Initially Solidified Shell Growth of Hypo-peritectic Carbon Steel in Continuous Casting Mold

Abstract

The occurrence of longitudinal surface cracks in hypo-peritectic carbon steel slabs depends largely on the cooling capacity of the mold and the flow velocity of molten steel below the meniscus. The influence of both flow velocity of the molten steel below the meniscus and the heat flux in the copper mold were examined using continuous casting tests and numerical simulation of the molten steel flow. The casting speed was fixed, and the meniscus flow velocity was controlled by adjusting the port size of the submerged entry nozzle. The molten steel flow velocity was predicted by a three-dimensional unsteady-state numerical simulation. Heat flux in the copper mold was calculated based on temperature readings from thermocouples arranged in the direction of both the mold width and mold length. When the difference in flow velocity of molten steel in the mold width direction became large, longitudinal surface cracks occurred in the central region of the slab. In these cases, the heat flux below the meniscus in the mold width direction was not constant. Small holes were drilled along the central region of the mold width. This decreased both the heat flux and tensile strength of the central region of the slab width, and successfully reduced the occurrence of longitudinal surface cracks.

1. Introduction

Hypo-peritectic carbon steel is widely used in the automobile and construction industries due to the material’s excellent strength. However, continuously cast slabs are prone to the development of longitudinal surface cracks. Understanding and controlling the growth mechanism of the initially solidified shell in the continuous casting mold are essential for minimizing the occurrence of surface cracks. A peritectic reaction takes place during the solidification of hypo-peritectic carbon steels, and the growth mechanism of the solidified shell is complex and difficult to understand.

The mechanism of non-uniform deformation^{1,2,3,4,5,6,7,8,9,10)} during initial shell solidification and the effects of heat flux in the mold on shell growth^{11,12,13,14,15)} have been studied. Longitudinal surface cracks in hypo-peritectic carbon steel slabs result from non-uniform solidification of the shell just below the meniscus of the mold. However, the factors contributing to the development of longitudinal surface cracks that occur at the center of the wide face of the hypo-peritectic carbon steel slabs are not fully understood. The relationship between solute redistribution behavior during solidification as well as the generation behavior of both tensile strength¹⁶⁾ and density¹⁷⁾ have been studied, revealing the mechanisms involved in the solidification of hypo-peritectic carbon steel. Furthermore, it has been established that higher velocities of molten steel lead to a lower growth velocity of the solidified shell.^3,8,18) It is thought that initial solidification of the shell in the mold is influenced by the molten steel flow.

This study aimed to investigate the effects of heat flux in the mold and the flow velocity of molten steel just below the meniscus on the development of longitudinal surface cracks in hypo -peritectic carbon steel slabs. An experimental machine was used to perform continuous casting, which could vary the discharge velocity from the port of the submerged entry nozzle at a fixed casting speed. To avoid the development of longitudinal surface cracks in the slabs, continuous casting was performed using a mold which could vary the cooling capacity in the mold width direction. The molten steel flow and the stress of the shell were predicted using numerical simulations. The relationship between the longitudinal surface cracks, heat flux in the mold and velocity of the molten steel flow below the meniscus was evaluated.

2. Experiment Procedures

2.1. Continuous Casting Mold

Figure 1 shows the schematic diagram of the mold used in the continuous casting tests. Small holes were drilled on the N-side of the mold to control its cooling capacity. The influence of the flow velocity of the molten steel on the development of longitudinal surface cracks was examined on the S-side of the mold, which had no holes. The effect of the small holes in decreasing longitudinal surface cracks was examined on the N-side of the mold.

Fig. 1.

Positions of thermocouples in the continuous casting mold.

Small holes of 5.0×10⁻³ m in diameter and 2.5×10⁻¹ m in depth were drilled at a 1.0×10⁻² m spacing down the center line of the mold width (see Figs. 1(b), 1(c)). The holes were arranged in front of the cooling slits (see Fig. 1(d)). The thermal resistance of the mold was increased while the heat flux was decreased. To obtain the accurate temperature measurements within the copper mold, K-type coated thermocouples with an outer diameter of 2.0×10⁻³ m and grounded at the tip were used. The response time of each thermocouple was 1.0×10⁻¹ s. The thermocouples were arranged along the center of the mold’s width at a depth of either 2.0×10⁻³ m or 7.0×10⁻³ m. Additional thermocouples were arranged at other positions on the mold surface at a depth of 2.0×10⁻³ m only, due to limited space in the mold. Heat flux was calculated based on the temperature gradient between 2.0×10⁻³ m and 7.0×10⁻³ m. The depth of the thermocouples is represented as shaded and unshaded points in Fig. 1(a). Temperature distribution in the mold width direction and heat flux in the mold was evaluated using the temperature measurements at 4.5×10⁻² m below the meniscus. Temperature distribution and heat flux were evaluated at the positions of center, 1/4W and 3/4W of the mold width.

