Continuous casting mold and method for continuously casting steel
11020794 · 2021-06-01
Assignee
Inventors
Cpc classification
B22D11/22
PERFORMING OPERATIONS; TRANSPORTING
International classification
Abstract
A continuous casting mold including a water-cooled copper mold having a mold copper plate including an inner wall surface, recessed portions disposed partially or entirely in a region of the inner wall surface of the water-cooled copper mold from at least a position located at a meniscus to a position located 20 mm lower than the meniscus, and material-filled layers disposed in the recessed portions with a metal or nonmetal having a thermal conductivity different from that of the mold copper plate of the water-cooled copper mold. A shape of each of the recessed portions at a surface of the mold copper plate includes a curved surface.
Claims
1. A continuous casting mold comprising: a water-cooled copper mold having a mold copper plate including an inner wall surface; recessed portions disposed partially or entirely in a region of the inner wall surface of the water-cooled copper mold from at least a position located at a meniscus to a position located 20 mm lower than the meniscus; and material-filled layers disposed in the recessed portions with a metal or nonmetal having a thermal conductivity different from that of the mold copper plate of the water-cooled copper mold, wherein a shape of each of the recessed portions at a surface of the mold copper plate includes a curved surface having a curvature in every direction and a flat surface, and the curved surface has a radius of curvature satisfying the formula (1) below:
d/2<R≤d (1) where d is a minimum opening width (mm) of the recessed portions at the inner wall surface of the mold copper plate, and R is an average radius of curvature (mm) of the recessed portions.
2. The continuous casting mold according to claim 1, wherein the radius of curvature is a constant value.
3. A method for continuously casting steel, the method comprising: providing the continuous casting mold according to claim 2; pouring molten steel in a tundish into the continuous casting mold; and continuously casting the molten steel.
4. The continuous casting mold according to claim 1, wherein an opening shape of one recessed portion at the inner wall surface of the mold copper plate is elliptic, and all adjacent recessed portions are not in contact with or connected to one another.
5. A method for continuously casting steel, the method comprising: providing the continuous casting mold according to claim 4; pouring molten steel in a tundish into the continuous casting mold; and continuously casting the molten steel.
6. The continuous casting mold according to claim 1, wherein an opening shape of one recessed portion at the inner wall surface of the mold copper plate is elliptic, and all or some adjacent recessed portions are in contact with or connected to one another.
7. A method for continuously casting steel, the method comprising: providing the continuous casting mold according to claim 6; pouring molten steel in a tundish into the continuous casting mold; and continuously casting the molten steel.
8. The continuous casting mold according to claim 1, wherein an opening shape of one recessed portion at the inner wall surface of the mold copper plate is circular, and all adjacent recessed portions are not in contact with or connected to one another.
9. A method for continuously casting steel, the method comprising: providing the continuous casting mold according to claim 8; pouring molten steel in a tundish into the continuous casting mold; and continuously casting the molten steel.
10. The continuous casting mold according to claim 1, wherein an opening shape of one recessed portion at the inner wall surface of the mold copper plate is circular, and all or some adjacent recessed portions are in contact with or connected to one another.
11. A method for continuously casting steel, the method comprising: providing the continuous casting mold according to claim 10; pouring molten steel in a tundish into the continuous casting mold; and continuously casting the molten steel.
12. A method for continuously casting steel, the method comprising: providing the continuous casting mold according to claim 1; pouring molten steel in a tundish into the continuous casting mold; and continuously casting the molten steel.
13. A continuous casting mold comprising: a water-cooled copper mold having a mold copper plate including an inner wall surface; recessed portions disposed partially or entirely in a region of the inner wall surface of the water-cooled copper mold from at least a position located at a meniscus to a position located 20 mm lower than the meniscus; and material-filled layers disposed in the recessed portions with a metal or nonmetal having a thermal conductivity different from that of the mold copper plate of the water-cooled copper mold, wherein a shape of each of the recessed portions at a surface of the mold copper plate, at any position of the recessed portion, is a curved surface having a curvature in every direction, and the curved surface has a radius of curvature satisfying the formula (1) below:
d/2<R≤d (1) where d is a minimum opening width (mm) of the recessed portions at the inner wall surface of the mold copper plate, and R is an average radius of curvature (mm) of the recessed portions.
