Effects of Nickel and Nitrogen on Austenite Phase Growth in Rapid Cooled Microstructure from High Temperature in Duplex Stainless Steel

Abstract

The growth of austenite phase from overcooled ferrite phase in duplex stainless steel was investigated to clarify the quantitative effects of nickel and nitrogen on that in isothermal heating process. The ratio of ferrite and austenite phase is very important factor to obtain the maximum performance such as toughness and corrosion resistance of the steels. However, the fraction of austenite phase in heat affected zone (HAZ) in weldments can be changed in the portion closed to fusion boundary during welding process.

The measurement of austenite phase fraction was conducted experimentally in the specimens after rapid cooled from 1653 K and isothermally heated at various temperature, employing the 25%Cr or 22%Cr duplex stainless steels containing various level of nickel and nitrogen. Applying those data obtained to the model proposed where the growth rate of austenite phase is determined as the function of isothermal temperature, the effects of nickel and nitrogen on the growth behavior of austenite phase was clarified by determining the parameters for each steel in that function. The validity of this manner was clarified by confirming the applicability of the model proposed to the experimental data obtained by another authors.

1. Introduction

Recently duplex stainless steels consisting of ferrite and austenite phase are widely used for various structural materials because of high performance for cost.^1,2,3,4) The high performance in terms of mechanical property and corrosion resistance is obtained in the condition with the optimum range of ferrite and austenite phase ratio in the duplex stainless steel.^{5,6,7,8,9,10)} Therefore the fraction of the phase is controlled in the optimum range of approximately 40% to 60% as the phase ratio during the manufacturing process including the heat treatment.^{11,12,13,14,15,16,17,18,19)} However, in the welded portion it is indispensable to be heated at the high temperature where the phase transformation is remarkable, therefore the fraction of the phase can be changed out of the optimum range in heat affected zone (HAZ) by weld thermal cycles. The duplex stainless steel that does not change so much in microstructure even in HAZ has been continuously developed.^3,4,5)

From that background many research works^{6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30)} have been conducted about the microstructure change in HAZ of duplex stainless steels. Those works were categorized as the following approaches. 1) the effects of Ni and N and cooling rate on the formation of austenite phase in HAZ cooled from high temperature where microstructure transforms toward a single phase of the ferrite. 2) the formation of austenite phase from the overcooled ferrite phase during the isothermal heating at the dual phase temperature range 3) the prediction of the austenite formation in the continuously cooled HAZ by using the data in the isothermal heating. Concerning the modeling of austenite phase formation from the overcooled ferrite phase in HAZ, the method of calculation to obtain the fraction of austenite phase has been established in those works^11,12,13) by applying the additivity rule using the known experimental data of growth rate in isothermal heating. In many works much of isothermal growth rate data of austenite phase have been obtained experimentally. However for practical application those data are required for the individual steels consisting of various chemical compositions at each temperature of isothermal heating. Therefore the physical model of growth rate constant of austenite phase has been proposed as an function of isothermal temperature in the previous work by the authors.²⁰⁾ That model was confirmed to be applicable to the duplex stainless steel consist of various chemical compositions. However the additional experimental dada were necessary for the application to new steels consisting of other chemical compositions, so that in this work the effect of chemical composition such as Ni and N on the parameters to determine the growth rate constant of each steel in that model was investigated experimentally and from the point of view of thermodynamics.

2. Experimental

The duplex stainless steels containing chromium of 25% or 22% listed in Table 1 were used. Those were melted in laboratory, hot forged and hot rolled to 12 mm thick plates in the range of 1373 to 1523 K then those were heat treated by water quench after holding at 1373 K for 1800 s. Those plates were machined to the specimens of 11 mm in thickness and 11 mm in width and 60 mm in length. The specimens were heated at 1653 K for 3 s and cooled rapidly with argon gas to the various test temperatures. And then those are held for various durations at a constant temperature and quenched with argon gas shower. The average cooling rate was approximately 100 K/s. To measure the initial fraction of austenite phase before holding at a constant temperature, some specimens were quenched with argon gas shower from 1653 K to the room temperature.

