Effects of Temperature and Strain Rate on TRIP Effect in SUS301L Metastable Austenitic Stainless Steel

Abstract

Effects of temperature and strain rate on tensile properties in metastable austenitic stainless steel SUS301L were studied in order to clarify the conditions of stress-induced martensitic transformation behavior for the maximum uniform elongation through the TRIP effect. The experimental results of the previously studied SUS304 steel were used to compare the conditions of metastable austenitic steels with different austenite stability. In the static tensile tests for the SUS301L steel at temperatures between 123 K and 373 K, the tensile strength increased with decreasing temperature, and uniform elongation reached a maximum at 323 K. The volume fraction of stress-induced martensite (V_α) at the same true strain increased with a decrease in temperature. For the strain-rate dependence on transformation kinetics, V_α decreased at strain rates higher than about 10^–2 s^–1 due to the temperature rise caused by adiabatic deformation. The equation for stress-induced transformation behavior proposed by Matsumura et al. was modified to consider the saturation value of stress-induced martensite, and the modified equation could describe the transformation kinetics precisely. The conditions of stress-induced transformation for the maximum uniform elongation through the TRIP effect were coincident between the SUS301L and the SUS304 with different austenite stability: the volume fraction of martensite at a true strain of 0.3 is approximately 5% and the maximum transformation rate is almost 2 at a higher true strain near uniform elongation.

1. Introduction

The transformation induced plasticity (TRIP) effect^1,2,3) is a feasible strengthening mechanism for the enhancement of uniform elongation due to stress-induced martensitic transformation during deformation. Thus far, metastable austenitic stainless steels,^{1,2,3,4,5,6,7,8,9,10,11,12,13,14)} 9% Ni steels,¹⁵⁾ and TRIP-aided multi-microstructure steels^16,17,18) have been investigated for TRIP steels. In our previous studies, we investigated the effects of temperature,¹⁹⁾ strain rate²⁰⁾ and Ni equivalent^21,22) on the TRIP effect and stress-strain curve^22,23) in metastable austenitic stainless steels. In terms of the temperature dependence on the TRIP effect in the SUS304 (Ni equivalent (Ni_eq.) is 23.1%),¹⁹⁾ the following two conditions were summarized for stress-induced martensitic transformation to obtain the maximum uniform elongation through the TRIP effect.

(i) The volume fraction of martensite at a true strain of 0.3 is approximately 5%.

(ii) The maximum rate of stress-induced martensitic transformation per unit strain is almost 2 and is reached at a higher strain near uniform elongation.

These conditions are closely correlated with a large deformation in the austenite phase before transformation^4,5) and the optimum amount of stress-induced martensite.^3,6) In terms of the TRIP effect in metastable austenitic stainless steels, the volume fraction of stress-induced martensite affects the tensile strength, and the conditions for obtaining excellent ductility have been qualitatively discussed using extensive experimental data.^{1,2,3,4,5,6,7,8,9,10)} The above conditions¹⁹⁾ should also be clarified by using other metastable austenitic steels with different austenite stability because transformation kinetics depend on chemical composition, temperature and strain rate. In this study, the commercial metastable austenitic stainless steel SUS301L (Ni_eq. = 21.9%)^20,22) was investigated.

On the other hand, we have also investigated the stress-induced transformation behavior by applying the following equation proposed by Matsumura et al.^17,24,25)   

$$V_{\alpha }=1-\frac{V_{{\gamma }_0}}{1+\left(k/q\right)\hspace{0.17em}{V}_{{\gamma }_0}\hspace{0.17em}{\epsilon }^q}\text{\hspace{0.17em},}$$(1)

where V_α is the volume fraction of stress-induced martensite, V_γ0 is the volume fraction of austenite before deformation, ε is the true plastic strain, and k and q are constants.²⁴⁾ Equation (1) can precisely describe various stress-induced transformation behavior. In Eq. (1), the estimated V_α always becomes 100%. However, this is not necessarily coincident with past studies.^1,6,9,14) That is, V_α approaches saturation below 100% depending on the deformation conditions. It is very important to consider such behavior for the description of stress-induced transformation in discussions on the TRIP effect.^1,6,7,14) We modified Eq. (1) to obtain the following equation, which takes into consideration the transformation kinetics:   