14. The continuous casting mold according to claim 13, wherein the radius of curvature is a constant value.
15. A method for continuously casting steel, the method comprising: providing the continuous casting mold according to claim 14; pouring molten steel in a tundish into the continuous casting mold; and continuously casting the molten steel.
16. A method for continuously casting steel, the method comprising: providing the continuous casting mold according to claim 13; pouring molten steel in a tundish into the continuous casting mold; and continuously casting the molten steel.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
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DETAILED DESCRIPTION
(14) The disclosed embodiments will be specifically described below with reference to the accompanying drawings.
(15) The continuous casting mold shown in
(16) As shown in
(17) As shown in
(18) The term “meniscus” refers to the “upper surface of molten steel in a mold”. Although its position is not determined when casting is not performed, the meniscus position is controlled to be about 50 mm to 200 mm lower than the upper end of the mold copper plate in an ordinary continuous casting operation for steel. Therefore, even in the case where the meniscus position is 50 mm or 200 mm lower than the upper end of the mold long-side copper plate 1, the dissimilar material-filled layers 3 are arranged so that the length Q and the length L satisfy the conditions according to this embodiment described below.
(19) In consideration of an influence on early stage solidification of a solidified shell, it is necessary that the dissimilar material-filled layers 3 be arranged at least in a region from the meniscus to a position located 20 mm lower than the meniscus. Therefore, it is necessary that the length L be 20 mm or more.
(20) The amount of heat removed through a continuous casting mold is larger in the vicinity of a meniscus position than at other positions. That is, the heat flux in the vicinity of the meniscus position is higher than the heat flux at other positions. The results of experiments conducted by the present inventors show that, although depending on the amount of cooling water fed to the mold and the cast-piece drawing speed, while the heat flux is lower than 1.5 MW/m.sup.2 at a position located 30 mm lower than the meniscus, the heat flux is generally 1.5 MW/m.sup.2 or more at a position located 20 mm lower than the meniscus.
(21) According to this embodiment, in order to prevent occurrence of surface cracks in a cast piece when high-speed casting is performed or when medium carbon steel is cast in which surface cracks are likely to occur in a cast piece, by forming dissimilar material-filled layers 3, thermal resistance is varied on the inner wall surface of the mold in the vicinity of the meniscus position. By forming the dissimilar material-filled layers 3, a periodic variation in heat flux is sufficiently secured, thereby preventing occurrence of surface cracks in a cast piece. In consideration of the influence on early stage solidification, it is necessary to arrange dissimilar material-filled layers 3 in a region from the meniscus to a position located 20 mm lower than the meniscus in which the heat flux is large. In the case where the length L is less than 20 mm, the effect of preventing surface cracks in a cast piece is insufficient. The upper limit of the length L is not limited, and the dissimilar material-filled layers 3 may be arranged so as to spread up to the lower end of the mold.
(22) On the other hand, the upper end of the dissimilar material-filled layers 3 may be located at any position as long as the position is located at the same position as the meniscus or at a position higher than the meniscus. The length Q shown in
(23) The thermal conductivity of the metal or nonmetal with which the recessed portions 2 are filled is in general lower than the thermal conductivity of pure copper or a copper alloy constituting the mold long-side copper plate 1. However, in the case where the mold long-side copper plate 1 is made of a copper alloy having a low thermal conductivity, the thermal conductivity of the metal or nonmetal used for filling may be higher. In the case where the material for filling is a metal, filling is achieved by a plating process or thermal spraying process. In the case where the material for filling is a nonmetal, filling is achieved by a thermal spraying process or by fitting a nonmetal, which has been worked to the shape of a recessed portion 2, into the recessed portion 2 (shrink fitting).
(24)
(25) By arranging dissimilar material-filled layers 3 in the width direction of a continuous casting mold and in the casting direction in the vicinity of a meniscus including the meniscus position, as shown in
(26) As a result of the regular and periodic increases and decreases in heat flux, stress caused by transformation from δ iron to γ iron and thermal stress are decreased, and the deformation of the solidified shell caused by these stresses decreases. Because of the decrease in the deformation of the solidified shell, occurrence of depression is suppressed, and uneven distribution of heat flux due to deformation of the solidified shell is uniformized, and the generated stresses are dispersed to decrease individual strains. As a result, occurrence of surface cracks on the surface of the solidified shell is suppressed.
