- Email: [email protected]
Modelling of the dynamic recrystallization of austenite in low alloy and microalloyed steels
Vol. 44, No. 1, pp. 165-171, 1996 Elsevier Science Ltd Copyright 0 1995 Acta Metallurgica Inc. Printed in Great Britain. All rights reserved 1359-6454196 $15.00 + 0.00
Actamater.
Pergamon
0956-7151(95)00154-9
MODELLING OF THE DYNAMIC OF AUSTENITE IN LOW ALLOY STEELS
RECRYSTALLIZATION AND MICROALLOYED
S. F. MEDINA’ and C. A. HERNANDEZ’ ‘Centro Madrid,
National de Investigaciones Metaltirgicas (CENIM-CSIC), Av. Gregorio de1 Amo 8, 28040Spain and Wniversidad Autbnoma de Mexico (UNAM), Facultad de Quimica D, 04510 D.F. Mexico
(Received 9 September 1994; in revised form 24 March 1995) Abstract-Using
torsional tests in the austenite phase, the dynamic recrystallization of a selection of low alloy and microalloyed steels was studied and Avrami’s equation was modelled. The model is based on the experimental determination of flow curves and their subsequent modelling, making it possible to
calculate the recrystallized fraction (X,) as a function of all the variables which intervene in hot deformation: temperature, strain rate, austenite grain size and the chemical composition of the steel. The influence of the first three variables is quantified using the Zener-Hollomon parameter where the activation energy is expressed as a function of the content of each alloy. The start of dynamic recrystallization was determined by regression, finding a value of 0.956,. In testing conditions all the elements were found in solution in the austenite, except Ti which was found partially precipitated. The results of these tests indicate that C, Si (low content), Mn and V have hardly any influence on the start of recrystallization while MO, Ti and especially Nb delay it. Finally, the dynamic recrystallization kinetics are illustrated through the study of the microstructure during deformation.
For a given steel the start of dynamic recrystallization depends basically on the temperature and the strain rate, and to a lesser degree on the austenite grain size. A reduction in the temperature has a qualitative influence similar to an increase in the strain rate, causing a delay in the appearance of the first recrystallized grains and in the obtainment of a totally recrystallized microstructure. In hot rolling the strain rate applied in each pass is greater than that mentioned above and the phenomenon of periodic recrystallization does not occur. The strain at which dynamic recrystallization starts has been the object of several studies, and almost all coincide in that it begins at a strain slightly below peak strain (or) [ 1 I-141. Several models have been proposed to calculate the dynamically recrystallized fraction (DRX), though they are only applicable to a certain type of families of steels, normally the C-Mn steels [15-191. It is generally admitted that DRX follows Avrami’s law and the most common expression to quantitatively interpret this phenomenon has the following form
1. INTRODUCTION When a low alloy steel is strained at relatively high rates in the austenite phase its flow curves present the typical regions of hot deformation: a hardening region characterized by an increasing dislocation density, followed by a dynamic recovery characterized by a polygonized austenite, and finally dynamic recrystallization where the build-up of dislocations leads to the nucleation and growth of recrystallized grains during the deformation until the steady state is reached where recrystallization is total and continuous. At first the stress increases until it reaches a maximum (a,), where the nucleation of some new grains has already begun, and then descends as recrystallization progresses until it reaches a constant value (a,) where recrystallization is 100% and continuous. When the strain rate is very low, normally to the order of 0.01 s-’ or less, and the temperatures are high, periodic recrystallizations may appear and the flow curve will show multiple peaks [I, 21. Several theories have been developed to explain the transition from periodic recrystallization to continuous recrystallization [3-71, but the theory of Sakai et al. [&IO] seems to be most in line with the experimental results obtained. This indicates that cyclic flow curves are associated with grain coarsening and that single peak flow curves are associated with grain refinement being the critical condition D, = D,, where D,, and D, are the initial and stable grain sizes respectively.
X,=
1 -exp[--krTr]
(1)
where k and m’ are generally constants, with values between: 0
166
MEDINA
and HERNANDEZ:
RECRYSTALLIZA-TION
Ot
AI,STENi’I‘F
--Steel C2
a b C
b C
01 0
I’,
’
1
0.5
I
1.5
2
’
2.5
0.5
3
Equivalent strain
Fig. I. Stress-strain curves calculated in accordance with the models of hardening plus recovery (a,), of dynamic recrystallization induced softening (Au) and the resulting flow curve (oe- Ao). Steel Cl. E = 3.628 SK’; (a) 900°C; (b) 1000°C; (c) 1100°C. Avrami’s law, with a form similar to the equation used for the statically recrystallized fraction [19]. The dynamically recrystallized grain size (Dd) does not depend upon the initial grain size and is a function only of the maximum stress (a,) or of the stress reached in the steady state (ass) [4,20-221. As (cr,,) depends on the strain rate and temperature, D, can be expressed as a function of the ZenerHollomon parameter (Z), following a power law. Some expressions have been proposed for CMn steels [14, 19, 231 and others for Nb microalloyed steels [24]. The modelling of dynamic recrystallization is of great importance in the prediction of microstructures in hot rolled steels as it is not normally advisable to reach strains above the strain at which recrystallization begins (at,) as this may give rise to heterogenous structures, as occurs in the conventional strip mill. However, in some types of rolling the aim is to obtain finer structures, as is the case in the newly designed controlled rolling procedures, which involve larger strains and provide significant proportions of dynamic recrystallization that in turn leads to finer austenite grains [25-281.
