Influence of heat flux different between wide and narrow face in continuous casting mould on unevenness of hypo-peritectic steel solidification at off-corner

Abstract

The effects of the difference of the heat flux between the wide face and narrow face of the mould, the mould taper, casting speed and cooling rate on unevenness of hypo-peritectic steel at the off-corner in the mould, which leads to longitudinal cracking, bleeding and breakout during continuous casting, were evaluated by a finite element model (FEM) simulation and a plant test with a commercial continuous caster. The simulation results show that an increase in the difference in the heat flux between the wide and narrow face increases the off-corner unevenness of solidification because the solidified shell on the low heat flux side is pulled toward the high heat flux side. The analysis results were in good agreement with the plant test results. These results revealed the importance of optimizing the heat flux ratio between the wide face and narrow face mould even under a high casting speed condition.

Introduction

In recent years, both high slab quality and high productivity have been required in continuous casting. Surface cracking of slabs during continuous casting is a serious problem. In particular, longitudinal cracks on the slab surface cause not only slab quality deterioration during high-speed casting, but also operational trouble such as bleeding and breakout [1–4]. It has been reported that slab longitudinal cracking occurs in hypo-peritectic steel (C = 0.09–0.17 wt-%) due to deflection of the solidified shell during the δ to γ transformation in the initial stage of solidification in the mould [5–11]. One of the primary uses of mould flux is to prevent uneven solidification and longitudinal cracking by stabilizing the heat transfer between the solidified shell and the mould [12–14]. It is also known that not only uneven solidification but also the air gap between the shell and the mould greatly affect the growth of the solidified shell and uneven solidification in the vicinity of the corner, leading to longitudinal cracking and bleeding in the vicinity of the slab corner. Since the mould taper value greatly affects shell growth and uneven solidification, the mould taper values of the wide side and narrow side need to be optimized corresponding to solidification shrinkage [15,16]. In order to minimize air gap formation between the solidified shell and the mould, which is more important in high-speed casting, a multi-tapered mould has been developed for the narrow side mould [17]. Kim et al. [18] reported that the difference in the heat flux between the wide side mould and the narrow side mould, as well as the mould taper, affected the unevenness of the solidified shell with complex solidified shell deformation in the vicinity of the corners, leading to longitudinal cracking, bleeding as shown in Figure 1. In high-speed casting, the unbalanced flow in the mould, the heat flux in the mould, and the variation of heat flux in the mould width direction become large [19,20], and the heat flux difference between the wide side mould and the narrow side mould also becomes large, which can result in further deterioration of the unevenness of solidification near the mould corner. However, there have been few reports on the influence of the difference of the heat flux of the wide side mould and the narrow side mould on the air gap between the solidified shell and the mould and the solidification behaviour in the vicinity of the corner. Therefore, in this study, a FEM analysis and experiment in the continuous casting machine were carried out in order to evaluate the effects of the heat flux difference between the wide side and narrow side of the mould, the taper value of the mould, the casting speed, and the cooling rate of the solidified shell in the mould on the air gap formation, the solidified shell deformation behaviour and the unevenness in the solidified shell near the corner in the mould during continuous casting.

Figure 1.

Example of solidified shell structure near corner in mould where severe crack and bleeding occurred [18].

Mathematical model

The heat transfer calculation and the calculation of the solidified shell deformation in the mould were carried out for a Fe-0.1 wt-% C hypo-peritectic steel with the commercial FE package ABAQUS. Figure 2 shows schematic illustrations of the heat transfer and solidified shell deformation models. The calculations were performed on a two-dimensional quarter cross-section of a slab 252 mm in thickness and 1000 mm in width with a regular square mesh [21].

Figure 2.

Schematic illustration of (a) heat transfer model and (b) solidified shell deformation model in the mould.

