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Numerical simulation of temperature fields in electroslag remelting slab ingots
Acta Metall. Sin.(Engl. Lett.)Vol.21 No.4 pp253-259 Aug. 2008
NUMERICAL SIMULATION OF TEMPERATURE FIELDS IN ELECTROSLAG REMELTING SLAB INGOTS L.Z. Chang∗ and B.Z. Li Department of Metallurgical Technology, Central Iron & Steel Research Institute, Beijing 100081, China Manuscript received 14 September 2007; in revised form 30 January 2008
The method based on transient heat transfer model is adopted to simulate electro-slag remelting process. The calculated results of the model show that the process is in the quasi-steady state, and the shape of pool remains unchanged when the height of ingot is approximately 2.5–3 times the thickness of slab ingot. The change in the shape of pool is found to be strongly dependent on the pattern of melting rate, and hence, the power input; the depth of the molten pool increases with the increase in melting speed. It is concluded that a transient heat transfer model has to be used to obtain reliable input information for the entire operating time. KEY WORDS ESR; Slab ingot; Mathematical model; Shape of molten metal pool
1. Introduction With the development of ship-building industry, nuclear and heat power engineering and some other branches of industries in China, a large-sized plate of high quality is required. It has been universally recognized that the application of the electroslag remelting (ESR) is rational for the production of large slab ingot[1,2] . ESR slab ingot with such excellent quality mainly lies in its solidification structure. The key to obtain good solidification structure is the selection of rational remelting speed. For the selection of suitable remelting speed, the information with regard to the thermal state of the ingot being solidified, such as, shape and depth of molten metal pool, extension of mushy zone and temperature field in the part of the ingot already solidified, is of significant importance. However, such information is very difficult to obtain experimentally, as it is expensive and labor-consuming. The methods of mathematical simulation are of special interest, because they can simulate all the above-mentioned parameters at minimum time and investment. In China, there are few references about the mathematical simulation for slab ingot, and in abroad, Nippon Steel Corporation had simulated temperature fields of a 40 t slab ingot[3] . Medovar[4] had ever simulated temperature fields of slab ingot. At present, there are several steelmaking plants in China that built large ESR furnace for slab ingots. The furnace can produce slabs with the thickness of 400 mm. ∗
Corresponding author. Tel.: +86 10 62181053. E-mail address: [email protected] (L.Z. Chang)
· 254 · The objective of this article is to simulate the temperature field of slab ingot, the shape of molten metal pool and extension of mushy zone, and to control the solidification structure of slab ingot. 2. Description of Mathematical Modeling 2.1 Assumptions of modeling (1) Two-dimensional heat transfer for the model; (2) Interface of slag-metal is horizontal; (3) Temperature of slag is a constant; (4) Convection in the molten metal pool is ignored; (5) Physical parameters in the solid metal and molten metal are constant. 2.2 Description of solidification model[5−8] Considering the dependence of thermal-physical properties on temperature and generation of latent heat of solidification within the temperature range, mathematical model can be expressed by equation: ρcp
∂ ∂t ∂ ∂t ∂t = λ + λ ∂τ ∂x ∂x ∂z ∂z
(1)
where ρ is density, cp is heat capacity, t is temperature, τ is time and λ is thermal conductivity. The most common method to simulate the generation of latent heat of solidification involves the artificial increase of specific heat within the liquidus and solidus temperature range, so that:
cp = cp,m +
L tl − ts
(ts < t < tl )
(2)
where cp is atomic heat capacity of metal, L is latent heat of solidification, tl is liquidus temperature and ts is solidus temperature. An effective thermal conductivity is used to account for the effect of convection motion in the liquid metal pool[9] : keff = km (1 + A)
(3)
where km is the atomic thermal conductivity of metal. A is a constant, usually fell in the range of 2–5. x − 0
Fig.1 Schematic diagram for mathematical description (1-Mould; 2-Consumable electrode; 3-Solidified ingot; 4-Mushy zone; 5-Molten metal pool; 6-Slag pool).
