; MicroalIoys; Grain size; Torsion simulation
1. Introduction The different factors influencing the thermomechanical steel treatments have been studied for decades on low carbon steels due to their importance in the optimization of the final products. Specifically, the austenitic grain refining induced in microalloyed steels, at a determined strain and strain rate, is of great importance to obtain improved mechanical properties [1-53 On studying the thermomechanical treatments, it is usual to give a paramount importance to the strain, and only a secondary relevance to the strain rate. The laboratory simulations usually follow strictly the temperature and the amount of deformation of the thermomechanical treatments. However, these simulations have usually been conducted at strain rates lower than those used in industrial processes. The object of this work is to demonstrate the influence of the strain rate on the final results, showing the importance of carrying out the simulations at strain rates similar to those used in industry. The final austenitic grain size is related to the size before simulation as a function of strain, strain rate and treatment
temperature. The simulations have been carried out by means of torsion tests on medium carbon steels (0.300.40%C) which are used in critical automotive components (wheel hubs, crank-shafts, etc.). 2. Materials and experimental procedure
Two microalloyed steels have been studied. Their compositions are shown in Table 1. The first steel is a typical medium carbon vanadium microalloyed steel. The second steel has a higher carbon content and a small percentage of titanium is added. Hot torsion tests have been conducted on these steels. The torsion machine, describe(t elsewhere [6], has a maximum speed of 2400 rpm. The torsion samples had a gauge length of 17 mm, 6 mm in diameter in the deformed region. A non-deformed region of 12 mm diameter is present in the head of the sample. The samples are heated by a high frequency induction furnace. The temperature measurement, by means of a two-colour pyrometer, is continuous. The samples are introduced in a silica tube, with a helium inlet, to ensure protection against oxidation and to minimize adiabatic heating (about 10 K at 14 s-1 and 1398 K).
156
M, Carsi et al. / Materials Science and Engineering A216 (I996) 155-160
Table 1' ChemicaI compositions in wt. % and p,p.m.* %C
%Mn
%Si
%S
%P
%Cr
%Ni
%Mo
%V
%Ti
%Cu
%Sn
%A1
N~
O~
0.29 0.38
1.30 1.30
0.41 0.48
0,026 0,039
0.021 0.020
0,09 0.15
0.10 0,14
0,02 0.04
0.10 0.12
0,003 0.011
0.24 0.21
0,02 0.02
0,029 0.030
0,0167 0.0147
30 34
Steel I Steel 2
The strain, e, and the strain rate, ~ can be obtained by means of the following expressions [7]: G=
=
27rRN
(1)
2rcR~
(2)
where R is the sample critical radius, N the number of turns, 3? the number of turns per second and L the effective sample length. The effective stress in a torsion test can be defined, at the critical radius, as [7] o--F _~j---~ ~( 53 -
+ 3 ( 0 + m))
(3)
where F is the torque, r the sample radius, 0 the work hardening exponent in the equation 0= dlnF d in e k r
(4)
and m the strain rate sensitivity in the equation m
=dlnF dln~l~,r
3. Results and discussion
Fig. 1 shows an example of torque-strain curves for steel 1 obtained directly from torsion tests at 1423 K. These curves can be transformed into stress-strain curves by means of Eqs. (3), (4) and (5). Fig. 2 shows these curves for the same steel in a plot cr versus e. The curves clearly show a decrease in stress, after reaching a maximum, until a constant value is obtained. The start of this regime, considered as the steady state, is obtained at increasing strains with increasing strain rates. However, the steady state is present in all curves at a strain of 1.5. The stress corresponding to this value of strain has been used for calculation of the Zener-Hollomon equations. The parameters given in Eq. (6) (Q, A, ~ and n) can be obtained from stress-strain curves in the steady state at different temperatures and strain rates by means of an algorithm [8,9]. Specifically, values of o', and T correspond to data given in Fig. 3 for steel 1 and in Fig. 4 for steel 2. The Zener-Hollomon equations particularized for both steels are the following: Steel 1:
(5)
exp(252 kJ/mol per RT) = 1.015 x 1011(Sinh 0.0064e) 5'21
Torsion tests to determine 0 and m were conducted to failure. The Zener-Hollomon equation, used to relate the temperature, strain rate and steady state stress, o-, is given as follows: exp(Qder/RT ) = A (Sinh c~¢)"
(6)
where (2a~ris the apparent activation energy, R = 8.314 J/mol the gas constant and A, ~ and n are material constants. The term ~ e x p ( 0 d d R T ) = Z is the ZenerHollomon parameter. The values of Qd~r, A, c
(7)
Correlation r = 0.997 Steel 2: exp(301 kJ/mol per RT)
(8)
= 4.360 x 1014(Sinh 0.0039~) 5'3° 4 14 s "1
3
F, Nm
i
2 s °1 t
t
0
0,5
I
1,5
2
2,5
3
Numberof turns Fig.' 1. Torque versus number of turns for Steel 1.
