Austenite Phase Growth Behaviour in Continuous Cooling from High Temperature in Duplex Stainless Steel

Abstract

Austenite phase growth behavior in continuous cooling process from high temperature in the 25%Cr and 22%Cr duplex stainless steels was investigated regarding various cooling rate conditions. 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 the heat affected zone (HAZ) in weldments can be changed in the portion closed to fusion boundary during welding process. In that portion the fraction of austenite phase is influenced by the welding condition as well as by the chemical composition in steels.

The way to predict that fraction in the continuous cooling was investigated applying the additivity rule to the physical model proposed regarding austenite phase growth during isothermal heating by the authors in another work. The measurement of austenite phase fraction was conducted experimentally in the specimens after continuous cooling from 1653 K employing 25%Cr or 22%Cr duplex stainless steels and the effect of cooling rate on that fraction was obtained. It was clarified the above-mentioned calculation results of austenite phase fraction in various cooling rate had good fit to the experimental data.

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 of approximately equal fraction of ferrite and austenite phase in the duplex stainless steel.^{5,6,7,8,9,10)} Therefore the fraction of the phase is controlled in the optimum range 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)} have been conducted about the microstructure change in HAZ of duplex stainless steels. In many works the change in microstructure in the continuous heating or cooling process has been calculated applying the additivity rule to the data obtained in the isothermal heating process. It has been reported^11,12) the fraction in HAZ of duplex stainless steels formed with the continuous cooling process can be calculated applying the additivity rule with the experimental data of the growth property of austenite phase during isothermal heating. By that way the effect of cooling condition on the fraction of austenite phase can be predicted. However in that way the experimental data of the growth property at all of the temperatures where the austenite growth is not negligible shall be prepared. Each set of experimental data shall be prepared for each steel consisting of the different chemical composition. Therefore in this work the simplified prediction way of austenite phase in HAZ was investigated using the physical model regarding the growth property of austenite phase proposed in the previous work.

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 continuously cooled to 973 K with controlling the various cooling rate by adjusting heating current and the flow rate of argon cooling gas. Those are gas quenched with argon gas shower after cooled to 973 K. For thermal cycles employed are shown in Fig. 1. The average cooling rates were 3 K/s, 10 K/s, 30 K/s and 60 K/s corresponding to the thermal cycles of (1) to (4) respectively. 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. The grain size of prior ferrite phase was measured by line cutting method referring JIS G 0551 using the optical micrograph of those specimens.

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
5CC	0.02	0.17	0.47	7.11	25.20	1.95	2.97	0.33
2CB	0.02	0.16	0.50	4.96	22.04	–	3.00	0.20

Fig. 1.

Measured thermal cycle chart applied to simulated HAZ specimens.

3. Application of Austenite Phase Growth Model to Continuous Cooling Process

3.1. Growth of Austenite Phase in Continuous Cooling Process

In the physical model proposed regarding austenite phase growth during isothermal heating by the authors in the previous work³²⁾ the growth of austenite is according to the following equation on the basis of Austin-Rickett rule.   

$$\mathrm{X}/(1-\mathrm{X})-{\mathrm{X}}_0/(1-{\mathrm{X}}_0)={\mathrm{k}}_{\mathrm{p}}\cdot \mathrm{t}$$(1)

where X is the ratio of transformation X(= f(t)/f_e), f(t) and f_e are the fraction of austenite at the time of t and at equilibrium condition respectively and X₀ is the initial condition of X for t = 0. The growth rate constant corresponding to k_p is described as the function of temperature shown as the following equation in that work.   

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

where T_eq (K) is the upper limit temperature for the stability of austenite phase, ΔT is the degree of supercooling which is the difference between T_eq and T, Δu_m is the constant equal to 1950 J/mol and k_p0 is the coefficient of growth rate constant which have been already obtained in the steel employed.²⁰⁾

The temperature changes every moment in the continuous cooling process but the calculation was conducted in the condition that temperature was assumed as constant so far within extremely short duration Δt. That Δt and T_i are defined as n equal dividing of the whole cooling duration and the temperature in the stage of number i in that equal dividing respectively. The temperature T_i−1 changes to T_i according to cooling rate after the duration Δt passed. Then the transformation ratio X_i is described as the following using the equivalent time ${\mathrm{t}}_{\mathrm{i}}^{\mathrm{e}\mathrm{q}}$ to achieve the same transformation to that in the stage number i-1 corresponding to the time t_i−1 by isothermal heating at the temperature T_i−1. Therefore the transformation ratio in the stage number i is described as the following using Eq. (1).   

