Investigation on the Solidification Structure of Q355 in 475 mm Extra-Thick Slabs Adopting Cellular Automaton-Finite Element Model

Abstract

The solidification structure characteristics are decisive for the production of extra-thick slabs. This study developed a solidification heat transfer model and a cellular automaton–finite element coupled model to investigate the solidification behavior and structure characteristics of a 475 mm extra-thick slab. The models were applied under various continuous casting process parameters and different alloy element content. The simulation results reveal that casting speed has the most significant effect on the solidification behavior of extra-thick slabs, surpassing the impact of specific water flow and superheat. The solidification structure characteristics of the 475 mm extra-thick slabs were investigated under various conditions. The findings indicate that at higher casting speeds and superheats, the average grain size increases and the grain number decreases. The average grain size initially decreases and then increases with the rise in specific water flow, reaching its minimum at approximately 0.17 L·kg⁻¹. Additionally, the average grain radius first decreases and then slightly increases with an increase in carbon content, achieving the minimum value of about 0.17% carbon. Compared with carbon and manganese, silicon has a greater impact on the solidification structure of ultra-thick slabs, and a moderate increase in silicon content can effectively refine the grain size. This study provides a theoretical foundation for understanding the changes in solidification structure characteristics and optimizing continuous casting process parameters for 475 mm extra-thick slabs.

1. Introduction

Extra-thick steel plates are primarily utilized in offshore engineering, the military industry, nuclear power, and high-rise buildings, among other critical technical equipment manufacturing fields [1,2]. It is a hot issue that the production of extra-thick steel plates using the ingot casting process results in a comparatively low metal yield. Given this situation, the continuous casting (CC) process is considered a more efficient method that contributes to energy saving and carbon reduction [3]. However, the CC process has numerous influencing factors, and the accessibility of the appropriate process parameters increases with the thickness of the slab, so the extra-thick slabs are prone to internal defects such as central segregation and porosity shrinkage [4,5]. The solidification structure characteristics determine the formation of the internal defects of slabs, the adequate improvement of which is a pivotal factor for the production of ultra-thick steel plates [6]. Furthermore, the wider equiaxed crystal zone in the center of the slab protects against the formation of mini-ingots, leading to severe V-shaped segregation and porosity shrinkage [7]. To some extent, the fluctuation of the alloy elements content, a non-negligible effect on the final solidification structure, also causes variations in the solidus temperature, liquidus temperature, and dendrite growth parameters [8]. Meanwhile, the tiny shrinkage holes in the slab are not wholly compressed in the subsequent rolling process, as the compaction ratio is limited. Also, hardly will the macroscopic chemical composition distribution maintain uniformity during the heat treatment process [9]. Therefore, it is essential for the realization of high-quality extra-thick slabs to explore the influence of CC process parameters and alloying element content on the solidification structure characteristics.

To date, numerous studies have been conducted on the effect of CC process parameters (e.g., superheat, casting speed, and specific water flow) on the solidification structure of slabs across a range of thicknesses [10,11,12]. The heat transfer rate in the primary and secondary cooling zones, the main factor influencing the local temperature gradient and solidification rate, is mainly determined by the CC process parameters during slab solidification. Additionally, Hunt et al. [13] concluded that the criterion for the columnar to equiaxed transition (CET) depends on both the temperature gradient and the solidification rate, which determines the distribution characteristics of the central equiaxial and columnar crystal zones in the billet. Unlike columnar crystals, equiaxed crystals have no specific direction in the growth process. Thus, the residual steel enriched with solute elements can be distributed relatively uniformly in the mushy zone, alleviating the central segregation of the slabs [14]. Zhang et al. [15] developed a macro-segregation model and a solidification structure model for 300 mm thick slabs, and the results showed that a lower superheat can reduce grain size, increase ECR, and lessen central segregation. Furthermore, Chen et al. [16] studied the microstructure of 400 mm extra-thick slabs by numerical simulation, and believed that the center ECR and the average grain size are little changed along with the change in casting speed and secondary cooling compared to superheat. In contrast to extra-thick slabs, however, the cooling intensity in the secondary cooling zone has a larger impact on the fluctuation of the solidification structure of the slab with common thickness. As for slabs with a thickness of 200 mm, Zhang et al. [17] found that reducing the specific water flow is conducive to enhancing the ECR of 24Mn steel slabs through a numerical–physical coupled simulation method. Sheng et al. [18] observed that the CET position near the corners of a 250 mm thick slab progressively moved towards the center of the slab and the ECR decreased due to the cooling intensity of the slab corners declining.