Heat transfer model

The temperature distribution in the solidified shell shown in Figure 2(a) was calculated by two-dimensional unsteady state heat transfer conduction by a heat transfer equation and a heat transfer boundary condition, i.e. (1) (2) where is heat capacity (J (kg·K)^–1), is density (kg m^–3), is the thermal conductivity of steel [15.9 + 0.01151 T W (m·K)^–1] [22], T is temperature (K), t is time (s), x and y are the distance in the width direction in the mould (m) and the distance from the strand surface (m), respectively, n is an outward-facing normal to the strand surface, and q(t) is the time-dependent heat flux on the strand surface (W m^–2).

The latent heat (ΔH [272.1 J g^–1] [23]) effect is considered by the apparent heat capacity method given by (3) (4) where T_L and T_S are the liquidus and solidus temperatures, which were calculated using the TCFE6 database of Thermo-Calc [24]. The initial temperature of the liquid steel was set to T_L + 10 K. The heat flux profiles measured by Kanazawa et al. [2] were used as the input heat flux values. Kanazawa measured the heat flux occurring when using different mould fluxes at a position 45 mm below the meniscus during continuous casting. In this study, the measurements for a high heat flux (mould flux A: q _MF-A (basicity = 0.95)) and low heat flux (mould flux B: q _MF-B (basicity = 1.22)) expressed by the casting speed were converted to the heat flux profiles expressed by the transit time from the meniscus [11,25]. Note that it was confirmed that there were no changes after 5 s in either q _MF-A or q _MF-B as shown in Figure 3. Since the heat flux distribution in the mould shown in Figure 3 is not a measured result near the corner in the mould, the influence of the air gap between the mould and the solidified shell cannot be considered. Therefore, the heat flux expressed by the following Equations (5) to (10), which can be calculated using the results of the gap values between the mould and the solidified shell obtained in each solidified shell deformation calculation step, was used in Figure 2(a). When the gap ( ) between the mould and the solidified shell at both the wide side and the narrow side of the mould is larger than the average mould flux film thickness ( ) determined from mould flux consumption, the calculation is performed under the condition of coexistence of the mould flux and an air gap ( ) [26].

Figure 3.

Heat flux as a function of transit time from the meniscus for mould flux A and mould flux B [11].

The average mould flux film thickness used in this study was calculated based on the relationship between the casting speed and the consumption of mould flux A and mould flux B, respectively, as reported by Kanazawa et al. [2] In this calculation, the solidified shell, air gap, mould flux film, and mould are considered as the heat transfer resistance in the mould [11]. The expressions for the heat flux of the narrow side and wide side moulds are shown in Equations (5) and (6). (5) (6)

The thermal resistance and without an air gap in the mould are expressed by Equations (7) and (8). (7) (8)

Further, the thermal resistance and on the wide side and the narrow side with the formation of an air gap can be expressed by Equations (9) and (10) [11]. (9) (10) where is the heat flux on the narrow side mould with an air gap (W m^–2), is the heat flux on the wide side mould with an air gap, is the temperature of water in the mould (298 K), i and j are constants, is the total thermal resistance on the narrow side mould without an air gap (m²K W^–1), is the total thermal resistance on the wide side mould without an air gap (m²K W^–1), is the baseline heat flux on the narrow side mould without an air gap (W m^–2), is the baseline heat flux on the wide side mould without an air gap (W m^–2), are the thermal resistivities of the solidified shell without an air gap on the narrow and wide side moulds (m²K W^–1), are the thermal resistivities of the mould flux on the narrow and wide side moulds (m²K W^–1), are the thermal resistivities of the mould on the narrow and wide side moulds (m²K W^–1), are the thermal resistivities of the air gap on the narrow and wide side moulds (m²K W^–1), and are the thermal resistivities of the solidified shell with an air gap on the narrow and wide side moulds (m² K W^–1).

are calculated from the conduction component from the air gap height at each node as and the radiation component between the mould and solidified shell. Where is the air gap height and is the thermal conductivity of air. The values of and were determined by performing additional heat transfer simulations without an air gap as (10a) (10b) where and are the shell surface temperatures at each site on the narrow and wide side moulds (K).

