Strength and Structural Changes under High Strain-rate

Hot Deformation of C Steels*

By Hiroshi YADA,** Nobuhiko MATSUZU,** Koe NAKAJIMA,**

Kazuo WA TANABE * * and Hidenori T OKI TA* *

Synopsis

For high-speed continuous rolling, such as in wire rod mill and hot strip mill, behaviors of various carbon steels under high strain-rate hot deforma-tion were investigated. For the purpose, a compression type hot deformation simulator of the following performance was developed; maximum strain rate, 300 sec-'; minimum time interval between each deformation, 15 msec; and maximum strain, over 2. A high speed rolling mill was also used, and a strain rate of 800 sec-' was obtained by this mill. A technique of two pass rolling was also developed.

Using these experimental devices, steels of 0.05 to 0.81 %C were tested in the temperature region between 800 °C and 1 100 °C. The main results obtained were as follows:

(1) The features of stress-strain curves did not change essentially with the increase in strain rate. It was shown that the dynamic recrystalliza-tion of austenite determined the form of the curves.

(2) In the simulator experiments, the maximum stress 6m, the steady state stress QS, and the mean resistance to deformation k fm, were all found describable satisfactorily well as a function of the Zener-Hollomon Parameter, Z, with an activation energy of 63 800 kcal/mol and with an exponent of Z lying between 0.09 N 0.17. The grain diameter of recrystallized austenite also seemed to be described as a function of Z.

(3) In the rolling experiments, kfm was also shown to be well described as a function of Z, as

kfm = CZr

provided that the calculated finishing temperature be taken as the tem-perature of deformation, k fm and r both showing a fair agreement with those obtained from the simulator experiment.

(4) The effects of successive deformation on the stress, with a short interval of 0.5 sec and below, are nearly the same as those of single deforma-tion, provided the overall strain is the same. Accordingly, the above con-clusions (1) and (2) should also apply to the cases of successive deformation as a rough approximation.

I. Introduction

In the modern hot rolling of steel, such as by hot

strip mills and wire rod mills, the rolling speed has been continuously increased, so that strain rates of

several hundreds per second are presently realized. Few investigations, however, have been reported yet on the structural changes or on the hot strength of

steel in such high speed deformation.

Tensile,' compressive,2~ and torsional3~ tests at high strain rates were conducted by many investiga-

tors. In these investigations, however, the amount of strain applied to the specimen was limited, and in

most cases, experimental conditions were not effec-tively controlled. Furthermore, new concepts are

needed to deal with the successive deformations ap-

plied at a very short interval, which is the case of all the high speed hot rolling, where the time interval between passes has become as small as some 20 msec

in wire rod mills. In the previous work,4~ some of the present authors

reported that in wire rod rolling the structure was consisted of fully recrystallized austenite after passing through a train of mills, and that the grain diameter was related to the Zener-Hollomon parameter Z of the last pass only, as shown in Fig. 1, Z being the equivalent, or the temperature-compensated, strain rate given by

z = k exp (Q /R T) .....................(1)

where, k : the strain rate

Q: the activation energy R : the gas constant

T: the absolute temperature. As seen in this figure, the relationship between grain size and Z coincides with that in one-pass rolling with a reduction exceeding 40 %. From these results they suggested that, when high strain rate deforma-tions are performed successively, as in a train of high speed hot rolling mills, strain is accumulated suc-cessively, so that after many passes the structure is substantially the same as in one-pass rolling with that much amount of strain, and that the structure is usually dynamically recrystallized.

The present work was undertaken to prove and develop further the above concept, using a newly developed hot deformation simulator and a high speed laboratory mill, and also to develop a formula-tion of the mean resistance to deformation based on this new concept.