(27) In the disclosed embodiments, pure copper or a copper alloy is used for the mold copper plate. As the copper alloy used for the mold copper plate, a copper alloy to which small amounts of chromium (Cr), zirconium (Zr), and the like are added, which is generally used for a mold copper plate for continuous casting, is used. The thermal conductivity of pure copper is 398 W/(m×K), while the thermal conductivity of a copper alloy is generally lower than that of pure copper, and even a copper alloy whose thermal conductivity is about ½ of that of pure copper is used for a continuous casting mold.
(28) As a material with which the recessed portions 2 are filled, preferably, a material whose thermal conductivity is 80% or less, or 125% or more of the thermal conductivity of the mold copper plate is used. In the case where the thermal conductivity of the material for filling is more than 80%, or less than 125% of that of the mold copper plate, the effect of a periodical variation in heat flux due to the presence of the dissimilar material-filled layers 3 becomes insufficient, and the effect of suppressing surface cracks in a cast piece becomes insufficient when high-speed casting is performed or when medium carbon steel is cast in which surface cracks are likely to occur in a cast piece.
(29) In this embodiment, the material with which the recessed portions 2 are filled is not particularly limited in kind. For reference, examples of a metal that can be suitably used as the material for filling include nickel (Ni, thermal conductivity: 90 W/(m×K)), chromium (Cr, thermal conductivity: 67 W/(m×K)), cobalt (Co, thermal conductivity: 70 W/(m×K)), and alloys containing these metals. These metals and alloys have a lower thermal conductivity than pure copper and copper alloys, and can be easily used for filling the recessed portions 2 by a plating process or thermal spraying process. Examples of a nonmetal that can be suitably used as the material for filling include ceramics, such as BN, AlN, and ZrO.sub.2. These materials have a low thermal conductivity and therefore are suitable as the material for filling.
(30)
(31) Regarding a continuous casting mold including dissimilar material-filled layers 3 in a region where a meniscus is located, which is configured as described above, studies were conducted on extension of mold life. Cracking mainly occurs on the mold copper plate side of an interface where a mold copper plate and a dissimilar material-filled layer 3 are in contact with each other, and the mold life is influenced by the cracking growth rate. Accordingly, studies were conducted on prevention of occurrence of cracking on the mold copper plate side of the interface.
(32) As a result of various studies, considering that, when there is a corner in a recessed portion 2, stress concentrates on the corner, and cracking is likely to occur on the mold copper plate side, it was studied to form the inner surface of a recessed portion 2 into a smooth shape.
(33) Specifically, as shown in
(34) A copper plate test piece provided with a recessed portion 2 having the shape shown in
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(37) Furthermore, the diameter of a dissimilar material-filled layer 3 at the copper plate wall surface, i.e., the minimum opening width of a recessed portion 2 formed of a curved surface having a curvature in every direction, was set to two levels: 5 mm and 6 mm, and copper plate test pieces (thermal conductivity: 360 W/(m×K)) having a recessed portion 2, which were different in the average radius of curvature constituting the recessed portion 2, were prepared. By carrying out the thermal fatigue test (JIS 2278, higher temperature: 700° C., lower temperature: 25° C.), the influence of the average radius of curvature of the recessed portion 2 on the number of thermal cycles at the time of occurrence of cracking on the surfaces of the copper plate test pieces was investigated. The opening shape of the recessed portion 2 at the copper plate wall surface was circular in all the test pieces. In the test, the dissimilar material-filled layer 3 was formed by filling the recessed portion 2 with pure nickel (conductivity: 90 W/(m×K)). The curvatures of the curved surface of the recessed portion 2 were measured by a CNC 3D measuring instrument and stored as digital data, and on the basis of this, the radii of curvature in the horizontal direction and in the vertical direction at each measuring point were obtained. The average radius of curvature was calculated by dividing the sum total of the measured radii of curvature by the measured number of radii of curvature. The average radius of curvature was calculated by excluding data with an infinite radius of curvature.
