Influence of Liquid Core Reduction on Stress-strain Distribution and Strand Deformation in a Thin Slab Caster

Abstract

A new numerical model called SteelSim, which is based on the Finite Element Method (FEM), has been developed in order to investigate the Liquid Core Reduction (LCR) section in a thin slab continuous caster. As a SteelSim application example, the influence of roll alignment on temperature distribution, solidification, stress-strain distribution and strand deformation has been studied. The thermo-elasto-viscoplastic constitutive equations and the Arbitrary Lagrangian Eulerian (ALE) kinematic description for the conservation equations were calculated in the SteelSim model. From the results, it can be seen that the roll configuration: (a) symmetrical alignment of rolls with LCR, (b) asymmetrical alignment of rolls with LCR, and (c) symmetrical alignment without LCR, has an influence on the local stress-strain distribution and thus local strand deformation, which in turn affects the evolving shape profile of the narrow face. Eventually, the SteelSim model can be utilized for determining optimal roll configurations and casting conditions for specific steel grades in order to avoid the formation of critical casting defects, such as: excessive bulging, macrosegregation, cracking etc., which may lead to poor product quality or even total failure of the casting process due to a breakout. The results presented here may allow us to further analyze and validate the model with actual plant casting data.

1. Introduction

The thin slab continuous casting technology has achieved great research focus due to the increasing industrial requirements, such as: lower production costs, larger energy savings and higher production efficiency, since this casting technology can be more suitable for achieving these requirements as compared with the conventional casting process.^1,2) In thin slab casting, the Liquid Core Reduction (LCR) is a critical section which allows fast strand reduction from the initial thickness, achieved at the mould exit, down to the final thickness requirement. The funnel-shaped mould, in a thin slab caster, allows for the placement of a larger nozzle which facilitates higher metal inflow, thus leading to higher casting speeds and production rates.^3,4) High casting velocities require good control of the rolling process in the Liquid Core Reduction section of a thin slab caster, whereby the mass flow needs to be in balance with the withdrawing rolling forces which provide the deformation of the strand. It is very important to study the local deformation of the solid shell during the LCR process, because non-uniform local heat flux, roll misalignment, unstable fluid flow conditions and inadequate casting speeds can induce casting defects in the strand such as: surface cracks, hot tearing, excess bulging, breakouts and irregular shaped narrow faces, especially when considering the large amount of deformation that can be achieved at the LCR section in the thin slab casting process.^5,6)

In recent years, having computational costs decreasing and more powerful modeling packages available, applying mathematical models to understand the complicated continuous casting process is becoming an accepted approach.⁷⁾ Thus, the numerical simulation of temperature distribution, solidification, stress-strain distribution and strand deformation during continuous casting has been the focus of many studies, which are of great interest to help the casting engineers and operators for optimizing their casting parameters such as: casting speed, cooling conditions, etc. For example, Ren and Wang⁸⁾ analyzed the influence of bulging and strain on the solidifying shell of a continuously cast strand with the thermo-elastic bending theory. It has been shown that negative bulging may occur in the caster due to changes in roll pitch and roll misalignment. Lin and Thomas showed the effects of roll pitch and misalignment on the strand deformation with a two dimensional model based on the Finite Element Method (FEM) code ABAQUS.⁹⁾ As a result, it was found that roll misalignment was a dominant factor in determining the shell deformation. Ha et al.¹⁰⁾ analyzed the influence of casting speed, cooling conditions and roll pitch on bulging deformation in a 3-D FEM model by using elasto-plastic constitutive equations including creep. Zhang et al.¹¹⁾ presented a thermo-mechanical model considering roll arrangement to predict the 3-D temperature distribution and strand deformation. Triolet et al.¹²⁾ conducted transient thermo-mechanical modeling of the continuous casting process using a software tool called TherCast and investigated the effects of roll arrangement and heat transfer on strand deformation, demonstrating that a roll misalignment may strongly disturb the bulging profile.