Fig . 1. Prior austenite grain size of quenched crop ends in wire-rod rolling and that of single-pass rolling with

large reduction. (Q=63 800 cal/mol)

* Presented to the Symposium of the 101st ISIJ Meeting, April 1981, at The University of Tokyo in Tokyo; preprinted in

to-Hagane, 67 (1981), A57, in Japanese. English manuscript received September 29, 1981. 0 1983 ISIJ * * Process Technology R & D Laboratories, Nippon Steel Corporation, Edamitsu, Yawatahigashi-ku, Kitakyushu 805.

Tetsu-

(loo) Research Article

Transactions ISIJ, Vol. 23, 1983 (101)

II. Experimental Work

1. Material

The steels used were obtained in the form of billet or slab from commercial stocks, and were soaked at 1200 to 1 250 °C then hot-rolled into plates of 6 to 15 mm thickness.

The chemical analyses are listed in Table 1: the carbon contents ranged from 0.05 to 0.81 %.

2. Experimental Method 1. Hot Deformation Simulator

A newly developed apparatus of impact flat-com-

pression type was used to simulate high-speed sequen-tial hot rolling.5'6~ Table 2 shows its main perfor-mance capabilities. The total system of the apparatus is schematically shown in Fig. 2. The apparatus has a servo-hydraulic system, as do the similar modern compression type machines, and thanks to the large servo-valve (4001/min) for its comparatively small load capacity, the ram velocity and the interval be-tween successive compression are the fastest and the shortest among those reported heretofore.7'8~ The ranges of strain rate and time interval achievable are shown in Fig. 3, as compared with those of com-mercial rolling mills. It will be appreciated that the simulator can cover almost the whole range of com-mercial operation.

The specimen is a bar with a rectangular section, and the form during or after deformation is shown in the figure attached to Photo. 1. After many tries,

those dimensions that are inscribed were decided upon, as giving a satisfactorily uniform distribution of strain within a specimen. Although, as is shown in Photo. 1, non-uniform distribution of strain is in-evitable at the center of the deformed part due to sticking, approximately uniform distribution of strain is obtained at either end of the deformed part (arrow A), and also it was found that the average strain in the direction of application of force does not vary within the deformed part. Also in this case the bulging to both sides was slight, and it was shown experimentally that plane-strain condition was nearly fulfilled with respect to stress.

Table 1. Chemical compositions of steels used. (wt %)

Table 2. Outline of the hot deformation simulator.

Fig. 2. Block diagram of the hot deformation simulator.

Fig. 3. Comparison of laboratory simulation methods of hot

rolling with commercial rolling mills.

Research Article

(102) Transactions ISIJ, Vol. 23, 1983

Specimens were usually heated to 1200 °C and maintained at that temperature for 3 min, and then

allowed to cool to the desired temperature of deforma-tion. The temperature of the part of the specimen

to be tested was measured by a thermocouple welded to a side of that portion, and was regulated so as to fit to the intended heat cycle.

After compression, specimens were usually quench-ed with water jet within 0.2 sec. The cooling rate was about 1 000 °C/sec. The metallographic observa-tion was made on the vertical section of the specimen including its long axis (see the dot-and-dash line in the figure attached to Photo. 1). This rapid cooling always enabled to produce martensitic structure, so that prior austenitic grain boundaries were revealed by an etchant consisting of alcoholic solution of picric acid added with sodium laurilbenzenesulfonate.

Displacement of the upper die is controlled by a

process computer, as shown in Fig. 4. In this figure, (a) is for a case of single deformation with a large amount of strain and (b) the sequential deformations, in which the same amount of strain was divided into 8 deformations. As seen in this example, the speci-men is always hit by the upper die after it has acquired a predetermined constant speed, and in the case of deformation of a large amount of strain, the speed was reduced stepwise so as to make the strain rate as constant as possible throughout the deformation. The records of actual displacement of the upper die and the accompanying change in load in this ex-ample are also shown in this figure.