Table 1. Chemical compositions of steels tested (mass%).

	C	Si	Mn	Ni	Cr	W	Mo	N
5CA	0.02	0.16	0.48	7.10	25.29	1.98	3.03	0.11
5CB	0.02	0.16	0.47	7.14	25.10	1.99	2.98	0.22
5CC	0.02	0.17	0.47	7.11	25.20	1.95	2.97	0.33
5CD	0.02	0.15	0.49	9.19	25.29	2.00	3.01	0.33
5CE	0.02	0.16	0.47	6.00	25.11	2.00	3.00	0.20
5CF	0.02	0.16	0.48	4.98	25.28	2.00	3.01	0.10
2CA	0.02	0.16	0.46	4.96	22.00	–	3.01	0.09
2CB	0.02	0.16	0.50	4.96	22.04	–	3.00	0.20
2CC	0.02	0.15	0.48	5.96	22.07	–	3.03	0.20
2CD	0.02	0.17	0.50	4.02	22.06	–	2.98	0.19
2CE	0.02	0.17	0.50	3.01	22.09	–	2.97	0.19

The heat treated specimens were buff polished in the cross section corresponding to the center of homogeneously heated zone. Then in that cross section the fraction of austenite phase was measured in the area of approximately 0.97 mm² using EBSD (Electron Back Scatter Diffraction) analysis.

3. Austenite Phase Growth Model

The model that disks consisting of austenite phase dispersed with the number density of Np and the average size of r_m was assumed, where that disks grow just to the radius (r_m) direction without growing to the thickness direction. In the condition of phase interface migration determined by diffusion with the flax balance and with the mass conservation using the linear gradient approximation²¹⁾ at the interface in the cylindrical coordinate system, the growth of r_m is described as the following equation.   

$${\mathrm{r}}_{\mathrm{m}}^2=2\mathrm{D}\phi \left(\omega \right)\mathrm{t}$$(1)

where φ(ω) is the term of supersaturation, which depends on the concentration of allying element at the moving phase interface of ferrite and austenite as shown in the previous work.²⁰⁾ D is the diffusion coefficient of Ni. In this model the extended volume of austenite phase V_ex corresponding to the total volume of disks is obtained as the following when the whole volume is V₀ and the average thickness of disks is L.   

$${\mathrm{V}}_{\mathrm{e}\mathrm{x}}={\mathrm{V}}_0{\mathrm{N}}_{\mathrm{p}}\pi {\mathrm{r}}_{\mathrm{m}}^2\mathrm{L}=2{\mathrm{V}}_0{\mathrm{N}}_{\mathrm{p}}\pi \mathrm{L}\mathrm{D}\phi \left(\omega \right)\mathrm{t}$$(2)

The equilibrium volume of austenite phase is ωV₀ so that the transformation ratio X_ex without considering impingement is the following equation.   

$${\mathrm{X}}_{\mathrm{e}\mathrm{x}}={\mathrm{V}}_{\mathrm{e}\mathrm{x}}/\left(\omega {\mathrm{V}}_0\right)={\mathrm{N}}_{\mathrm{p}}\pi {\mathrm{r}}_{\mathrm{m}}^2\mathrm{L}/\omega =2{\mathrm{N}}_{\mathrm{p}}\pi \mathrm{L}\mathrm{D}\phi \left(\omega \right)/\omega \cdot \mathrm{t}$$(3)

It has been confirmed that growth property is according to the Austin-Rickett rule.¹¹⁾ Considering the effect of impingement by Austin-Rickett rule¹¹⁾ the equation austenite phase growth was obtained as the following.   

$$\mathrm{X}/\left(1-\mathrm{X}\right)-{\mathrm{X}}_0/\left(1-{\mathrm{X}}_0\right)=2\pi {\mathrm{N}}_{\mathrm{p}}\mathrm{L}\mathrm{D}\phi \left(\omega \right)/\omega \cdot \mathrm{t}={\mathrm{k}}_{\mathrm{p}}\cdot \mathrm{t}$$(4)

, where X₀ is the initial condition of X for t=0 and growth rate constant k_p corresponds to 2πN_pLDφ(ω)/ω.