Also, the variations in the alloy element content have an essential influence on the thermophysical properties of the steel grade, which determines the solidification structure development of the slab with defined CC process parameters [8,19,20]. Cai et al. [21] concluded that the ECR initially increased and then decreased when the carbon (C) content was improved from 0.09% to 0.53%, and the ECR is at a peak at a C content of 0.3%. Moreover, the dendrite arm spacing is a fundamental feature parameter for characterizing the compactness degree of the solidification structure. Zhang et al. [22], through a combination of numerical simulations and experiments, found that decreasing the silicon (Si) and C content can reduce the spacing of secondary dendrite arms (SDAS) in slabs with a thickness of 295 mm, promoting the improvement of central segregation. Likewise, Li et al. [23] analyzed the relationships between Si, Cr, manganese (Mn) contents, and solidification structure based on the numerical simulations method for a 72 mm thickness slab. Yuan et al. [24] discovered that higher Mn and C contents would suffer from coarse solidification structure and carbide, which made it difficult to find suitable parameters for a continuous casting process, using various experimental methods for Mn13 steel slab with a 230 mm thickness. Gao et al. [19] developed the solidification structure model and SDAS model for a 370 mm extra-thick slab. It was found that the increase in Nb and V contents can refine the grain, and SDAS has enormous fluctuation with the elevation of Ti element contents. However, there are limited reports related to the influence of alloying element content on the solidification structure.

Analyzing the solidification structure evolution of billets through numerical simulation can save a huge amount of resources and time compared to traditional metallurgical analysis methods [25]. Current simulation methods for solidification structures include stochastic methods, deterministic methods, and phase-field methods [26]. Furthermore, the cellular automaton (CA) method is one of the stochastic methods, which has the physical background mechanism of dendrite tip growth kinetics and the characteristics of high simulation accuracy [27]. Combining it with the finite element (FE) model of macroscopic heat transfer contributes to handling nonlinearity and complexity problems [28]. Utilizing the cellular automaton–finite element (CAFÉ) model, Lu et al. [29] determined the optimal combination for temperature distribution and ECR within the specified parameter range of thin slab by cross-scale and full-process calculations. A unique CAFÉ analysis approach was suggested by Tan et al. [30] and is appropriate for the solidification structure simulation of 38CrMoAl large round bloom considering mold and final electromagnetic stirring. Nonetheless, the solidification structures simulated by the CAFÉ model are primarily billets, thin slabs, and round blooms, while there are relatively few simulations of ultra-thick slabs over 400 mm.

In addition, it is crucial to emphasize that the slab thickness is closely related to solidification structure characteristics. The bigger section size will give rise to slower solidification in the central region and longer local solidification times, which is more severe in comparison with the internal quality of the thin slabs [31]. Zhang et al. [32] compared the relationship between the solidification structure and central segregation of slabs with thicknesses ranging from 245 mm to 440 mm by numerical simulation. It was observed that the central segregation region and ECR are expanded with the increase in billet thickness. In addition, Xu et al. [33] analyzed the microstructure evolution with 420 mm extra-thick slab under different casting speeds, superheats, and specific water flow, and the findings provide strategic guidance for optimizing the CC process and alleviating the central segregation of extra-thick slabs. Currently, the maximum thickness of extra-thick slabs produced by the vertical curved continuous caster is up to 475 mm [34]. There is no doubt that the occurrence of internal defects in the slab obviously rises with the thickness of the casting slab. However, the study of the solidification behavior and solidification structure of extra-thick slabs with a thickness of 475 mm has not yet been reported.

In the present study, models for the solidification heat transfer and the cellular automaton–finite element of high-strength structural steel Q355 were established, with a section size of 475 mm × 2000 mm. The accuracy of these models was verified through nail penetration experiments, surface temperature measurements, and acid-etching tests. Moreover, the influence rules of various casting speeds, specific water flow, and superheats on the solidification behavior of extra-thick slabs were investigated in detail. Finally, the solidification structure characteristics of extra-thick slabs with different CC process parameters and alloy element content were calculated and analyzed. The outcomes from this study are expected to shed light on a better understanding of the changing characteristics of the solidification structure in 475 mm ultra-thick slabs, leading to a theoretical basis to achieve higher quality extra-thick steel plates.

2. Model Parameters and Method Descriptions

In this study, numerical simulation methods have been adopted to investigate the solidification process of an extra-thick slab with the advantages of rapidity, low cost, and visualization. Furthermore, the continuous casting process of slabs is dynamic and continuous. The solidification structure of billets evolves dynamically with the distance from the meniscus and the influence of the process parameters. Therefore, this paper simulated the solidification process of slabs using the slice-moving method to improve the computational efficiency of the model. The overall idea is described in Figure 1.

2.1. Experimental Material and Main Technological Parameters of CC

In this paper, the main chemical compositions of the high-strength structural steel Q355 supplied by a domestic steel plant are listed in

Table 1. The main chemical composition of the test steel.

Element	Fe	C	S	Mn	Si	P	Cr	Al	Ti
Concentration (wt.%)	97.9198	0.163	0.0042	1.525	0.286	0.021	0.021	0.044	0.016

. The thermal conductivity, enthalpy, solid fraction (the proportion of solid phase in the two-phase zone), and density were obtained from the material database of the ProCAST (version 13.5) software in accordance with the composition of the steel (the viscosity is neglected). The results of the obtained thermophysical parameters are shown in Figure 2. The liquidus and solidus temperatures are 1784 K and 1742 K, respectively.