$${\mathrm{X}}_{\mathrm{i}}/(1-{\mathrm{X}}_{\mathrm{i}})-{\mathrm{X}}_{\mathrm{i},0}/(1-{\mathrm{X}}_{\mathrm{i},0})={\mathrm{k}}_{\mathrm{p}}({\mathrm{T}}_{\mathrm{i}})({\mathrm{t}}_{\mathrm{i}}^{\mathrm{e}\mathrm{q}}+\mathrm{\Delta }\mathrm{t})$$(3)

  

$${\mathrm{t}}_{\mathrm{i}}^{\mathrm{e}\mathrm{q}}=\left[{\mathrm{X}}_{\mathrm{i}-1}/(1-{\mathrm{X}}_{\mathrm{i}-1})-{\mathrm{X}}_{\mathrm{i}-1,0}/(1-{\mathrm{X}}_{\mathrm{i}-1,0})\right]/{\mathrm{k}}_{\mathrm{p}}({\mathrm{T}}_{\mathrm{i}})$$(4)

, where X_i,0 is the initial transformation ratio at the stage number i in isothermal heating.

From Eqs. (3) and (4)   

$$\begin{array}{l}{\mathrm{X}}_{\mathrm{i}}/(1-{\mathrm{X}}_{\mathrm{i}})={\mathrm{X}}_{\mathrm{i}-1}/(1-{\mathrm{X}}_{\mathrm{i}-1})+{\mathrm{X}}_{\mathrm{i},0}/(1-{\mathrm{X}}_{\mathrm{i},0})\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-{\mathrm{X}}_{\mathrm{i}-1,0}/(1-{\mathrm{X}}_{\mathrm{i}-1,0})+{\mathrm{k}}_{\mathrm{p}}({\mathrm{T}}_{\mathrm{i}})\mathrm{\Delta }\mathrm{t}\end{array}$$(5)

The transformation ratio after cooling to a temperature T_n is obtained as the following by the integration of Eq. (5).   

$${\mathrm{X}}_{\mathrm{n}}/(1-{\mathrm{X}}_{\mathrm{n}})={\mathrm{X}}_{\mathrm{n},0}/(1-{\mathrm{X}}_{\mathrm{n},0})+{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{k}}_{\mathrm{p}}({\mathrm{T}}_{\mathrm{i}})\mathrm{\Delta }\mathrm{t}$$(6)

The fraction of austenite phase f in the continuously cooled portion was obtained as the following due to the definition of X_n as the ratio of f and f_e.   

$$\begin{array}{l}\mathrm{f}/({\mathrm{f}}_{\mathrm{e}}-\mathrm{f})={\mathrm{f}}_0/({\mathrm{f}}_{\mathrm{e}}-{\mathrm{f}}_0)+{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{k}}_{\mathrm{p}}({\mathrm{T}}_{\mathrm{i}})\mathrm{\Delta }\mathrm{t}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}={\mathrm{f}}_0/({\mathrm{f}}_{\mathrm{e}}-{\mathrm{f}}_0)+\int {\mathrm{k}}_{\mathrm{p}}({\mathrm{T}}_{\mathrm{i}})\mathrm{d}\mathrm{t}\end{array}$$(7)

3.2. Grain Growth in Continuous Cooling Process

The effect of grain growth on k_p0 was negligible in the isothermal heating test to determine the value of k_p0 because of rapid cooling to the temperature enough low for ceasing the grain growth. However the grain growth of prior ferrite phase can be caused in the continuous cooling process to simulate the HAZ. Therefore the effect of grain growth on k_p0 was reflected by the followings. As shown in previous work²⁰⁾ k_p0 (m⁻²) is described as Eq. (8).   

$${\mathrm{k}}_{\mathrm{p}0}=2\pi \mathrm{L}\mathrm{\Omega }{\mathrm{N}}_0$$(8)

L: Thickness of disk like austenite phase (m)

Ω: Term of supersaturation of Ni

N₀: Maximum density of austenite phase formation site (m⁻³)

Assuming the formation site is on the edges of grain boundary in the Kelvin’s fourteen hedron, the maximum number of the site per volume N₀ is the following.²⁰⁾   

$${\mathrm{N}}_0=6\sqrt{2}(\mathrm{N}/\mathrm{V}){}^{1/3}/{\mathrm{R}}_{\mathrm{G}}{}^2$$(9)

, where R_G is the diameter of ferrite grain.