157
3I. Carsi et al./ Materials Science and Eugineering A216 (199.6) I55-I60 140
. . . .
1206080
~
. . . .
~
. . . .
,
. . . .
,
. . . .
10 tlS~ [
J ~
Z
..... l
o, MPa
,,~x, I oo,',~,,
',Y,I~ : {
........
E,s "1
40
~ o • C • © •
20
0.5
1
1.5
2
2.5
K K K K K
i
60
Fig. 2. Stress vs. strain at various temperaturesand strain rates.
1323 1353 1393 1423 1453 1473
10.0 c~,MPa
Correlation r = 0.996 The Zener-Hollomon approach is usually used to describe the creep behavior in a wide range of strain rates and temperatures. From a more basic approach, it is usual to analyze the data by means of a power law equation of the form: i = K exp(Qa~f/RT)crn'
(9)
where K is a material constant and n', the stress exponent, shofild be equal to n when the Sinh is equivalent to the arc. Independently of n', the Qdefvalue should be the same as that obtained from the Zener-Hollomon equation. Figs. 3 and 4 show strain rate versus stress curves for steels 1 and 2, respectively. The figures show that the experimental data obtained at six different temperatures can be accurately described by Eq. (9). The n values at the different temperatures are close to 6. The difference between this value and that obtained from the Zener-Hollomon equation can be attributed to the c~G producthaving a valffe higher than 0.8 and therefore to the Sinh(c~o-) being higher than c~a. The activation energy for deformation of both steel's can be obtained from Figs. 3 and 4 by plotting the strain rate at a given stress as a function of the inverse of the absolute temperature. The results are presented in Figs. 5 and 6 at a stress of 90 and 80 MPa for steels 1 and 2, respectively. The Qdefvalues are 255 and 295 k J/tool for steels 1 and 2, respectively. These values coincide with those obtained using the Zener-Hollomon equation (252 and 301 kJ/mol). It is known that the final austenitic grain size under static recrystallization conditions can be related to the Zener-Hollomon parameter, Z, by the equation [1114]: Drec = ]':D0~ ; Z q
Fig. 3. Strain rate vs. stress for Steel 1. The study of these steels under static recrystallization conditions was carried out considering deformations lower than 0.8 times the cteformation at the peak stress. Figs. 7 and 8 show thefinal austenitic grain size under static recrysiatliz.atiori, conditions as a function of deformation at various strain rates for initial austenitic grain sizes of 1t0 and 70 ~m for steels 1 and 2, respectively. The data from Figs. 7 arid'8 can be used to obtain the parameters k, p, and q of Eq. (10). This has been done using the regression plane derived from Eq. (10). Its general expressionis logDr~o=logk+logDo+p(lbge)+q(logZ)
(11)
The activation energies used, included in Z, are those obtained by the mathematical algorithm of the ZenerHollomon equations. Initial austenitic grain sizes in the range 125-55 pm were considered. The following relations were obtained: Steel 1:
D r e o = 2 1 . 2 D o e - ° ' 4 2 Z -°'I8°
(12)
Steel 2:
Drec= 317.3Doe-°'21Z -°''-35
(13)
. . . .
i
•
10
~, S-1
///
/
~
~
•
1353 K ,~73 K
--x--- 1398 K
(1 O)
where k is a material constant, D~o the recrystallized austenitic grain diameter, Do the initial austenitic grain size, and p and q are parameters describing the static recrystallization process.
t
),~ 1423 K ,
60
,
,
~, MPa
1
r
I00
Fig. 4. Strain rate vs. stress for SteeI 2.