The strain rate-strain and the stress-strain curves were calculated from these records as shown in Fig. 5. As shown, the fluctuation of strain rate is smaller in the single deformation, within about 30 % of the average value, while it varies within 70 % of the average value. In the latter case, however, the feature of the change resembles that of rolling, the strain rate being highest at the moment of contact and then falling. 2. Rolling Experiment

A 2-high laboratory mill of 400 mm rolls and equipped with a large flywheel was used for high speed

Photo. 1. Metal flow of specimen formation simulator. longitudinal section)

after testing by

(multiple layer

the hot de-

clad steel,

Fig. 4. Examples of deformation program and records of the actual displacement and load. (Simulator)

Research Article

Transactions ISIJ, Vol. 23, 1983 (103)

rolling. The 2-pass sequential rolling was performed using a looper guide, the diameter of which is 630 mm, attached to the mill as shown in Fig. 6. An ordinary laboratory mill of 350 mm rolls, was also used in some experiments.

The specimens used were 4 to 6 mm thick, 30 to 50 mm wide and 500 to 1 000 mm long. They were usually heated to 1 200 °C for 5 min, and then trans-ferred during cooling to another furnace, which was kept at 700 to 1200 °C beforehand. They were rolled within 0.2 to 2 sec after extraction from the second furnace, in which they were held at least 10 min.

After rolling, specimens were immediately quenched in water. The roll speed was between 120 and 1 600 rpm, and reduction was up to 40 %. The mean strain rate was calculated from the reduction in the thickness of the specimen and the rolling speed, and it ranged from 40 to 800 sec-1, as is shown in Fig. 7. The two-pass rolling was done with a roll speed of either 1 000 or 1 500 rpm. The interval between the two passes was 0.11 and 0.07 sec, respectively.

III. Results and Discussion

r. Hot Deformation Simulator Experiment

1. Single Deformation Typical stress-strain curves of austenite, with varied

strain rates and temperatures, are shown in Fig. 8. Generally speaking, the stress increases with strain at first to reach a maximum a at a strain of 0.2 to 0.5, then converges to a constant level o. For strain rates of about 5 sec-1, however, the stress increases again at higher strain. This anomaly is most likely due to the decrease in temperature, which amounted to 50 °C in this case. All the steels investigated showed similar stress-strain behavior.

Structural changes are exemplified in Photo. 2 (a) in correspondence with the stress-strain curve pre-sented by the solid line in Photo. 2 (b). As already reported in a previous work though in a lower strain-

Research Article

Fig . 5. Example of actual strain

from the records of Fig. 4.

rate and stress

(Simulator)

derived

Fig. 6. Experimental metho d of high-speed two pass rolling.

Fig . 7. Mean strain rates obtained in the high

rolling.

speed mill

Fig. 8. Stress-strain curves. (Simulator)

(104) Transactions ISIJ, Vol. 23, 1983

rate range,8) the decreasing rate of stress at the first stage corresponds to the beginning of recrystalliza-tion, and the steady state reached at higher strains

(between 0.8 to 1.3) corresponds to the region of complete recrystallization.

Because of the rapid cooling, which should be considered as sufficient to suppress effectively the progress of static recrystallization, this structural change is most likely due to dynamic recrystallization. The features of those stress-strain curves correspond well to this thought.

The maximum stress 6m and the steady state stress QS are plotted on a log-log scale against the Zener-Hollomon parameter Z as shown in Fig. 9. For the activation energy Q of Eq. (1), 63 800 calf mol, the value which was deduced by Sakai et al. from tensile tests with high carbon steels,9~ was adopted.

A linear relationship seems to hold between the two stresses and Z, so that Qm and QS are expressed as

Qm = AZp ...........................(2)

QS = BZq ...........................(3)

where, A, B, p, q ; the constants independent of strain rate and temperature.