Table 1. Conditions of the torsional tests for the study of the microstructure during deformation of steel C2: temperatures, strain rates, deformations of quenching, values of cP and of Z/A calculated in accordance with Refs 129,301 Temperature (“C)
Strain rate (SK’)
900
3.628
I100
5.224
II00
0.544
1
1.5
2
;5
Equivalent strain
Strain
L.
Z/A
0.46 I .09 I.57 3.27 0.26 0.66 0.91 I .67 0.23 0.37 0.45 1.20
0.73
595.74
0.40
14.44
Fig. 2. Flow curves, experimental lated
(dotted lines) and calcu(solid lines) for steel C2. (a) 900°C; 3.628 SS’; (b) 1100°C; 5.224 s- ‘: (c) 1100°C; 0.544 s-l.
The aim of this work is to obtain a model for dynamic recrystallization, in accordance with equation (I), which can be applied to all low alloy and microalloyed steels, whatever their chemical composition. As will be seen later, the model is based on the prior modelling of the Z parameter and of peak strain as a function of the chemical composition of the steel. 2. EXPERIMENTAL
The steels used in this study are the same as those used to mode1 the Zener-Hollomon parameter [29], peak strain [30] and flow curves [31], as a function of temperature, strain rate, austenite grain size and the chemical composition of the steel. The conditions under which the torsional tests were carried out have already been described [29-311, nevertheless it is worth repeating that at the reheating temperature (1230°C) all the precipitates (carbides and nitrides) of V and Nb were completely dissolved and only Ti nitrides were partially dissolved [32, 331. Furthermore, at the temperatures (900, 1000 and IlOOC) and strain rates (0.544, 1.451, 3.628 and 5.224 SK’) applied in the tests there was no precipitation during deformation. The magnitudes of torsion, torque and number of turns were transformed applying Von Mises yielding criterion to equivalent stresses and strains, respectively [34]. The main features of the torsion machine used have already been described [35] and the possibility should be noted, in relation with this work, of quenching the specimen using a stream of water which passes through the quartz tube where the specimen is protected from oxidation. The torsion specimens had a useful length of 50 mm and were 6 mm in diameter. 3. RESULTS
0.28
1.50
PROCEDURE
AND DISCUSSION
Flow curves were determined for all the steels, temperatures and strain rates cited above to an equivalent strain of approx. 2.5, amply reaching the steady state where the stress becomes constant [29].
MEDINA and HERNANDEZ:
RECRYSTALLIZATION
OF AUSTENITE
167
200
s a E 8 $ m
150
100
s 7 '3 w"
50
1
1.5
Equivalent strain Fig. 3. Flow curves at 900°C and 3.628 ss’ and microstructures obtained by quenching at different strains: 0.46: 1.09: 1.57: 3.27. The values of the maximum stress or peak stress (u,) and of the corresponding strain (6,) were measured and the activation energy for the deformation (Q) was modelled as a function of the content of all the alloying elements, including the microalloys (Ti, V, Nb), and in this way the Z parameter was also modelled. Finally (a,) was modelled as a function of a dimensionless parameter given by the Z/A relation, A being the coefficient of the second side of the Sellars-Tegart equation [36]. In the same way, L, was modelled as a function of the chemical composition of the austenite, arriving at the conclusion that small quantities of MO, Ti, V and Nb produced the same effect as other larger quantities, always of the most common compositions of the low alloy steels [30]. In a third study [31] a model was established to calculate the flow curve as a result of subtracting from one expression, which predicts the stress in the hardening region plus the dynamic recovery region, a second expression, which predicts the softening effect of dynamic recrystallization, in other words the model predicts the evolution of the microstructure during deformation. The aim of this work
is to model dynamic recrystallization and expression which predicts softening due to phenomenon is [31]
B’ = 26.0310
k =O.*974exp[
m’=
? o.‘35’ 0A
the this
(3)
1.2333(s)‘]
(4)
1.0901 exp[ 0.0264($].
(5)
represents the The coefficient B’ mathematically value of Acr when the strain tends towards infinity, but physically this equality should be checked when the stress reaches the steady state. The parenthesis of equation (2) represents the recrystallized fraction which starts at 0.956, and should be equal to one when the steady state is reached. The value of 0.95 was given by regression calculations and represents the optimum value, with minimum error, in the fitting
MEDINA
168
and HERNANDEZ:
RECRYS’fALLIZATION
of the flow curves. The expression for the dynamically recrystallized fraction is therefore
Equation (6), together with equations (4) and (5) make it possible to predict the dynamically recrystallized fraction as a function of the strain, temperature, strain rate, initial grain size and chemical composition of a broad selection of steels. The main differences between this model and others already published are the following: (a) The model is not only valid for one specific steel or one family of steels but for a broad selection, in other words the low alloy and microalloyed steels. (b) k and m’ are not constants and clearly depend on the temperature. strain rate and the chemical composition of the steel, and this dependence is expressed by the dimensionless parameter Z/A.