Therefore k_p0a was defined as the coefficient of austenite growth rate constant including the effect of the grain growth as shown in the following.   

$${\mathrm{k}}_{\mathrm{p}0\mathrm{a}}={\mathrm{k}}_{\mathrm{p}0}{({\mathrm{R}}_{\mathrm{G}0}/{\mathrm{R}}_{\mathrm{G}})}^2$$(10)

  

$${\mathrm{k}}_{\mathrm{p}}={\mathrm{k}}_{\mathrm{p}0\mathrm{a}}\mathrm{D}exp\left(-\mathrm{\Delta }{\mathrm{u}}_{\mathrm{m}}{({\mathrm{T}}_{\mathrm{e}\mathrm{q}}/\mathrm{\Delta }\mathrm{T})}^2/\mathrm{R}\mathrm{T}\right)$$(11)

Experimental formula to describe the grain growth of ferrite phase in duplex steel in the isothermal conditions has been reported as shown in Eq. (12) in the Nakaos’ work.¹²⁾   

$${\mathrm{R}}_{\mathrm{G}}^3-{\mathrm{R}}_{\mathrm{G}0}^3={\mathrm{A}}_{0}exp(-{\mathrm{Q}}_{\mathrm{a}}/\mathrm{R}\mathrm{T})\cdot \mathrm{t}$$(12)

, where Q_a is effective activation energy of grain growth and A₀ is the constant.

Applying the additivity rule to this results the grain growth of ferrite phase in the continuous cooling process has been also reported¹²⁾ as shown in the following.   

$${\mathrm{R}}_{\mathrm{G}\mathrm{i}}^3-{\mathrm{R}}_{\mathrm{G}0}^3={\sum }_{\mathrm{j}=1}^{\mathrm{i}}{\mathrm{A}}_{0}exp(-{\mathrm{Q}}_{\mathrm{a}}/\mathrm{R}{\mathrm{T}}_{\mathrm{j}})\cdot \mathrm{\Delta }\mathrm{t}$$(13)

, where R_Gi and R_G0 are the grain size at a time t_i on the way of cooling process and that in the initial respectively and the term of Δt is defined as n equal dividing of the whole cooling duration as mentioned above.

In conclusion using Eqs. (7), (10), (11) and (13) the growth of austenite phase in continuous cooling process is calculated.

4. Effect of Cooling Rate on Growth of Austenite Phase

4.1. Experimental Results of Growth of Austenite Phase

The microstructures in the simulated HAZ of the 25%Cr-7%Ni-3%Mo-2%W-0.1/0.3%N and the 22%Cr-5%Ni-3%Mo-0.2%N steels after continuous cooling from 1653 K with various cooling rates are shown in Fig. 2. Fraction of austenite phase in all of those tested tended to decrease with the increase of cooling rate. The 25%Cr-7%Ni-3%Mo-2%W-0.1%N had smaller fraction of that than the other two steels in all of the cooling rate conditions. Figure 3 shows examples of image of EBSD analysis to evaluate quantitatively the fraction of austenite phase in various cooling conditions. That fraction in the simulated HAZ of austenite phase in the 25%Cr-7%Ni-3%Mo-2%W-0.1/0.3%N and the 22%Cr-5%Ni-3%Mo-0.2%N steels after continuous cooling from 1653 K with various cooling rates is shown in Figs. 4, 5, 6. The 25%Cr-7Ni-3%Mo-2%W-0.3%N steel had the fractions in the range of 30 to 70% which has been known as the recommendable range from the point of view of the performance in weldments in all of the cooling conditions tested as shown in Fig. 4. The effect of cooling rate on those fractions was not large in this steel but that fraction increased slightly with the decrease of cooling rate except for the case of the maximum cooling rate. Contrary the 25%Cr-7Ni-3%Mo-2%W-0.1%N steel containing low N had low fractions in the range of 5% to 20% and those decreased remarkably with the increase of cooling rate as shown in Fig. 5. The effect of cooling rate on the grain size of prior ferrite phase is shown in Fig. 7. In the smaller cooling rate condition that grain size was the larger due to the longer heating duration in the high temperature range where the grain growth can occur. The 22%Cr-5%Ni-3%Mo-0.2%N steel also had the fractions in the range of 30 to 70% as shown in Fig. 6. In this steel that fraction decreased with the increase of cooling rate ,however the effect of cooling rate was not remarkable comparing to that in the 25%Cr-7Ni-3%Mo-2%W-0.1%N steel.

Fig. 2.

Example of optical micrograph of 25%Cr and 22%Cr duplex stainless steels tested after continuous cooling from 1653 K with various cooling rate conditions.

Fig. 3.