2.2. Model Assumptions and Mesh Generation

The solidification heat transfer in extra-thick slabs is a remarkably complex non-stationary process, which makes the calculations difficult to realize and match in practice if all the details are taken into account. Therefore, the following assumptions are made to improve computational efficiency without losing precision [35]:

(1)

The slab volumetric shrinkage and the gravity effect are both ignored during the solidification;

(2)

The heat transfer along the casting direction is ignored, and it is also assumed that the heat transfer in the slab is two-dimensional;

(3)

The heat transfer of each part in the secondary cooling zone is uniform, and the heat transfer conditions on the fixed side and loose side are consistent;

(4)

The heat transfer in the mold is processed by the average heat flux;

(5)

The physical parameters of the slab vary only with temperature;

(6)

The equivalent handling of the effect of flow on heat transfer by increasing the thermal conductivity in the liquid-phase and mushy zones [36].

The main production conditions of the Q355 extra-thick slab are listed in

Table 2. Main technological CC process parameters.

Parameters	Value
Sectional dimension (mm2)	475 × 2000
The effective length of mold (m)	0.80
Caster radius (m)	12.10
Submerged entry nozzle type	Quick-change type
Casting speed (m·min−1)	0.45
Superheating (K)	21
Specific water flow (L·kg−1)	0.17

. Based on the above assumptions, the solidification process of the slab was calculated using the slice-moving method, with a 1/2 cross-section selected for modeling [22]. A computational domain of 1000 mm × 475 mm × 10 mm was created by the SolidWorks (version 2018) software, and then hexahedral meshes, 608,875 volume meshes, were carried out through the ProCAST software. In addition, in order to simulate the entire continuous casting process of the slabs from the mold, the secondary cooling zone to the air-cooling zone, the distance passed by the slab in each zone can be equated to the residence time of the casting slab in each zone, and then set up different heat transfer boundary conditions during the residence time. Nevertheless, the contact conditions of the slab and the mold wall had a more significant impact on the distribution of heat flux distribution; the molten steel in the mold, due to solidification shrinkage, will produce an air gap so that the heat transfer efficiency of the slab is drastically reduced. As shown in Figure 3, the meshes of the edges of the geometrical model were refined, and a rounded corner model was used to deal with the air gap problem at the corners of the extra-thick slab in order to ensure the accuracy of the simulation process [37].

2.3. Establishing the Solidification Heat Transfer Model

2.3.1. Governing Equations of Solidification Heat Transfer

The solidification heat transfer calculations in the ProCAST software are performed by the enthalpy method. The heat transfer governing equations are as follows [32]:

$${\displaystyle \frac{\partial }{\partial x}}\left(\lambda {\displaystyle \frac{\partial T}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(\lambda {\displaystyle \frac{\partial T}{\partial y}}\right)=\rho {\displaystyle \frac{\partial H}{\partial t}}$$

(1)

$$H={\displaystyle {\int }_0^T{C}_{p}dT+L\left(1-f_S\right)}$$

(2)

where λ is the thermal conductivity, W·m⁻¹·K⁻¹; ρ is the density, kg·m⁻³; L is the latent heat, J·kg⁻¹; f_s is the solid phase rate; c_p is the specific heat, J·kg⁻¹·K⁻¹; H is the enthalpy, kJ·kg⁻¹; and T is the local temperature, K.

2.3.2. Thermal Boundary Conditions Setting

The initial condition (i.e., the casting temperature) is given by Equation (3):

$$T_0=T_1=1805 \mathrm{K}$$

(3)

where T₀ is the initial temperature, K; and T₁ is the casting temperature, K.

In order to simplify the analysis, the heat loss of the free surface is neglected due to the protective slag on the free surface playing a role in adiabatic heat preservation. The instantaneous heat flux distribution proposed by Savsge et al. [38] is used in the mold:

$$q_m=\left(2.688-B\sqrt{\mathrm{t}}\right)\times {10}^3$$

(4)

$$B={\displaystyle \frac{3}{2\sqrt{l/v}}}\left(2.688\times {10}^3-q_a\right)$$

(5)

where q_m is the heat flux of the mold, kW·m⁻²; B is a coefficient related to mold cooling conditions, kW·m⁻²·s^−1/2; t is the residence time of molten steel in the mold, s; q_a is the broadface (or narrow face) average heat flux, 898.15 (or 979.28) kW·m⁻²; l is the length of mold, 0.8 m; and v is the casting speed, m·s⁻¹. The foot roller section, secondary cooling zone, and air-cooling zone are water spray cooling, air-mist cooling, and radiation heat transfer, respectively. The boundary conditions and the parameters of the secondary cooling zone are shown in

Table 3. Related parameters and boundary conditions of the secondary cooling zone.