Of- .AUSl-th1-l L:
The dependence of k and m’ on Z..,l has been stated previously [31] and, although it is relatively small, the high correlation coefficient obtained (> 0.95) demonstrates that they should not be taken as constants. Both functions arc different. while li is decreasing with Z/A. m’ is increasing. A graph of the hardening plus recovery equations. and of the recrystallization induced softening equation (2), as well as the resulting flow curve (0, - Ao)), are shown in Fig. 1 which corresponds to steel Cl (wt%: 0.15C: 0.21 Si: 0.74Mn). where the important contribution of recrystallization to the softening of the austenite can be seen, this contribution being greater as the temperature decreases or the strain rate increases. To clearly show the evolution of the microstructure during deformation. especially in the transition region. i.e. from a strain close to the start of dynamic recrystallization tp, to strains belonging to the steady state, steel C2 (wt”/,: 0.36 C; 0.20 Si: 0.82 Mn) was selected due to the fact that its hardenability was sufficient to allow the austenite grain boundaries to
100 Z5 8
80
g u) E a,
60
F ._ g w
40
20
0 0.5
1
1.5
2
2.5
Equivalent strain Fig. 4. Flow curves at 1100°C and 5.224SV’and microstructures obtained by quenching at different strains: 0.26; 0.66; 0.91: I .67.
MEDINA
and HERNANDEZ:
RECRYSTALLIZATION
v
60
\
OF AUSTENITE
169
,
Equivalent strain Fig. 5. Flow curves at 1100°C and 0.544 SK’and microstructures obtained 0.23; 0.37; 0.45; 1.20.
be fixed by quenching with water. Table 1 presents the conditions of temperature and strain rate at which the tests were carried out, as well as the strains at which the specimens were quenched. The temperatures and strain rates were chosen with the intention of obtaining three different values of Z/A which would allow a relation to be established between this parameter and the dynamically recrystallized grain size. The values of Z/A and tr calculated for the testing conditions and for steel C2 are shown in Table 1. Figure 2 displays the flow curves determined experimentally at the temperatures and strain rates indicated in Table 1, as well as the flow curves calculated in accordance with the equations of adiabatic modelling [31]. The model’s prediction of the flow curves and thus of the transition region can be seen to be good. The specimens quenched at the strains indicated in Table 1 were prepared for microscopic observation. From each quenched specimen a sample surface 20mm in length, situated in the central part of the specimen and at 0.3 mm from the surface, was metallographically prepared and attacked in a saturated solution of picric acid with some drops of dissolved
by quenching
at different strains:
teepol, and the resulting microstructures are shown in Figs 3-5 where the experimental flow curves corresponding to each temperature and strain rate, respectively, have also been drawn, with arrows indicating the position corresponding to each microstructure. In this way it is easier to relate each microstructure with the corresponding values of stress and strain of the austenite at the moment it was quenched. In each specimen the recrystallized fraction and the mean austenite grain size was measured by the observation of approx. 10 fields with an optic microscope and the results as a function of the strain are shown in Figs 6 and 7, respectively. In Fig. 6 the recrystallization curves have also been drawn, calculated with the aid of Sellars-Tegart’s equation [29], of peak strain [30] and equations (4x6) of the text, and each curve corresponds to one of the values of Z/A noted in Table 1. As the strain increases the mean austenite grain size (Fig. 7) tends to a constant value which represents the grain size in the steady state region, or the size of the grain recrystallized in continuous dynamic recrystallization. Observation of the microstructures, especially those corresponding to the greatest value of Z/A, allows Sakai and Jonas’
170
MEDINA
and HERNANDEZ:
RECRYSTALLIZATION
C)I- AUSTENITE
I Steel C2 0.8
,,_.___i
O0.1
0.2
0.5
1
2
5
10
0.1
Equivalent strain Fig. 6. Recrystallization curves calculated in accordance with the model and recrystallized fraction measured in quenched specimens. conclusions [8] regarding the preferential nucleation on the grain boundaries and the appearance of a necklace-like form to be checked. However, grains with intragranular nucleation (in the interior of the grain) are also found. It has also been observed that the recrystallized grain remains practically constant as recrystallization advances, as has already been reported by other authors [20]. Figure 8 shows the recrystallized austenite grain size as a function of Z/A, it being seen that this follows the power law mentioned above, whose regression line obeys the following expression Dd
(7)
The dynamically recrystallized grain size, in accordance with equation (7), gives values which coincide approximately with Sellars’ model [14, 231, when the Z parameter is high, and with the model developed by Namba et al. [19], when the Z parameter is relatively low. Finally, the alloying elements influence recrystallization kinetics in so far as they affect the value of peak strain [30] and the activation energy for the
E
1
240
0 IIOOYI; 0.5445“ 0 lloo~c; A 900°C;
5.224
s-1
3.628
s-’
Steel
1
10
loo
1,000
z!A Fig. 8. Dynamically recrystallized grain size as a function of the dimensionless parameter Z/A. strain [29]. In this respect, and by way of summary, it may be said that an increase in the C, Si or Mn content has no effect on tp while an increase of V, MO, Ti or particularly Nb increases the value of tp. With regard to the activation energy, all the elements contribute to a greater or lesser degree to increasing the activation energy, except carbon which tends to reduce it, Nb being the element which most contributes to the hardening of the austenite and therefore to increasing the activation energy. 4. CONCLUSIONS 1. The model created to calculate the dynamically recrystallized fraction establishes that the term k and the exponent m’ are not constants and depend on the dimensionless parameter Z/A. 2. The model makes it possible to calculate the dynamically recrystallized fraction of any low alloy or microalloyed steel as a function of the strain, temperature, strain rate and austenite grain size. 3. The recrystallized grain size depends less on the Z/A parameter than other models established as a function of Z alone. 4. All the alloying elements, except carbon, tend to delay the start of dynamic recrystallization, especially niobium. Acknowledgements-This work has been undertaken in CENIM (Madrid) and the authors are grateful for the financial support of the DGICYT of Spain (Project PB890022). Hernandez’s studies are sponsored by the UNAM (Mexico).