Example of EBSD phase map in simulated HAZ specimens with various cooling conditions of a) 3 K/s, b) 10 K/s and c) 30 K/s d) 60 K/s (25Cr-7Ni-3-Mo-2W-0.1N). (Online version in color.)

Fig. 4.

Fraction of austenite in simulated HAZ with various continuous cooling conditions (25Cr-7Ni-3Mo-2W-0.3N) [Cooling condition: (1) to (4) shown in Fig. 1].

Fig. 5.

Fraction of austenite in simulated HAZ with various continuous cooling conditions (25Cr-7Ni-3Mo-2W-0.1N) [Cooling condition: (1) to (4) shown in Fig. 1].

Fig. 6.

Fraction of austenite in simulated HAZ with various continuous cooling conditions (22Cr-5Ni-3Mo-0.2N) [Cooling condition: (1) to (4) shown in Fig. 1].

Fig. 7.

Effect of cooling rate on growth of prior ferrite grain size in 22Cr-5Ni-3Mo-0.2Nsteel (Broken line: calculated value).

4.2. Calculation of Growth of Austenite Phase

First the validity of grain growth property shown in Eq. (13) was confirmed. The measured data of grain size and results of calculated using Eq. (13) drawn as a curve of broken line were shown in Fig. 7, applying 390 μm to R_G0, 1.2 × 10⁻² μm³ to A₀ and 274 kJ/mol to Q_a respectively by referring the reported value.¹²⁾ That curve calculated had rather fit to the measured data.

Comparison between results of fraction of austenite calculated with and without grain growth in the simulated HAZ is shown in Fig. 8. The calculation considering the grain was conducted using Eqs. (7), (10), (11) and (13). The calculation without considering the grain growth was conducted with applying 1.0 constantly to the term of (R_G0/R_G)² in Eq. (10). For calculations the values referred from the previous work³²⁾ shown in Table 2 were applied to k_p0 in Eq. (10) and f₀ in Eq. (7). For the values of f_e in Eq. (7) the data shown in Fig. 9 calculated using the thermodynamic data base²³⁾ were used. The fraction of austenite phase calculated without considering grain growth was larger than that with considering grain growth. The reason is understand to be due to the value of k_p0a resulting in the difference of the term of the integration $\int {\text{k}}_{\text{p}}({\text{T}}_{\text{i}})\text{dt}$ during cooling process.

Fig. 8.

Comparison between calculated results of fraction of austenite with and without grain growth in simulated HAZ with various continuous cooling conditions.

Table 2. Parameters applied in calculation.

	kp0 (m−2)	Teq (K)	f0 (%)
25Cr-7Ni-3Mo-2W-0.3N	4.0 × 1014	1668	50
25Cr-7Ni-3Mo-2W-0.1N	1.1 × 1014	1618	0
22Cr-5Ni-3Mo-0.2N	3.3 × 1014	1656	35

Fig. 9.

Equilibrium fraction of austenite phase in various temperature calculated using thermodynamic data base.

Figure 10 shows the results drawn as the lines calculated in the simulated HAZ of the three sorts of steels tested and those experimental data plotted against cooling rate. The calculated lines of the fraction of austenite phase in Fig. 10 were obtained using Eq. (7) with considering the grain growth. The calculated results had rather fit to the experimental data for all the steels. From the results the validity of the calculation using the model proposed was confirmed.

Fig. 10.

Comparison between experimental data and calculated results of fraction of austenite with grain growth in simulated HAZ with various continuous cooling conditions. (Online version in color.)

5. Discussion

The fraction of austenite phase in HAZ in weldments can be changed especially in the portion closed to fusion boundary during welding process. That fraction shall be controlled in the optimum range due to remarkable influence on the performance such as toughness and corrosion resistance of the weldment. In this section the prior factors regarding the effect of cooling condition and the chemical composition of steels on the fraction of austenite phase in the simulated HAZ was to be considered. The experimental results had rather fit to the calculated results using the model proposed so that those effects can be understood referring the model described such as Eq. (7). The equilibrium fraction of austenite f_e and f₀, the growth rate constant k_p and the upper limit temperature for the stability of austenite phase T_eq are were reflected in that effect of cooling rate. Transforming Eq. (7) to describe the austenite fraction in continuous cooled HAZ f, the following equation was obtained.   

$$\mathrm{f}={\mathrm{f}}_{\mathrm{e}}/\left\{1+1/[{\mathrm{f}}_0/({\mathrm{f}}_{\mathrm{e}}-{\mathrm{f}}_0)+\int {\mathrm{k}}_{\mathrm{p}}({\mathrm{T}}_{\mathrm{i}})\mathrm{d}\mathrm{t}]\right\}$$(14)