$$V_{\alpha }=V_{\alpha s}\left(1–\frac{V_{{\gamma }_0}}{1+\left(k/q\right)\hspace{0.17em}{V}_{{\gamma }_0}{\epsilon }^q}\right)\text{\hspace{0.17em},}$$(2)

where V_αs is the saturation value of stress-induced martensite and is governed by the driving force for the martensitic transformation.¹⁴⁾ The V_αs is also associated with the austenite stability and depends on many parameters such as chemical compositions, temperature, strain rate and microstructures.^{1,5,12,13,14,19,20,21)} In Eq. (2), the calculated V_α never exceeds V_αs. In this study, V_αs was considered as the V_α of the fractured specimen, which was measured by x-ray diffraction experiments. The conditions of stress-induced martensitic transformation for the maximum uniform elongation were discussed based on Eq. (2) using the experimental results of not only the SUS301L steel but also the previously investigated SUS304 steel.

In this study, we aimed at clarifying the conditions of stress-induced martensitic transformation for the maximum uniform elongation through the TRIP effect in metastable austenitic steels. We summarized the temperature and strain-rate dependence of stress-induced transformation behavior and discussed the conditions of temperature and strain rate to obtain the maximum uniform elongation in metastable austenitic stainless steels with different austenite stability.

2. Experimental Procedures

The commercial metastable austenitic stainless steel JIS-SUS301L, with a thickness of 1.5 mm, was used in this study. The chemical composition of the SUS301L and SUS304 steels and the Ni equivalent (Ni_eq.) are listed in Table 1. By employing the equation used by Sanga et al.,²⁶⁾ the Ni_eq. of SUS301L was calculated to be 21.9%. It was found from the estimated Ni_eq. that the austenite stability for SUS301L is lower than that for SUS304 (Ni_eq. = 23.1%). Figure 1 shows an optical micrograph of the SUS301L steel for which the average austenite grain size measured by the line intercept method was 26 μm.

Table 1. Chemical compositions of the JIS-SUS301L and JIS-SUS304 steels (mass%) and the Ni equivalent (Ni_eq.) estimated by Sanga et al.’s equation.²⁶⁾

	C	Si	Mn	P	S	Ni	Cr	N	Nieq. (%)
SUS301L	0.028	0.47	1.04	0.03	0.0015	7.1	17.3	0.127	21.9
SUS304	0.05	0.4	0.98	0.03	0.008	8.2	18.2	0.023	23.1

Fig. 1.

Optical micrographs of SUS301L steel used in this study.

Tensile tests were conducted at various temperatures and strain rates.^19,20,27) In terms of the effect of temperature on the stress-strain curve, static tensile tests with an initial strain rate of 3.3 × 10^–4 s^–1 were conducted at test temperatures between 123 K and 373 K. In terms of the strain rate dependence on the stress-strain curve, tensile tests were performed with strain rates between 10³ s^–1 and 3.3 × 10^–6 s^–1 at 296 K. Details of the experimental procedures for tensile tests are described in the references.^{18,19,20,21,22,27)} In order to investigate the effects of temperature and strain rate on the stress-induced martensitic transformation kinetics, test samples deformed by various amounts of ε were also prepared for x-ray diffraction analysis. Details of the quantitative estimation of the austenite and martensite phases by x-ray diffraction are also summarized in our previous papers.^19,20)