Recently, a new numerical FEM model called SteelSim has been developed by the Norwegian Institute for Energy Technology in cooperation with Tata Steel in order to better understand the deformation of the strand during thin slab casting. The model uses the thermo-elasto-viscoplastic constitutive equations and employs the ALE algorithm in order to realize the displacement and vertical expansion of the grid (simulating the dynamic deformation and vertical displacement during continuous casting). This study shows the SteelSim numerical simulations of temperature distribution, solidification, stress-strain distribution and mechanical deformation of the solid shell and mushy zone (i.e. semi-solid solidification transition region) for a low-carbon steel 0.045C, 0.2Mn (wt%) considering three roll configurations: (a) symmetrical alignment of rolls with LCR, (b) asymmetrical alignment of rolls with LCR, and (c) symmetrical alignment without LCR. The study focuses on the deformation of the narrow face shape, since the bulging of the non-constrained narrow face is more evident and can serve as a measurable characteristic for validating the model with actual plant data. Eventually, the model can be used for determining the optimal casting parameters for different steel grades.

2. SteelSim Numerical Model

2.1. Heat Transfer and Fluid Flow

The model for heat transfer and fluid flow is based on a continuum mixture model¹³⁾ for the solid-liquid material. A Darcy force is used in the mixture momentum equations which accounts for the interfacial friction due to the different velocities of the solid and the liquid. The current mixture model is simplified by neglecting the local solidification shrinkage and the solute transport caused by gradients in chemical composition. Thermal convection is included by the Boussinesq approximation. The mixture velocity is defined by:   

$$u_i=g^l{u}_i^l+g^s{u}_i^s$$(1)

where g^l, g^s are the volume fractions of the liquid and the solid phases respectively, and $u_i^l$ , $u_i^s$ are the volume averaged velocities of the liquid and the solid phases, respectively. The Darcy force is given as follows:   

$$S_i=\{\begin{array}{c}0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{\hspace{0.17em} }\hspace{1em}\hspace{1em}\mathrm{\hspace{0.17em} }for\hspace{1em}\hspace{0.17em} T>T_l\\ \hspace{1em}\hspace{1em}\frac{\nu }{K}\left(u_i^s-u_i\right)\hspace{1em}\hspace{1em}\hspace{1em}for\hspace{1em}\hspace{0.17em} T_s<T<T_l\\ M\left(u_i^s-u_i\right)\hspace{1em}\hspace{1em}\hspace{1em}for\hspace{1em}\hspace{0.17em} T<T_s\end{array}$$(2)

Where v and K are the kinematic viscosity of the liquid and the permeability of the mush, respectively. M is a number which forces the mixture flow field to be equal to the solid velocity in the solid region. T_l and T_s are the liquidus and solidus temperatures, respectively. The permeability K is dependent on the morphology of the mush. It is here numerically described by the Kozeny-Carman equation:¹⁴⁾   

$$K=K_0\frac{{\left(g^l\right)}^3}{{\left(1-g^l\right)}^2}$$(3)

K₀ numerically describes the influence of the structure on permeability. In this case, the secondary dendrite arm spacing DAS is considered for this estimation as follows:   

$$K_0=\frac{{(DAS)}^2}{180}$$(4)

The buoyancy force f_i is given by:   

$$f_i=\frac{\mathrm{\Delta }\rho }{{\rho }_0}{g}_i$$(5)

where Δρ is the density difference from the liquidus temperature, ρ₀ and g_i and are the constant density and the acceleration of gravity, respectively. The mass and momentum conservation equations are solved as follows:   

$$\frac{\partial u_i}{\partial x_i}=0$$(6)

  

$$\frac{\partial u_i}{\partial t}+\left(u_j-{\omega }_j\right)\frac{\partial u_i}{\partial x_j}=-\frac{1}{{\rho }_0}\frac{\partial p}{\partial x_i}+\frac{\partial }{\partial x_j}\nu \frac{\partial u_i}{\partial x_j}+f_i+S_i$$(7)

where p and ω are the pressure and the velocity of the computational nodes, respectively. The mixture energy equation is:   

$$\rho \frac{\partial h}{\partial t}+\rho \left(u_j-{\omega }_j\right)\frac{\partial h}{\partial x_j}=\frac{\partial }{\partial x_j}\lambda \frac{\partial T}{\partial x_j}$$(8)

where h, T and λ are the mixture enthalpy, temperature and thermal conductivity, respectively. Free solid material in the mush is neglected, and it is assumed that the whole solid is connected to the dendritic structure. More details on the model and the numerical solution techniques of the equations presented here can be found in Ref. 15).