In order to evaluate the influence of the heat flux difference between the narrow side mould and the wide side mould on the solidification unevenness of the corner, the baseline heat flux ratio of the narrow side mould (

) to the that of the wide side mould (

) given in Figure 3 was defined as R, as expressed by Equation (11). (11)

The thermophysical properties of the steel used in these model calculations are summarized in Table 1.

Table 1.

Thermophysical properties of steel used in the heat-transfer model.

Symbol	Property	Value
C_p	Heat capacity	0.68 (kJ kg^–1 K^–1) [22]
ρ	Density	7360 (kg m^–3) [23]
k	Thermal conductivity	15.9 + 0.01151T (W m^–1 K^–1) [22]
ΔH	Latent heat	272.1 (J g^–1) [23]

Mechanical model of solidified shell deformation

A shell deformation static analysis of the two-dimensional cross section shown in Figure 2(b) was performed under the same conditions as the width, thickness, mesh size, and number of meshes used in the heat transfer calculation. A pressure P (Pa) is applied at the boundary between the liquid and the solidified shell corresponding to the ferrostatic pressure, as expressed by Equation (12). (12) where is gravitational acceleration (m s^–2), v_c is the casting speed (m s^–1), and Z is the distance from the meniscus (m).

The elastic modulus was based on the experimental data of Mizukami et al. [27] was used, and Poisson's ratio was assumed to be 0.3. In the experiment by Mizukami et al. [27], the elastic modulus of Fe–0.08%C–0.19%Si–0.66%Mn–0.019%P was measured. This composition can be regarded as hypo-peritectic steel from the equivalent carbon content (C_eq = 0.10 wt-%), considering the effects of the various elements proposed by Xu et al. [28] to predict if a steel exhibits peritectic behaviour.

The strain rate dependent plasticity constitutive equation expressed by Equation (13) was used to predict the temperature and strain-rate dependence on flow stress [29]. (13) (14) where , , and m are constants, R is the gas constant (J (K·mol)^–1), Q is the activation energy for deformation (J mol^–1), K is the strength coefficient, n is the strain hardening exponent, is the effective plastic strain, and is the effective plastic strain rate (1/s). The values of , , Q, and m in and are taken from Han et al. [30]. A rule of mixtures is used to calculate the effective yield stress of the / composite. Here, it should be noted that the constitutive behaviour of the liquid metal was characterized by using a low elastic modulus (100 MPa) and a high yield stress (100 GPa) to ensure low stress levels and no plastic strain accumulation in the liquid metal region [31]. A flowchart of this calculation model is shown in Figure 4. First, the thermal simulation is initiated to extract heat from the surface of the solidified shell. Second, the velocity of the wide face mould (V_W ) and narrow face mould (V_N ) is given to each mould according to the taper values (M_TN and M_TW ) of the narrow side mould and the wide side mould shown in Equations (15) and (16), respectively, and the solidified shell deformation calculation is performed using the temperature distribution. (15) (16) where is the mould width at the top of the mould (m), is the mould width at the bottom of the mould (m), L is the mould length (m), is the mould thickness at the top of the mould (m), and is the mould thickness at the bottom of the mould (m).

Figure 4.

Flowchart of calculation procedure.

Note that friction between the solidified shell and the mould was neglected in this model for simplicity. The heat flux was calculated considering the size of the gap between the solidified shell and the mould obtained from the solidified shell static deformation calculation expressed by Equations (5) to (10), and the result was used as the heat flux for the next step of the heat transfer calculation. The calculation was carried out under the conditions that the time step of the calculation was 0.1 s, the length from the meniscus to the bottom of the mould was 800 mm, and the casting speed (V_c ) was 1.5, 3.0, or 5.0 (m min^–1).

Further, this model also considers the effect of the cooling rate on the density and thermal expansion resulting from the to transformation. The evolution of amount of during the to transformation was calculated in order to estimate the average density and thermal expansion coefficient. The model employed is the one-dimensional model of carbon diffusion in the phase proposed by Konishi et al. [25]. In this model, the carbon diffusion in the gamma phase is expressed by (17) where is the carbon concentration in the phase, and is the diffusion coefficient of carbon in (m² s^–1) [32].