Photo. 2. Comparison of the

single deformation.

stress-strain curve and quenched structure of multi-pass

Interval between successive deformations in multi-pass,

deformation with those 50 msec. (Simulator)

of a

Fig. 9. Dependence of deformation stress mon parameter Z. (Simulator)

on Zener-Hollo-

Research Article

Transactions ISIJ, Vol. 23, 1983 (105)

The values of p and q obtained in this experiment are shown in Table 3. No obvious relationship can be found between these values and the carbon con-tents. The grain diameter of dynamically recrystallized austenite is also expected to show a similar relation-ship with Z as the deformation stress does.9~ This plot is shown in Fig. 10. The scattering of the data, which is wider than that in the rolling experiment shown in Fig. 1, seems partly due to the effect of the initial grain diameter as shown in this figure, and also

probably partly due to the effect of the unevenness of strain distribution. From this figure it is not certain whether grain diameter d can be expressed in the same from as Q in Eqs. (2) and (3), as was the case in the experiments at lower strain-rates.9~ This problem will be discussed in detail elsewhere.

From above considerations, it may be concluded that at high strains the dynamical recrystallization determines both the deformation stress and the struc-ture after deformation up to the high strain-rate range. 2. Sequential Deformation Experiment

An example of sequential deformation is shown in Photo. 2 (b) by the dotted line, and the resultant structure in Photo. 2 (c). In this experiment, the total strain, the same as that of the single deformation (the solid line in Photo. 2 (b)), was divided into 4 equal parts, with an interval of 50 msec between

deformations. As shown in Photo. 2 (b), the four stress-strain curves, when depicted against the accumulated strain, may be synthesized into one enveloping curve, which resembles that of the single deformation (solid line). This result indicates that a sequential deformation with very short intervals between deformations should be considered as substantially equal to a single deformation with the same total amount of strain.

In Fig. 11 are shown the results of the experiment, which was done to determine the limit of the interval between deformations within which the above con-clusion holds. As shown in Fig. 11, an interval of less than 0.5 sec does not affect much on the stress-strain behavior.

2. Rolling Experiment

1. Single Pass Rolling In Fig. 12, results obtained from high-speed rolling

experiments for the mean resistance to deformation

Table 3. Values of exponents in

pression of deformation terms of Z.

the exponential

stresses and k1m

ex-

in

- vava -''-V "- k,'- ci' v. VJ V'~ 1 1VV \.1

Fig. 10. Dependence of grain diameter of prior austenite on Zener-Hollomon parameter Z. (Simulator)

Fig. 11. Comparison

deformation

of stress-strain curves in sequential

with time intervals changed.

Fig. 12. Temperature

deformation.

dependence of mean

(Rolling)

resistance to

Research Article

(106) Transactions ISIJ, Vol. 23, 1983

k fm of Steel A are depicted against the rolling tem-perature, that is, the temperature of the holding furnace, with the strain rate widely varied. Also in this figure, the k fm values calculated from Shida's empirical formula,10~ which is now frequently used for actual rolling in the strain-rate regions lower than 100 sec-1, are presented by the broken lines. The deflection in these two groups of curves below about 900 °C correspond to the transformation of austenite to ferrite. Here discussions will be confined to the fully austenitic region, because the transformation behavior differs widely depending on the initial micro-structure, and needs more elaborate considerations.

The present result shows that Shida's empirical formula (which is expressed using the rolling tem-

perature that was actually the temperature of the holding furnace and did not represent the real tem-

perature of the specimens) is far from correct, especial-ly in the higher strain-rate range. It was suspected that one of the causes of this discrepancy might be the failure of accounting for the temperature change that should take place during rolling due to high strain rate. Therefore, the temperature change after extraction from the heating furnace was calculated using a computer simulation program which was successfully applied to hot strip mills.11 The results are shown in Fig. 13.

The finishing temperature is shown to differ widely depending on the strain rate : the difference in the finishing temperatures between the lowest

(6 sec-1) and the highest (630 sec-') amounts to 100 to 180 °C for the same temperature of extraction from the furnace. It will be noticed further that the temperature drop is considerable only for lower strain rates at a high strain rates. This is because at a high strain rate the heat generated by plastic work and by the friction between the plate and the rolls com-pensates, or exceeds, the heat lost by radiation into the atmosphere and by conduction to the rolls.