2.2. Expanding Geometry

The current model contains three sub-domains within the calculated strand domain: the Eulerian, the Expansion, and the Lagrangian sub-domains. The Arbitrary Lagrangian-Eulerian (ALE) numerical approach was used for simulating the continuous casting process by having an expanding region in the Expansion sub-domain and having elements continuously added to the Lagrangian lower domain following the specified casting speed for the vertical displacement of the nodes. Further details of the ALE description can be found elsewhere in Refs. 16), 17), 18).

2.3. Stress-strain Distribution

The thermo-elasto-viscoplastic constitutive equations were used in this study without considering heat produced from viscoplastic deformation. During strand solidification, the total strain is divided into elastic ${\epsilon }_s^e$ , viscoplastic ${\epsilon }_s^p$ , and a thermal part ${\epsilon }_s^T$ , thereby having the formulation as follows:¹⁹⁾   

$$\epsilon ={\epsilon }_s^e+{\epsilon }_s^p+{\epsilon }_s^T$$(9)

The constitutive equation for elasticity describes the influence of elastic strain ${\epsilon }_s^e$ on the stress σ. This is given by the Hook’s generalized law, which is written in the form:   

$$\sigma =D(T)\cdot {\epsilon }_s^e$$(10)

where the Young’s modulus and the Poisson’s ratio are entered into the matrix D as a function of temperature.¹⁹⁾ The Young’s modulus E and the Poisson’s ratio v as a function of temperature are listed in Table 1. Intermediate values are obtained accordingly by linear interpolation.

Table 1. The constitutive parameters of low carbon steel.

Temperature, °C	F MPa	n	m	Young’s modulus E, GPa	Poisson’s ratio ν
0	610	0.25	0.22	200	0.33
200	523	0.25	0.22	180	0.33
400	435	0.25	0.22	150	0.33
600	348	0.25	0.22	130	0.33
800	260	0.35	0.22	78	0.33
1000	221	0.35	0.22	15	0.33
1200	109	0.35	0.22	5	0.33
1400	4	0.1	0.22	5	0.33
1500	0.1	0.1	0.22	–	0.33

The thermal strain component is described by Bellet and Fachinotti as an integral:²⁰⁾   

$${\epsilon }_s^T=-\frac{1}{3}\underset{T}{\overset{T_{coh}}{\int }}{\beta }_T(T)dT\cdot I$$(11)

where the volumetric thermal expansion coefficient β_T is set as constant, and the mechanical coherency temperature T_coh, for the current steel, is considered as 1520°C.

Plastic flow is determined by the constitutive equations applied earlier by Fjær and Mo,¹⁹⁾ whereby the flow stress $\overline{\sigma }$ is determined as a function of temperature T and viscoplastic strain rate ${\stackrel{•}{\overline{\epsilon }}}_p$   

$$\begin{array}{c}\overline{\sigma }=F(T)\cdot {(\varphi {}_0+\varphi )}^{n(T)}\cdot {({\stackrel{•}{\overline{\epsilon }}}_p)}^{m(T)}\\ d\varphi =\{\begin{array}{c}d{\overline{\epsilon }}_p,T\le T_0\\ 0,T>T_0\end{array}\end{array}$$(12)

where F(T), n(T) and m(T) are nonlinear functions of T. F(T) accounts for the temperature dependence of the flow stress $\overline{\sigma }$ , whereas n(T) and m(T) are the strain hardening exponent and strain rate sensitivity coefficient, respectively. These functions can be attained through a fitting method from the measured true stress-strain curves of the steel. The fitted specific values F(T), n(T), m(T) are listed in Table 1. Here, ϕ₀ is assigned a value of 0.0001. Work hardening occurs bellow the T₀ temperature, which in this case is considered as 1500°C.