When the number density of austenite phase formation sites N_p is according to Boltzmann distribution, that N_p is described as the following equation.²²⁾   

$${\mathrm{N}}_{\mathrm{p}}={\mathrm{N}}_{0}exp\left(-\mathrm{\Delta }{\mathrm{u}}_{\mathrm{m}}{\left({\mathrm{T}}_{\mathrm{e}\mathrm{q}}/\mathrm{\Delta }\mathrm{T}\right)}^2/\mathrm{R}\mathrm{T}\right)$$(5)

, where T_eq is the upper limit temperature for the stability of austenite phase, ΔT is equal to T_eq−T and Δu_m (T_eq/ΔT)² is the term regarding the energy barrier in the transformation of ferrite to austenite phase. The value of N₀ is the maximum number of austenite phase formation sites per volume and R is the gas constant.

From Eqs. (4) and (5)   

$$\mathrm{X}=2\pi \mathrm{L}\mathrm{D}{\mathrm{N}}_{0}exp\left(-\mathrm{\Delta }{\mathrm{u}}_{\mathrm{m}}{\left({\mathrm{T}}_{\mathrm{e}\mathrm{q}}/\mathrm{\Delta }\mathrm{T}\right)}^2/\mathrm{R}\mathrm{T}\right)\phi \left(\omega \right)/\omega \cdot \mathrm{t}={\mathrm{k}}_{\mathrm{p}}\cdot \mathrm{t}$$(6)

  

$${\text{k}}_{\text{p}}={\text{k}}_{\text{p}0}\text{Dexp}\left(-\mathrm{\Delta }{\text{u}}_{\text{m}}{\left({\text{T}}_{\text{eq}}/\mathrm{\Delta }\text{T}\right)}^2/\text{RT}\right)$$(7)

, where the coefficient of growth rate constant k_p0 is defined as the following when φ(ω)/ω is described as Ω.   

$${\mathrm{k}}_{\mathrm{p}0}=2\pi \mathrm{L}{\mathrm{N}}_0\phi \left(\omega \right)/\omega =2\pi \mathrm{L}{\mathrm{N}}_0\mathrm{\Omega }$$(8)

4. Effect of Ni and N on Growth of Austenite Phase

The examples of microstructure of the 25%Cr-Ni-3%Mo-2%W-N and the 22%Cr-Ni-3%Mo-0.2%N steels held at 1173 K for various durations after overcooled from 1653 K is shown in Figs. 1 and 2 respectively. Fraction of austenite phase in all of the specimens tested increased gradually during isothermal heating. The initial fraction of austenite phase after rapid cooling was larger in the steel containing higher level of Ni and N. The fractions of austenite phase f(t) were obtained with EBSD analysis in all the specimens of the steels treated with various heating conditions. Using those data of f(t), Eq. (4) regarding transformation ratio X(=f(t)/f_e) were calculated with the following equation.   

$$\mathrm{X}/\left(1-\mathrm{X}\right)-{\mathrm{X}}_0/\left(1-{\mathrm{X}}_0\right)=\mathrm{f}\left(\mathrm{t}\right)/\left({\mathrm{f}}_{\mathrm{e}}-\mathrm{f}\left(\mathrm{t}\right)\right)-{\mathrm{f}}_0/\left({\mathrm{f}}_{\mathrm{e}}-{\mathrm{f}}_0\right)$$(9)

where f_e is the equilibrium fraction of austenite at a temperature and f₀ is the initial fraction of austenite phase corresponding to the heating time of 0 s which were shown in Fig. 3 as the results measured in the specimens quenched to the room temperature. The values of f_e shown in Fig. 4 are obtained by using the thermodynamic data (2017a, database:TCFe8).²³⁾

Fig. 1.