· 255 · 2.3 Boundary and initialization conditions 2.3.1 Boundary condition at liquid metal-slag interface The equation of balance of heat flows will be expressed as follows[9] : q = qsl + qr
(4)
where q is total heat flows entering in the molten metal pool; qsl is heat flow entering in the molten metal pool from slag pool; qr is heat flow brought with the electrode metal drops. These two components will be expressed as follows: qr = mc[tk − t(x, z, τ )]
(5)
qsl = hsl [tsl − t(x, z, τ )]
(6)
where m is weight of metal drops, kg; C specific heat, J/(kg·◦ C); tk temperature of metal drops, ◦ C; tsl temperature of slag pool, ◦ C; hsl coefficient of heat-exchange between slag and metal pools. Thus, the final boundary condition at z=f (τ ) is as follows: −λ
∂t | = hsl (tsl − t(x, z, τ )) + M c[tk − t(x, z, τ )] ∂z z=f (τ )
(7)
The temperature of slag is assumed to be 1650◦ C. Coefficient of heat-exchange between slag and metal pool is assumed to be equal to 2840 W/(m2 ·◦ C) and temperature of cooling water is 20◦ C. 2.3.2 Boundary condition at the bottom of the ingot ∂t (8) = hb (t − tb ), z = 0 ∂z where tb is temperature of cooling water, ◦ C; hb effective coefficient of heat-exchange between cooling water and bottom plate. −k
2.3.3 Boundary condition at the lateral surface of the ingot ∂t = htw (t − tw ), 0 < z < f (τ ) (9) ∂x where htw is effective coefficient of heat-exchange between cooling water and lateral surface of the ingot; t is temperature of cooling water, ◦ C; f (τ ) is ingot height. −λ
2.3.4 Boundary condition at the axis of the ingot Assuming that the temperature field of the ingot is symmetric with respect to plane x=0. This means that heat flow in the direction normal to this plane is zero. 0 < z < f (τ ),
x=0
−λ
∂t =0 ∂x
(10)
2.3.5 Initial condition In the initial moment of time it is assumed that there is already a small layer of the deposited metal, having T0 temperature.
· 256 · 2.4 Computation method In this article, finite difference method is used to solve the mathematical equation. Because of the strong temperature dependence on thermal conductivity and heat capacity, it is desirable to limit the size of the integration time step. Time step was 1 s and a 10 mm×10 mm grid size was used. The growth of ingot is considered by adding a new grid row after several time increments. The program for computer was compiled in the language “Visual Basic”. CrNiMo steel is simulated and the thermal-physical parameters used are shown in Table 1. Table 1 Thermal-physical parameters of CrNiMo steel Thermal-physical parameters Liquidus/◦ C Solidus/◦ C Thermal conductivity of molten metal/W·m−1 ·K−1 Thermal conductivity of solid metal/W·m−1 ·K−1 Atomic heat capacity of molten metal/J·kg−1 ·K−1 Atomic heat capacity of solid metal/J·kg−1 ·K−1 Density of molten metal/kg·m−3 Density of solid metal/kg·m−3 Latent heat of solidification/J·kg−1
Symbols Tl Ts λl λs cp,l cp,s ρl ρs ∆h
Values 1499 1460 15.48 29.4 840 680 7000 7400 2.72×105
3. Results and Discussion Fig.2 shows the calculated shape of molten metal pool at various ingot heights while melting rate is 3 mm/min (1100 kg/h), and Fig.3 shows the depth of calculated pool and thickness of mushy zone as functions of time and ingot height. As can be seen from Fig.2, at the initial stage, because of the strong cooling effect from bottom, the depth of pool is shallow, the thickness of mushy zone is thin, and Ushape pool is formed. With the increase in ingot height, as the cooling effect from bottom becomes weak, V-shape pool is gradually formed and depth of pool increases. The thermal condition in ESR system can be reproducible in time after the ingot has grown to a length approximately 2.5−3 times higher than the thickness of slab ingot. Fig.3 shows that the depth of liquidus rapidly increases from zero to approximately 220 mm within 300 min, which corresponds to the heights of ingot from 0 to approximately 1000 mm; the solidus temperature rapidly increases from zero to approximately 260 mm within 300 min, which corresponds to the heights of ingot from 0 to about 1000 mm. At the initial stage, the isotherm velocity of the liquidus temperature rapidly increases than that of the solidus temperature, which shows that thickness of mushy zone increases with time. When the height of ingot is approximately 2.5−3 times the thickness, the two isotherm velocities are at the same time, thickness of mushy zone does not change. Figs.4 and 5 show the calculated shape of molten metal pool, depth of pool and thickness of mushy zone while melting rate is 4 mm/min (1500 kg/h). Figs.6 and 7 show the calculated shape of molten metal pool, depth of pool and thickness of mushy zone while melting rate is 5 mm/min (1900 kg/h). As can be seen from Figs.2–7, with the increase in melting speed, the depth of molten metal pool also increases. The depth of pool reaches 400 mm and thickness of
· 257 ·
Fig.2 Pool shape at various ingot heights (ν=1100 kg/h).
