**2.4. Mechanics calculations ( FU JianXun et al.2011(a))**

In the secondary cooling zone, the slab has to release sensible heat and latent heat to avoid complete solidification and to maintain the surface temperature according to the technical requirements of the metallurgy process. In this zone, the stress and strain of the slab are the result of mechanical action and thermal effects (S. Kobayashi et al,1988). Some parts of the slab may have a low temperature, which causes thermal stress in the secondary cooling zone. The thermal stress of the slab in the secondary cooling zone is small enough to be ignored compared to the stress caused by the bulging and the roller disalignment. Thus, mechanical stresses, includes the bending stress, straightening stress, roller-misalignment stress, the stress of rollers acting on the slab, and the static pressure of molten steel, determine the degree of slab broadening.

The bulging stress of a slab is defined as (Sheng Y et al ,1993) :

$$\mathcal{S} = \frac{pl^4}{32E\_\text{x}S^3} + \frac{pl^4}{32E\_\text{x}S^3} \text{(1sqrt(t))},\tag{3}$$

where Ex is the equivalent elastic modular ratio, expressed as:(Sheng Y et al ,1993)

$$E\_{\chi} = \frac{T\_{So} - T\_{m}}{T\_{so} - 100} \times 10^{6} \,\text{ }\tag{4}$$

Roller ID

Slab shell thickness (10-2 m)

**3. Model and parameters** 

JianXun et al. 2010(b-c); 2011(b)):

divided into several stages.

calculation boundaries are placed at the rollers.

to be a linear object.

independent sub-model.

**3.1. Finite element model** 

Casting speed (m·s-1)

disalignment do not cause the broadening of a slab.

Bulging (10-2 m)

64 10.8 0.0167 0.08 0.145 0.0202 0.0202 65 10.9 0.0167 0.08 0.142 0.0203 0.0203

Tables 2 and 3 reveal that the bending, straightening, and disalignment stresses are far lower than the stress of bulging. Therefore, the stresses of bending, straightening, and

Building a satisfactory three-dimensional (3D) finite element model for the numerical simulation of continuous casting in the secondary cooling zone is quite complex. Thus, to simplify the problem, the following assumptions are made, as in our previous work((FU

1. The bending and straightening effects of the slab are ignored, and the slab is considered

2. In the simulations, time, space, the characteristics of steel, and the temperature field in the slab are continuous, and the effects of the initial mechanical conditions of the slab on the deformation are ignored. The continuous caster in the secondary cooling zone is

3. Because of symmetry, 1/4 of the slab and rollers on one side is used for the calculation. 4. The slab is deformable, the rollers are stiff, and the gap between rollers is variable. The

Based on these assumptions, the thermal-mechanical coupled model of the whole secondary cooling zone is divided into 6 independent sub-models for calculation. The 15 segments of the secondary cooling zone are divided into 6 groups. The first 5 groups each contain 2 segments; the remaining 5 segments make up the last group as a completely solidified slab. A 2-m slab is used for the simulation. The slab goes through the roll arrangement at a given speed. The simulation is performed continuously from the first group to the last group, and the results of a group of rollers are taken as the initial inputs for the subsequent group.

Eight-node isoparametric elements are used for the geometric discretization of the computational domain in the model. The slab comprises 4500 elements and 5250 nodes. Figure 2 shows the finite element models of the rollers and the slab in the caster. Figure 3(a) shows the rollers and the slab in the 3rd independent sub-model. Figure 3(b) shows the 6th

Due to the symmetry of the slab in the width direction, one half of the slab was simulated. The grid units at the start plane of the slab move forward at a given speed. The static

**Table 3.** Comparison of slab stresses in the straightening zone( FU JianXun et al.2011(a))

Numerical Simulation of Slab Broadening in Continuous Casting of Steel 561

Disalignment strain(%)

Bending strain (%)

Bulging strain(%)

The stress of bending and straightening is expressed as:(Lei H et al ,2007)

$$\omega\_i = \left(\frac{D\_s}{2} - S\_i\right) \left(\frac{1}{Ri - \frac{D\_s}{2}} - \frac{1}{R\_{i+1} - \frac{D\_s}{2}}\right) \times 100\%\_\prime \tag{5}$$

The stress of disalignment is expressed as: (Chen J,1990)

$$
\varepsilon\_{\rm q} = \frac{300s\_i \delta}{l^2} \times 100\% \,\tag{6}
$$

The values of these stresses calculated for the Q235 slab are listed in Tables 2 and 3. The calculations were based on the parameters of the continuous casters of Maanshan Iron and Steel Co. Ltd. A casting speed of 0.0167 m·s-1 was used. The bending zone of the continuous caster is at the 10th~15th rollers of the 2nd segments, and the straightening zone is at the 60th~65th rollers of the 9th segments. A negative stress indicates that a pushing stress acts on the contact surface between the slab and rollers whereas a positive stress indicates a tensile stress acting on the contact surface.





**Table 3.** Comparison of slab stresses in the straightening zone( FU JianXun et al.2011(a))

Tables 2 and 3 reveal that the bending, straightening, and disalignment stresses are far lower than the stress of bulging. Therefore, the stresses of bending, straightening, and disalignment do not cause the broadening of a slab.