Example of optical micrograph of 25Cr-Ni-3Mo-2W-N steel heated at 1223 K for various time after rapidly cooled from 1653 K.

Fig. 2.

Example of optical micrograph of 22Cr-Ni-3Mo-0.2N steel heated at 1223 K for various time after rapidly cooled from 1653 K.

Fig. 3.

Initial fraction of austenite phase quenched from 1653 K in steels containing various levels of Cr, Ni and N.

Fig. 4.

Equilibrium fraction of austenite phase calculated using thermodynamic data. a) 25Cr-Ni-3Mo-2W-N, b) 22Cr-Ni-3Mo-0.2N.

As the examples, Fig. 5 shows the experimental results plotted against the logarithm of heating time t according to Austin-Reckett rule.¹¹⁾ The values in vertical axis corresponding to the left side of Eq. (9) increased almost proportionally to the logarithm of heating time with the inclination of 1.0 as same as those reported in other works.^11,12,13,20) The values of the intercept in vertical axis obtained from the linear relation of those experimental plots correspond to the growth rate constant k_p in the Eq. (6). The obtained growth rate constants of k_p are Arrhenius plotted against the temperature of isothermal heating shown in Fig. 6. It has been reported in the previous work²⁰⁾ the optimum values of k_p0 was determined by the minimizing the difference between the experimental results and the calculated value by using Eq. (7) with the value of Δu_m of 1950 kJ/mol.²⁰⁾ The diffusion coefficient of Ni was applied for Eq. (7) as same in previous work.²⁰⁾ The values of T_eq are employed by compensating the values obtained using the thermodynamic data (2017a, database:TCFe8)²³⁾ as shown in Eq. (10). Because effective equilibrium temperature of austenite T_eq tended to lower than obtained equilibrium values by the thermodynamic data. So that the following compensation was applied to minimize the difference between the experimental results and the calculated equilibrium value [T_eq]_td by using Eq. (7).   

$${\mathrm{T}}_{\mathrm{e}\mathrm{q}}=0.42{\left[{\mathrm{T}}_{\mathrm{e}\mathrm{q}}\right]}_{\mathrm{t}\mathrm{d}}+980$$(10)

Fig. 5.

Examples of Austin-Rikett plot of austenite phase precipitation at 1223 K from overcooled ferrite during isothermal heating.

Fig. 6.

Effect of temperature on growth rate constant of austenite phase from overcooled ferrite in 25Cr or 22Cr steel containing various levels of Ni and N.

Effects of Ni and N content on the coefficient of growth rate constant k_p0 obtained in the above manners is shown in Figs. 7 and 8 respectively. The coefficient of growth rate constants k_p0 increased simply with the increase of N in steels. Those also increased with the increase of Ni in steels within low Ni content. However those did not increase with the increase of Ni and rather did decrease in the steel containing Ni of 9%.

Fig. 7.

Effect of N content on coefficient of growth rate constant k_po.

Fig. 8.

Effect of Ni content on coefficient of growth rate constant k_po.