c2
REFERENCES 0
0.4 0.8 1.2 Equivalent
Fig. 7. Mean austenite
1.6 2.0 24 strain
2.8
grain size as a function
3.2
3.6
of the strain.
I. C. Rossard and P. Blain, Mtm. Scient. Rec. M6taN. 56, 285 (1959). 2. R. A. Petrovic, M. J. Luton and J. J. Jonas, Q. 14, 137 (1975).
Can. Metall.
MEDINA
and HERNANDEZ:
RECRYSTALLIZATION
3. S. Steinemann, Bectriige Geol. Scheweiz (Hydrol) 10, 1 (1985). 4. M. J. Luton and C. M. Sellars, Acta metall. 17, 1033 (1969). and C. M. Sellars, Indian 5. J. P. Sah, G. J. Richardson J. Technol. 11, 445 (1973). 6. R. Sandstrom and R. Lagneborg, Acta metall. 23, 387 (1975). 7. W. Roberts, H. Boden and B. Ahlblom, Metal Sci. 13, 195 (1979). 8. T. Sakai and J. J. Jonas, Acta metall. 32, 189 (1984). 9. T. Sakai, M. G. Akben and J. J. Jonas, Thermomechanical Processing of Microalloyed Austenite (edited by A. J. DeArdo, G. A. Ratz and P. J. Wray), p. 237. A.I.M.E., Warrendale, Pa (1982). 10. T. Sakai, M. G. Akben and J. J. Jonas, Acta metall. 31, 631 (1983). and C. Rossard, M&m. 11. A. Le Bon, J. Rofes-Vernis Scient. Rev. M&all. 55, 573 (1973). 12. A. Le Bon, J. Rofes-Vemis and C. Rossard, Metal. Sci. 9, 36 (1975). 13. J. P. Michel, M. Akben and J. J. Jonas, Revue MeYaN. 78, 823 (1981). 14. C. M. Sellars, Hot Working and Forming Processes (edited by C. M. Sellars and G. J. Davies), p. 3. The Metals Society, London (1980). 15. C. M. Sellars, Czech. J. Phys. B 35, 239 (1985). 16. J. H. Benyon and C. M. Sellars, ISZJZnt. 32,359 (1992). and J. J. Jonas, ISIJ Int. 31, 95 (1991). 17. A. Laasraoui MPm. Scient. Rev. 18. S. F. Medina and C. A. Hernandez, M&t. 66, 217 (1992).
OF AUSTENITE
171
19. S. Nanba, M. Kitamura, M. Shimada, M. Katsumata, T. Inque, H. Imamura, Y. Maeda and S. Hattori, ISZ.7 Int. 3i, 377 (1992). 20. J. P. Sah. G. J. Richardson and C. M. Sellars. Metal. Sci. 8, 3255 (1974). 21. G. Glover and C. M. Sellars, Metall. Trans. 4, 765 (1973). 22. H. J. McQueen and S. Bergerson, Metal. Sri. 6, 25 (1972). 23. C. M. Sellars, Metal. Sci. Technol. 6, 1072 (1990). 24. R. A. Barbosa and H. C. Braga, ISIJInt. 32,257 (1992). 25. F. H. Samuel, S. Yue, J. J. Jonas and B. A. Zbinden, ISIJ Int. 29, 1221 (1989). 26. F. H. Samuel. S. Yue. J. J. Jonas and K. R. Barnes. ISZJ Int. 30, 216 (1990). 27. L. N. Pussegoda, S. Yue and J. J. Jonas, Metall. Trans. 21A, 153 (1990). 28. L. N. Pussegoda and J. J. Jonas, ISZJInt. 31,278 (1991). 29. S. F. Medina and C. Hernandez, Acta mater. 44, 137. 30. S. F. Medina and C. Hernandez, Acta mater. 44. 149. 31. C. Hernandez, S. F. Medina and J. Ruiz, Acta mater. 44, 155. 32. J. Kunze, Metal. Sci. 16, 217 (1982). 33. S. F. Medina and J. E. Mantilla, Scripta metall. mater. 30, 73 (1994). 34. A. Faessel, Rev. M&all., Cah. if: Tech. 4, 875 (1976). 35. S. F. Medina, Rev. Metal. Madrid 23, 419 (1987). 36. C. M. Sellars and W. J. M. Tegart, M&m. I&d. Sci. Rev. M&all. 63, 731 (1966).