The experimental conditions for continuous casting are given in Table 1. The flow velocity of the molten steel below the meniscus was adjusted using the port size of the submerged entry nozzle, which varied the average discharge velocity from the nozzle. The average discharge velocity was the volume of molten steel discharging from the port of the nozzle per second divided by the cross-sectional area of the port. The casting speed was assumed to be affected by the change in velocity. This influences the thickness of the solidified shell in the mold. To avoid a change in the thickness of the solidified shell, the casting speed was kept constant. The heat flux was calculated based on its relationship with the temperature measured within the mold. Numerical simulations of heat conduction in the mold were performed for varying heat flux at the mold surface. The physical properties used for the numerical simulations are listed in Table 2. The two-dimensional heat transfer in the copper mold, containing cooling slits and small holes, was calculated. It was assumed that the small holes were filled with air. The temperature of the back side of the copper mold, which was in contact with the back frame, as well as the temperature of the cooling water was measured.

Table 1. Experimental conditions.

case		A	B	C	D
steel composition (mass%)		0.11%C-0.10%Si-0.48%Mn-0.02%P-0.008%S
mold cavity (mm)		100×800
casting speed (m·min−1)		2.0
nozzle	port size (mm)	35×60	35×36	30×30	25×25
	discharge velocity (ms−1)	0.6	1.0	1.5	2.0
	depth (mm)	180
	downward angle (°)	30

Table 2. Physical properties for calculation.

parameter	value	ref.
thermal conductivity of shell (Wm−1K−1)	33.0	27)
specific heat of shell (Jm−3K−1)	5.73×106	27)
latent heat of shell (Jm−3)	1.93×109	28)
thermal conductivity of copper mold (Wm−1K−1)	393	29)
specific heat of copper mold (Jm−3K−1)	3.0×106	29)
density of copper mold (kgm−3)	8.94×103	29)
temperature of copper mold contact with back frame (K)	303	–
thermal conductivity of air in small hole (Wm−1K−1)	2.41×10−2	30)
specific heat of air (Jm−3K−1)	1.0×103	30)
density of air (kgm−3)	6.52×10−1	30)
temperature of cooling water (K)	303	–
heat transfer coefficient between water and mold in cooling slit (Wm−2K−1)	2.3×104	31)
liquid temperature of steel (K)	1800	27)
solidus temperature of steel (K)	1764	27)
thermal conductivity of molten steel (Wm−1K−1)	35.0	27)
viscosity coefficient of molten steel (kgm−1s−1)	6.1×10−3	32)
Young’s modulus (MPa)	4400	26)
Poisson’s ratio (–)	0.38	26)
work hardening coefficient (MPa)	20	26)

Figure 2 shows the relationship between the calculated heat flux and temperature at 2.0×10⁻³ m from the mold surface. When the heat flux at the mold surface was constant, the temperature at the thermocouple position of the N-side (with small holes) of the mold was higher. When the temperature was constant, the heat flux of the N-side was smaller. The heat flux based on the thermocouple measurements at 2.0×10⁻³ m from the mold surface (4.4×10⁻² m from the mold center) was compared with the heat flux based on the temperature difference between 2.0×10⁻³ m (4.4×10⁻² m from the mold center) and 7.0×10⁻³ m depth (6.4×10⁻² m from the mold center) in the case of test case C. This comparison was used to evaluate the validity of the simulations. The calculated results were highly correlated, as shown in Fig. 3. Thus, the heat flux from the numerical simulation based on the temperatures at 2.0×10⁻³ m was reliable.

Fig. 2.

Relationship between heat flux in the mold and temperature at 2.0×10⁻³ m from mold surface.

Fig. 3.

Comparison between heat flux by numerical calculation and heat flux by thermocouple.

Prior to the inclusion of small holes in the mold, a numerical simulation of the heat conduction in the mold was conducted to avoid non-uniform cooling. This enabled the selection of the suitable number and position of the holes. An example of the calculated temperature profile in the cross section of the copper mold with a heat flux of 3.0 MWm⁻² at the mold surface is given in Fig. 4. The isothermal lines were distorted around the small holes. However, the temperature distribution between the surface and the hole was flat, indicating that the cooling capacity of the N-side of the mold was uniform.

Fig. 4.

Calculated temperature profile in the copper mold (a) with holes and (b) without holes.