5. Discussion

It was confirmed the change in austenite phase fraction in the steels consisting of various chemical composition was according to the Austin-Rickett rule and that was uniquely described using Eq. (4) consisting of the growth rate constant k_p, initial fraction f₀ and equilibrium fraction f_e. The growth rate constant of austenite phase k_p has been described as the function of temperature shown in Eq. (7), where the effect of chemical composition was reflected in just two valuables of k_p0 and T_eq. Then the influence mechanism regarding the effects of Ni and N on the value of k_p0 can be considered by analyzing the constitution of physical model proposed. Referring Eq. (8) the coefficient of growth rate constant k_p0 corresponds to 2πLN₀Ω in the physical model. The value of Ω is calculated as the solution of phase interface migration determined by diffusion with the flax balance and with the mass conservation at the interface in the cylindrical coordinate system using thermodynamic data base. The parameter Ω is the function of supersaturation ω which increases with the increase of ω and ω is increased by the austenite phase stabilizing elements of Ni and N. Because ω means the ratio of the difference of Ni or N content between steel and ferrite phase to that between ferrite and austenite at phase interface. The maximum number of number density of austenite phase N₀ tends to decrease in the larger grain of prior ferrite phase due to the smaller grain boundary area.³¹⁾ The grain of prior ferrite phase tends to grow in the steel with the lower equilibrium temperature of austenite T_eq due to the larger temperature range of ferrite single phase during heating up to peak temperature of 1653 K. Therefore it is understand qualitatively the effect on the value of N₀ is considering to be reflected by T_eq. As shown in Fig. 9 T_eq tended to elevate with the increase of Ni and N content. From the experimental results, the value of k_p0 increased with the increase of N content within the tested range of N content. It is understand to be due to the increase of the value of Ω by N and elevating of T_eq resulting in decrease of grain size and the increase of N₀.^20,31) From the experimental results, the value of k_p0 also increased with the increase of Ni content within the Ni content lower than 7%. It is understand to be due to the same reason in the case of N. However in the steel of high Ni content such as 9% the value of k_p0 did not increase with the increase of Ni content and rather decreased in the 25%Cr steel. That is understood to be due to the large amount of initial fraction of austenite phase at isothermal heating. At the initial of the isothermal heating there has already been sufficient austenite phase because austenite phase was stable even heated at 1653 K in the steel containing high Ni. Therefore it is assumed to be low driving force for the growth of austenite phase resulting in low value of k_p0.

Fig. 9.

Effect of Ni content on effective equilibrium temperature of austenite phase Teq.

The value of Ω regarding some of the steels, 25%Cr-7%Ni-3%Mo-2%W-0.3%N, 25%Cr-7%Ni-3%Mo-2%W-0.1%N and 22%Cr-5%Ni-3%Mo-0.2%N tested was calculated. That was calculated using the linear gradient approximation²¹⁾ at the interface in the cylindrical coordinate system in the condition of phase interface migration determined by diffusion with the flax balance and with the mass conservation. As results the relation between the coefficient of growth rate constant k_p0 and the parameter of Ω/[Ω]₀T_eq/[T_eq]₀ is obtained as shown in Fig. 10. The horizontal axis in the figure is shown using the relative value normalized by [Ω]_td and [T_eq]₀ which are the value in 25%Cr-7%Ni-3%Mo-2%W-0.3%N steel. The coefficient of growth rate constant k_p0 increased linearly with the value Ω/[Ω]₀T_eq/[T_eq]₀. From the result the following experimental formula was obtained.   

$${\mathrm{k}}_{\mathrm{p}0}=\left\{4.9\mathrm{\Omega }/{\left[\mathrm{\Omega }\right]}_0{\mathrm{T}}_{\mathrm{e}\mathrm{q}}/{\left[{\mathrm{T}}_{\mathrm{e}\mathrm{q}}\right]}_0-0.92\right\}\times {10}^{14}$$(11)

Fig. 10.

Relation between parameter of Ω/[Ω]₀Teq/[T_eq]₀ and coefficient of growth rate constant k_po.

Using the experimental formula and calculated values of Ω and T_eq the coefficient of growth rate constant k_p0 in various steels can be predicted.

To clarifying validity and extendability, the applicability of this manner of prediction using Eq. (11) to the duplex stainless steel shown in another work^11,12) was employed. The experimental data were referred from the Nakaos’ work.^11,12) Those works have included the experimental data regarding the growth properties of austenite phase from overcooled ferrite phased in the 25%Cr-5.5%Ni-1.8%Mo-0.07%N duplex stainless steel specified as SUS329J1. The values of Ω at 1223 K and T_eq in the steel of 25%Cr-5.5%Ni-1.8%Mo-0.07%N were calculated applying the above mentioned way using thermodynamic data and those were obtained as 0.81 and 1640 K respectively. The calculated curve of growth rate constant obtained by applying the values of Ω and T_eq to the Eqs. (7) and (11). The result is shown in Fig. 11, where the experimental data referred from the Nakaos’ work were plotted together with the dot line calculated using the experimental formula by quartic function regression shown in that work.¹²⁾ The curve of solid line calculated by the model in this work had good fit to the experimental data plotted from another work within the temperature range where experimental data existed. From the results the validity and extendability of this model proposed were confirmed due to the applicability of another duplex stainless steel consisting of different chemical composition.