3. Geometry Model, Thermo-physical Properties and Boundary Conditions

3.1. Geometry

In this study, the SteelSim model was set-up for simulating the temperature distribution, solidification, stress-strain distribution and strand deformation during continuous thin slab casting. The main casting parameters, part of the layout of the LCR and strand cooling conditions are based on data obtained from the Tata Steel thin slab caster located in IJmuiden, The Netherlands. The submerged entry nozzle and funnel shape of the actual casting set-up were not considered in the current model, instead a fluid flow with a uniform velocity at the metal level inlet was included. For this study, a rectangular mould geometry was used. The LCR section is a critical part in the casting process whereby rolling forces influence the development of the solid shell. An optimal distribution of stresses in the solid shell is required in order to provide further deformation of the strand without failure. For this study we only consider the influence of roll configuration on the narrow face development at the upper part of the LCR. In this region, the early solidifying shell is no longer constrained by the mould walls, thus bulging at the narrow face, due to the inner ferrostatic pressure, is the most critical.

Figure 1(a) demonstrates the half-symmetry geometry and the distinctive computational domains and sub-domains for the SteelSim modeling as described before. The LCR section below the mould includes 2 sets of guiding rolls (foot rolls), and 6 sets of rolls that are a part of the LCR section, as shown in Fig. 1(b). The rolls at the LCR section are set-up to have a strand thickness reduction of 10.9 mm at the exit of the roll pair no. 8. The effect roll of alignment on strand deformation was studied by considering three different roll configurations: (a) symmetrical alignment of rolls with LCR (having symmetrical closure of rolls), (b) asymmetrical alignment of rolls with LCR (having a single-sided closure of rolls), and (c) symmetrical alignment without LCR (fully vertical arrangement of rolls at both sides), as shown in Fig. 2. For the asymmetrical case, the row of rolls closing in the LCR (having the inwards roll displacement) is located at the loose side of the LCR, while the roll configuration at the fixed side remains fully vertical. A set-up without LCR is used at the start of casting to allow passing of a dummy bar and avoid excessive forces during the start-up. The corresponding casting machine geometry and casting parameters are shown in Table 2.

Fig. 1.

Computational model: (a) The rectangular casting geometry, (b) Liquid Core Reduction Section.

Fig. 2.

The configurations in roll alignment: (a) symmetrical alignment of rolls with LCR, (b) asymmetrical alignment of rolls with LCR, and (c) symmetrical alignment with no LCR.

Table 2. The casting machine geometry and casting parameters.

Mould cross section dimension thickness, m × width, m	0.09×1.25
Mould length, m	1.1
Mould wall thickness, m	0.025
Distance from meniscus to the top of mould, m	0.1
Strand width, m	1.25
Strand thickness, m	0.09
Roll diameter, m	0.13
Distance between mould and roll pair no. 1, m	0.12
Distance between roll pair no. 1 and 2, m	0.155
Distance between roll pair no. 2 and 3, m	0.155
Distance between roll pair no. 3 and 4, m	0.155
Distance between roll pair no. 4 and 5, m	0.155
Distance between roll pair no. 5 and 6, m	0.16
Distance between roll pair no. 6 and 7, m	0.16
Distance between roll pair no. 7 and 8, m	0.16
Casting speed, m·min–1	5
Pouring temperature, °C	1540
Cooling water temperature, °C	50