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(39) On the basis of the results described above, a test was further carried out by using an actual continuous casting machine for slab. In the actual machine test, mainly, the occurrence state of surface defects in cast slab was checked. In the actual machine test, three levels were tested: a continuous casting mold having a mold long-side copper plate 1 provided with a recessed portion 2 shown in
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(41) Furthermore, regarding a mold long-side copper plate 1 having a recessed portion 2 in which the opening shape of the recessed portion 2 at the inner wall surface of the copper plate is circular and the shape of the recessed portion 2 at the surface of the mold copper plate is a curved surface having a curvature in every direction, the diameter of a dissimilar material-filled layer 3 at the copper plate inner wall surface, i.e., the minimum opening width of the recessed portion 2, was set to two levels: 5 mm and 6 mm, and the average radius of curvature constituting the recessed portion 2 was varied. The influence of the average radius of curvature of the recessed portion 2 on the number density of surface cracks in cast slab was investigated. In the test, a copper alloy having a thermal conductivity of 360 W/(m×K) was used as the mold long-side copper plate 1, and pure nickel having a thermal conductivity of 90 W/(m×K) was used as the material with which the recessed portion 2 was filled. The length Q was set at 50 mm, and the length L was set at 200 mm.
(42)
(43) On the basis of the test results described above, in this embodiment, it is necessary that the shape of the recessed portion 2 at the surface of the mold copper plate, at an arbitrary position of the recessed portion 2, be a curved surface having a curvature in every direction. Here, the term “curved surface having a curvature in every direction” refers to a curved surface, such as a spherical crown surface that is a part of a spherical surface, or a part of an ellipsoid. In such a case, preferably, the average radius of curvature constituting the recessed portion 2 satisfies the formula (1) below.
d/2<R≤d (1)
(44) In the formula (1), d is the minimum opening width (mm) of the recessed portion at the inner wall surface of the mold copper plate, and R is the average radius of curvature (mm) of the recessed portion.
(45) The reason for this is considered to be that, as described above, in the case where the average radius of curvature constituting the recessed portion 2 is ½ or less of the minimum opening width d of the recessed portion 2, stress at the interface between the dissimilar material-filled layer 3 and the mold copper plate increases, and cracking is likely to occur. On the other hand, it is considered that, in the case where the average radius of curvature constituting the recessed portion 2 is more than the minimum opening width d of the recessed portion 2, the volume of the dissimilar material-filled layer 3 is decreased, and the effect of suppressing surface cracks in cast slab is decreased.
(46) In this embodiment, when the radii of curvature constituting the recessed portion 2 are constant, designing and processing for the recessed portion 2 are facilitated, which is preferable, however, as long as the curved surface has a curvature in every direction, the radii of curvature may not be constant.
(47) Although
(48) The minimum opening width d in the formula (1) is defined by the length of the shortest straight line among the straight lines that pass through the center of an opening shape of the recessed portion 2 at the inner wall surface of the mold long-side copper plate 1, i.e., defined by the length of the shortest straight line among the straight lines that pass through the center of a shape of the dissimilar material-filled layer 3 at the inner wall surface of the mold long-side copper plate 1. Accordingly, the minimum opening width d corresponds to the diameter of a circle when the opening shape of the recessed portion 2 at the inner wall surface of the mold long-side copper plate 1 is circular, and corresponds to the minor axis of an ellipse when the opening shape is elliptic. In the case where the opening shape of the recessed portion 2 at the inner wall surface of the mold long-side copper plate 1 is circular and the average radius of curvature R constituting the recessed portion 2 satisfies the formula (1), a recessed portion 2 can be formed with a constant radius of curvature of the recessed portion 2.
(49) The diameter (equivalent circle diameter in the case of a quasi-circle) of the dissimilar material-filled layer 3 is preferably 2 to 20 mm. By setting the diameter of the dissimilar material-filled layer 3 to be 2 mm or more, the decrease in the heat flux in the dissimilar material-filled layer 3 becomes sufficient, and an effect of suppressing surface cracks can be obtained. By setting the diameter of the dissimilar material-filled layer 3 to be 2 mm or more, the recessed portion 2 can be easily filled with a metal by a plating process or thermal spraying process. On the other hand, by setting the diameter (equivalent circle diameter in the case of a quasi-circle) of the dissimilar material-filled layer 3 to be 20 mm or less, delay in solidification at the dissimilar material-filled layer 3 is suppressed, stress concentration locally on the solidified shell is prevented, and it is possible to suppress occurrence of surface cracks in the solidified shell. The equivalent circle diameter is calculated, assuming that the quasi-circle is a circle, from an area of a quasi-circular dissimilar material-filled layer 3.