The thickness of the initially solidified shell was evaluated by immersing Fe–S alloy lumps in the molten steel in the tundish during casting. Plate-like samples were taken from the continuous cast slabs and the thickness of the initially solidified shell in the mold was measured using a sulfur print test.

2.2. Analysis of Molten Steel Flow

The port size of the submerged entry nozzle was adjusted to vary the flow velocity of the molten steel below the meniscus. The relationship between the flow velocity and frequency of longitudinal surface cracks on the slabs was investigated. The molten steel flow was calculated using the non-steady three-dimensional fluid flow simulation with solidification. The turbulent flow was considered by the Large Eddy Simulation method.^19,20,21) The basic equations were the following:

equations of energy:   

$$\frac{\partial T}{\partial t}+\frac{\partial \left(u_{i}T\right)}{\partial x_i}=\frac{k_0}{\rho C_p}\frac{\partial }{\partial x_i}\frac{\partial T}{\partial x_j}+\frac{\mathrm{\Delta }H}{c_p}\frac{\partial f_S}{\partial t}$$(1)

  

$$f_S=\frac{T_L-T}{T_L-T_S}$$(2)

equation of continuity   

$$\frac{\partial u_i}{\partial x_i}=0$$(3)

equations of momentum   

$$\begin{array}{l}{\displaystyle \frac{\partial u_i}{\partial t}}+{\displaystyle \frac{\partial \left(u_i{u}_j\right)}{\partial x_i}}\\ =-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial p}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_i}}\left({\mu }_0+{\mu }_t\right)\left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}}\right)+\beta \left(T-T_L\right) g_i\end{array}$$(4)

  

$$S_{ij}=\frac{1}{2}\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)$$(5)

  

$${\mu }_t={\left(C_S\mathrm{\Delta }\right)}^2\left|S\right|\hspace{1em}\mathrm{\Delta }={\left(\mathrm{\Delta }x\mathrm{\Delta }y\mathrm{\Delta }z\right)}^{\frac{1}{3}}\hspace{1em}{C}_S=1.0\hspace{1em}\left|S\right|={\left(2S_{ij}{S}_{ji}\right)}^{\frac{1}{2}}$$(6)

Here, T: temperature (K), f_S: fraction of solid (–), t: time (s), u_i: velocity in i (= x, y, z) direction (ms⁻¹), P: pressure (Pa), and Δi: mesh size of i (= x, y, z) (m).

Heat flux values within the mold calculated based on the temperature measurement were used for the boundary condition of the solidified shell, as discussed below. Heat flux at the lower end of the mold was used as the boundary condition for the lower side of the mold. The physical properties used for numerical simulations are given in Table 2. The molten steel from the upper part of the submerged entry nozzle was assumed to flow out from the bottom of the slab, where the length was 5.0 m and operated at a casting speed 2.0 m·min⁻¹.

2.3. Analysis of Thermal Stress

Longitudinal surface cracks in the steel slabs are caused by the tensile stress along the width of the solidifying shell. To evaluate the tensile strength, thermal-stress analysis was conducted considering the boundary conditions of the heat flux.

Elasto-plastic and solidification analysis models were developed for the mold and the solidifying shell, as shown in Fig. 5. The 8 nodes of isoparametric quadrilateral elements, comprising 1600 elements for the two-dimensional cross section of the mold and the solidifying shell, were used to analyze the deformation behavior using a finite element method.^22,23,24,25) A time interval of 1.0×10⁻³ s was used due to the rapid formation of the solidified shell. The two-dimensional cross section of the solidifying shell was assumed to develop in the direction of casting from the meniscus, and the heat flux obtained from the experiments was used as a boundary condition.

Fig. 5.

Boundary conditions for elasto-plastic and solidification analysis for (a) the mold and (b) the solidifying shell.

The non-steady state heat transfer equation used for solidification analysis of the initially solidified shell and the heat conduction of the mold was:   

$$\left[\mathrm{K}\right]\left\{\mathrm{\Phi }\right\}+\left[\mathrm{C}\right]\left\{\mathrm{\Delta }\mathrm{\Phi }\right\}=\left\{\mathrm{F}\right\}$$(7)

where, {Φ}: vector of nodal temperature, {F}: vector of heat flux, [K]: matrix of heat conduction, and [C]: matrix of heat capacity. The latent heat during solidification was accounted for in the matrix [C] by using the equivalent specific heat method. The cooling behavior of the solidified shell was determined using the thermal boundary conditions between the shell and chill plate. These conditions were taken in the vector {F} as a product of heat flux.