Fig.4 Pool shape at various ingot heights (ν=1500 kg/h).
Fig.3 Calculated pool depth and mushy zone thickness as functions of time and ingot height (ν=1100 kg/h).
Fig.5 Calculated pool depth and mushy zone thickness as functions of time and ingot height (ν=1500 kg/h).
· 258 ·
Fig.6 Pool shape at various ingot heights (ν=1900 kg/h).
Fig.7 Calculated pool depth and mushy zone thickness as functions of time and ingot height (ν=1900 kg/h).
mushy zone is 130 mm while melting rate is 1900 kg/h. In general, solidification proceeds perpendicularly to the liquid-solid interface. The depth and shape of the molten metal pool as established and maintained during the remelting operation will be of paramount influence on the as-cast structure of the remelted ingot, such as center looseness, macro segregation, inclusion removal, impact strength and so on. All parameters influencing the thermal balance of the process have an influence on the melting rate of the consumable electrode that affects the shape of the molten metal pool and consequently the as-cast structure of the ingot. The depth of molten metal pool can be varied with varying melting rate of ingot. Hence it is probable to reduce the depth of metal pool to any extent by decreasing the melting rate. However, it is not the case in practice. That is, if melting rate is too low, it will cause difficulties in melting. Particularly, a thick slag blanket will be formed that not only retard the solidification of ingot but also roughen the surface of ingot. Melting rate cannot be too low, but too high melting rate will deteriorate the crystallization quality. So, based on the calculated pool shape (depth), the reasonable processing parameter (melting rate) can be constituted in the course of the remelting. At the initial stage, the depth of pool is shallow at the different melting rates (3 mm/min, 4 mm/min, 5 mm/min). When system is in the quasisteady state, the depth of pool is too deep with melting rate 5 mm/min. So, melting rate of 5 mm/min can be adopted at the initial stage and can be gradually lowered to the extent of 3 mm/min or 4 mm/min finally, while system is in the quasi-steady state. 4. Conclusions A transient heat transfer model is
· 259 · developed for the calculation of pool shape and mushy zone thickness. The calculated results of the model show that the process is in the quasi-steady state when the height of ingot is approximately 2.5–3 times the thickness of slab ingot. The change in the pool shape is found to be strongly dependent on the pattern of melting rate, and hence, the power input. It is concluded that a transient heat transfer model has to be used to obtain reliable input information for the entire operating time. Acknowledgements—This study was supported by Angang Steel Company Limited. REFERENCES [1] Z.B. Li, Translation Assembles for Electroslag Remelting 2nd (Metallurgical Industry Press, Beijing, 1990) p.110 (in Chinese). [2] K. Moriyama, H. Yoshimura and K. Kaku, Trans. ISIJ 23 (1983) 434. [3] M. Nishiwaki, T. Yamaguchi, M. Koba, N. Sato and K. Okohira, Proc. of the 5th Int. Conf. on Vacuum Metallurgy and ESR Processes (Leybold-Heraeus GmbH & Co.KG Press, Munich, 1976). [4] B.I. Medovar, , V.F. Demchenko, A.G. Bogachenko, N.I. Tarasevich and Yu.P. Shtanko, Proc. of the 5th Int. Conf. on Vacuum Metallurgy and ESR Processes (Leybold-Heraeus GmbH & Co.KG Press, Munich, 1976). [5] A. Mitchell, Mater. Sci. Eng. A413-414 (2005) 10. [6] K.M. Kelkar, J. Mok1 and S.V. Patankar, J. Phys. IV 120 (2004) 421. [7] P.M. Guo, J.W. Zhang and Z.B. Li, J. Iron Steel Res. Int. 7 (2000) 27. [8] Y. Hirose, K. Okohira, T. Shimizu, N. Sato, M. Hikai and M. Nishiwaki, Tetsu-to-Hagane 63 (1977) 2208. [9] K.O. Yu, C.B. Adasczik and W.H. Sutton, Proc. of the 7th Int. Conf. on Vacuum Metallurgy ISIJ, Tokyo, 1982).