The key assumptions of the model are that undercooling below the peritectic temperature is negligible, carbon diffusion is controlling for the growth of the phase, the grain size is assumed to correspond to the primary dendrite-arm spacing and this can be linked to the cooling rate as where and CR are given in (µm) and (K s^–1) [33], the carbon concentration within the δ phase is uniform, and a local equilibrium exists at the δ/γ interface is used as where is the equilibrium carbon concentration of the gamma phase at temperature T. Based on the results of the calculated volume fraction of and the linear shrinkage of the solidified shell as a function of temperature with different cooling rates, it has been reported that the cooling rate affects the density and coefficient of thermal expansion [11]. In particular, the solidified shell near the mould corner has a large cooling rate, and the cooling rate dependence of the density and coefficient of thermal expansion can be important for the evaluation of the solidified shell deformation on the off-corner in the mould.

In this calculation and the experiment, the unevenness near the corner of the narrow side ( ) and wide side ( ) mould in solidification expressed by Equations (18) and (19) were evaluated. The unevenness in the solidified shell was defined as being within 50 mm from the corner because the part where solidification is most retarded is within 50 mm from the corner and there is no change in the solidified shell thickness over 50 mm from the corner on either the wide side or the narrow side. (18) (19) where is the solidified shell thickness on the wide side (at x = 50 mm) (mm), is the minimum solidified shell thickness on the wide side (mm), is the solidified shell thickness on the narrow side (at y = 50 mm) (mm), and is the minimum solidified shell thickness on the narrow side (mm).

Experimental method

Next, an experiment was conducted under the experimental continuous casting conditions shown in Table 2. The chemical compositions of the steels were Fe–(0.08–0.13)%C–0.20%Si–(0.80–1.45)%Mn–0.01%P–0.002%S of the hypo-peritectic steel range (C_eq [28] = 0.13–0.16 wt-%), the continuous casting speed was 1.5 m min^–1, the basicity of the mould flux was 0.92, and the wide side mould taper M_TW and the narrow side mould taper M_TN were 0.9–1.1%/m. The slab thickness and width were 250 and 2100 mm, respectively. After the casting experiment, slab samples were cut, and

and

were evaluated by measuring the white band [34] on the cut surface revealed by etching with picric acid. The white band can be formed at the solidified shell-liquid interface continuously at off-corner in the cross section perpendicular to the casting direction due to the discharge flow from the submerged entry nozzle and reverse flow on the narrow side mould. Although heat flux in the mould and mould temperature can be measured by installing the thermocouples in the mould [35], it is difficult for continuous measurement and continuous evaluation of shell thickness behaviour along width direction at off-corner because each thermocouple can not be installed continuously along width direction in the mould. Therefore, in this study, the observation of the white band in the slab samples was adopted as a method for evaluation of

and

Table 2.

Casting conditions.

Steel grade	Fe–(0.08∼0.13)%C–0.20%Si–(0.80–1.45)%Mn–0.01%P–0.002%S
Equivalent carbon content [28] (wt-%)	0.13–0.16
Casting speed (m min^–1)	1.5
Slab size (mm)	250 × 2100
Mould taper (%/m)	M _Tw = M _TN = 0.9∼1.1
Basicity of mould flux	0.95

Furthermore, a comparison with and without longitudinal cracks caused by uneven solidification in the vicinity of the mould corner was also carried out. R was obtained by calculating the heat fluxes in the mould [36] from the results of temperature measurements 50 mm below the meniscus using thermocouples embedded in the centre of the width of the wide side mould and the centre of the thickness of the narrow side mould.