The constituent equation used for the thermal-stress analysis was:   

$$([{\mathrm{k}}^{\mathrm{e}}]+[{\mathrm{k}}^{\mathrm{p}}])\left\{\mathrm{\Delta }\mathrm{d}\right\}=\left\{{\mathrm{f}}^{\mathrm{s}}\right\}+\left\{{\mathrm{f}}^{\mathrm{v}}\right\}+\left\{{\mathrm{f}}_{\mathrm{t}}^{\mathrm{e}}\right\}+\left\{{\mathrm{f}}_{\mathrm{t}}^{\mathrm{p}}\right\}$$(8)

where, [k^e]: elastic matrix, [k^p]: plastic matrix, {Δd}: vector of nodal displacement, {f^s}: vector of nodal load by surface force, {f^v}: vector of nodal load by volume force, {f_t^e}: elastic component of the nodal load by thermal strain and {f_t^p}: plastic component of the nodal load by thermal strain.

Numerical simulations for solidification and thermal-stress were calculated based on the physical properties listed in Table 2. It was assumed that the solidified shell was an elasto-plastic body and that the mold was a rigid body. The deformation of the solidified shell did not progress to the mold side and the shell was restrained. As the solidified shell was elasto-plastic in the thermal stress analysis and the transition from elastic to plastic followed the von Mises yield criterion, friction between the solidified shell and the mold was ignored. The boundary between the solidified shell and the molten steel was loaded with static pressure. Solidification analysis was performed first, and the thermal stress analysis was initiated once the nodal temperature of the shell surface corresponded to a solid fraction value of 0.8. The thermal stress was dependent on the physical properties at high temperatures, such as the tensile strength and the linear expansion coefficient, and it was necessary to use physical properties for the hypo-peritectic carbon steel. The density¹⁶⁾ and the tensile strength¹⁷⁾ used are provided in Fig. 6. Other properties were treated as constant values to investigate the influence of the tensile strength and density.

Fig. 6.

Change in phase of fraction, density and tensile strength with temperature for hypo-peritectic carbon steel.

3. Results and Discussion

3.1. Effect of Molten Steel Flow on Surface Crack

3.1.1. Cooling Capacity in the Mold Width Direction

Figure 7 shows the temperature distribution in the direction of the copper mold width at 4.5×10⁻² m below the meniscus, when the port size of the submerged entry nozzle changes. Unshaded points indicate the average temperature on the S-side of the mold (no holes). The N-side of the mold, in which holes were drilled, was shown as shaded points. The temperatures were measured using thermocouples at 2.0×10⁻³ m from the mold surface. The temperatures on the S-side reached a maximum at 1.5×10⁻¹ m to 2.6×10⁻¹ m and −1.5×10⁻¹ m to −2.6×10⁻¹ m from the mold center. The center of the mold was found to have the lowest temperature. A decreased submerged entry nozzle port area resulted in a higher flow velocity from the port, and the difference between the maximum value and the minimum temperatures largely increased.

Fig. 7.

Temperature profile in the direction of mold width at 4.5×10⁻² m from the meniscus in (a) case A, (b) case B, (c) case C and (d) case D. Points indicate average temperature, lines indicate maximum and minimal temperature.

The heat flux profile on the S-side of the mold was analyzed at 4.5×10⁻² m below the meniscus along the mold width, as shown in Fig. 8. Maximum heat flux values were observed in the ranges 1.5×10⁻¹ m to 2.6×10⁻¹ m and −1.5×10⁻¹ m to −2.6×10⁻¹ m from the mold, while the heat flux at the center showed the minimum value. A smaller nozzle port area led to higher flow velocity, which contributed to a higher difference in heat flux.

Fig. 8.

Heat flux profile in the direction of mold width at 4.5×10⁻² m from the meniscus in (a) case A, (b) case B, (c) case C and (d) case D. Points indicate average heat flux, lines indicate maximum and minimal heat flux.

3.1.2. Cooling Capacity of the Mold in the Casting Direction

Figure 9 shows the measurement results of temperatures for the S-side mold in the direction of casting at 2.0×10⁻³ m from the surface of the mold.

Fig. 9.

Temperature profile in the direction of casting of S-side mold at (a) 4.4×10⁻² m from mold center, (b) 2.6×10⁻¹ m and (c) −2.6×10⁻¹ m from the mold center.

The temperature profile at 4.4×10⁻² m from the center of the mold width demonstrated that the temperature decreased with increasing distance from the mold top, as shown in Fig. 9(a). The temperatures in the direction of casting at 2.6×10⁻¹ m and −2.6×10⁻¹ m from the center of the mold width are given in Figs. 9(b) and 9(c), respectively. The temperature decreased with increasing the distance from the mold top. The temperatures increased at 3.0×10⁻¹ m from the top, which was due to the discharge velocity from and the high temperatures of the submerged entry nozzle.