Fig. 11.

Comparison of austenite phase growth rate constant measured experimentally in another work and calculated values by model of this work. (Online version in color.)

By applying the values of T_eq and Ω to be obtained using thermodynamic data base to Eqs. (7) and (11) in the model proposed, the growth rate constant k_p in a steel containing some chemical composition at each temperature can be calculated without experiment. Using that k_p calculated the change of austenite phase fraction during isothermal heating can be calculated when the initial value of the fraction f₀ was obtained experimentally.

6. Conclusion

The following results were obtained by the investigation regarding the effect of Ni and N on isothermal growth property of austenite phase from overcooled ferrite phase in the steel of 25%Cr and 22%Cr duplex stainless steels.

(1) The change in austenite phase fraction in the steels consisting of various chemical compositions used was according to the Austin-Rickett rule and that was uniquely described using the equation consisting of the growth rate constant k_p, initial fraction f₀ and equilibrium fraction f_e.

(2) The effects of Ni and N on the coefficient of growth rate constant k_p0 which determines the growth rate constant k_p in each of steel were experimentally clarified.

(3) The relation between the coefficient of growth rate constant k_p0 and the thermodynamic parameter as a function of supersaturation was clarified as a formula which can predict the unknown value of k_p0 in some steels without the experiment.

(4) The validity and extendability of this model proposed were confirmed by that the growth rate constant k_p calculated using the model had good fit to experimental data reported in another duplex stainless steel consisting of different chemical composition.

Acknowledgement

The author wish to acknowledge for providing research infrastructure and resource by Nippon Steel Corporation.