3. Results and Discussion

3.1. Effects of Temperature and Strain Rate on Tensile Properties in SUS301L Steel

Figure 2 shows nominal stress-strain curves in the SUS301L steel at various temperatures (a) and strain rates (b). The mechanical properties obtained at various temperatures and strain rates are summarized in Tables 2 and 3. As can be seen, the stress-strain curves and mechanical properties are much more dependent on the temperature than on the strain rate.^1,19,20) Figure 3 shows the true stress and work-hardening rate as a function of the true strain at various temperatures in the SUS301L. The work-hardening rate stopped decreasing and began to increase again below 323 K. Such behavior seems to have led to the changes in the flow curve and tensile properties, as seen in Fig. 2(a)^8,19,22) and are closely associated with the stress-induced martensitic transformation behavior.^19,20) The enhancement of uniform elongation in metastable austenitic steels can be obtained because a work-hardening rate higher than the flow stress can be maintained until a higher strain.^3,4,5,6,19) Figure 4 shows the mechanical properties of the SUS301L and SUS304 steels¹⁹⁾ as a function of temperature. In the SUS301L, the 0.2% proof stress and tensile strength increased with a decrease in the temperature and the uniform elongation reached its maximum at 323 K. In the SUS304,¹⁹⁾ the maximum uniform elongation was obtained at 308 K, which was lower than that for the SUS301L. The maximum value of uniform elongation for the SUS301L (90.4%) was larger than that for the SUS304 (82.7%), which seems to be associated with not only the stress-induced transformation behavior but also the work-hardening behavior of austenite,²⁸⁾ stress partitioning between the phases and so on. In the comparison of uniform elongation between the SUS301L and the SUS304, the uniform elongation near room temperature for the SUS301L was larger than that for the SUS304, but that at low temperatures below 243 K was reversed. The 0.2% proof stress of SUS304 decreased below 243 K because this is associated with the transformation strain of stress-induced martensite formed before yielding of the austenite. The $M_S^{\sigma }$ temperature for SUS304 steel thereby appears to be approximately 243 K,¹⁹⁾ which is almost coincident with Huang et al.’s study.⁷⁾ Judging from the difference in Ni_eq., the $M_S^{\sigma }$ temperature for the SUS301L seems to be higher than that for the SUS304. However, the 0.2% proof stress of SUS301L increased with a decrease in temperature. This may be related to the effect of nitrogen (N) on tensile properties^29,30) because the SUS301L contains N content of 0.127 mass%. Miura et al.²⁹⁾ investigated the effects of N and carbon (C) content on the deformation behavior at low temperatures using SUS304 and SUS316 steels. The effect of temperature on 0.2% proof stress in the SUS304 with N content of 0.128 mass%²⁹⁾ agreed well with that of the SUS301L.

Fig. 2.

Nominal stress−strain curves in the SUS301L steel obtained by the static tensile tests at various temperatures (a) and strain rates (b). (Online version in color.)

Table 2. Mechanical properties of the SUS301L steel obtained by tensile tests at various temperatures with an initial strain rate of 3.3 × 10^–4 s^–1.

Temperature (K)	0.2% proof stress (MPa)	Tensile strength (MPa)	Uniform elongation (%)
123	504	1560	35.5
173	500	1401	37.8
213	443	1244	41.3
223	425	1204	44.7
233	417	1177	45.5
243	400	1151	47.3
258	378	1070	52.5
273	364	1058	56.0
296	328	880	76.8
323	313	744	90.4
348	290	647	73.6
373	296	622	55.3

Table 3. Mechanical properties of the SUS301L steel obtained by tensile tests with various strain rates at 296 K.²⁰⁾

Strain rate (s–1)	0.2% proof stress (MPa)	Tensile strength (MPa)	Uniform elongation (%)
3.3 × 10–6	302	893	81.9
3.3 × 10–5	323	897	77.0
3.3 × 10–4	328	880	76.8
10–3	321	844	74.6
10–2	357	784	72.2
10–1	390	747	55.7
100	420	738	43.1
101	450	715	37.2
102	483	742	35.5
103	–	814	37.2

Fig. 3.

True stress and work-hardening rate as functions of true strain at various temperatures in the SUS301L steel.

Fig. 4.

0.2% proof stress, tensile strength and uniform elongation as functions of temperature in the SUS301L and SUS304¹⁹⁾ steels. (Online version in color.)