Figure 10 shows the change in the heat flux of the S-side of the mold in the direction of casting. The heat flux profile at 4.4×10⁻² m from the center of the mold width indicated that the meniscus had the maximum value, which decreased with increasing distance from the mold top, as shown in Fig. 10(a). The heat flux profile in the direction of casting at 2.6×10⁻¹ m and −2.6×10⁻¹ m is shown in Figs. 10(b) and 10(c), respectively. Again, the heat flux was observed to decrease with an increasing distance. Similarly, the heat flux increased at 3.0×10⁻¹ m from the top, due to the discharge velocity and the high temperatures of the submerged entry nozzle.

Fig. 10.

Heat flux profile in the direction of casting of S-side mold at (a) 4.4×10⁻² m from mold center, (b) 2.6×10⁻¹ m and (c) −2.6×10⁻¹ m from the mold center.

3.1.3. Longitudinal Cracks on the Slab Surface

The generation behavior of the longitudinal surface crack on continuous casting steel slabs was studied, whereby the position and length of the cracks were measured. Before measurement, the scales adhering to the slab surface were removed using a wire brush.

The longitudinal surface crack index is the value of the total length of the cracks divided by the slab length. Figure 11 shows the relationship between the longitudinal surface crack index and the distance from the center of the slab width. When the discharge velocity from the port of the submerged entry nozzle was 0.6 ms⁻¹, a small index was measured on the S-side of the mold, as shown in Fig. 11(a). As shown in Figs. 11(b) and 11(c), an increased discharge velocity resulted in a greater occurrence of surface cracks around the central region of the slab width. This clearly demonstrates that the formation of surface cracks on the slabs was affected by the discharge flow velocity from the submerged entry nozzle. An increased discharge flow velocity resulted in an increased flow velocity below the meniscus, as was predicted by the numerical simulation.

Fig. 11.

Relationship between index of longitudinal surface crack and distance from center in (a) case A, (b) case B, (c) case C and (d) case D.

3.1.4. Flow Velocity of Molten Steel in the Mold

Thermal boundary conditions were required for the numerical simulation of fluid flow during solidification. The heat flux of the wide face of the mold was interpolated to obtain a representative mold temperature based on the heat flux shown in Figs. 8 and 10. The heat flux distribution used as a boundary condition for the numerical simulation is given in Fig. 12. Thermocouples were arranged in the direction of casting at 4.4×10⁻² m from the center of the mold width, but not at −4.4×10⁻² m. However, it was assumed that the temperature distribution was symmetrical and that the temperatures at both points were equal. The temperature distribution was converted into heat flux distribution using the relationship given in Fig. 2. The temperature distribution on the narrow face of the mold was predicted based on the gradient of the temperature from the top to the bottom of the wide face of the mold, and temperature distribution was converted to heat flux distribution. The heat flux beneath the mold was substituted by the heat flux at the bottom of the mold for both the wide and narrow faces.

Fig. 12.

Heat flux profile in the mold for the numerical simulation.

The molten steel flow pattern was calculated at the central vertical section of the slab thickness at 600 s after beginning the calculation from the meniscus to 1.3 m, as shown in Figs. 13(a)–13(d). The discharge flow from the port of the submerged entry nozzle was divided into upward flow and downward flow when it reached the narrow face of the mold. The upward flow turned toward the direction of the submerged entry nozzle below the meniscus. This behavior remained constant when the discharge velocity changed. At high discharge velocity, the molten steel flow below the meniscus was easy to turbulent.

Fig. 13.

Flow field at the half thickness of slab in (a) case A, (b) case B, (c) case C and (d) case D.

Figures 14(a)–14(d) show the calculated flow pattern of the molten steel in the horizontal section at 4.5×10⁻² m from the meniscus at 600 s after beginning the calculation. The molten steel flowed from the submerged entry nozzle to the narrow face of the mold, where the direction of the flow was almost parallel to the wide face of the mold near the mold surface. However, the direction of the molten steel flow was not always parallel to the wide face in the central region of the mold cavity. When the discharge velocity increased, the molten steel flow tended to become turbulent.

Fig. 14.

Flow field at 4.5×10^-2 m below the meniscus in (a) case A, (b) case B, (c) case C and (d) case D.