Results and discussion

Effect of narrow side mould taper

In the present heat transfer calculation, as described above, the calculations were carried out under the condition that both the mould flux and an air gap can coexist between the mould and the solidified shell. Figure 5 shows the result of a preliminary evaluation of the effect of the heat transfer in the gap between the mould and the solidified shell on the unevenness of the solidified shell near the mould corner. Three cases were evaluated: existence of only the air gap, existence of only the mould flux as determined from the consumption of mould flux, and coexistence of the air gap and the mould flux in the gap part. The figure shows the unevenness near the corner of the narrow side mould in solidification ( ) at 100, 300, 500 and 800 mm below the meniscus under the conditions of M_TW = 0%/m, M_TN = 1.1%/m, V_c = 1.5 m min^–1 and R = 1.0. Under these three calculation conditions, σ _N deteriorates in the order of only air gap, coexistence of mould flux and air gap, and only mould flux, and the influence is especially large in the vicinity of the meniscus. When an air gap is generated between the mould and the solidified shell, the air gap is considered to greatly affect the solidified shell growth, (i.e. the unevenness of the solidified shell) because the thermal conductivity of air is remarkably smaller than that of mould flux [6,37]. The following calculation results show the results under the condition where the mould flux and the air gap coexist. Figure 6 shows the transition of the solidified shell temperature and the shell deformation near the corner at 100, 300, 500, and 800 mm below the meniscus, and Figure 7 shows , , , and of the corner as a function of the transit time from the meniscus under the conditions of mould flux A (M_TW = 0%/m, M_TN = 1.1%/m, V_c = 1.5 m min^–1 and R = 1.0). Here, the deformation geometry of the solidified shell in Figure 6 has been enlarged by 5 times. In the upper part of the mould, a gap is generated between the mould and the solidified shell in the vicinity of the corner, and the gap on the wide side mould increases in the lower part of the mould due to the smaller taper (M_TW = 0%/m) of the wide side mould. These behaviours in the gap between the mould and the solidified shell are in good agreement with the previous calculation results for M_TW = 0%/m [21,30]. The difference between and or and shown in Figure 7 corresponds to the influence of the air gap between the mould and the solidified shell.

Figure 5.

σ_N as a function of distance from the meniscus with only an air gap, air gap + mould flux, and only mould flux (mould flux A, M_TW = 0%/m, M_TN = 1.1%/m, V _c = 1.5 m min^–1, R = 1.0).

Figure 6.

Deformed geometries of solidified shell and air gap at (a) 100 mm, (b) 300 mm,(c) 500 mm, and (d) 800 mm from meniscus (mould flux A, M_TW = 0%/m, M_TN = 1.1%/m, V _c = 1.5 m min^–1, R = 1.0).

Figure 7.

, , , and of the corner as a function of transit time from the meniscus (mould flux A, M_TW = 0%/m, M_TN = 1.1%/m, V_c = 1.5 m min^–1, R = 1.0).

Figure 8 shows the relationship between the narrow side mould taper M_TN and the air gap thickness between the corner solidified shell and the narrow side mould (a) or the wide side mould (b) in the case of mould flux A, M_TW = 0%/m, V_c = 1.5 m min^–1, and R = 1.0. When M_TN decreases, the air gap thickness on the narrow side mould becomes larger, and the air gap on the wide side mould becomes smaller. Thus, the taper on the narrow side mould affects not only the narrow side mould but also the air gap thickness on the wide side mould. Figure 9 shows the effect of the mould flux on the relationship between M_TW and at 300 mm below the meniscus under the conditions of M_TW = 0%/m, V_c = m min^–1, and R = 1.0. Kim et al. [18] reported that the origin of bleeding was at a position about 300 mm below the meniscus due to the uneven solidification which occurred in the vicinity of the corner of the narrow side mould due to the heat flux difference between the wide side and narrow side moulds. Since the results in Figure 7 also indicated that the thickness of the air gap at the corner of the narrow side mould became large at a position about 300 mm below the meniscus, the evaluation in this paper focuses especially on the position 300 mm below the meniscus. In the case of strong cooling (mould flux A), increases and decreases with decreasing M_TN corresponding to the air gap behaviour. On the other hand, under the mild cooling condition (mould flux B), increases when M_TN is decreased to 0.6%/m, but under the same taper condition, greatly decreases as a result of mild cooling, and also decreases in comparison with strong cooling with mould flux A. It is considered that tends to be larger than with both mould fluxes because M_TW is smaller than M_TN . In the case of mould flux A with M_TN of less than 1.0%/m, the solidified shell formation on the narrow side was suppressed by the large air gap between the mould and the solidified shell corresponding to the small heat flux.