Cooling Zone		Length/(m)	Water Flow Rate/ (L·min−1)	Computational Formula
Secondary Cooling Zone	Foot roll section (N)	1.82	78.20	$h=\alpha \cdot \left[581W^{0.541}(1-0.0075T_w)\right]$ [39]
	Foot roll section (W)	1.09	126.00
	II	2.02	76.40	$h=\beta \cdot \left[0.35+0.13W\right]$ [39]
	III	3.52	75.10
	IV	5.08	74.70
	V	7.13	34.80
	VI	9.19	27.70
	VII	13.53	29.30
	VIII	18.08	22.50
	IX	20.37	9.20
	X	25.51	18.60
Air cooling Zone	/		$q=\epsilon \sigma (T_b^4-{T_{amb}}^4)$
			$\epsilon =0.85/[1+exp{\left(42.68-0.02682T_b\right)}^{0.0115}]$ [40]

. h is heat transfer coefficient of slab, kW·m⁻²·K⁻¹; W is the water flow rate, L·m⁻²·s⁻¹; α and β represent the correction factors, and the value is 0.9; T_w is the temperature of cooling water, K. ε is the radiation coefficient; σ is Stefan–Boltzmann constant, 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴; T_b is the strand surface temperature, K; and T_amb is the ambient temperature, K.

2.4. Establishing the Solidification Structure Model

2.4.1. Nucleation Model

A continuous heterogeneous nucleation model based on the normal distribution proposed by Rappaz and Gandin et al. [41,42] is adopted, and the relationship between the nucleation density and the undercooling obeys the following law:

$$n\left(\mathsf{\Delta }T\right)={\displaystyle {\int }_0^{\mathsf{\Delta }T}\frac{dn}{d\left(\mathsf{\Delta }T\right)}d\left(\mathsf{\Delta }T\right)}$$

(6)

$${\displaystyle \frac{dn}{d\left(\mathsf{\Delta }T\right)}}={\displaystyle \frac{n_{\max }}{\sqrt{2\pi }\mathsf{\Delta }{T}_{\sigma }}}\exp \left[-{\displaystyle \frac{1}{2}}{\left({\displaystyle \frac{\mathsf{\Delta }T-\mathsf{\Delta }{T}_n}{\mathsf{\Delta }{T}_{\sigma }}}\right)}^2\right]$$

(7)

where ΔT_n is the mean undercooling, K; ΔT_σ represents the standard deviation undercooling, K; n_max is the maximum nucleation density, which integrates the normal distribution from 0 to ∞, m⁻³; and ΔT is the undercooling, K. The nucleation parameters and growth parameters are described in

Table 4. Nucleation parameters in CAFÉ model.

Nucleation Parameter	ΔTS,max/K	ΔTS,σ/K	nS	ΔTV,max/K	ΔTV,σ/K	nV
value	1	0.1	1 × 108	4.3	1.1	3 × 1010

, where ΔT_s,max, ΔT_s,σ, n_s and ΔT_v,max, and ΔT_v,σ and n_v are the surface nucleation, the surface standard deviation undercooling, the surface nucleation density, and the volume nucleation, the volume standard deviation undercooling, the volume nucleation density, respectively.

2.4.2. Dendrite Tip Growth Model

The growth of grains and crystals depends on the undercooling at the dendrite front during the solidification of the slab. The undercooling consists of four parts: the constitutional undercooling ΔT_c, the thermodynamic undercooling ΔT_t, the dynamics undercooling ΔT_k, and solid–liquid interface curvature undercooling ΔT_r, which is given by the following expression:

$$\mathsf{\Delta }T=\mathsf{\Delta }{T}_c+\mathsf{\Delta }{T}_t+\mathsf{\Delta }{T}_k+\mathsf{\Delta }{T}_r$$

(8)

The effects of ΔT_t, ΔT_k, and ΔT_r on dendrite growth are so mild that they can be neglected for most alloys. Based on the actual experimental procedure, Equation (9) for the relationship between undercooling and growth velocity can be obtained from the KGT model to calculate the dendrite tip growth kinetics [30,43]:

$$v={\alpha }_2\mathsf{\Delta }{T}^2+{\alpha }_3\mathsf{\Delta }{T}^3$$

(9)

$${\alpha }_2=[{\displaystyle \frac{-\rho }{2m{c}_0{(1-k)}^2\mathsf{\Gamma }k}}+{\displaystyle \frac{1}{m{c}_0(1-k)D}}]{\displaystyle \frac{D^2}{{\pi }^2\mathsf{\Gamma }}}$$

(10)

$${\alpha }_3={\displaystyle \frac{D}{\pi \mathsf{\Gamma }}}\cdot {\displaystyle \frac{1}{{(m{c}_0)}^2(1-k)}}$$

(11)

where α₂ and α₃ are the fitted polynomial coefficients of the dendrite tips kinetic parameters related to the alloy composition, and the units are m·s⁻¹·K⁻², and m·s⁻¹·K⁻³, respectively. ρ is the density of steel. The Q355 high-strength structural steel is divided into eight binary systems of Fe-C, Fe-S, Fe-Mn, Fe-Si, Fe-P, Fe-Cr, Fe-Al, and Fe-Ti. The composition of molten steel c₀, equilibrium solute partition coefficient k, Gibbs–Thompson coefficient Γ [44] liquidus slope m, and solute diffusion coefficient D [45] are shown in

Table 5. Kinetic parameters of dendrite growth in CAFÉ model.