(50)
(51) By configuring dissimilar material-filled layers 3 to a shape as shown in
(52) Preferably, the area ratio ε (ε=(B/A)×100), which is a ratio of the total sum B (mm.sup.2) of areas of all the dissimilar material-filled layers 3 to the area A (mm.sup.2) of the inner wall surface of the mold copper plate in a region where the dissimilar material-filled layers 3 are disposed, is 10% or more. By securing an area ratio ε of 10% or more, the area occupied by the dissimilar material-filled layers 3 with low heat flux is secured, and a difference in heat flux between the dissimilar material-filled layer 3 and the pure copper portion or copper alloy portion can be obtained. Thus, the effect of suppressing surface cracks in a cast piece can be stably obtained. Although the upper limit of the area ratio ε may not be necessarily specified, when the area ratio ε is 50% or more, the effect of suppressing surface cracks in a cast piece due to the periodic difference in heat flux is saturated. Therefore, an upper limit of 50% is sufficient.
(53)
(54) Regarding continuous casting of a cast piece by using a continuous casting mold configured as described above, the mold is suitably used for, in particular, continuous casting of a cast slab (thickness: 200 mm or more) of medium carbon steel having a carbon content of 0.08 to 0.17% by mass, which is highly susceptible to surface cracks. Hitherto, in the case where a cast slab of medium carbon steel is continuously cast, in order to prevent surface cracks in the cast piece, the cast-piece drawing speed has been generally decreased. By using the continuous casting mold according to this embodiment, surface cracks in a cast piece can be suppressed. Therefore, even at a cast-piece drawing speed of 1.5 m/min or more, a cast piece free from surface cracks or with a very small number of surface cracks can be continuously cast.
(55) As described above, in a continuous casting mold including dissimilar material-filled layers 3 on an inner wall surface of a water-cooled copper mold, since the shape of a recessed portion 2 forming each dissimilar material-filled layer 3 at the surface of the mold copper plate is, at an arbitrary position of the recessed portion, a curved surface having a curvature in every direction, concentration of stress does not occur on the surface of the mold copper plate in contact with the dissimilar material-filled layer 3. Therefore, occurrence of cracking in the mold copper plate can be suppressed, and the number of usable times of the continuous casting mold including the dissimilar material-filled layers 3 can be greatly extended.
(56) The above description has been given on continuous casting of a cast slab. However, this embodiment is not limited to continuous casting of a cast slab, but can also be applied to continuous casting of a cast bloom or cast billet.
Examples
(57) 300 tons of medium carbon steel (chemical composition, C: 0.08 to 0.17% by mass, Si: 0.10 to 0.30% by mass, Mn: 0.50 to 1.20% by mass, P: 0.010 to 0.030% by mass, S: 0.005 to 0.015% by mass, and Al: 0.020 to 0.040% by mass) was continuously cast using water-cooled molds made of a copper alloy in which dissimilar material-filled layers were formed on inner wall surfaces thereof under various conditions. Tests were carried out to check the number of surface cracks in cast slabs after casting and the number of occurrences of cracking on the surfaces of the mold copper plates (Examples and Comparative Examples). The water-cooled molds made of a copper alloy used had an inner space in which the length of the long side was 1.8 m and the length of the short side was 0.22 m. For comparison, tests were also carried out on a water-cooled mold made of a copper alloy in which dissimilar material-filled layers were not formed (Conventional Example).
(58) In each of the water-cooled molds made of a copper alloy, the length from the upper end to the lower end of the mold was 950 mm, the position of a meniscus (upper surface of molten steel in the mold) during steady casting was set to be 100 mm lower than the upper end of the mold, and dissimilar material-filled layers were disposed in a region from a position 60 mm lower than the upper end of the mold to a position 400 mm lower than the upper end of the mold.
(59) A copper alloy having a thermal conductivity of 360 W/(m×K) was used as the mold copper plates, and pure nickel (thermal conductivity: 90 W/(m×K)) was used as the filler material for the dissimilar material-filled layers. The opening shape of each recessed portion at the inner wall surface of the mold long-side copper plate was set to be circular or elliptic. Recessed portions formed with various average radii of curvature were filled with pure nickel by a plating process to form dissimilar material-filled layers. Table 1 shows the minimum opening width d of the recessed portion, the average radius of curvature R, and the shape of the filled portion. In Examples 19 and 20, the opening shape of each recessed portion is circular, and the shape of the filled portion is spherical crown-shaped with a flat surface bottom.