Figure 5 shows the mechanical properties of the SUS301L²⁰⁾ and SUS304 steels¹⁹⁾ as a function of the strain rate. In terms of the strain rate dependence on tensile properties, the 0.2% proof stress increased with an increase in strain rate. The tensile strength decreased with an increase in strain rate up to 10⁰ s^–1, but increased again with strain rates higher than 10¹ s^–1.^9,20) The uniform elongation decreased with increasing strain rate and changed largely at strain rates between about 10^–2 and 10⁰ s^–1. The mechanical properties of the SUS301L in Fig. 5 were larger than those of the SUS304 in most cases. However, at high strain rates above 10⁰ s^–1, the uniform elongation of SUS304 was larger than that of SUS301L.

Fig. 5.

0.2% proof stress, tensile strength and uniform elongation as functions of strain rate in the SUS301L²⁰⁾ and SUS304 steels. (Online version in color.)

Figure 6 shows the tensile strength − uniform elongation balance at various temperatures and strain rates in the SUS301L and SUS304 steels. The dashed lines in Fig. 5 are contour lines of the product of tensile strength and uniform elongation. As can be seen, the temperature led to a large change in both tensile strength and uniform elongation whereas the strain rate mainly affected the uniform elongation. A better balance of tensile strength and uniform elongation was also obtained under other conditions of temperature and strain rate where the maximum uniform elongation was observed, mostly at low strain rates below 10^–4 s^–1 in the vicinity of room temperature.

Fig. 6.

Tensile strength − uniform elongation balance of the SUS301L²⁰⁾ and SUS304¹⁹⁾ steels at various temperatures and strain rates. (Online version in color.)

3.2. Temperature and Strain Rate Dependence on Stress-induced Martensitic Transformation Behavior in SUS301L and SUS304 Steels

Next, stress-induced martensitic transformation behavior at various temperatures and strain rates are discussed. Figures 7 and 8 show the volume fraction of stress-induced martensite (V_α) (a) and transformation rate (b) as a function of ε at various temperatures (Fig. 7) and strain rates (Fig. 8) in the SUS301L steel.²⁰⁾ The plots in Figs. 7(a) and 8(a) are the measured results obtained by x-ray diffraction analysis, and the solid or dashed lines are described by Eq. (2). The solid lines show the calculated results before necking and the dashed lines show those for higher strains.^19,20) The constants k, q and V_αs in Eq. (2) determined by the curve fitting of experimental results²⁴⁾ are summarized in Tables 4 and 5. In Fig. 7(a), V_α at the same ε increased with decreasing deformation temperature. Figure 7(b) shows the rate of stress-induced transformation per unit strain (dV_α/dε), which denotes the slope of the curves in Fig. 7(a) as a function of ε. The value of dV_α/dε at each temperature increased to the maximum after the start of deformation and decreased after the maximum rate.^7,19) The maximum rate of stress-induced transformation (dV_α/dε)_max became high, but dV_α/dε decreased abruptly with a decrease in temperature. On the other hand, as seen in Fig. 8, the effect of the strain rate on stress-induced transformation behavior changed at the strain rate of 10^–3 s^–1.²⁰⁾ At strain rates between 10^–3 s^–1 and 3.3 × 10^–6 s^–1, V_α at the same ε increased with an increase in strain rate. However, V_α at the same ε decreased at strain rates between 10^–2 s^–1 and 10⁰ s^–1. As seen in Table 5, V_αs was almost the same at about 20% at strain rates higher than 10¹ s^–1. The stress-induced transformation behavior at high strain rates agrees with the past studies on SUS304.^9,10) In Fig. 9, V_α (a) and dV_α/dε (b) in the SUS304 steel were summarized by using Eq. (2) as a function of ε at various temperatures.¹⁹⁾ The constants k, q and V_αs in Eq. (2) are summarized in Table 6. At temperatures below 273 K, constants k and q were the same as in the previous study¹⁹⁾ because V_αs was 1.0. It was found that the transformation kinetics near room temperature, in which the value of V_αs is below 100%, can be described more precisely by using Eq. (2). When the effect of the temperature on stress-induced transformation behavior was compared between the SUS301L (Fig. 7) and the SUS304 (Fig. 9), V_α at the same ε and the same temperature in the SUS301L was larger than that of the SUS304. This is associated with the stability of austenite or the Ni_eq. as seen in Table 1 and is also valid for dV_α/dε.

Fig. 7.