Actamater.
Pergamon
0956-7151(95)00154-9
MODELLING OF THE DYNAMIC OF AUSTENITE IN LOW ALLOY STEELS
RECRYSTALLIZATION AND MICROALLOYED
S. F. MEDINA’ and C. A. HERNANDEZ’ ‘Centro Madrid,
National de Investigaciones Metaltirgicas (CENIM-CSIC), Av. Gregorio de1 Amo 8, 28040Spain and Wniversidad Autbnoma de Mexico (UNAM), Facultad de Quimica D, 04510 D.F. Mexico
(Received 9 September 1994; in revised form 24 March 1995) Abstract-Using
torsional tests in the austenite phase, the dynamic recrystallization of a selection of low alloy and microalloyed steels was studied and Avrami’s equation was modelled. The model is based on the experimental determination of flow curves and their subsequent modelling, making it possible to
calculate the recrystallized fraction (X,) as a function of all the variables which intervene in hot deformation: temperature, strain rate, austenite grain size and the chemical composition of the steel. The influence of the first three variables is quantified using the Zener-Hollomon parameter where the activation energy is expressed as a function of the content of each alloy. The start of dynamic recrystallization was determined by regression, finding a value of 0.956,. In testing conditions all the elements were found in solution in the austenite, except Ti which was found partially precipitated. The results of these tests indicate that C, Si (low content), Mn and V have hardly any influence on the start of recrystallization while MO, Ti and especially Nb delay it. Finally, the dynamic recrystallization kinetics are illustrated through the study of the microstructure during deformation.
For a given steel the start of dynamic recrystallization depends basically on the temperature and the strain rate, and to a lesser degree on the austenite grain size. A reduction in the temperature has a qualitative influence similar to an increase in the strain rate, causing a delay in the appearance of the first recrystallized grains and in the obtainment of a totally recrystallized microstructure. In hot rolling the strain rate applied in each pass is greater than that mentioned above and the phenomenon of periodic recrystallization does not occur. The strain at which dynamic recrystallization starts has been the object of several studies, and almost all coincide in that it begins at a strain slightly below peak strain (or) [ 1 I-141. Several models have been proposed to calculate the dynamically recrystallized fraction (DRX), though they are only applicable to a certain type of families of steels, normally the C-Mn steels [15-191. It is generally admitted that DRX follows Avrami’s law and the most common expression to quantitatively interpret this phenomenon has the following form
1. INTRODUCTION When a low alloy steel is strained at relatively high rates in the austenite phase its flow curves present the typical regions of hot deformation: a hardening region characterized by an increasing dislocation density, followed by a dynamic recovery characterized by a polygonized austenite, and finally dynamic recrystallization where the build-up of dislocations leads to the nucleation and growth of recrystallized grains during the deformation until the steady state is reached where recrystallization is total and continuous. At first the stress increases until it reaches a maximum (a,), where the nucleation of some new grains has already begun, and then descends as recrystallization progresses until it reaches a constant value (a,) where recrystallization is 100% and continuous. When the strain rate is very low, normally to the order of 0.01 s-’ or less, and the temperatures are high, periodic recrystallizations may appear and the flow curve will show multiple peaks [I, 21. Several theories have been developed to explain the transition from periodic recrystallization to continuous recrystallization [3-71, but the theory of Sakai et al. [&IO] seems to be most in line with the experimental results obtained. This indicates that cyclic flow curves are associated with grain coarsening and that single peak flow curves are associated with grain refinement being the critical condition D, = D,, where D,, and D, are the initial and stable grain sizes respectively.
X,=
1 -exp[--krTr]
(1)
where k and m’ are generally constants, with values between: 0
166
MEDINA
and HERNANDEZ:
RECRYSTALLIZA-TION
Ot
AI,STENi’I‘F
--Steel C2
a b C
b C
01 0
I’,
’
1
0.5
I
1.5
2
’
2.5
0.5
3
Equivalent strain
Fig. I. Stress-strain curves calculated in accordance with the models of hardening plus recovery (a,), of dynamic recrystallization induced softening (Au) and the resulting flow curve (oe- Ao). Steel Cl. E = 3.628 SK’; (a) 900°C; (b) 1000°C; (c) 1100°C. Avrami’s law, with a form similar to the equation used for the statically recrystallized fraction [19]. The dynamically recrystallized grain size (Dd) does not depend upon the initial grain size and is a function only of the maximum stress (a,) or of the stress reached in the steady state (ass) [4,20-221. As (cr,,) depends on the strain rate and temperature, D, can be expressed as a function of the ZenerHollomon parameter (Z), following a power law. Some expressions have been proposed for CMn steels [14, 19, 231 and others for Nb microalloyed steels [24]. The modelling of dynamic recrystallization is of great importance in the prediction of microstructures in hot rolled steels as it is not normally advisable to reach strains above the strain at which recrystallization begins (at,) as this may give rise to heterogenous structures, as occurs in the conventional strip mill. However, in some types of rolling the aim is to obtain finer structures, as is the case in the newly designed controlled rolling procedures, which involve larger strains and provide significant proportions of dynamic recrystallization that in turn leads to finer austenite grains [25-281.