References

• 1)   W. A.  Baeslack III and  J. C.  Lippold: Met. Constr., 20 (1988), 26R.
• 2)   R. N.  Gunn: Duplex Stainless Steels, Abington Publishing, Cambridge, UK, (1997), 110. https://doi.org/10.1533/9781845698775
• 3)   J.-O.  Nilsson and  A.  Wilson: Mater. Sci. Technol., 9 (1993), 545. https://doi.org/10.1179/mst.1993.9.7.545
• 4)   H.  Okamoto: Proc. Applications of Stainless Steel ’92, (Stockholm), Stainless steel world, Netherlands, (1992), 360.
• 5)   K.  Ogawa,  H.  Okamoto,  M.  Ueda,  M.  Igarashi,  T.  Mori and  T.  Kobayashi: Weld. Int., 10 (1996), 466. https://doi.org/10.1080/09507119609549032
• 6)   K.  Ogawa,  H.  Okamoto,  M.  Igarashi,  M.  Ueda,  T.  Mori and  T.  Kobayashi: Weld. Int., 11 (1997), 14. https://doi.org/10.1080/09507119709454409
• 7)   E. B.  Haugan,  M.  Næss,  C. T.  Rodriguez,  R.  Johnsen and  M.  Iannuzzi: Corrosion, 73 (2017), 53. https://doi.org/10.5006/2185
• 8)   S.-H.  Jeon,  I.-J.  Park,  H.-J.  Kim,  S.-T.  Kim,  Y.-K.  Lee and  Y.-S.  Park: Mater. Trans., 55 (2014), 971. https://doi.org/10.2320/matertrans.M2013471
• 9)   K.  Ogawa and  T.  Osuki: ISIJ Int., 60 (2020), 1016. https://doi.org/10.2355/isijinternational.ISIJINT-2019-537
• 10)   S.  Atamert and  J. E.  King: Mater. Sci. Technol., 8 (1992), 896. https://doi.org/10.1179/mst.1992.8.10.896
• 11)   Y.  Nakao,  K.  Nishimoto and  S.  Inoue: J. Jpn. Weld. Soc., 50 (1981), 514 (in Japanese). https://doi.org/10.2207/qjjws1943.50.514
• 12)   Y.  Nakao,  K.  Nishimoto and  S.  Inoue: J. Jpn. Weld. Soc., 50 (1981), 1107 (in Japanese). https://doi.org/10.2207/qjjws1943.50.1107
• 13)   K.  Yasuda,  R. N.  Gunn and  T. G.  Gooch: Q. J. Jpn. Weld. Soc., 20 (2002), 68 (in Japanese). https://doi.org/10.2207/qjjws.20.68
• 14)   Y.  Tanabe,  K.  Onishi,  T.  Ogura,  K.  Saida,  K.  Nishimoto and  Y.  Oikawa: Proc. National Meeting of JWS, Vol. 95, JWS, Tokyo, (2014), 230 (in Japanese). https://doi.org/10.14920/jwstaikai.2014f.0_230
• 15)   H.  Liou,  R.  Hsieh and  W.  Tsai: Mater. Chem. Phys., 74 (2002), 33. https://doi.org/10.1016/S0254-0584(01)00409-6
• 16)   J. C.  Lippold,  I.  Varol and  W. A.  Baeslack III: Weld. J., 73 (1994), 75-s.
• 17)   A. J.  Ramirez,  J. C.  Lippold and  S. D.  Brandi: Metall. Mater. Trans. A, 34 (2003), 1575. https://doi.org/10.1007/s11661-003-0304-9
• 18)   J.  Liao: ISIJ Int., 41 (2001), 460. https://doi.org/10.2355/isijinternational.41.460
• 19)   I.  Calliari,  E.  Ramous and  P.  Bassani: Materials Science Forum online, 638–642 (2010), 2986. https://doi.org/10.4028/www.scientific.net/MSF.638-642.2986
• 20)   K.  Ogawa and  A.  Seki: ISIJ Int., 59 (2019), 1614. https://doi.org/10.2355/isijinternational.ISIJINT-2018-869
• 21)   M.  Enomoto: The Japan Institute of Metals and Materials Seminar, Base and Application of Phase Diagram and Transformation in Material Science, JIM, Sendai, (1992), 73 (in Japanese).
• 22)   T.  Nishizawa: Thermodynamics of Microstructures, ASM International, Materials Park, (2008), 91.
• 23)  Thermo-Calc Software: Computational Materials Engineering, https://www.thermo-calc.com, (accessed 2021-06-25).
• 24)   I. F.  Machado and  A. F.  Padilha: ISIJ Int., 40 (2000), 719. https://doi.org/10.2355/isijinternational.40.719
• 25)   Y.  Shimoide,  J.  Cui,  C.-Y.  Kang and  K.  Miyahara: ISIJ Int., 39 (1999), 191. https://doi.org/10.2355/isijinternational.39.191
• 26)   S.  Jeon,  S.  Kim,  S.  Kim,  M.  Choi and  Y.  Park: Mater. Trans., 54 (2013), 1473. https://doi.org/10.2320/matertrans.M2012402
• 27)   K.  Ogawa,  Y.  Komizo,  S.  Azuma and  T.  Kudo: Trans. Jpn. Weld. Soc., 23 (1992), 40.
• 28)   H.  Xu,  W.  Hu,  C.  Kang,  W.  Li and  X.  Sha: ISIJ Int., 61 (2021), 967. https://doi.org/10.2355/isijinternational.ISIJINT-2020-559
• 29)   H.  Kajimura,  K.  Ogawa and  H.  Nagano: ISIJ Int., 31 (1991), 216. https://doi.org/10.2355/isijinternational.31.216
• 30)   L.  Karlsson,  L.  Ryen and  S.  Pak: Weld. J., 74 (1995), 28-s.
• 31)   M.  Umemoto and  I.  Tamura: Bull. Jpn. Inst. Met., 24 (1985), 262 (in Japanese). https://doi.org/10.2320/materia1962.24.262