Volume fraction of stress-induced martensite (a) and rate of stress-induced martensitic transformation (b) as functions of true strain at various temperatures in the SUS301L steel. (Online version in color.)

Fig. 8.

Volume fraction of stress-induced martensite (a) and rate of stress-induced martensitic transformation (b) as functions of true strain at various strain rates in the SUS301L steel.²⁰⁾ (Online version in color.)

Table 4. Constants k, q and V_αs in Eq. (2) at various temperatures in the SUS301L steel.

Temperature (K)	k	q	Vαs
123	1558	2.55	1.0
243	2098	3.62	1.0
296	191.0	3.64	0.885
323	225.5	5.20	0.663

Table 5. Constants k, q and V_αs in Eq. (2) at various strain rates in the SUS301L steel.²⁰⁾

Strain rate (s–1)	k	q	Vαs
3.3 × 10–6	730.6	5.21	0.797
3.3 × 10–5	588.9	4.51	0.791
3.3 × 10–4	191.0	3.64	0.885
10–3	76.43	2.54	0.809
10–2	140.8	2.49	0.480
10–1	12.89	1.48	0.431
100	184.6	3.45	0.222
101	−	−	0.254
102	−	−	0.219
103	−	−	0.216

Fig. 9.

Volume fraction of stress-induced martensite (a) and rate of stress-induced martensitic transformation (b) as functions of true strain at various temperatures in the SUS304 steel.¹⁹⁾ Here, some data in the previous study were summarized by using Eq. (2) again. (Online version in color.)

Table 6. Constants k, q and V_αs in Eq. (2) at various temperatures in the SUS304 steel.¹⁹⁾

Temperature (K)	k	q	Vαs
123	1761.3	2.83	1.0
243	450.2	2.98	1.0
273	172.8	3.01	1.0
296	4639	6.1	0.551
308	374.1	5.2	0.506
323	1803.6	6.93	0.166

Here, the differences in tensile properties between the SUS301L and the SUS304 are discussed from the viewpoint of the stress-induced transformation behavior. As seen in Fig. 4, the uniform elongation of the SUS301L was larger than that of the SUS304 in the vicinity of room temperature, but at temperatures below 243 K, the uniform elongation of the SUS304 was larger than that for the SUS301L. The effect of temperature on uniform elongation seems to be small at low temperatures because the austenite phase was easily transformed to stress-induced martensite.^1,6,7,19) Thus, in the case where most of the austenite transformed to martensite at small strains below 243 K, the larger the tensile strength was, the smaller the uniform elongation became. On the other hand, tensile deformation behavior at high strain rates was similar to that of stable austenitic steels²⁰⁾ because the formation of martensite was prevented by the adiabatic heating at high strain rates above 10⁰ s^–1.^9,10,20) Thus, the TRIP effect on mechanical properties is smaller at high strain rates. The decrease in V_α at high strain rates leads to the change in balance between tensile strength and uniform elongation, as seen in Fig. 5. The reason why the uniform elongation between 10^–3 s^–1 and 10^–1 s^–1 in the SUS304 was smaller than that for the SUS301L is associated with the stability of austenite. V_α in the SUS304 seems to be smaller than that of the SUS301L because of the higher austenite stability in the SUS304.

3.3. Conditions of Stress-induced Transformation for the Maximum Uniform Elongation through the TRIP Effect in Metastable Austenitic Steels