158
M. Carsl et al./ Materials Science and Engineer#zg A216 (1996) 155-160 .
10
40
.
2/;:
.
.
.
i
~,s-1 ~=90 MPa < ' ~ Q=255 kJ/Mol
2 r
i
6.6 10.4
r
I
I
r
t
7.0
'
i
,
i
I
1 0 .4
i
r
r
7.4
I
,
I
20
'
i
h
i
l/T, K"~
i
1
1.00
0,30
1 0 "4
Fig. 7. Static recrystallization behavior. Final austenitic grdn size vs. strain at different strain rates for Steel 1.
Fig. 5. Strain rate vs. 1/T at ~r = 90 MPa for Steel 1.
Eqs. 12 and 13 clearly shows the similar values of the exponents p and q, within th~ same order of magnitude, for the case of static recfystallization conditions. This means that the strain rate carl be as important as the strain to influence the final microstructure and therefore the mechanical properties of the final product. Therefore, it is important to simulate the industrial process at strain rates similar to those used in production. The study of these steels under dynamic recrystallization conditions was carried out considering deformations higher than e = 2. The final austenitic grain size under dynamic recrystallization conditions can be related to the Zener-Hollomon parameter by the equation [11-14]:
D~o = k'Zq'
r
(14)
where k' is a material constant and q' is a parameter describing the dynamic recrystallization process. Fig. 9 and Table 2 shows the final austenitic grain size under dynamic recrystallization conditions as a function of deformation for both steels at different austenitizing
temperatures. The data were related by means of the regression line corresponding to the equation log Dre c = log K' + q' log Z
(15)
using various initial austenitic grain sizes in the range 150-60/Lm. The final austenitic grain size was found to be independent of the initial grain size for both steels. The following relations were obtained fl'om the experimental data: Steel 1:
D = 2 6 1 5 Z -°'2°°
(16)
Steel 2:
D = 42 446Z-°'266
(17)
It is inferred by comparison of Eqs. (12), (13), (16) and (17) that q and q' have values less than zero and that are lower for steel 2 than for steel 1 ( - 0.23 < 0.18 and - 0.27 < - 0.20). Assuming q and q' less than zero, it can be demonstrated that the grain size increment diminishes with increasing values of Qdef with the condition Qa~r> - RT/q (or Qdot"> -- RT/q'). The maximum value of the activation energy is 72 kJ/mol
10 -.--o.--14
•
s"l
.=
S'1
or= 8 0 Q= 295 kJ/Mol
3
30
.i,I.ll,Frl,rl.rrll,r,,tr.I,Fr,,rPrll
7.0 10.4
7.2 10.4
7.4 10.4
~ ,3
,
r
e
l/T, K" Fig. 6. Strain rate vs. 1/T at o-= 80 beiPa for Steel 2.
Fig. 8. Static recrystallization behavior. Final austenRic grain size vs. strain at different strain rates for Steel 2,
M. Carsi et al. / Materials Science and Engineering A216 (I996) i55-I60 40
159
80 Static rec. Dynamictee.
6 0
"/0
zx A
60 /x
._= 50
g
AZ~ &
..= 20
.=
× •
Steel I (I353 K)
•
Steel 1 (1398 K)
X
Steel 2 (1353K)
•
Steel 2 (1398 KI
A&
40
•
A ;
30
rn~
×
Z~ A &
rT~ A []
20 12
I ,
10
t
i
10
20
10
20
Fig. 9. D y n a m i c recrystaliization behavior. Final austenitic grain size vs. strain rate for the two steels.