NUMERICAL SIMULATION OF TEMPERATURE FIELDS IN ELECTROSLAG REMELTING SLAB INGOTS L.Z. Chang∗ and B.Z. Li Department of Metallurgical Technology, Central Iron & Steel Research Institute, Beijing 100081, China Manuscript received 14 September 2007; in revised form 30 January 2008
The method based on transient heat transfer model is adopted to simulate electro-slag remelting process. The calculated results of the model show that the process is in the quasi-steady state, and the shape of pool remains unchanged when the height of ingot is approximately 2.5–3 times the thickness of slab ingot. The change in the shape of pool is found to be strongly dependent on the pattern of melting rate, and hence, the power input; the depth of the molten pool increases with the increase in melting speed. It is concluded that a transient heat transfer model has to be used to obtain reliable input information for the entire operating time. KEY WORDS ESR; Slab ingot; Mathematical model; Shape of molten metal pool
1. Introduction With the development of ship-building industry, nuclear and heat power engineering and some other branches of industries in China, a large-sized plate of high quality is required. It has been universally recognized that the application of the electroslag remelting (ESR) is rational for the production of large slab ingot[1,2] . ESR slab ingot with such excellent quality mainly lies in its solidification structure. The key to obtain good solidification structure is the selection of rational remelting speed. For the selection of suitable remelting speed, the information with regard to the thermal state of the ingot being solidified, such as, shape and depth of molten metal pool, extension of mushy zone and temperature field in the part of the ingot already solidified, is of significant importance. However, such information is very difficult to obtain experimentally, as it is expensive and labor-consuming. The methods of mathematical simulation are of special interest, because they can simulate all the above-mentioned parameters at minimum time and investment. In China, there are few references about the mathematical simulation for slab ingot, and in abroad, Nippon Steel Corporation had simulated temperature fields of a 40 t slab ingot[3] . Medovar[4] had ever simulated temperature fields of slab ingot. At present, there are several steelmaking plants in China that built large ESR furnace for slab ingots. The furnace can produce slabs with the thickness of 400 mm. ∗
Corresponding author. Tel.: +86 10 62181053. E-mail address: [email protected] (L.Z. Chang)
· 254 · The objective of this article is to simulate the temperature field of slab ingot, the shape of molten metal pool and extension of mushy zone, and to control the solidification structure of slab ingot. 2. Description of Mathematical Modeling 2.1 Assumptions of modeling (1) Two-dimensional heat transfer for the model; (2) Interface of slag-metal is horizontal; (3) Temperature of slag is a constant; (4) Convection in the molten metal pool is ignored; (5) Physical parameters in the solid metal and molten metal are constant. 2.2 Description of solidification model[5−8] Considering the dependence of thermal-physical properties on temperature and generation of latent heat of solidification within the temperature range, mathematical model can be expressed by equation: ρcp
∂ ∂t ∂ ∂t ∂t = λ + λ ∂τ ∂x ∂x ∂z ∂z
(1)
where ρ is density, cp is heat capacity, t is temperature, τ is time and λ is thermal conductivity. The most common method to simulate the generation of latent heat of solidification involves the artificial increase of specific heat within the liquidus and solidus temperature range, so that:
cp = cp,m +
L tl − ts
(ts < t < tl )
(2)
where cp is atomic heat capacity of metal, L is latent heat of solidification, tl is liquidus temperature and ts is solidus temperature. An effective thermal conductivity is used to account for the effect of convection motion in the liquid metal pool[9] : keff = km (1 + A)
(3)
where km is the atomic thermal conductivity of metal. A is a constant, usually fell in the range of 2–5. x − 0
Fig.1 Schematic diagram for mathematical description (1-Mould; 2-Consumable electrode; 3-Solidified ingot; 4-Mushy zone; 5-Molten metal pool; 6-Slag pool).