Table 1. Conditions of the torsional tests for the study of the microstructure during deformation of steel C2: temperatures, strain rates, deformations of quenching, values of cP and of Z/A calculated in accordance with Refs 129,301 Temperature (“C)
Strain rate (SK’)
900
3.628
I100
5.224
II00
0.544
1
1.5
2
;5
Equivalent strain
Strain
L.
Z/A
0.46 I .09 I.57 3.27 0.26 0.66 0.91 I .67 0.23 0.37 0.45 1.20
0.73
595.74
0.40
14.44
Fig. 2. Flow curves, experimental lated
(dotted lines) and calcu(solid lines) for steel C2. (a) 900°C; 3.628 SS’; (b) 1100°C; 5.224 s- ‘: (c) 1100°C; 0.544 s-l.
The aim of this work is to obtain a model for dynamic recrystallization, in accordance with equation (I), which can be applied to all low alloy and microalloyed steels, whatever their chemical composition. As will be seen later, the model is based on the prior modelling of the Z parameter and of peak strain as a function of the chemical composition of the steel. 2. EXPERIMENTAL
The steels used in this study are the same as those used to mode1 the Zener-Hollomon parameter [29], peak strain [30] and flow curves [31], as a function of temperature, strain rate, austenite grain size and the chemical composition of the steel. The conditions under which the torsional tests were carried out have already been described [29-311, nevertheless it is worth repeating that at the reheating temperature (1230°C) all the precipitates (carbides and nitrides) of V and Nb were completely dissolved and only Ti nitrides were partially dissolved [32, 331. Furthermore, at the temperatures (900, 1000 and IlOOC) and strain rates (0.544, 1.451, 3.628 and 5.224 SK’) applied in the tests there was no precipitation during deformation. The magnitudes of torsion, torque and number of turns were transformed applying Von Mises yielding criterion to equivalent stresses and strains, respectively [34]. The main features of the torsion machine used have already been described [35] and the possibility should be noted, in relation with this work, of quenching the specimen using a stream of water which passes through the quartz tube where the specimen is protected from oxidation. The torsion specimens had a useful length of 50 mm and were 6 mm in diameter. 3. RESULTS
0.28
1.50
PROCEDURE
AND DISCUSSION
Flow curves were determined for all the steels, temperatures and strain rates cited above to an equivalent strain of approx. 2.5, amply reaching the steady state where the stress becomes constant [29].
MEDINA and HERNANDEZ:
RECRYSTALLIZATION
OF AUSTENITE
167
200
s a E 8 $ m
150
100
s 7 '3 w"
50
1
1.5
Equivalent strain Fig. 3. Flow curves at 900°C and 3.628 ss’ and microstructures obtained by quenching at different strains: 0.46: 1.09: 1.57: 3.27. The values of the maximum stress or peak stress (u,) and of the corresponding strain (6,) were measured and the activation energy for the deformation (Q) was modelled as a function of the content of all the alloying elements, including the microalloys (Ti, V, Nb), and in this way the Z parameter was also modelled. Finally (a,) was modelled as a function of a dimensionless parameter given by the Z/A relation, A being the coefficient of the second side of the Sellars-Tegart equation [36]. In the same way, L, was modelled as a function of the chemical composition of the austenite, arriving at the conclusion that small quantities of MO, Ti, V and Nb produced the same effect as other larger quantities, always of the most common compositions of the low alloy steels [30]. In a third study [31] a model was established to calculate the flow curve as a result of subtracting from one expression, which predicts the stress in the hardening region plus the dynamic recovery region, a second expression, which predicts the softening effect of dynamic recrystallization, in other words the model predicts the evolution of the microstructure during deformation. The aim of this work
is to model dynamic recrystallization and expression which predicts softening due to phenomenon is [31]
B’ = 26.0310
k =O.*974exp[
m’=
? o.‘35’ 0A
the this
(3)
1.2333(s)‘]
(4)
1.0901 exp[ 0.0264($].
(5)
represents the The coefficient B’ mathematically value of Acr when the strain tends towards infinity, but physically this equality should be checked when the stress reaches the steady state. The parenthesis of equation (2) represents the recrystallized fraction which starts at 0.956, and should be equal to one when the steady state is reached. The value of 0.95 was given by regression calculations and represents the optimum value, with minimum error, in the fitting
MEDINA
168
and HERNANDEZ:
RECRYS’fALLIZATION
of the flow curves. The expression for the dynamically recrystallized fraction is therefore
Equation (6), together with equations (4) and (5) make it possible to predict the dynamically recrystallized fraction as a function of the strain, temperature, strain rate, initial grain size and chemical composition of a broad selection of steels. The main differences between this model and others already published are the following: (a) The model is not only valid for one specific steel or one family of steels but for a broad selection, in other words the low alloy and microalloyed steels. (b) k and m’ are not constants and clearly depend on the temperature. strain rate and the chemical composition of the steel, and this dependence is expressed by the dimensionless parameter Z/A.