The difference of temperature between 4.4×10⁻² m and 1.5×10⁻¹ m from the center of the mold width was dependent on the discharge velocity from the submerged entry nozzle. An increased discharge velocity led to a higher flow velocity below the meniscus. Therefore, the relationship between the discharge velocity and flow velocity below the meniscus was examined. The relationship between the maximum flow velocity parallel at the solidified shell interface and the discharge flow velocity from the submerged entry nozzle, specifically at both 4.4×10⁻² m and 1.5×10⁻¹ m from the center of the mold, was found to be directly proportional, as shown in Fig. 15. A high discharge velocity resulted in a higher flow velocity parallel to the solidification interface. Thus, the velocity at the center of the mold width was lower than the velocity at 2.0×10⁻¹m, as the molten steel could not easily flow between the mold and submerged entry nozzle.

Fig. 15.

Relationship between calculated maximum velocity parallel to mold wide face and discharge velocity from submerged entry nozzle.

As shown in Fig. 8, the heat flux profile exhibited a concave shape in the center of the mold where the longitudinal surface crack index was high. The curve became more concave with increasing discharge velocity. Furthermore, the flow velocity below the meniscus decreased at the center of the mold. The difference in the flow velocity below the meniscus increased at higher discharge velocities at the center, as shown in Fig. 15.

Figure 16 shows the relationship between the difference in heat flux of the S-side and the difference in the velocity parallel to the mold wide face. The maximum difference in heat flux was found between 4.4×10⁻² m and 1.5×10⁻¹ m from the center of the mold width. The maximum difference in the flow velocity was found between 4.4×10⁻² m and 1.5×10⁻¹ m from the center of the mold width. The difference in heat flux increased with an increasing the difference in the flow velocity of the molten steel below the meniscus.

Fig. 16.

Relationship between difference in heat flux and difference in velocity parallel to mold wide face between 4.4×10⁻² m and 1.5×10⁻¹ m from mold center.

Figure 17 shows the relationship between the index of total longitudinal surface cracks and the difference in the heat flux in case of the S-side mold. The maximum difference in heat flux was found between 4.4×10⁻² m and 1.5×10⁻¹ m from the center of the mold width. The index of total longitudinal surface cracks increased with an increasing difference in the heat flux.

Fig. 17.

Relationship between total index of longitudinal surface crack and difference in heat flux between 4.4×10⁻² m and 1.5×10⁻¹ m from the mold center of the S-side mold.

3.2. Effect of Small Holes in the Mold

3.2.1. Cooling Capacity in the Mold Width Direction

The temperature profile along the mold width direction at 4.5×10⁻² m below the meniscus on the N-side of the mold (with holes) is shown in Fig. 7. The temperature in the central region of the mold increased. However, the temperature of the area on the side at which holes had not been drilled did not increase and showed similar behavior to the S-side of the mold (no holes). This clearly demonstrated that the temperature in the mold increased due to the presence of the holes.

The heat flux profile in the mold width direction at 4.5×10⁻² m below the meniscus in the region with small holes is shown in Fig. 8. Even with holes, the heat flux became lower at the center of the mold width. The heat flux of the N-side was smaller than that of the S-side, but the difference at the center of the mold width between the N-side and S-side was small. This was due to an increase in discharge velocity from the port of the submerged entry nozzle. The holes tended to decrease heat flux due to an increased thermal resistance and a decreased temperature gradient. The region in which heat flux was decreased was limited to the area where the holes had been drilled, even if the flow velocity from the port varied.

3.2.2. Cooling Capacity of the Mold in the Casting Direction

Figure 18 shows the measurement results of the temperature at 2.0×10⁻³ m from the mold surface in the direction of casting in case A. The temperature profile at 4.4×10⁻² m from the center of the mold width revealed that the temperature deceased when moving further from the meniscus on both the N-side and S-side of the mold, as shown in Fig. 18(a). The temperature of the region on the N-side with the small holes was higher than that on the S-side. Instead, the region on the N-side without holes exhibited temperatures similar to those on the S-side. These findings demonstrated that the area affected by the small holes was limited. The temperatures in the direction of casting at 2.6×10⁻¹ m and −2.6×10⁻¹ m from the center for the N-side and S-side are given in Figs. 18(a) and 18(b), respectively. There were no holes at either of these positions. The temperatures were almost identical, further demonstrating that the rise in temperature could be limited to the areas in which the small holes were placed.

Fig. 18.

Temperature profile in the mold for casting direction of case A at (a) 4.4×10⁻² m, (b) 2.6×10⁻¹ m and (c) −2.6×10⁻¹ m from the mold center.

The heat flux profile in the direction of casting at 4.4×10⁻² m from the center demonstrated that the heat flux of the N-side (with holes) was smaller than that of the S-side (no holes) within the area from the top of the mold to a depth of 2.0×10⁻¹ m, as shown in Fig. 19(a). This confirmed that there was a mild cooling effect on the N-side of the mold. In the area of the N-side devoid of holes, there was no difference in the heat flux between the N-side and S-side. The heat flux profiles in the direction of casting at 2.6×10⁻¹ m and −2.6×10⁻¹ m from the center are provided in Figs. 19(b) and 19(c). There were no holes at either of these positions, which led to similar heat flux values, and there was no difference in cooling capacity. The use of small holes was found to control the cooling capacity in the copper mold only in confined areas.