This may probably be good enough to explain the inadequacy of conventional fromulae and shows that a new expression for kfm is necessary for the high strain-rate region. In order to obtain such a formula, the conventional procedure has been to investigate the strain rate dependence of k fm at fixed temperatures. In the high strain rate region, however, this method cannot be used, because experimentally it is difficult

to hold the temperature constant against the heat being generated. Consequently, an expression which allows the effect of temperature to be lumped together with that of strain rate, or vice versa, as is done in Eqs. (2) and (3), is also necessary for k fm.

In Fig. 14, consequently, the kfm values taken from Fig. 12 are plotted on a log-log scale against Z, which was calculated from the estimated finishing temperature as in Fig. 13. The results obtained from ordinary-mill experiments are also included in this figure. As is seen, an excellent linear relationship is obtained as a whole, excepting two groups of data. One group (those points that are surrounded by broken line in Fig. 14) represents the cases of rolling conducted at 1200 °C, in which dynamic recrystal-lization was presumed to have occurred in view of the results of metallographic examination of the rolled specimen. The other group (marked with asterisks) corresponds to the cases of rolling in the intercritical and ferritic microstructure ranges.

From this result, it can be concluded that k fm may also be expressed as

k fm = CZr ...........................(4)

where, C, r: constants, regardless of strain rate and temperature.

The value of the exponent r, 0.12, was the same for the steel C.

Figure 15 is a similar representation of k fm of the same steel as in Fig. 14 for the case where the rolling was done at the heating temperature. For com-

parison's sake, the two straight lines of Fig. 14 are inscribed. At lower values of Z the plots coincide with the solid line, while at 1013 to 1015 they deviate downward from it, due probably to the difference in initial grain diameter, which was about 80 pm at 900 °C and about 130 pm at 1200 °C. Also, in the intercritical and ferritic regions, a considerable reduc-

Fig. 13. Calculated finishing

experiment of Steel A

temperature in

(e=0.3). (Roll

the ing)

rolling

Fig. 14. Dependence of mean resistance to deformation on equivalent strain rate, with the calculated tempera-

ture adopted. (Rolling)

Research Article

Transactions ISIJ, Vol. 23, 1983 (107)

tion in kfm is seen compared with the kfm value in Fig. 14. This result suggests that, to determine exact

values of 'fm , it is necessary to choose such a heat

cycle for each series of experiments that the structure before deformation will be nearly the same for all

samples. 2. Two-pass Rolling

A typical result of sequential rolling is shown in Fig. 16. In this figure kfm values of two-pass rolling

are plotted against accumulated strain, together with

strain values of one-pass rolling. All the kfm values of both the first and the second passes, together with those of one-pass rolling, conform to a single curve

against strain. This result confirms the conclusion derived from

the simulator experiments that the strains of preceding deformations are accumulated almost perfectly in

sequential deformations separated by very short in-tervals.

3. Comparison between Simulator and Rolling Experiments

The kfm values of the simulator experiment may be calculated from the stress-strain curves as shown in Fig. 8 by using

kfm $f(s)ds = .................... ~ .(5)

where, f (s) : the stress-strain curve. They are compared with the values of the rolling experiments as a function of carbon content in Fig. 17. Agreement is quite satisfactory. From this result it might be reasoned that (i) the plastic deformation behavior of the rolling can well be simulated by the hot deformation simulator used in this study, and also that (ii) the finishing temperature obtained from the computer simulation program proved to be a good representation of the effective deformation tempera-ture, which cannot be measured directly in the rolling experiment.

This calculated finishing temperature was used successfully by some of the present authors in formu-lating the structure just after deformation as shown in Fig. 1.4' In the case at hand, however, the resis-tance to deformation might be better expressed by the average temperature during deformation. So the above conclusion (ii) might remain tentative until a more exact one would be obtained from the analysis of the relation between the strain distribution and concurrent temperature change during rolling.