3.2. Thermo-physical Properties and Boundary Conditions

The material considered for the simulations corresponds to a low carbon steel having a composition of 0.045C, 0.2Mn (wt%). The corresponding thermo-physical properties such as density, specific heat capacity, thermal conductivity, kinematic viscosity etc. are shown in Table 3. The fluid flow is assumed as free up to a fraction of solid of 0.3 (with a fixed linear increase in viscosity from the liquidus), and from a fraction of solid of 0.3 to 1.0, a solidification source term is applied which accounts for the friction against the solid network. The heat transfer at the copper mould and at the LCR section are set-up according to the data from the Tata Steel, IJmuiden thin slab caster, considering both the actual primary and secondary cooling for the given steel at the specified casting conditions. The heat flux set-up at the rolls section follows the description of the 5 cooling zones as shown in Fig. 3. During the simulation, the meniscus level is fixed in space i.e. free surface modelling is not considered in the current model. The model assumes full contact of the strand surface with the mould walls, thus the influence of air gap formation on heat transfer is calculated in the model but already included in the total heat flux set-up database. From the bottom of the mould down to roll pair no. 8, free surface mechanical boundary conditions are applied where the strand is not in contact with the rolls, thus enabling the prediction of the strand deformation. Moreover, at the LCR section the finite element grid adjusts according to the amount of deformation, i.e. having nodal displacement calculated during the simulation. The model is arbitrarily adjusted below the domain of interest by having a large increase of stiffness and cooling after roll pair no. 8 where the strand continues to be pulled downwards. This was done in order to have a stable numerical calculation by avoiding an excessive bulging deformation due to the metallostatic pressure, and to simplify the geometry by assuming a fully vertical cast strand. Also, the caster start-up procedure was simplified and accelerated. Given the current simplifications in the model, it was found that a steady state can be achieved at a time of 60 s. The results presented in the following parts are down to roll pair no. 7, i.e. down to 2.0 m from the meniscus. It is considered that the above restrictions and artificial boundary conditions, below roll pair no. 8, have no influence on the steady-state results from roll pair no. 7 upwards.

Table 3. The thermo-physical properties of the low carbon steel.

Temperature, °C	Density, kg·m–3	Specific heat capacity, J·kg–1·K–1	Thermal conductivity, W·m–1·K–1	Kinematic viscosity, m2·s–1
25	7863	446	74.7	–
689	7639	903	35.7	–
723	7648	886	34.1	–
766	7647	882	32.2	–
853	7661	600	28.3	–
1000	7587	623	29.6	–
1450	7317	729	33.6	–
1512	7287	738	34.2	–
1531	7132	785	34.8	1.60E-05
1533	7030	817	35	8.03E-07
2230	6449	795	35	3.27E-07
Thermal expansion coefficient, K–1		1.2×10–5
Liquidus temperature, °C		1533
Solidus temperature , °C		1461
Latent heat of fusion, kJ·kg–1		244

Fig. 3.

Cooling zones at the rolls section.

4. Results and Discussion

4.1. Heat Transfer and Solidification

Figure 4 shows the temperature profile of the strands for the three roll configurations when the continuous casting time is ~60 s, i.e. at the steady state. The images show the temperature contours at the wide face, loose side (the rolls are hidden at this face in order to reveal the results). It can be observed that the temperature of the strand surface between the adjacent rolls is lower due to the simulated high cooling rate provided by the water sprays. It was found that the three roll configurations show little differences on the temperature distribution at the wide face.

Fig. 4.

Temperature profile of the strands for the three roll alignments: (a) symmetrical alignment of rolls with LCR, (b) asymmetrical alignment of rolls with LCR, and (c) symmetrical alignment with no LCR.

For all three cases, it is found that strand solidification starts at about 30 mm below the meniscus. From this point downwards the solid skin develops continuously. The solid skin thickness at the mould exit is about 10 mm. Figure 5 exhibits the local surface temperature profiles at the centre of the narrow face (45 mm from the wide face surface of the strand) from the meniscus down to 2.0 m. It can be seen in Fig. 5 that the surface temperature tends to decrease inside the mould and then increases after leaving the mould due to the reduced cooling intensity at the secondary cooling zone. It can also be noticed that there are no obvious differences in temperature distribution between the three roll alignments. Also, it was found that there are no significant differences, between the three roll alignments, on the development of the solidification region of the strand (demonstrated by the inner solid fraction development) (see Fig. 6).

Fig. 5.

The local surface temperature profiles at the centre of the narrow face from the meniscus down to 2 m in length for three roll alignments.

Fig. 6.