Fig. 19.

Heat flux profile in the mold for casting direction of case A at (a) 4.4×10⁻² m, (b) 2.6×10⁻¹ m and (c) −2.6×10⁻¹ m from the mold center.

3.2.3. Longitudinal Cracks on the Slab Surface

The relationship between the longitudinal surface crack index and the distance from the center of the slab width is shown in Fig. 11. At lower discharge velocities, such as 1.0 and 1.5 ms⁻¹, surface cracks did not occur in the N-side slab. However, slight cracks began to form when the discharge velocity was increased to 2.0 ms⁻¹. The occurrence of longitudinal surface cracks was suppressed when the heat flux was decreased due to the small holes in the central area of the copper mold near the meniscus.

3.3. Growth Behavior of the Solidified Shell

The effectiveness of the small holes in decreasing the heat flux and the thickness of the initially solidified shell was measured. The relationship between the thickness of the initially solidified shell at 1/2W and 1/4W of the slab width and time (square root) for case A is illustrated in Fig. 20, where the region of the N-side with the small holes was shown. The regression lines of 0.15 min^0.5 were used, and corresponded to a casting length of 4.5×10⁻² m. The thickness of the solidified shell at 1/2W of the slab width increased with as time progressed. However, the thickness of the solidified shell on the N-side (with holes) was smaller than that on the S-side (no holes) until 0.15 min^0.5, and the growth velocity on the N-side decreased. Beyond 0.15 min^0.5, it was observed that the differences between the N-side and S-side became minimal. Furthermore, there was no difference in the shell thickness between the N-side and S-side at any point in time at 1/4W of the slab width, and the thickness of the solidified shell increased with time. The growth rate of the solidified shell was large until 0.15 min^0.5, after which the growth rate became small and the deviation of the thickness became large.

Fig. 20.

Relationship between shell thickness at initial stage of solidification and time of case A at (a) 1/2W and (b) 1/4W of the mold width.

The growth velocity of the initially solidified shell between the N-side and S-side was compared by evaluating the solidification constant until 0.15 min^0.5, and a difference in the shell thickness was observed. The solidification constant of the initially solidified shell at 1/2W of the slab width for the N-side and S-side is given in Fig. 21(a). The solidification constant corresponds to the gradient of the regression line in Fig. 20. The solidification constant on the N-side was smaller than that of on the S-side due to the mild cooling from the holes. The solidification constant of the initially solidified shell at 1/4W of the slab width was almost the same for the N-side and S-side, as there were no holes in these regions, as shown in Fig. 21(b).

Fig. 21.

Solidification constant at initial stage of solidification at (a) 1/2W and (b) 1/4W of the mold width.

Figure 22 shows the thickness of the solidified shell in the direction of the slab width at 4.5×10⁻² m, 1.0×10⁻¹ m and 1.5×10⁻¹ m from the meniscus in the half region of the slab width.

Fig. 22.

Relationship between shell thickness and distance from mold center of case A at (a) 4.5×10⁻² m, (b) 1.0×10⁻¹ m and (c) 1.5×10⁻¹ m below the meniscus.

The thickness of the solidified shell on the S-side was thicker than that on the N-side at 4.5×10⁻² m from the meniscus, as shown in Fig. 22(a). The submerged entry nozzle was located near this position in the mold cavity and the distance between the shell and the submerged entry nozzle became narrow. Therefore, the velocity of molten steel flow decreased and the amount of superheated molten steel was reduced. This caused an increased cooling and the shell became thicker. However, with sufficient heat supply from the molten steel outside the region of the nozzle, the thickness of the solidified shell became thinner. Around the submerged entry nozzle, the thickness of the solidified shell of on the N-side (with holes) became thinner than the S-side, while there was little difference in the thickness between the two sides further from the nozzle. The small holes on the N-side close to the submerged entry nozzle contributed to the decreased growth rate of the solidified shell. As shown in Figs. 22(b) and 22(c), the differences in shell thickness between the N-side and S-side were not observed at 1.0×10⁻¹ m and 1.5×10⁻¹ m from the meniscus, likely due to the lack of holes on both sides. The growth of the solidified shell was only suppressed by the small holes in the area from the meniscus to 4.5×10⁻² m. Thus, holes were found to be effective in decreasing the heat flux in the central region of the mold, and contribute to minimizing longitudinal surface cracks in hypo-peritectic carbon steel slabs.