Figure 8.

Air gap thickness at (a) narrow face corner and (b) wide face corner as a function of the mould taper of the narrow face (mould flux A, M_TW = 0%, V_c = 1.5 m min^–1, R = 1.0).

Figure 9.

Influence of mould taper of the narrow face on σ_N and σ_W 300 mm from the meniscus with mould flux A and mould flux B (M_TW = 0%, V_c = 1.5 m min^–1, R = 1.0).

Effect of wide side mould taper

Figure 10 shows the relationship between the wide side taper and or at 100, 300, 500, and 800 mm below the meniscus at M_TN = 1.1%/m, V_c = 1.5 m min^–1, and R = 1.0 with mould flux A. Here, it was found that both and greatly decreased with increasing M_TN. From these results, it is considered that the wide side taper, as well as the narrow side taper, is effective for reducing uneven solidification near the corner.

Figure 10.

Influence of mould taper of the wide face on (a) σ_N and (b) σ_W at 100, 300, 500, and 800 mm from the meniscus (mould flux A, M_TN = 1.1%/m, V_c = 1.5 m min^–1, R = 1.0).

Effect of heat flux difference between wide and narrow sides

The influence of the heat flux difference ratio R between the wide side mould and the narrow side mould given by Equation (11) on the unevenness of the solidified shell near the corner was evaluated. Figure 11 shows the solidified shell temperature distribution and the shell deformation at 300 mm below the meniscus under the conditions of mould flux A, M_TW = 0%/m, M_TN = 1.1%/m, V_c = 1.5 m min^–1 and R = 0.70, 0.80, 0.90, 1.00, 1.11, 1.25, or 1.43. It is confirmed that this calculation results show a solidification retardation area near the corner due to the unevenness of solidified shell and this simulation results of solidified shell structure are similar to the actual macro structure where bleeding occurred during continuous casting shown in Figure 1. Figure 12 shows the average solidified shell temperature and the average solidified shell temperature difference within 50 mm from the corner on the narrow side and the wide side moulds. These results confirmed that the solidified shell temperature at the wide side increases with increasing R because of the smaller heat flux. Further, Figure 13 shows the total surface solidified shell deformation with shrinkage of the wide side mould along the x-direction and narrow side mould along the y-direction at different values of R. The amount of deformation in the x-direction increases with smaller values of R, whereas that in the y-direction increases with increasing R. From the results shown in Figures 11 and 12, it is found that the heat flux difference between the wide side and narrow side moulds affects the solidified shell deformation due to the shrinkage of the solidified shell. As the mechanism of this phenomenon, it is considered that the solidified shell is deformed in the direction of the larger heat flux side from the smaller heat flux side, and as a result, a gap is formed on the smaller heat flux side. Figure 14 shows the relationship between R and or under the conditions of mould flux A (M_TW = 0%/m, M_TN = 1.1%/m, V_c = 1.5 m min^–1) at 300 mm below the meniscus and mould flux B (M_TW = 0%/m, M_TN = 1.1%/m, V_c = 1.5 m min^–1 and M_TW = 0%/m, M_TN = 0.6%/m, V_c = 1.5 m min^–1) as an evaluation of the effect of the mould flux on uneven solidification due to a heat flux difference between the narrow side and the wide side moulds. It was found that both and can be reduced at all values of R by using mould flux B, that is, mild cooling, and uneven solidification can be further reduced by using the optimized taper. Figure 15 shows the temperature of the solidified shell corner at 0 mm to 300 mm below the meniscus under the conditions of mould flux A and mould flux B (M_TW = 0%/m, M_TN = 1.1%/m, V_c = 1.5 m min^–1, R = 1.0). It was found that the mild cooling mould flux (mould flux B) suppresses the reduction of heat flux, leading to a lower corner temperature at the position 300 mm below the meniscus, because the gap between the mould and the solidified shell is smaller than that under the strong cooling mould flux condition (mould flux A). Moreover, these results also confirmed that the maximum and minimum temperature differences in the solidified shell temperature gradient in the solidified shell at 50 mm from the corner at the position 300 mm below the meniscus were reduced from 41.9°C mm^–1 for the wide side mould and 45.5°C mm^–1 for the narrow side mould with mould flux A, to 34.9°C for the wide side mould and 34.9°C mm^–1 for the narrow side mould with mould flux B, respectively.