Composition	c0/wt.%	m/K·(wt.%)−1	K0	D/m2·s−1	Γ/m·K
C	0.163	−80.61	0.16	1.10 × 10−8	3 × 10−7
Si	0.0286	−16.64	0.55	8.50 × 10−9
Mn	0.525	−5.20	0.71	2.40 × 10−9
P	0.021	−28.65	0.26	4.60 × 10−9
S	0.0042	−38.23	0.03	3.50 × 10−9
Cr	0.021	−1.63	0.91	3.30 × 10−9
Al	0.044	4.74	1.17	2.47 × 10−8
Ti	0.016	−13.86	0.28	4.4 × 10−9

.

3. Model Validation

3.1. Validation of Solidification Heat Transfer Model

It is verified that the agreement is consistent between the solidification heat transfer model and the solidification process of extra-thick slabs in actual production by the nail-shooting experiment. The installation location of the nail shooting device is located at the end of the 10th, 11th, and 12th segment of the CC caster (the distances from the meniscus are 27.76 m, 30.03 m, and 32.31 m, respectively), and the sampling (provided by Rizhao Steel Yingkou Medium Plate Co., Ltd., Yingkou, China) schematic is shown in Figure 4. During the experiment, the nail (material is 60Si2Mn) was melted in the liquid core after being hit into the solidifying slab. Then, the sulfur (S) rapidly distributed into the molten steel. Ultimately, the accurate liquid core width and the solidified shell thickness were judged based on the diffusion of sulfur in the specimens. The macroscopic morphology results after pickling are shown in Figure 5. As shown in Figure 5a, the liquid core thickness at the end of the 10th segment is 81 mm and the actual shell thickness is 184.5 mm. The liquid core thickness at the end of the 11th segment is 63 mm and the actual shell thickness is 193.5 mm, as shown in Figure 5b. From Figure 5c, it can be seen that the liquid core thickness at the end of the 12th segment is 40 mm and the actual shell thickness is 205 mm. The comparison results are shown in Figure 6 between the measured and predicted values of the solidified shell thickness. The simulated shell thicknesses at the end of sections 10, 11, and 12 are 183.3 mm, 192.6 mm, and 201.6 mm, respectively, and the error between them and the actual shell thickness is within 2%. The temperatures of the extra-thick slab at one-quarter of the broad surface and half of the narrow surface measured by infrared thermometer were compared with the simulation results further to verify the precision of the heat transfer model, as shown in Figure 6. The error between the experimental results and the simulated temperatures is within 3%, and the absolute error is not more than 33 K, which powerfully demonstrates the reliability of the heat transfer model. Therefore, the numerical solidification heat transfer model can accurately predict the solidification process of the extra-thick slab.

3.2. Validation of Solidification Structure Model

The comparison of the solidification structure between those calculated by the CAFÉ model and the macrograph after pickling is demonstrated in Figure 7. The experimental solidification structure results of Figure 7b reveal that the columnar crystals on the fixed side are hindered by the nuclei settled by gravity, leading to inconsistent evolution patterns of the solidification structure on the loose side and fixed side. The equiaxed crystal region with a center ECR of 26.44% is shifted to the fixed side. The CAFÉ model, hardly considering gravity, predicts a solidification structure, as shown in Figure 7a, with a central ECR of 25.56%. Different colors in Figure 7a represent grain orientation. The measured and simulated ECR have a slight error of less than 1%, which indicates that the CAFE numerical model is reliable.

4. Results and Discussion

4.1. Effect of CC Process Parameters on Solidification Heat Transfer

4.1.1. Effect of Casting Speed on Solidification Heat Transfer

The effect of different casting speeds (0.39, 0.42, 0.45, and 0.48 m·min⁻¹) on the solidification heat transfer of the extra-thick slab was analyzed at the pouring temperature (1805 K) and the specific water flow (0.170 L/kg⁻¹). As shown in Figure 8a, it can be found that as the casting speed increases, the residence time of the slab in each section of the second cooling zone is shortened. Thus, the heat carried away by the cooling water is reduced, leading to a significant improvement in the slab surface temperature. The increase of 0.03 m·min⁻¹ resulted in 18 K in slab surface temperature at the exit of the caster (34.36 m from the meniscus). Besides, combined with the center solid fraction curve and the center temperature curve in Figure 8a, it can be seen that the center temperature change is relatively small due to the continuous release of latent heat from the liquid core in the slab before the slab is fully solidified, while the center temperature decline is sharply accelerated after the complete solidification of the slab.