The inner solid fraction profile of the strand from roll pair no. 1 to roll pair no. 6 for three different roll alignments: (a) symmetrical case with LCR, (b) asymmetrical case with LCR, and (c) symmetrical case with No-LCR.

4.2. Stress-strain Distribution

Figure 7 shows the mean stress distribution at the surface of the strands for the three roll alignments. It can be seen that the compressive and tensile forces act over the wide surface of the strand during rolling. The wide face shows the compressive stress at the contact surface between the strand and roll, while the tensile stress can be noticed at the free surface between the rolls due to the metallostatic pressure and the inhomogeneous thermal contraction due to the water sprays. Slightly higher stress values are observed in the asymmetric LCR case. At the narrow face, due to the influence of strand thickness reduction, local compressive stresses can be noticed for the symmetric and asymmetric cases with the LCR. The largest compressive stresses can be observed at the contact region between the strand and rolls.

Fig. 7.

The mean stress distribution (MPa) of the strands for the roll alignments: (a) symmetrical alignment of rolls with LCR, (b) asymmetrical alignment of rolls with LCR, and (c) symmetrical alignment with no LCR.

Besides the surface stress distribution, it was found that the roll configuration influences the internal distribution of stresses and strains. Figure 8 exhibits the mean stress distribution in the strand for the three different roll alignments at 60 s. As seen in Fig. 8, the local compressive/tensile stresses within the mushy zone in the asymmetrical case (Fig. 8(b)) are larger than that for the symmetrical cases with and without LCR (Figs. 8(a) and 8(c)). For illustrative purposes, an isoline at the subsurface of the wide face of the strand is shown indicating the fraction of solid of 0.5. This shows that there are stresses developing around this region, and these may influence the nucleation and propagation of cracks during solidification. The larger tensile stresses found in the asymmetrical case with LCR can be indicative of higher internal crack susceptibility as compared with the other two cases. This observable feature can assist us in determining cracking susceptibility. Cracking may occur if the tensile stress at the solidification front exceeds the critical stress value of the steel at the given casting conditions. If cracking propagation occurs in the mushy zone, the integrity of the strand in the LCR can be hampered, and in the worst case scenario, this can even lead to a breakout. This is an important observation because it can give us an indication on how the casting set-up and parameters influence the full stability of strand.

Fig. 8.

The inner mean stress distribution of the strands for the roll alignments: (a) symmetrical alignment of rolls with LCR, (b) asymmetrical alignment of rolls with LCR, and (c) symmetrical alignment with no LCR.

Figure 9 illustrates the mean stress determined at the surface of the narrow face in between roll pair no. 2, 4 and 6. The cases with LCR show larger compressive forces at the extremes of the narrow face whereby the strand is in direct contact with the roll. The compressive forces become more evident as the strand is pulled further down the LCR section, which can be seen at roll pair no. 4 and 6. Moreover, for the symmetrical case with LCR, the stresses become symmetrically distributed around the centreline of the narrow face, whereas for the asymmetric case, the strand side in contact with vertical rolls show larger compressive stress values as compared with the opposite side having inward inclination of the rolls (i.e. loose side of the LCR).

Fig. 9.

The mean stress distribution at the transverse section of the narrow face between: (a) roll pair no. 2, (b) roll pair no. 4, and (c) roll pair no. 6.

Figure 10 exhibits the mean stress at the contact point between strand and roll near the narrow face for the different roll alignments. As compared with the case without LCR, the cases with LCR exhibit a compressive stress that is larger by one order of magnitude and becomes more pronounced as the amount of reduction increases.

Fig. 10.

The maximum mean stress at the contact between the strands and rolls near the narrow face with the different roll configurations.