(for q = -0.18 and T = 1573 K). This value is much lower than the Qdefvalue of any steel. This implies that the grain size increment of steel 2 should be lower than that of steel 1 since the activation energy is higher in steel 2 than in steel 1. This is in agreement with the experimental observations and also in agreement with the role of titanium as grain growth inhibitor [11,15,16]. The recrystallized grain size for both steels are of the same order of magnitude. However, the solutions obtained from Eqs. 10 and 14 give different orders of magnitude for lc and k'. This is because the term Z is an order of magnitude lower in steel 2 than in steel 1 (Q~ef and q' are higher in steel 2 than in steel 1). Therefore, k and k' have to be an order of magnitude higher in steel 2. The values of the Z exponent are similar to, those found in the literature and close to those obtained by Yoshimura et al. [13]. A good concordance also exists between the predicted values of Q from the algorithm method and the experimental data. The mathematical solution for the Zener-Hollomon equation provides a Qdof value that is probably more accurate ( + 5 kJ/mol) than that obtained from Figs. 5 and 6. According to Tamura et al. [11] the grain size depends exclusively on the Zener-Hollomon parameter if dynamic recrystallization processes occur. This is in agreement with observations of the grain size for steel 1 at different strain rates and initial austenitic grain sizes (Fig. 9 and Table 2). For e/> 2 the final austenitic grain size is independent of the initial one. It can be observed that for 110 Izm or 65/~m initial austenitic grain sizes, the final austenitic grain size is about 18 /zm. The constancy of the final austenitic grain size means that the steady state stress has been reached. Therefore, only dynamic recrystallization mechanisms may operate in this region. Steel 2 has a similar behavior but the steady state starts at e = 1.6.
30 40 50 60 70 Experimenial grain size, ; m
80
Fig. 10
Finally, Fig. 10 gives the caIculated final austenitic grain size by means of Eqs. (12) and (16) as a function of the experimental one for steel 1. Similarly, Fig. 11 gives the calculated final austenitic grain size by means of Eqs. (13) and (17) as a function of the experimental one for steel 2. A good concordance between the predicted and experimental values is observed in both steels. This confirms the important role of the strain rate as a factor influencing the hot forming simulation of medium carbon microalloyed steels.
4. Conclusions
(1) The behavior of the two medium carbon~microal= loyed steels investigated is similar to that observed for low carbon microalloyed steels. (2) Two equations describing the evolution of grain size for both cases, static and dynamic recrystallization, have been obtained. These equations are similar to
60
50
0
Static rec.
a
Dynamicrec.
©
'Pa
©
40
~o $
30
©
O~
J ©,x
20 A
r
10 10
t
r
,
I
i
,
I
23 36 49 Experimental grain size,gm Fig. 11.
62
dV[. Ca~'sl er ~a[./ Materials Science and Engifwering A216 (I996) 155-160
160 Table 2 Experimental results for high strain
Steel 1
SteeI 2
Acknowledgements
e
~ (s -1)
T (K)
DO (~m)
D~¢o (,urn)
2 2 2 2 2 4 4 2 " 2
2 2 7 7 2 2 7 7 14 14
1398 I398 1423 1323 1398 1398 1398 1398 1398 1398
110 150 125 125 65 65 65 65 65 i10
28 30 25 18 30 30 30 22 19 I8
50 50 50 50 70 70 70
28 22 19 15 37 29 19
4 ~ 2 4 7 4 14 4 2I 4 2 4 7 4 21
1353 , 1353 I35~ 1353 1398 1398 1398
those describing the evolution of grain size of low carbon microalloyed steels. (3) In the case of static recrystallization, the exponent q of the Zener-Hollomon parameter is of the same order of magnitude of that corresponding to the strain, p. This implies that the contributiOri of the strain rate, included in the Zener-Hollomon parameter, is important and has to be taken into consideration in the simulation of industrial processes. This contribution is important even at low deformation. (4) In the case of dynamic recrystallization, the importance of the strain rate contribution js even more obvious since the final grain size is exclusively a function of Z.
This research was carried out under the sponsorship of Comisidn Interministerial de Ciencia y Tecnologia (C.I.C.Y.T.), Program MAT 95-0186.
References