In this experiment kfm was shown to increase considerably with carbon content when the carbon content is below 0.6 %. Because the value of ex-ponent r in Eq. (4) does not change consistently with the chemical composition, and the activation energy used in calculating Z in Eqs. (2) to (4) is assumed constant through this work, the above dependency of kfm on carbon is attributed mainly to that of the constant C in Eq. (4). This conclusion also holds

Fig. 15. Dependence of mean resistance to deformation on equivalent strain rate when starting structures are varied. (Rolling)

i~liY Vl..l l.1V11U Vl 1V11 ,l~l• 1 VVV^1 JVV 1111

Fig. 16. Mean resistance to deformation in high-speed, two-

pass rolling.

Fig. 17. Dependence o

C content.

f mean resistance to deformation on

Research Article

(108) Transactions ISIJ, Vol. 23, 1983

for 6m and cS in Eqs. (2) and (3). Consequently, the constants A, B and C in Eqs. (2) to (4) may be con-sidered generally as the functions of strain only, and, therefore, represent the geometry of the stress-strain curves.

4. Basic Formula of the Resistance to Deformation If in the following general equation for deformation

stress a is assumed to be

Q = g (~, composition, initial structure). ZS ...(6)

where initial structure may be replaced by initial austenite grain size in most cases, and g is a function expressing the geometry of the stress-strain curve and independent of strain rate and temperature, then, it follows from Eqs. (5) and (6) as

kfm = 1 o dE

E

= ZS gds .....................(7)

E This is the same form as Eq. (4). In this case, the exponents p, q, r, s must respectively be the same for the same steel and the same initial structure. This situation is approximately realized in Table 3. The values of p and q do not differ widely from those of r, as well as from that obtained from the rolling ex-

periments, 0.12. This result suggests that, if the exact form of the

stress-strain curve and its change with the initial

grain diameter are known for one particular condition of strain-rate and temperature, kfm may be predicted for any strain, strain-rate and temperature. On the other hand, however, it will be noticed in that the form of g of Eq. (6) also seems to change somewhat according to strain rate and temperature. More detailed work is underway to find a more exact form of stress-strain curves, as well as to determine more exactly the constants in Eqs. (1) to (4) for various kinds of steels.

Conventionally resistance to deformation k f, i.e., the a in Eq. (6), is written as

k f exp (E /T) ...............(8)

where, D, n, m, E: the constants that depend on composition and the conditions of deforma-

tion.lo,i1) From the results obtained here, however, it is clear that the term & does not express properly the effect of strain for the high-speed sequential rolling as may be judged in Fig. 8.

5. Correspondence to the Actual Rolling Practice

The results obtained in this work reveal basic features of resistance to deformation in high-speed continuous rolling : that the strain is accumulated at a later stage of sequential rolling, and that the struc-ture and the stress may be predicted from the one-pass rolling with large strain. The accumulation of strain will be nearly complete in the finishing train of the

wire rod mill (block mill), though in most cases the effect of static restoration between passes may not be neglected. In any case, however, at the last stage of a tandem mill, that of hot strip mills also, the ac-cumulated strain should become so large that the dynamic recrystallization occurs in the temperature region in which the carbon steels are austenitic, and that for this reason the resistance to deformation would actually be lower than that predicted from conven-tional formulae.

Accordingly, to describe the resistance to deforma-tion in continuous rolling, a completely new expres-sion will have to be constructed on the basis of Eq. (4), and it should also include the static restoration during interpass time.

Iv. Summary and Conclusion

For high-speed continuous rolling such as in wire rod mills and hot strip mills, behaviors of various carbon steels under high strain-rate hot deformation were investigated. For the purpose, a compression type hot deformation simulator of the following per-formance was developed : maximum strain rate, 300 sec-1; minimum time interval between each deforma-tion, 15 msec; and maximum strain, over 2. A high-speed rolling mill was also used, and a strain rate of 800 sec-1 was obtained by this mill. A technique of two-pass rolling was also developed.