· 255 · 2.3 Boundary and initialization conditions 2.3.1 Boundary condition at liquid metal-slag interface The equation of balance of heat flows will be expressed as follows[9] : q = qsl + qr
(4)
where q is total heat flows entering in the molten metal pool; qsl is heat flow entering in the molten metal pool from slag pool; qr is heat flow brought with the electrode metal drops. These two components will be expressed as follows: qr = mc[tk − t(x, z, τ )]
(5)
qsl = hsl [tsl − t(x, z, τ )]
(6)
where m is weight of metal drops, kg; C specific heat, J/(kg·◦ C); tk temperature of metal drops, ◦ C; tsl temperature of slag pool, ◦ C; hsl coefficient of heat-exchange between slag and metal pools. Thus, the final boundary condition at z=f (τ ) is as follows: −λ
∂t | = hsl (tsl − t(x, z, τ )) + M c[tk − t(x, z, τ )] ∂z z=f (τ )
(7)
The temperature of slag is assumed to be 1650◦ C. Coefficient of heat-exchange between slag and metal pool is assumed to be equal to 2840 W/(m2 ·◦ C) and temperature of cooling water is 20◦ C. 2.3.2 Boundary condition at the bottom of the ingot ∂t (8) = hb (t − tb ), z = 0 ∂z where tb is temperature of cooling water, ◦ C; hb effective coefficient of heat-exchange between cooling water and bottom plate. −k
2.3.3 Boundary condition at the lateral surface of the ingot ∂t = htw (t − tw ), 0 < z < f (τ ) (9) ∂x where htw is effective coefficient of heat-exchange between cooling water and lateral surface of the ingot; t is temperature of cooling water, ◦ C; f (τ ) is ingot height. −λ
2.3.4 Boundary condition at the axis of the ingot Assuming that the temperature field of the ingot is symmetric with respect to plane x=0. This means that heat flow in the direction normal to this plane is zero. 0 < z < f (τ ),
x=0
−λ
∂t =0 ∂x
(10)
2.3.5 Initial condition In the initial moment of time it is assumed that there is already a small layer of the deposited metal, having T0 temperature.
· 256 · 2.4 Computation method In this article, finite difference method is used to solve the mathematical equation. Because of the strong temperature dependence on thermal conductivity and heat capacity, it is desirable to limit the size of the integration time step. Time step was 1 s and a 10 mm×10 mm grid size was used. The growth of ingot is considered by adding a new grid row after several time increments. The program for computer was compiled in the language “Visual Basic”. CrNiMo steel is simulated and the thermal-physical parameters used are shown in Table 1. Table 1 Thermal-physical parameters of CrNiMo steel Thermal-physical parameters Liquidus/◦ C Solidus/◦ C Thermal conductivity of molten metal/W·m−1 ·K−1 Thermal conductivity of solid metal/W·m−1 ·K−1 Atomic heat capacity of molten metal/J·kg−1 ·K−1 Atomic heat capacity of solid metal/J·kg−1 ·K−1 Density of molten metal/kg·m−3 Density of solid metal/kg·m−3 Latent heat of solidification/J·kg−1
Symbols Tl Ts λl λs cp,l cp,s ρl ρs ∆h
Values 1499 1460 15.48 29.4 840 680 7000 7400 2.72×105
3. Results and Discussion Fig.2 shows the calculated shape of molten metal pool at various ingot heights while melting rate is 3 mm/min (1100 kg/h), and Fig.3 shows the depth of calculated pool and thickness of mushy zone as functions of time and ingot height. As can be seen from Fig.2, at the initial stage, because of the strong cooling effect from bottom, the depth of pool is shallow, the thickness of mushy zone is thin, and Ushape pool is formed. With the increase in ingot height, as the cooling effect from bottom becomes weak, V-shape pool is gradually formed and depth of pool increases. The thermal condition in ESR system can be reproducible in time after the ingot has grown to a length approximately 2.5−3 times higher than the thickness of slab ingot. Fig.3 shows that the depth of liquidus rapidly increases from zero to approximately 220 mm within 300 min, which corresponds to the heights of ingot from 0 to approximately 1000 mm; the solidus temperature rapidly increases from zero to approximately 260 mm within 300 min, which corresponds to the heights of ingot from 0 to about 1000 mm. At the initial stage, the isotherm velocity of the liquidus temperature rapidly increases than that of the solidus temperature, which shows that thickness of mushy zone increases with time. When the height of ingot is approximately 2.5−3 times the thickness, the two isotherm velocities are at the same time, thickness of mushy zone does not change. Figs.4 and 5 show the calculated shape of molten metal pool, depth of pool and thickness of mushy zone while melting rate is 4 mm/min (1500 kg/h). Figs.6 and 7 show the calculated shape of molten metal pool, depth of pool and thickness of mushy zone while melting rate is 5 mm/min (1900 kg/h). As can be seen from Figs.2–7, with the increase in melting speed, the depth of molten metal pool also increases. The depth of pool reaches 400 mm and thickness of
· 257 ·
Fig.2 Pool shape at various ingot heights (ν=1100 kg/h).