Of- .AUSl-th1-l L:
The dependence of k and m’ on Z..,l has been stated previously [31] and, although it is relatively small, the high correlation coefficient obtained (> 0.95) demonstrates that they should not be taken as constants. Both functions arc different. while li is decreasing with Z/A. m’ is increasing. A graph of the hardening plus recovery equations. and of the recrystallization induced softening equation (2), as well as the resulting flow curve (0, - Ao)), are shown in Fig. 1 which corresponds to steel Cl (wt%: 0.15C: 0.21 Si: 0.74Mn). where the important contribution of recrystallization to the softening of the austenite can be seen, this contribution being greater as the temperature decreases or the strain rate increases. To clearly show the evolution of the microstructure during deformation. especially in the transition region. i.e. from a strain close to the start of dynamic recrystallization tp, to strains belonging to the steady state, steel C2 (wt”/,: 0.36 C; 0.20 Si: 0.82 Mn) was selected due to the fact that its hardenability was sufficient to allow the austenite grain boundaries to
100 Z5 8
80
g u) E a,
60
F ._ g w
40
20
0 0.5
1
1.5
2
2.5
Equivalent strain Fig. 4. Flow curves at 1100°C and 5.224SV’and microstructures obtained by quenching at different strains: 0.26; 0.66; 0.91: I .67.
MEDINA
and HERNANDEZ:
RECRYSTALLIZATION
v
60
\
OF AUSTENITE
169
,
Equivalent strain Fig. 5. Flow curves at 1100°C and 0.544 SK’and microstructures obtained 0.23; 0.37; 0.45; 1.20.
be fixed by quenching with water. Table 1 presents the conditions of temperature and strain rate at which the tests were carried out, as well as the strains at which the specimens were quenched. The temperatures and strain rates were chosen with the intention of obtaining three different values of Z/A which would allow a relation to be established between this parameter and the dynamically recrystallized grain size. The values of Z/A and tr calculated for the testing conditions and for steel C2 are shown in Table 1. Figure 2 displays the flow curves determined experimentally at the temperatures and strain rates indicated in Table 1, as well as the flow curves calculated in accordance with the equations of adiabatic modelling [31]. The model’s prediction of the flow curves and thus of the transition region can be seen to be good. The specimens quenched at the strains indicated in Table 1 were prepared for microscopic observation. From each quenched specimen a sample surface 20mm in length, situated in the central part of the specimen and at 0.3 mm from the surface, was metallographically prepared and attacked in a saturated solution of picric acid with some drops of dissolved
by quenching
at different strains:
teepol, and the resulting microstructures are shown in Figs 3-5 where the experimental flow curves corresponding to each temperature and strain rate, respectively, have also been drawn, with arrows indicating the position corresponding to each microstructure. In this way it is easier to relate each microstructure with the corresponding values of stress and strain of the austenite at the moment it was quenched. In each specimen the recrystallized fraction and the mean austenite grain size was measured by the observation of approx. 10 fields with an optic microscope and the results as a function of the strain are shown in Figs 6 and 7, respectively. In Fig. 6 the recrystallization curves have also been drawn, calculated with the aid of Sellars-Tegart’s equation [29], of peak strain [30] and equations (4x6) of the text, and each curve corresponds to one of the values of Z/A noted in Table 1. As the strain increases the mean austenite grain size (Fig. 7) tends to a constant value which represents the grain size in the steady state region, or the size of the grain recrystallized in continuous dynamic recrystallization. Observation of the microstructures, especially those corresponding to the greatest value of Z/A, allows Sakai and Jonas’
170
MEDINA
and HERNANDEZ:
RECRYSTALLIZATION
C)I- AUSTENITE
I Steel C2 0.8
,,_.___i
O0.1
0.2
0.5
1
2
5
10
0.1
Equivalent strain Fig. 6. Recrystallization curves calculated in accordance with the model and recrystallized fraction measured in quenched specimens. conclusions [8] regarding the preferential nucleation on the grain boundaries and the appearance of a necklace-like form to be checked. However, grains with intragranular nucleation (in the interior of the grain) are also found. It has also been observed that the recrystallized grain remains practically constant as recrystallization advances, as has already been reported by other authors [20]. Figure 8 shows the recrystallized austenite grain size as a function of Z/A, it being seen that this follows the power law mentioned above, whose regression line obeys the following expression Dd
(7)
The dynamically recrystallized grain size, in accordance with equation (7), gives values which coincide approximately with Sellars’ model [14, 231, when the Z parameter is high, and with the model developed by Namba et al. [19], when the Z parameter is relatively low. Finally, the alloying elements influence recrystallization kinetics in so far as they affect the value of peak strain [30] and the activation energy for the
E
1
240
0 IIOOYI; 0.5445“ 0 lloo~c; A 900°C;
5.224
s-1
3.628
s-’
Steel
1
10
loo
1,000
z!A Fig. 8. Dynamically recrystallized grain size as a function of the dimensionless parameter Z/A. strain [29]. In this respect, and by way of summary, it may be said that an increase in the C, Si or Mn content has no effect on tp while an increase of V, MO, Ti or particularly Nb increases the value of tp. With regard to the activation energy, all the elements contribute to a greater or lesser degree to increasing the activation energy, except carbon which tends to reduce it, Nb being the element which most contributes to the hardening of the austenite and therefore to increasing the activation energy. 4. CONCLUSIONS 1. The model created to calculate the dynamically recrystallized fraction establishes that the term k and the exponent m’ are not constants and depend on the dimensionless parameter Z/A. 2. The model makes it possible to calculate the dynamically recrystallized fraction of any low alloy or microalloyed steel as a function of the strain, temperature, strain rate and austenite grain size. 3. The recrystallized grain size depends less on the Z/A parameter than other models established as a function of Z alone. 4. All the alloying elements, except carbon, tend to delay the start of dynamic recrystallization, especially niobium. Acknowledgements-This work has been undertaken in CENIM (Madrid) and the authors are grateful for the financial support of the DGICYT of Spain (Project PB890022). Hernandez’s studies are sponsored by the UNAM (Mexico).