4.3. Narrow Face Deformation

The shape of the narrow face is an important feature that can reflect the influence of the casting parameters on the deformation of the strand. Bulging becomes more evident at the narrow face during the LCR. It can serve as an indicative characteristic that can allow us controlling the casting process in order to avoid the formation of casting defects. This feature can also be used for experimental validation of the model. Figure 11 presents the equivalent strain distribution (in %) at the cross plane of the strand while it passes through roll pair no. 2, 4, and 6, for the three cases. It can be seen that the strain is distributed symmetrically for the symmetrical cases, whereas the strain distribution becomes asymmetrical for the asymmetrical case. The largest strain values in the strand at roll pair no. 6 are: 0.14%, 0.18%, 0.02%, for the symmetric LCR case, asymmetric LCR case and the case without LCR, respectively. The narrow faces show noticeable bulging deformation for the cases with LCR, as the rolling reduction increases, the bulging deformation also increases. The highest strain was attained in the asymmetric case.

Fig. 11.

The equivalent strain distribution (in %) at cross plane section of the strand while it passes through the roll pairs no. 2, 4, and 6, for the three different roll configurations: (a) symmetrical alignment of rolls with LCR, (b) asymmetrical alignment of rolls with LCR, and (c) symmetrical alignment with no LCR.

Figure 12 shows the development of the narrow face shape profiles in between the adjacent rolls. The shape profile develops symmetrically for the symmetrical cases, whereas the shape profile becomes asymmetrical for the asymmetrical case due to the roll alignment affecting the local stress-strain distribution as described earlier. The maximum bulging displacement for the asymmetric case is the largest among the three roll configurations with an orientation of the shape profile towards the loose side. The largest displacement (i.e. 2.5 mm) was attained in the asymmetrical case, at the roll pair no. 5 and 6, as compared with the other two cases. Without LCR, the narrow face profile remains virtually unaltered from roll pair no. 2 down to roll pair no. 6.

Fig. 12.

The narrow face shape profiles at different positions: (a) between rolls 1–2, (b) between rolls 3–4, and (c) between rolls 5–6.

Figure 13 exhibits the displacement at the center of narrow face from the bottom of the mould down to 2 m of strand length. It can be observed in Fig. 13 that, from 1.3 m downwards (after passing through the foot rolls), the shape profile displacement becomes more pronounced (evidenced by the change in slope in the curve) for the symmetric and asymmetric cases with LCR. Moreover, the displacement approaches 2.4 mm and 2.9 mm, at 2 m from the meniscus, for the symmetric and asymmetric cases, respectively. This indicates that the displacement is much larger for the asymmetric case as compared with the symmetric case. On the other hand, a negative displacement of the narrow face due to the low compressive stresses imposed by the rolls in combination with the local thermal contraction of the strand can be attained for the symmetrical case without LCR.

Fig. 13.

The maximum displacement at the centre of narrow face from the bottom of the mould down to 2 m of the strand length.

Figure 14 shows the topology of the narrow face in 3D and mean stress distribution for the three different roll configurations. The balance between compressive (blue) and tensile (green) stresses, from both sides, will determine the development of shape, depth and orientation of the narrow face profile. In the asymmetric case with LCR, there are slightly higher tensile stresses at the narrow face next to the loose side of the wide face as compared with the other 2 cases. The compressive stresses between the rolls (blue regions in Fig. 14) will push the strand at the edges of the narrow face inwards, while tensile stresses (evident at the narrow face after roll contact. i.e. green regions in Fig. 14) will push the strand surface narrow face outwards. This analysis on the stress-stress distribution and shape profile development can be used as parameters for establishing adequate casting conditions for achieving good steel castability.

Fig. 14.

The topology of the narrow face in 3D and stress distribution for the three different roll alignments: (a) symmetrical alignment of rolls with LCR, (b) asymmetrical alignment of rolls with LCR, and (c) symmetrical alignment with no LCR.

5. Conclusions

This paper presents a simulation of strand thermo-mechanical behaviour during the Liquid Core Reduction (LCR) in a thin slab caster by using the SteelSim modelling software tool. Three different roll configurations were investigated: (a) symmetrical alignment of rolls with LCR, (b) asymmetrical alignment of rolls with LCR, and (c) symmetrical alignment without LCR. Summarizing all the results, the following conclusions can be given:

(1) The roll configurations in the current study have relatively little influence on the heat transfer. On the other hand, the roll configuration has an evident influence on the stress-strain distribution and thus local deformation of the narrow face.