As can be seen in Figure 8b, there is a robust correlation between the solidification end and the casting speed. Moreover, the solidification end is shifted back by about 2.8 m for every 0.03 m·min⁻¹ increase in the casting speed. The equation can be obtained by linear fitting: y = 94.73v − 3.179, where y is the solidification end, m; v is the casting speed, m·min−1. Increasing the casting speed causes the overall temperature of the slab to increase, and the cooling rate at the solidification front slows down, thus gradually increasing the length of the mushy zone. The length of the mushy zone (the length of the zone corresponding to the center solid fraction from 0 to 1) increased by about 0.98 m for every 0.03 m·min⁻¹ increase in the casting speed. The equation l = 32.70v − 0.657 was obtained by linear fitting, where l is the length of the mushy zone, m. From Figure 8b, it is noticed that the solidification end is located beyond the caster length (34.36 m) when the casting speed is 0.45 m·min⁻¹, which will be unfavorable to the effective application of soft reduction technique in the actual production [46]. Therefore, considering the rhythm of production, the pulling speed should be maintained from 0.39 to 0.42 m·min⁻¹.

4.1.2. Effect of Specific Water Flow on Solidification Heat Transfer

The specific water flow is the ratio of the total water volume consumed in the secondary cooling zone to the slab mass passing through the secondary cooling zone per unit time, which represents the indicator of the secondary cooling intensity. With the casting speed of 0.45 m·min⁻¹ and the pouring temperature of 1806 K, the solidification process was simulated for different specific water flows (increasing or decreasing by 15%). It is observed from Figure 9a that the surface temperature and the center temperature of the slab vary to a lesser extent with the increase in the specific water flow. Figure 9b shows a negative correlation between the specific water flow and the solidification end, where the solidification end is shifted forward by about 0.45 m with each 15% increase in the specific water flow. The linear fitting of the specific water flow and the solidification end yielded the equation y = −16.57w + 42.284, where w is the specific water flow, L·kg⁻¹. The increase in specific water flow raises the cooling rate at the solidification front, and the length of the mush zone is gradually reduced. The equation l = −4.52w + 14.838 is obtained by the linear fitting.

4.1.3. Effect of Superheat on Solidification Heat Transfer

Under the condition of a casting speed of 0.45 m·min⁻¹ and specific water flow of 0.170 L·kg⁻¹, the solidification processes were simulated for the different superheats of 11, 21, 31, and 41 K, respectively. It can be noted from Figure 10a that the center temperature goes up with the increase in superheat in the early stage of slab solidification, and the center temperature tends to be the same at 21~23 m from the meniscus. As shown in Figure 10b, the solidification end is prolonged by about 1.06 m for every 10 K elevation in superheat, and the superheat and the solidification end of the slab are derived from a linear fit to y = 0.11b + 37.219, where b is the superheat, K. The length of the mush zone was slightly decreased with the rising to superheat, and the equation l = −0.03b + 14.847 was obtained by linear fitting.

4.2. Effect of CC Process Parameters on ECR and Grain Parameters

4.2.1. Effect of Casting Speed on ECR and Grain Parameters

The impact of different casting speeds on the solidification structure of the extra-thick slab was analyzed when the superheat and specific water flow were invariable. Since the loose and fixed sides of the slab are symmetrical during the simulation, the simulation area of the solidification structure is only half of the full thickness of the slab at the 1/4 position of the broad face. As shown in Figure 11, the center ECR of the extra-thick slab is 27.33%, 26.22%, 25.56%, and 24.44% when the casting speed is 0.39, 0.42, 0.45, and 0.48 m·min⁻¹, respectively. This is mainly attributed to the fact that as the casting speed rises, the solidification time of the slab increases along with the temperature gradient during solidification, resulting in the growth of columnar crystals being facilitated [23,33].

The variation curves of the cooling rate from the surface to the center of the slab at different casting speeds are shown in Figure 12. Since the cooling intensity is more significant in the mold and foot roll zone during the pre-solidification period, the variation in the average heat flux on the slab surface is lower. Hence, there is a minor difference in the cooling rate at different casting speeds within 20 mm from the slab surface, as shown in Figure 12a. At the same time, a higher cooling intensity will produce a significant undercooling, which leads to the formation of the chilled layer consisting of fine equiaxed crystals on the slab’s surface in a short time. As shown in Figure 12b, in the range of 20~45 mm from the slab surface, the cooling rate declined with the rise in casting speed. The main reason is the decrease in the residence time of the molten steel in the mold and the secondary cooling zone, which was not conducive to the export of superheat. This promotes the growth of columnar crystals and reduces the ECR [33]. The cooling water volume weakens constantly, and the difference disappears as the solidification process of the extra-thick slab progresses. Hence, the cooling rate is consistent from the 40 mm position off the surface to the center, as depicted in Figure 12c. The short residence time of the slab in each cooling zone under high casting speeds delays the export of superheat, which facilitates the growth of columnar crystals and reduces the number of nuclei in the molten steel; thus, the number of grains is diminished with the rise in the casting speed, and the size of the grains is progressively increased, as shown in Figure 13. This would be unfavorable for grain refinement and improvement of internal defects in the slab.

4.2.2. Effect of Superheat on ECR and Grain Parameters

The simulation results of the solidification structure of the extra-thick slab under various superheats with the same casting speed and specific water flow are shown in Figure 14. With the increase in superheat from 11 to 41 K, the ECR is 30.89%, 25.56%, 22.67%, and 21.56%, respectively. The magnitude of the change in the central ECR is significantly reduced when the superheat is higher than 21 K. Since the 475 mm ultra-thick slab has a relatively large cross-section, the temperature gradient at the solid–liquid interface increases much slower when the thickness of the solidified shell increases to a certain degree. Thus, the transformation from columnar crystal to equiaxed crystal is facilitated [47].