Figure 11.

Deformed geometries of solidified shell and air gap of (a) R = 0.70, (b) R = 0.80, (c) R = 0.90, (d) R = 1.00, (e) R = 1.11, (f) R = 1.25, and (g) R = 1.43 at 300 mm from the meniscus (mould flux A, M_TW = 0%/m, M_TN = 1.1%/m, V_c = 1.5 m min^–1).

Figure 12.

(a) Average solidified shell temperature within 50 mm of the corner on the narrow side mould and the wide side mould and (b) average solidified shell temperature difference within 50 mm from the corner on the narrow side and the wide side mould (mould flux A, M_TW = 0%/m, M_TN = 1.1%/m, V_c = 1.5 m min^–1).

Figure 13.

Total surface solidified shell deformation of (a) wide side mould along x direction and (b) narrow side mould along y direction (mould flux A, M_TW = 0%/m, M_TN = 1.1%/m, V_c = 1.5 m min^–1).

Figure 14.

Relationship between R and (a) σ_N and (b) σ_W with mould flux A and mould flux B at 300 mm from the meniscus (M_TW = 0%/m, V_c = 1.5 m min^–1).

Figure 15.

Relationship between distance from the meniscus and temperature with mould flux A and mould flux B (M_TW = 0%/m, M_TN = 1.1%/m, V_c = 1.5 m min^–1, R = 1.0).

Influence of casting speed

Next, the influence of the casting speed on uneven solidification within 50 mm of the corner was evaluated. Figure 16 shows the relationship between the casting speed v_c and or with mould flux A (M_TW = 0%/m, M_TN = 1.1%/m, R = 0.9, 1.0) at a transit time of 5 s from the meniscus. The time of 5 s corresponds to a minimum solidified shell thickness in the range of 1–2 mm, which leads to large uneven solidification, depression, and longitudinal cracking on the slab surface [1,9,38]. increased with increasing v_c , and became larger than with the increase of V_c because of the smaller wide side mould taper (M_TW = 0%/m). Figure 17 shows the relationship between the distance from the corner along the wide side mould at the transit time of 5 s below the meniscus and the temperature of the solidified shell surface. With increasing V_c , the temperature of the corner portion decreased and the shell temperature variation in the width direction increased. Larger uneven solidification and a larger air gap formed with the larger V_c caused by the smaller average mould flux film thickness (as determined from mould flux consumption), which resulted in a higher cooling rate as V_c increased. These results show that when V_c is increased, the degree of uneven solidification in the vicinity of the corner deteriorates. This result is consistent with the experimental result reported by Matoba et al. [17] that the number of longitudinal cracks in the vicinity of the corner increased due to an increase of V_c in an actual continuous casting machine. It was found that the surface temperature of the solidified shell shows a peak at the same position, corresponding to the position where the larger air gap is formed, and the temperature values are almost the same as at the transit time of 5 s below the meniscus independent of changes in the casting speed. This is thought to be due to the fact that the conditions of the taper values of both the wide and the narrow side mould and the baseline heat flux profile of both the wide and the narrow side mould as a function of transit time from the meniscus are the same, significantly affecting the solidified shell deformation and air gap formation.

Figure 16.

Influence of casting speed on σ_N and σ_W at 5 s from the meniscus (mould flux A, M_TW = 0%/m, M_TN = 1.1%/m).

Figure 17.

Relationship between distance from the corner along the wide side mould and the temperature of the solidified shell surface.