Fig.4 Pool shape at various ingot heights (ν=1500 kg/h).
Fig.3 Calculated pool depth and mushy zone thickness as functions of time and ingot height (ν=1100 kg/h).
Fig.5 Calculated pool depth and mushy zone thickness as functions of time and ingot height (ν=1500 kg/h).
· 258 ·
Fig.6 Pool shape at various ingot heights (ν=1900 kg/h).
Fig.7 Calculated pool depth and mushy zone thickness as functions of time and ingot height (ν=1900 kg/h).
mushy zone is 130 mm while melting rate is 1900 kg/h. In general, solidification proceeds perpendicularly to the liquid-solid interface. The depth and shape of the molten metal pool as established and maintained during the remelting operation will be of paramount influence on the as-cast structure of the remelted ingot, such as center looseness, macro segregation, inclusion removal, impact strength and so on. All parameters influencing the thermal balance of the process have an influence on the melting rate of the consumable electrode that affects the shape of the molten metal pool and consequently the as-cast structure of the ingot. The depth of molten metal pool can be varied with varying melting rate of ingot. Hence it is probable to reduce the depth of metal pool to any extent by decreasing the melting rate. However, it is not the case in practice. That is, if melting rate is too low, it will cause difficulties in melting. Particularly, a thick slag blanket will be formed that not only retard the solidification of ingot but also roughen the surface of ingot. Melting rate cannot be too low, but too high melting rate will deteriorate the crystallization quality. So, based on the calculated pool shape (depth), the reasonable processing parameter (melting rate) can be constituted in the course of the remelting. At the initial stage, the depth of pool is shallow at the different melting rates (3 mm/min, 4 mm/min, 5 mm/min). When system is in the quasisteady state, the depth of pool is too deep with melting rate 5 mm/min. So, melting rate of 5 mm/min can be adopted at the initial stage and can be gradually lowered to the extent of 3 mm/min or 4 mm/min finally, while system is in the quasi-steady state. 4. Conclusions A transient heat transfer model is
· 259 · developed for the calculation of pool shape and mushy zone thickness. The calculated results of the model show that the process is in the quasi-steady state when the height of ingot is approximately 2.5–3 times the thickness of slab ingot. The change in the pool shape is found to be strongly dependent on the pattern of melting rate, and hence, the power input. It is concluded that a transient heat transfer model has to be used to obtain reliable input information for the entire operating time. Acknowledgements—This study was supported by Angang Steel Company Limited. REFERENCES [1] Z.B. Li, Translation Assembles for Electroslag Remelting 2nd (Metallurgical Industry Press, Beijing, 1990) p.110 (in Chinese). [2] K. Moriyama, H. Yoshimura and K. Kaku, Trans. ISIJ 23 (1983) 434. [3] M. Nishiwaki, T. Yamaguchi, M. Koba, N. Sato and K. Okohira, Proc. of the 5th Int. Conf. on Vacuum Metallurgy and ESR Processes (Leybold-Heraeus GmbH & Co.KG Press, Munich, 1976). [4] B.I. Medovar, , V.F. Demchenko, A.G. Bogachenko, N.I. Tarasevich and Yu.P. Shtanko, Proc. of the 5th Int. Conf. on Vacuum Metallurgy and ESR Processes (Leybold-Heraeus GmbH & Co.KG Press, Munich, 1976). [5] A. Mitchell, Mater. Sci. Eng. A413-414 (2005) 10. [6] K.M. Kelkar, J. Mok1 and S.V. Patankar, J. Phys. IV 120 (2004) 421. [7] P.M. Guo, J.W. Zhang and Z.B. Li, J. Iron Steel Res. Int. 7 (2000) 27. [8] Y. Hirose, K. Okohira, T. Shimizu, N. Sato, M. Hikai and M. Nishiwaki, Tetsu-to-Hagane 63 (1977) 2208. [9] K.O. Yu, C.B. Adasczik and W.H. Sutton, Proc. of the 7th Int. Conf. on Vacuum Metallurgy ISIJ, Tokyo, 1982).