From the statistics of grain parameters under different superheats in

Table 6. Statistical results of grain parameters in the simulated area under different superheats.

Superheat/K	Grain Number	Mean Area/m2	Mean Radius/m	Max Area/m2
11	16,602	1.1615 × 10−6	0.96564 × 10−3	1.18242 × 10−4
21	14,200	1.3579 × 10−6	1.07544 × 10−3	3.35568 × 10−4
31	12,306	1.5669 × 10−6	1.14223 × 10−3	4.19956 × 10−4
41	10,053	1.9181 × 10−6	1.25151 × 10−3	6.20197 × 10−4

, it can be observed that the number of grains drops remarkably with the increase in superheat. The reason may be that the rise in superheat reduces the undercooling at the solidification front, resulting in a low nucleus formation rate in the molten steel. Meanwhile, the higher superheat will melt the nonhomogeneous nucleation particles in the molten steel, which causes a considerable reduction in the number of grains. In addition, the shrinking of nucleation particles decreases the probability of nucleation at the front of columnar crystals, and the elevated superheat enables an increase in the temperature gradient, which favors the development of the columnar crystals. As a consequence, when the superheat was raised from 11 K to 41 K, the average grain radius enlarged from 0.96564 × 10⁻³ m to 1.25151 × 10⁻³ m, the average grain area augmented from 1.1615 × 10⁻⁶ m² to 1.9181 × 10⁻⁶ m², and the maximum grain area increased from 1.18242 × 10⁻⁴ m² to 6.20197 × 10⁻⁴ m². In addition, too low superheat can cause difficulty in floating inclusions and nozzle clogging. Accordingly, it is recommended to keep the superheat in the range of 11~21 K to obtain high ECR and fine grains.

4.2.3. Effect of Specific Water Flow on ECR and Grain Parameters

The influence of different specific water flows (increase or decrease by 15% based on the original specific water flow of 0.170 L·kg⁻¹) on the solidification structures under the identical superheat and casting speed was also investigated. It can be revealed from Figure 15 that the ECR progressively decreases with the increase in specific water flow, and the corresponding ECRs are 26.67%, 25.56%, 23.56%, and 21.77% when the specific water flow is 0.146, 0.170, 0.196, and 0.221 L·kg⁻¹, respectively. It may be explained by the fact that the surface cooling intensity of the slab expands with the increase in the specific water flow, enabling an elevated temperature gradient at the solidification front. Hence, the columnar crystal region is enlarged, while the central equiaxed crystal region is reduced.

The average grain size results under different specific water flows are shown in Figure 16, which first decline and then ascend with the specific water flow, and the average grain radius reaches a minimum value, i.e., 1.07544 mm, when the specific water flow is about 0.17 L·kg⁻¹. The undercooling at the solidification front of the molten steel keeps increasing as the specific water flow increases from 0.146 to 0.17 L·kg⁻¹, gradually decreasing center equiaxed grain size and grain refinement [12]. However, as the specific water volume continued to increase from 0.17 L·kg⁻¹ to 0.221 L·kg⁻¹, the steady increase in the temperature gradient at the solidification front benefits the growth of columnar crystals. The columnar crystals became coarser so that the fine equiaxed crystals were not sufficient to counteract the tendency to enlarge the grain size. Hence, the specific water flow should be adjusted to about 0.17 L·kg⁻¹ so as to achieve grain refinement.

4.3. Effect of CC Alloy Element on Solidification Structure of the Ultra-Thick Slab

The influence of alloy elements on the macrostructure of the extra-thick slab is investigated by varying the Si, Mn, and C contents within the range of Q355 steel composition under certain conditions of CC process parameters. The solidus T_S, liquidus T_L temperature, and dendrite tip growth kinetic parameters α₃ for different Si, C, and Mn contents are demonstrated in

Table 7. T_S, T_L, and α₃ of experimental steels varying in Si contents.

Number	Si wt %	TL (K)	TS (K)	α3 (m·s−1·K−3)
Si1	0.20	1785	1744	9.954 × 10−6
Si2	0.30	1784	1741	8.770 × 10−6
Si3	0.40	1782	1738	7.791 × 10−6
Si4	0.50	1780	1735	6.974 × 10−6

,

Table 8. T_S, T_L, and α₃ of experimental steels varying in C contents.

Number	C wt %	TL (K)	TS (K)	α3 (m·s−1·K−3)
C1	0.15	1784	1744	1.004 × 10−5
C2	0.16	1784	1742	9.161 × 10−6
C3	0.17	1783	1740	8.396 × 10−6
C4	0.18	1782	1738	7.723 × 10−6

and

Table 9. T_S, T_L, and α₃ of experimental steels varying in Mn contents.