(2) The roll alignment influences the displacement, depth and orientation of the narrow face shape profile.

(3) The internal stresses and equivalent strains are distributed symmetrically in the symmetrical cases, whereas they become asymmetrically distributed in the asymmetrical case. With the strand thickness reduction increasing, the tensile and compressive stresses on the strand surface increase proportionally.

(4) The largest shape profile displacement at the narrow face was attained in the asymmetrical case. The narrow face profile can be utilized as a parameter for validating the model and thereby providing a better understanding on the formation of casting defects in order to improve the castability of difficult steel grades.

(5) The model has given good results and can provide new steel casting insights for optimizing the thin slab continuous casting process.

Acknowledgements

The SteelSim model development is being done in cooperation with the Institute for Energy Technology (IFE), the University of Science and Technology Beijing (USTB) and the Direct Sheet Plant (DSP) of Tata Steel in IJmuiden. We would like to thank André Burghardt, Henk Visser and Fokko Mensonides for their useful input for developing the model.

References

• 1)   W. R.  Irving: Continuous Casting of Steel, The Institute of Materials, London, (1993), 153.
• 2)   B. G.  Thomas: The Encyclopedia of Advanced Materials, Vol. 2, Pergamon Press, Oxford, UK, (2001), 1.
• 3)   T.  Nakagawa,  T.  Umeda,  J.  Murata,  Y.  Kamimura and  N.  Niwa: ISIJ Int., 35 (1995), 723.
• 4)   F.  Costes,  A.  Heinrich and  M.  Bellet: Proc. 10th Int. Conf. on Modeling of Casting, Welding and Advanced Solidification Processes, TMS, Warrendale, PA, (2003), 393.
• 5)   J. K.  Brimacombe,  I. V.  Samarasekera and  J. E.  Lait: Continuous Casting-Heat Flow, Solidification and Crack Formation. Iron and Steel Society, AIME, New York, (1984).
• 6)   D. G.  Eskin, Suyitno and L. Katgerman: Prog. Mater. Sci., 49 (2004), 629.
• 7)   B. G.  Thomas: Metall. Mater. Trans. B, 33B (2002), 795.
• 8)   J.  Ren and  Z.  Wang: Ironmaking Steelmaking, 25 (1998), 394.
• 9)   K. J.  Lin and  B. G.  Thomas: Thermal Stress Analysis of Bulging with Roll Misalignment for Various Strand Cooling Intensities, Report, Continuous Casting Consortium, University of Illinois, Urbana, IL, (2001).
• 10)   S.  Ha,  J. R.  Cho and  B. Y.  Lee: J. Mater. Process. Technol., 113 (2001), 257.
• 11)   J.  Zhang,  H. F.  Shen and  T. Y.  Huang: Adv. Mater. Res., 154 (2005), 1456.
• 12)   N.  Triolet,  M.  Bellet and  L.  Avedian: Rev. Metall-CIT, 102 (2005), 343.
• 13)   W. D.  Bennon and  F. P.  Incropera: Int. J. Heat Mass Transf., 30 (1987), 2161.
• 14)   S.  Asai and  I.  Muchi: Trans. Iron Steel Inst. Jpn., 18 (1978), 90.
• 15)   D.  Mortensen: Metall. Tran. B., 30B (1999), 119.
• 16)   S.  Ghosh: Mater. Shap. Tech., 8 (1990), 53.
• 17)   S.  Ghosh and  N.  Kikuchi: Comput. Methods Appl. Mech. Eng., 86 (1991), 127.
• 18)   R. W.  Lewis,  K.  Morgan,  H. R.  Thomas and  K. N.  Seetharamu: The Finite Element Method in Heat Transfer Analysis, Wiley, Colchester, (1996), 25.
• 19)   H. G.  Fjær and  A.  Mo: Model. Identif. Control, 14 (1990), 193.
• 20)   M.  Bellet and  V. D.  Fachinotti: Comput. Methods. Appl. Mech. Eng., 193 (2004), 4355.