3.4. Stress Sate in the Solidified Shell

Tensile strength and thermal-stress analyses were conducted to determine the boundary conditions for the heat flux calculations. The analysis was conducted according to the heat flux distribution of case D in Fig. 12.

Figure 23 shows the distribution of stress in the solidified shell in the direction of the slab width at 4.5×10⁻² m below the meniscus. As shown in Fig. 6(c), a tensile strength of 3.5 MPa at the solidus temperature was assumed to be the critical value for surface crack generation in the slab.

Fig. 23.

Stress distribution in the direction of slab width at 4.5×10⁻² m below the meniscus on the (a) S-side mold and (b) N-side mold.

Figure 23(a) shows the stress distribution in the solidified shell on the S-side. A tensile strength of 3.5 MPa in the direction of the slab width was observed in the central region. This value at ±2.0×10⁻¹ m from the center corresponded to the range in which the surface cracks were observed, as shown in Fig. 11(d).

Figure 23(b) shows the stress distribution in the solidified shell on the N-side. Compared with the S-side of the slab, the critical value for the generation of surface cracks was decreased.

Overall, the tensile strength corresponding to the critical value of crack formation for hypo-peritectic carbon steel was located at 4.5×10⁻² m below the meniscus in the central region of the slab width.

3.5. Generation and Control of the Longitudinal Surface Cracks of the Hypo-peritectic Carbon Steel Slab

The solidified shell that formed at 4.5×10⁻² m under the meniscus became thick in the central region of the slab width, particularly in the region of the mold cavity near the submerged entry nozzle. The distance between the mold and submerged entry nozzle became narrow, which restricted the flow velocity of molten steel and the heat supply from molten steel. This led to a more rapid growth of the solidified shell. As a result, the thickness of the solidified shell became non-uniform in the direction of the slab width, which contributed to tensile stress in the central region of the shell. These factors contributed to the formation of longitudinal surface cracks.

In areas where a gap between the mold and solidified shell was formed due to the deformation of the shell, the heat flux in the mold decreased, particularly in the central region at 4.5×10⁻² m under the meniscus. Deformation of the initially solidified shell occurs at approximately 0.5 s after solidification.¹¹⁾ The results suggest that the solidified shell reached 4.5×10⁻² m from the meniscus at about 1.4 s after casting. Thus, deformation had occurred within this time frame.

Controlling the growth of the initially solidified shell from the meniscus to 4.5×10⁻² m in the central region of the slab width was found to be essential in avoiding the development of longitudinal surface cracks in the hypo-peritectic carbon steel slab. Therefore, it is necessary to decrease the heat flux and encourage mild cooling in the central region of the mold width. To change the cooling capacity of the mold, small holes were drilled along the central region of the copper mold. The use of small holes near the meniscus was found to be effective. This slowed the growth of the solidified shell and led to a more uniform thickness.

4. Conclusions

To improve the surface quality of continuously cast slabs in the hypo-peritectic carbon range, it is important to avoid the formation of longitudinal surface cracks in the central region of the slab width. It is thought that these cracks depend on both the cooling capacity of the mold and the flow velocity of molten steel below the meniscus. In this study, to eliminate the influence of a continuous casting speed of the slabs, the experiments were conducted at various discharge velocities from the submerged entry nozzle under a fixed casting speed condition. Moreover, to change the cooling capacity of the mold, small holes were arranged in the central region of the copper mold. From both the experimental results of the continuous casting test and the numerical simulation for the flow velocity of molten steel and the stress of the shell, the following results are obtained.

(1) The temperature profile in the mold width direction below the meniscus was not uniform, and the temperature at the central region of the mold width was lower than that at both 1/4W and 3/4W of the width. The heat flux profile in the mold width direction was also not uniform, where the heat flux at the central region was lower than that at both 1/4W and 3/4W of the width. Small holes led to a local temperature increase and heat flux decrease in the central region of the mold width.

(2) In the direction of casting, the temperature in the copper mold was highest at the meniscus. When small holes were arranged in the copper mold, the temperature was elevated locally, and heat flux decreased.

(3) Small holes encouraged the uniformity in the thickness of the solidified shell in the mold width direction below the meniscus.

(4) The longitudinal surface crack index of the slabs became large when the discharge velocity from the submerged entry nozzle was large, particularly when the difference in heat flux in the mold width direction was also large. Heat flux differences were dependent on the difference in the flow velocity in the mold width direction. Small holes decreased the occurrence of the longitudinal surface cracks. According to the thermal-stress analysis, the tensile strength in the direction of the slab width decreased.

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