Number	Mn wt %	TL (K)	TS (K)	α3 (m·s−1·K−3)
Mn1	1.45	1784	1742	9.135 × 10−6
Mn2	1.50	1784	1742	8.992 × 10−6
Mn3	1.55	1784	1741	8.852 × 10−6
Mn4	1.60	1783	1741	8.715 × 10−6

, and the solidification structure simulation results are shown in Figure 17, Figure 18 and Figure 19. The solidification structure simulation results demonstrate that the center ECR of the slab rises gradually with the enhancement of Si, C, and Mn content. Yet, the variations in the Si element have a noticeable effect on the ECR of the extra-thick slab in comparison with C and Mn, and the ECR of the slab is enhanced from 19.11% to 29.78% when the Si element is increased from 0.2 to 0.5.

As for the heterogeneous nucleation, the maximum nucleus formation rate is obtained when the undercooling at the solidification front is about 0.02 times the theoretical crystallization temperature (i.e., liquidus temperature) [48]. According to the calculation results in Table 7 and Figure 20a, the liquidus temperature drops obviously with the increase in Si content, whereby the nucleation undercooling requirement for steel crystallization decreases, and the nucleation power increases [49]. When the Si content was added from 0.2% to 0.5%, the number of grains rose from 11,322 to 18,660, and the average grain radius reduced from 0.91308 × 10⁻³ m to 1.22347 × 10⁻³ m. Furthermore, the dendrite growth kinetic parameter decreases with increasing Si content, which restricts the tendency of columnar crystals to grow. Therefore, the center ECR of the extra-thick slab gradually rises [23]. Figure 20a presents the results of the enthalpy of phase change (i.e., the latent heat of phase change) calculated by the Jmatpro (version 7.0) software. With the increase in Si content, the enthalpy of phase change decreases significantly, which causes the shortening of the crystallization time of the molten steel during solidification and the suppression of the trend in grain growth, and results in a gradual increase in the degree of grain refinement [8].

In combination with Table 8 and Figure 20b, it can be noticed that the enthalpy of phase change and the dendrite growth kinetic parameter α₃ decrease progressively with the rise of C content, which serves to refine the grains. Consequently, it has been discovered from the simulation results of Figure 21b grain parameters that the average area of grains decreases and the number of grains rises with the increasing of C content, and the average grain radius decreases from 1.16594 × 10⁻³ m to 1.05279 × 10⁻³ m when the C content increases from 0.15% to 0.17%. The average grain radius reaches a minimum at a C content of about 0.17%; the average grain radius increased minimally from 1.05279 × 10⁻³ m to 1.06993 × 10⁻³ m when C content increased from 0.17% to 0.18%. As can be observed from Table 8, this is principally explained by the fact that the liquidus and solidus temperature can be lowered by suitably increasing the C content in the molten steel, as well as the declining trend in the solidus is more remarkable compared to the variation in liquidus. Thus, the extension of the slab’s solidification time further expanded the grain growth tendency, and the grain refinement was inadequate to compensate for the grain growth caused by the increase in the solidification time. As depicted in Table 9 and Figure 20c, the T_L, T_S, α₃, and the enthalpy of phase change only very mildly with the change in Mn content. In the integrated analysis of those as mentioned above, Si has the greatest impact on the solidification structure of the extra-thick slab compared with C and Mn, and an appropriate elevation of the Si content favors grain refinement.

5. Conclusions

(1)

Compared to the specific water flow and superheat, the casting speed has the most powerful influence on the solidification process of the extra-thick slab. For every 0.03 m·min⁻¹ increase in the casting speed, the surface temperature of the slab at the exit of the CC caster increases by about 18 K, and the solidification end is backward shifted by about 2.8 m. The length of the mushy zone shortens with increasing specific water flow and superheat but keeps enlarging with higher casting speed.

(2)

The center ECR of the extra-thick slab reduces progressively with rising casting speed and specific water flow. The superheat has a noteworthy impact on the solidification structure of the extra-thick slab. Since lower superheat will increase nucleation particles in molten steel, the center ECR drops from 30.89% to 21.56% when the superheat is elevated from 11 K to 41 K.

(3)

The average grain size enlarges, and the number of grains reduces as the casting speed increases and the superheat decreases. The average grain size decreases and then enlarges with the rise in specific water flow, reaching its minimum value when the specific water flow is about 0.17 L·kg⁻¹.

(4)

The number of grains in the extra-thick slab progressively increases with the increasing Si, C, and Mn element contents, and the average grain area keeps shrinking. The average grain radius reduces gradually with the rise in Si and Mn content, while the average grain radius decreases and then marginally increases with the rise in C content and reaches the minimum value at a C content of about 0.17%. In contrast to C and Mn, Si has the most substantial effect on the solidification structure of the extra-thick slab, and a proportional rise in the Si content serves to refine the grains.

(5)

Considering the simulation results under various continuous casting process conditions, the optimum process conditions are as follows: casting speed at 0.39~0.42 m min⁻¹, superheat at 11~21 K, and specific water flow about 0.17 L kg⁻¹.