Using these experimental devices, steels of 0.05 to 0.81 % C were tested in the temperature region between 800 °C and 1 100 °C. The main results obtained were as follows :

(1) The features of stress-strain curves measured by the simulator do not change essentially with in-crease in strain rate. After the initial steep rise the stress reaches maximum at a strain slightly smaller than that at which dynamic recrystallization starts, and then converges to an approximately constant level as the dynamic recrystallization completes.

Both the maximum stress o and the steady-state stress a were shown to be described by

am = AZ~

a = BZq

where, Z: the Zener-Hollomon parameter calculated from strain rate and temperature using 63

800 cal/mol as the activation energy for all the steels, and

A, B, p, q : constants. The values of p and q were between 0.10 and 0.16, and showed no obvious effect of carbon. The grain diameter of fully recrystallized austenite also seemed to be related to Z, though the exact formula to describe the relationship was not obtained.

(2) Sequential deformation with a short interval of 0.05 sec or less gives a nearly complete accumula-tion of strain so that it may be regarded as a single deformation with corresponding amount of strain. Further no conspicuous effects were seen on the de-formation stress by extending the interval to 0.5 sec.

(3) The mean resistance to deformation k 1m,

Transactions ISIJ, Vol. 23, 1983 (109)

obtained from the rolling experiment,

to be described well aswas also shown

k fm = CZr

where, C, r: constants. In this equation, the rolling temperature was the one that was calculated, instead of the extraction tem-

perature of the specimen, which is more common. The large difference between these temperatures seemed to account for the apparent discrepancy be-tween the resistances estimated by conventional for-mulae and those of this experiment when compared at the same level of the extraction temperature.

(4) The two-pass rolling experiments with inter-vals of 0.07 and 0.11 sec showed a complete ac-cumulation of strain, agreeing with the simulator experiment.

(5) The values of k f,,, calculated from the stress--strain curves showed a good agreement with those obtained from rolling experiment. The values of exponent r ranged from 0.09 to 0.17 for the former, which fairly agree with the value of 0.12 for the latter.

(6) From these results the new basic equation of the following form

S .

kf . = _E gds

is tentatively proposed, where s is the material con-stant and g is a function of strain, composition and

initial structure.

REFERENCES

1) For example, T. Toshima: Tetsu-to-Hagane, 41 (1955), 344. 2) For example, H. Suzuki, S. Hashizume, Y. Yabuki, Y.

Iehihara, S. Nakajima and K. Kenmochi : Rep. Inst. In- dustrial Science, The University of Tokyo, 18 (1968), No. 3, 139.

3) For example, Y. Ohtakara, T. Nakamura and S. Sakui: Trans. ISIJ, 12 (1972), 36.

4) H. Yada, H. Matsuzu, H. Sekine, Y. Matsumura and Y. Miura : Tetsu-to-Hagane, 65 (1979), 5880.

5) H. Yada, N. Matsuzu, H. Sekine and T. Futamura: Tetsu- to-Hagane, 66 (1980), 5992.

6) N. Matsuzu, H. Yada and K. Shimohashi : Tetsu-to-Hagand, 66 (1980), 5993.

7) L. J. Cuddy: The Hot Deformation of Austenite, ed. by

J. B. Ballance, AIMS, (1977), 169. 8) 0. Pawelski, U. Rudiger and R. Kasper: Stahl u. Eisen.,

98 (1978), 181. 9) For example, S. Sakui, T. Sakai and K. Takechi: Trans.

ISIJ, 17 (1977), 718. 10) S. Shida: Hitachi Hyoron, 47 (1965), 57. 11) K. Inoue : Tetsu-to-Hagane, 41 (1955), 506, 593 & 869. 12) S. Hamauzu, T. Kikuma, K. Nakajima and N. Hosomi:

Proceedings of 1980, Spring Joint Meeting of Sosei Kako

(Plastic Working), The Japan Soc. for Tech. of Plasticity, Tokyo, (1980), 53.

13) For example, S. Yamamoto, Y. Fujita, T. Okita, T. Ouchi and T. Osuga : Tetsu-to-Hagane, 67 (1981), A49.