Plant test results

Figure 18 shows the heat flux of both the wide and narrow side moulds at 50 mm below the meniscus and each R conditions are given as indicated by the numbers in parentheses. Figure 19 shows the relationship between R and or in the both plant test and simulation results. Comparison of casting conditions between plant test and simulation in Figure 19 is shown in Table 3. and of plant tests were evaluated by the white band observation in the slab samples and it is confirmed that the distance between the white band and the surface of the slab samples in the plant tests were equivalent to the values of solidified shell thickness near the mould corner at 300 mm below the meniscus used for the calculation of or in the model calculations as shown in Figure 19. It was found that dramatically increases when R ≦ 0.8, corresponding to a smaller heat flux ratio of the narrow side mould to the wide side mould. Under that condition, longitudinal cracking due to uneven solidification occurs easily in the vicinity of the corner on the narrow side mould. This tendency is also consistent with the present model calculation results in which is increased by a decrease in R. Further, this test also confirmed that increased with increasing R. Based on the above results and considerations from the simulation and plant test, optimization of the heat flux difference between the wide side and narrow side moulds is required in order to suppress uneven solidification near the corner in the mould. Although this heat flux difference between the wide side and narrow side moulds can be affected by the unbalanced flow due to the molten steel flow and the mould flux infiltration during continuous casting, it is considered that the heat flux difference between the wide side and narrow side moulds can be controlled by optimizing the mould thickness, material, coating, and taper of both the wide side and narrow side.

Figure 18.

Relationship between heat flux of the wide and narrow side moulds at 50 mm below the meniscus.

Figure 19.

Relationship between R and σ_N or σ_W in the both plant test and calculation results.

Table 3.

Comparison of casting conditions between plant test and simulation in Figure 19.

	Plant test	Simulation
Steel grade	Fe–(0.08∼0.13)%C–0.20%Si–(0.80-1.45)%Mn–0.01%P–0.002%S	Fe–0.1%C
Equivalent carbon content [28] (wt-%)	0.13-0.16	0.1
Casting speed (m min^–1)	1.5	1.5
Slab size (mm)	250 × 2100	252 × 1000
Mould taper (%/m)	M_Tw = M_TN = 0.9∼1.1	M_Tw = 0, M_TN = 1.1
Basicity of mould flux	0.92	0.95

Conclusion

The effects of the heat flux difference between the wide side and narrow side of the mould, the taper value of the mould, the casting speed, and the cooling rate of the solidified shell in the mould on the air gap formation, the solidified shell deformation behaviour and the unevenness in the solidified shell near the corner in the mould were evaluated through a FEM analysis and plant tests using a commercial slab continuous caster. The results are summarized as follows.

Optimization of the taper values of both the wide side mould and the narrow side mould is important for reducing uneven solidification near the corner, as the taper values affect the solidified shell deformation on both the wide side and the narrow side.

At high casting speeds, the thickness of the mould flux infiltration in the gap becomes small, and it is considered that this condition causes increased solidification unevenness.

The heat flux difference between the wide side and narrow side moulds affects the solidified shell deformation due to the shrinkage of the solidified shell. The solidified shell is deformed in the direction of the larger heat flux side from the smaller heat flux side, and as a result, uneven solidification increases on the smaller heat flux mould side. This study also clarified the fact that mild cooling by using an appropriate mould flux is effective for decreasing this uneven solidification.

The heat flux difference between the wide side mould and the narrow side mould and the uneven solidification in the vicinity of the corner were evaluated by plant tests with a commercial slab continuous caster. It was found that longitudinal cracks were easily generated in the vicinity of the corner when the heat flux difference and uneven solidification between the wide side mould and the narrow side mould were large, and the agreement of the experimental results of the unevenness of the solidified shell with the results of the model calculations was confirmed. Based on the above results and considerations from simulation and plant test, the optimization of the heat flux difference between the wide side and narrow side moulds is required in order to suppress the uneven solidification near the corner in the mould.

Footnotes

Disclosure statement

No potential conflict of interest was reported by the author(s).

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