From that equation the austenite fraction in continuously cooled HAZ f is proportional to the equilibrium fraction of austenite f_e. Therefore it is easily understand the experimental results of the largest fraction of austenite phase in the steels containing 0.3%N is owing to the largest value of f_e among the steels tested. Using the above-mentioned equation the effect of the ratio of initial and equilibrium fraction f₀/f_e on the fraction ratio f/f_e in simulated HAZ calculated using Eq. (14) is shown in Fig. 11. And the effect of the term of integration of increase of austenite during cooling process $\int {\text{k}}_{\text{p}}({\text{T}}_{\text{i}})\text{dt}$ on that fraction in simulated HAZ calculated using Eq. (14) was shown in Fig. 12. The cooling rate has no influence on the term of f₀/f_e and just has the influence on the term of $\int {\text{k}}_{\text{p}}({\text{T}}_{\text{i}})\text{dt}$. The value of $\int {\text{k}}_{\text{p}}({\text{T}}_{\text{i}})\text{dt}$in the HAZ of the same steel increased with the decrease of cooling rate. Referring the calculation results in the case of the smaller ratio of f₀/f_e the fraction of austenite phase in the simulated HAZ can be more influenced by the value of $\int {\text{k}}_{\text{p}}({\text{T}}_{\text{i}})\text{dt}$ and that means to be more sensitive to the cooling rate. This explains the experimental results that the austenite fraction was more sensitive to the cooling rate in the steel containing lower nitrogen with smaller ratio of f₀/f_e. Referring this model the fraction of austenite phase in the simulated HAZ can be larger in the steel with the larger value of k_p in the same cooling rate because $\int {\text{k}}_{\text{p}}({\text{T}}_{\text{i}})\text{dt}$ increases with the increase of the value of k_p. As shown in the previous work³²⁾ the value of k_p depends on the temperature for the stability of austenite phase T_eq and the coefficient term of k_p0 which is determined in each steel. That is also influenced by the prior grain size of ferrite phase but the effect is included in the term of T_eq due to the prevention of grain growth in the steel with high value of T_eq in the same cooling condition. The value of T_eq is high and the constant term of k_p0 is large in the steel consisting of small amount of ferrite stabilizing elements such as Cr and Mo and of large amount of austenite stabilizing elements such as Ni and N. Those have already been known qualitatively but in this work those was indicated quantitatively using the parameters in the model proposed.

Fig. 11.

Effect of ratio of initial and equilibrium fraction of austenite phase on that fraction in simulated HAZ calculated using model proposed. (Online version in color.)

Fig. 12.

Effect of integration of change in austenite fraction during cooling process on that fraction in simulated HAZ calculated using model proposed. (Online version in color.)

In conclusion the requirements for the steel to obtain the optimum range of the fraction of austenite phase even in HAZ from the point of view of the performance in weldments were clarified by applying the model proposed when any welding condition is given. For example to obtain the fractions in the preferable range of 30 to 70% from the point of view of the performance in weldments, the steel which has the high values of f₀, f_e and T_eq such as the 25%Cr-7%Ni-3%Mo-2%W-0.3%N containing high nitrogen was recommendable with the logical reason.

6. Conclusion

The following results were obtained regarding the simulated HAZ of 25%Cr and 22%Cr duplex stainless steels from the point of view of the growth property of austenite phase in the continuous cooling from high temperature close to fusion point.

(1) The 25%Cr-7%Ni-3%Mo-2%W-0.3%N steel containing high nitrogen and 22%Cr-5%Ni-3%Mo-0.2%N steel had the fractions of austenite phase in the range of 30 to 70% preferable for the performance in weldment in all of the cooling condition of 3 K/s to 60 K/s. Contrary the 25%Cr-7%Ni-3%Mo-2%W-0.1%N steel containing low N had low fractions in the range of 5% to 20% and those decreased remarkably with the increase of cooling rate.

(2) Applying the additivity rule to the austenite phase growth model obtained in the isothermal heating the austenite fraction in HAZ consisting of continuous cooling process was calculated. Those results calculated were confirmed to have rather fit to experimental data.

(3) The requirements for the steel to obtain the optimum range of the fraction of austenite phase in HAZ from the point of view of the performance in weldments were clarified by applying the model proposed when any welding condition is given.

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: Mater. Sci. Forum, 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, http://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
• 32)   K.  Ogawa: ISIJ Int., 62 (2022), 726