(60) TABLE-US-00001 TABLE 1 ½ × Number index Minimum Minimum Average Number density of cracking on opening opening radius of of surface the surface of width width curvature cracks in cast mold copper d d/2 R piece plate (mm) (mm) (mm) Shape of filled portion (number/m.sup.2) (—) Conventional — — — — 1.23 1.00 Example Example 1 5.0 2.5 3.0 Spherical crown-shaped 0.21 0.90 Example 2 6.0 3.0 3.1 Spherical crown-shaped 0.19 1.10 Example 3 6.0 3.0 4.0 Spherical crown-shaped 0.18 1.20 Example 4 7.0 3.5 5.0 Spherical crown-shaped 0.22 0.80 Example 5 8.0 4.0 6.0 Spherical crown-shaped 0.23 0.90 Example 6 10.0 5.0 5.5 Spherical crown-shaped 0.20 1.00 Example 7 6.0 3.0 3.2 Spherical crown-shaped 0.21 1.00 Example 8 12.0 6.0 6.2 Spherical crown-shaped 0.18 1.10 Example 9 4.0 2.0 2.5 Spherical crown-shaped 0.22 1.20 Example 10 6.0 3.0 3.5 Spherical crown-shaped 0.21 1.00 Example 11 3.0 1.5 2.0 Spherical crown-shaped 0.23 0.90 Example 12 6.0 3.0 2.5 Spherical crown-shaped 0.23 1.00 Example 13 6.0 3.0 6.5 Spherical crown-shaped 0.65 0.95 Example 14 5.0 2.5 2.0 Spherical crown-shaped 0.23 0.91 Example 15 10.0 5.0 3.0 Spherical crown-shaped 0.24 1.02 Example 16 7.0 3.5 8.1 Spherical crown-shaped 0.45 0.93 Example 17 8.0 4.0 9.0 Spherical crown-shaped 0.46 0.99 Example 18 4.0 2.0 1.9 Spherical crown-shaped 0.20 1.02 Example 19 12.0 6.0 6.2 Spherical zone-shaped with 0.19 1.12 a flat surface bottom having a diameter of 6 mm Example 20 5.0 2.5 2.0 Spherical zone-shaped with 0.24 0.94 a flat surface bottom having a diameter of 2 mm Comparative 5.0 2.5 — Cylindrical 0.78 1.23 Example 1 Comparative 6.0 3.0 — Quadrangular prismatic 0.82 1.32 Example 2 Comparative 8.0 4.0 — Triangular prismatic 0.79 1.35 Example 3 Comparative 4.0 2.0 — Cylindrical 0.76 1.42 Example 4 Comparative 7.6 3.8 — Cylindrical 0.83 1.32 Example 5
(61) After completion of continuous casting, an area of 21 m.sup.2 or more on the surface of a cast slab after casting was checked by a dye penetrant test, the number of surface cracks with a length of 1.0 mm or more was measured, and by dividing the total sum thereof by the measured area of the cast piece, a number density of surfaces cracks in the cast piece was obtained. By using the number density, the occurrence state of surface cracks in the cast piece was evaluated. After completion of continuous casting, the number of cracks on the surface of the mold copper plate was measured to evaluate the mold life. Table 1 also shows the investigation results of the number density of surface cracks in cast slab and the number index of cracking on the surface of the mold copper plate. The number index of cracking on the surface of the mold copper plate was calculated by dividing the measured number of cracks by the number of cracks measured in Conventional Example.
(62)
(63)
(64) On the other hand, among Examples, in the case where the average radius of curvature R of the recessed portion is more than ½ of the minimum opening width d of the recessed portion and in the case where the average radius of curvature R of the recessed portion is ½ or less of the minimum opening width d of the recessed portion, as shown in
(65) In Table 1, although there is a slight variation, the number index of cracking on the surface of the mold copper plate differs depending on the magnitude relationship between the average radius of curvature R of the recessed portion and ½ of the minimum opening width d of the recessed portion. In Table 1, in the case where the average radius of curvature R of the recessed portion is ½ or less of the minimum opening width d of the recessed portion, in 3 out of 4 examples, the number index of cracking is equal to or more than that of Conventional Example, while in the case where the average radius of curvature R of the recessed portion is more than ½ of the minimum opening width d of the recessed portion, in 7 out of 14 examples, the number index of cracking is equal to or more than that of Conventional Example. Thus, it is evident that, by setting the average radius of curvature R of the recessed portion to be more than ½ of the minimum opening width d of the recessed portion, it is possible to further reduce the occurrence of cracking on the surface of the mold copper plate. As is evident from these results and the results of