c2
REFERENCES 0
0.4 0.8 1.2 Equivalent
Fig. 7. Mean austenite
1.6 2.0 24 strain
2.8
grain size as a function
3.2
3.6
of the strain.
I. C. Rossard and P. Blain, Mtm. Scient. Rec. M6taN. 56, 285 (1959). 2. R. A. Petrovic, M. J. Luton and J. J. Jonas, Q. 14, 137 (1975).
Can. Metall.
MEDINA
and HERNANDEZ:
RECRYSTALLIZATION
3. S. Steinemann, Bectriige Geol. Scheweiz (Hydrol) 10, 1 (1985). 4. M. J. Luton and C. M. Sellars, Acta metall. 17, 1033 (1969). and C. M. Sellars, Indian 5. J. P. Sah, G. J. Richardson J. Technol. 11, 445 (1973). 6. R. Sandstrom and R. Lagneborg, Acta metall. 23, 387 (1975). 7. W. Roberts, H. Boden and B. Ahlblom, Metal Sci. 13, 195 (1979). 8. T. Sakai and J. J. Jonas, Acta metall. 32, 189 (1984). 9. T. Sakai, M. G. Akben and J. J. Jonas, Thermomechanical Processing of Microalloyed Austenite (edited by A. J. DeArdo, G. A. Ratz and P. J. Wray), p. 237. A.I.M.E., Warrendale, Pa (1982). 10. T. Sakai, M. G. Akben and J. J. Jonas, Acta metall. 31, 631 (1983). and C. Rossard, M&m. 11. A. Le Bon, J. Rofes-Vernis Scient. Rev. M&all. 55, 573 (1973). 12. A. Le Bon, J. Rofes-Vemis and C. Rossard, Metal. Sci. 9, 36 (1975). 13. J. P. Michel, M. Akben and J. J. Jonas, Revue MeYaN. 78, 823 (1981). 14. C. M. Sellars, Hot Working and Forming Processes (edited by C. M. Sellars and G. J. Davies), p. 3. The Metals Society, London (1980). 15. C. M. Sellars, Czech. J. Phys. B 35, 239 (1985). 16. J. H. Benyon and C. M. Sellars, ISZJZnt. 32,359 (1992). and J. J. Jonas, ISIJ Int. 31, 95 (1991). 17. A. Laasraoui MPm. Scient. Rev. 18. S. F. Medina and C. A. Hernandez, M&t. 66, 217 (1992).
OF AUSTENITE
171
19. S. Nanba, M. Kitamura, M. Shimada, M. Katsumata, T. Inque, H. Imamura, Y. Maeda and S. Hattori, ISZ.7 Int. 3i, 377 (1992). 20. J. P. Sah. G. J. Richardson and C. M. Sellars. Metal. Sci. 8, 3255 (1974). 21. G. Glover and C. M. Sellars, Metall. Trans. 4, 765 (1973). 22. H. J. McQueen and S. Bergerson, Metal. Sri. 6, 25 (1972). 23. C. M. Sellars, Metal. Sci. Technol. 6, 1072 (1990). 24. R. A. Barbosa and H. C. Braga, ISIJInt. 32,257 (1992). 25. F. H. Samuel, S. Yue, J. J. Jonas and B. A. Zbinden, ISIJ Int. 29, 1221 (1989). 26. F. H. Samuel. S. Yue. J. J. Jonas and K. R. Barnes. ISZJ Int. 30, 216 (1990). 27. L. N. Pussegoda, S. Yue and J. J. Jonas, Metall. Trans. 21A, 153 (1990). 28. L. N. Pussegoda and J. J. Jonas, ISZJInt. 31,278 (1991). 29. S. F. Medina and C. Hernandez, Acta mater. 44, 137. 30. S. F. Medina and C. Hernandez, Acta mater. 44. 149. 31. C. Hernandez, S. F. Medina and J. Ruiz, Acta mater. 44, 155. 32. J. Kunze, Metal. Sci. 16, 217 (1982). 33. S. F. Medina and J. E. Mantilla, Scripta metall. mater. 30, 73 (1994). 34. A. Faessel, Rev. M&all., Cah. if: Tech. 4, 875 (1976). 35. S. F. Medina, Rev. Metal. Madrid 23, 419 (1987). 36. C. M. Sellars and W. J. M. Tegart, M&m. I&d. Sci. Rev. M&all. 63, 731 (1966).