By summarizing the stress-induced martensitic transformation behavior of the SUS301L and SUS304 steels at various temperatures and strain rates, the conditions for the maximum uniform elongation were discussed. The maximum uniform elongation was obtained with a strain rate of 3.3 × 10^–4 s^–1 at 323 K (SUS301L) and at 308 K (SUS304). In our previous paper,¹⁹⁾ the two conditions described in the introduction were summarized by using Eq. (1). As can be seen in Figs. 7 and 9, these two conditions were coincident with the present study at which the stress-induced transformation behavior was discussed by using Eq. (2). Therefore, the conditions of stress-induced martensitic transformation for the maximum uniform elongation through the TRIP effect are almost the same in the metastable austenitic stainless steels with different Ni_eq.. Because the transformation kinetic was almost the same between the SUS301L and the SUS304 at the maximum uniform elongation, the temperature at the maximum uniform elongation was dependent on the Ni_eq., i.e., the chemical composition.^5,21) The higher the Ni_eq. was, the lower the temperature became at the maximum uniform elongation. On the other hand, (dV_α/dε)_max and ε at the maximum uniform elongation for the SUS304 at 308 K became slightly smaller than in the previous study¹⁹⁾ by using Eq. (2). Figure 10 summarizes the stress-induced transformation behavior from Figs. 7, 8, 9. As mentioned earlier, the maximum uniform elongation of the SUS301L was larger than that of the SUS304. When the stress-induced transformation behavior is compared between the two conditions in Fig. 10, it is found that dV_α/dε at the latter stage of deformation at ε greater than 0.5 in the SUS301L is higher than that in the SUS304. As the austenite is constantly transformed to martensite until ε is close to plastic instability, a larger uniform elongation is apparently obtained in the SUS301L.^3,6) In order to clarify this point, more detailed discussions including on the work-hardening behavior of austenite and the stress partitioning between the phases are required.

Fig. 10.

Stress-induced martensitic transformation behaviors at which the better tensile properties were obtained in the SUS301L and SUS304 steels. (Online version in color.)

On the other hand, as seen in Fig. 6, the better tensile strength − uniform elongation balance can be obtained under other conditions in the case of the maximum uniform elongation. These are strain rates of 3.3 × 10^–6 s^–1 and 3.3 × 10^–5 s^–1 at 296 K for the SUS301L. In Fig. 10, this transformation behavior is also shown. As can be seen, V_α at the same ε was larger than in the case of the maximum uniform elongation. The increase in V_α correlates with an increase in tensile strength.^3,4,5,6) This means that the tensile strength − uniform elongation balance can improve even if V_α increases compared with the transformation kinetics at the maximum uniform elongation. From Fig. 10, the condition for better tensile strength − uniform elongation balance is that (dV_α/dε)_max of less than 3 is approached at ε of more than 0.3.

4. Conclusions

In this study, the effects of temperature and strain rate on the tensile properties in metastable austenitic stainless steel SUS301L were studied. The conditions for the maximum uniform elongation through the TRIP effect were discussed by using the experimental results for the SUS301L and SUS304 steels with different austenite stability. The main conclusions are as follows:

(1) In the static tensile tests for the SUS301L steel at temperatures between 123 K and 373 K, the tensile strength increased with decreasing temperature, and uniform elongation reached a maximum at 323 K.

(2) The volume fraction of stress-induced martensite at the same true strain increased with a decrease in temperature. In terms of the effect of strain rate on transformation kinetics, it decreased at strain rates higher than about 10^–2 s^–1 due to the temperature rise caused by adiabatic deformation. The proposed equation for the stress-induced transformation behavior considering the saturation value of stress-induced martensite can precisely describe the transformation kinetics.

(3) The conditions of stress-induced transformation for the maximum uniform elongation through the TRIP effect were coincident between the SUS301L and the SUS304 with different austenite stability: the volume fraction of martensite at a true strain of 0.3 is approximately 5% and the maximum transformation rate is almost 2 at higher true strain near uniform elongation.

(4) The conditions of stress-induced transformation for an excellent tensile strength − uniform elongation balance were a maximum transformation rate of less than 3 approached at a true strain of more than 0.3.

References

• 1)   T.  Angel: J. Iron Steel Inst., 177 (1954), 165.
• 2)   V. F.  Zackay,  E. R.  Parker,  D.  Fahr and  R.  Bush: Trans. Am. Soc. Met., 60 (1967), 252.
• 3)   I.  Tamura,  T.  Maki and  H.  Hato: Trans. Iron Steel Inst. Jpn., 10 (1970), 163.
• 4)   I.  Tamura,  T.  Maki,  H.  Hato and  K.  Aburai: J. Jpn. Inst. Met., 33 (1969), 1383.
• 5)   Y.  Fukase,  K.  Ebato,  N.  Ohkubo and  S.  Murao: Trans. Iron Steel Inst. Jpn., 8 (1968), 311.
• 6)   C. P.  Livitsanos and  P. F.  Thomson: Mater. Sci. Eng., 30 (1977), 93.
• 7)   G. L.  Huang,  D. K.  Matlock and  G.  Krauss: Metall. Mater. Trans. A, 20A (1989), 1239.
• 8)   T. S.  Byun,  N.  Hashimoto and  K.  Farrell: Acta Mater., 52 (2004), 3889.
• 9)   J.  Talonen,  P.  Nenonen,  G.  Pape and  H.  Hanninen: Metall. Mater. Trans. A, 36A (2005), 421.
• 10)   S. S.  Hecker,  M. G.  Stout,  K. P.  Staudhammer and  J. L.  Smith: Metall. Trans. A, 13A (1982), 619.
• 11)   L. E.  Murr,  K. P.  Staudhammer and  S. S.  Hecker: Metall. Trans. A, 13A (1982), 627.
• 12)   Y.  Iwasaki,  Y.  Nakasone,  T.  Shimizu and  N.  Kobayashi: Trans. Jpn. Soc. Mech. Eng. A, 72 (2006), 1561.
• 13)   T.  Ogata,  T.  Yuri and  Y.  Ono: J. Cryo. Soc. Jpn., 42 (2007), 10.
• 14)   G. B.  Olson and  M.  Cohen: Metall. Trans. A, 6A (1975), 791.
• 15)   K.  Nagai,  K.  Shibata,  T.  Fujita and  Y.  Ujiie: Trans. Iron Steel Inst. Jpn., 22 (1986), 696.
• 16)   K.  Sugimoto,  M.  Kobayashi and  S.  Hashimoto: Metall. Trans. A, 23A (1992), 3085.
• 17)   O.  Matsumura,  Y.  Sakuma and  H.  Takechi: Trans. Iron Steel Inst. Jpn., 27 (1987), 570.
• 18)   N.  Tsuchida,  T.  Araki,  Y.  Yamaguchi and  K.  Fukaura: Tetsu-to-Hagané, 98 (2012), 558.
• 19)   N.  Tsuchida,  Y.  Morimoto,  T.  Tonan,  Y.  Shibata,  K.  Fukaura and  R.  Ueji: ISIJ Int., 51 (2011), 124.
• 20)   Y.  Takagi,  R.  Ueji,  T.  Mizuguchi and  N.  Tsuchida: Tetsu-to-Hagané, 97 (2011), 450.
• 21)   N.  Tsuchida,  S.  Kawabata,  K.  Fukaura and  R.  Ueji: J. Alloy. Compd., in press.
• 22)   N.  Tsuchida. Y. Morimoto, S. Okamoto, K. Fukaura, Y. Harada and R. Ueji: J. Jpn. Inst. Met., 72 (2008), 769.
• 23)   N.  Tsuchida and  Y.  Tomota: Mater. Sci. Eng., A285 (2000), 345.
• 24)   O.  Matsumura,  Y.  Sakuma and  H.  Takechi: Scr. Mater., 21 (1987), 1301.
• 25)   O.  Matsumura,  Y.  Sakuma,  Y.  Ishii and  J.  Zhao: ISIJ Int., 32 (1992), 1110.
• 26)   M.  Sanga,  N.  Yukawa and  T.  Ishikawa: J. JSTP, 41 (2000), 64.
• 27)   N.  Tsuchida,  Y.  Izaki,  T.  Tanaka and  K.  Fukaura: ISIJ Int., 52 (2012), 729.
• 28)   N.  Tsuchida,  K.  Fukaura,  Y.  Tomota,  A.  Moriai and  H.  Suzuki: Mater. Sci. Forum, 652 (2010), 233.
• 29)   R.  Miura,  K.  Ohnishi,  H.  Nakajima and  S.  Shimamoto: Tetsu-to-Hagané, 73 (1987), 715.
• 30)   J.-H.  Park,  M.  Kanda,  N.  Tsuchida and  Y.  Tomota: J. Jpn. Inst. Met., 69 (2005), 867.