**2.1. Index definition**

In order to measure slab broadening, the ratio of apparent shrinkage (RAS) and the ratio of ultimate broadening (RUB) were defined respectively as:

$$\text{RAS} = \left(\text{U} / \text{W} - 1\right) \times 100\% \tag{1}$$

Numerical Simulation of Slab Broadening in Continuous Casting of Steel 559

Table 1 lists the RAS and RUB values obtained for five companies. The data in the right column is from a handbook (XIONG Yi-gang, 1994). The RAS values range from 0.47% to 2.16%, with most being higher than the handbook data. The linear shrinkage of carbon steel from the initial shell to the cooled slab is 2.5%. The RUB values range from 0.34% to 2.03%, which is the result that the linear shrinkage subtracting the RAS. In general, the width of a slab is smaller than the top width of a mold. Broadening may overcome shrinkage under

The width of a cooled slab is larger than the ultimate width when broadening exists. To obtain a slab with the desired dimensions, the top and bottom widths of the mold must be reset. Therefore, the measured width (W) could replace the ultimate width (T). The RAS of a slab can thus be set by changing the values of the top and bottom widths of the mold. Then compare these values with the linear shrinkage of each steel grade, and it could consequently be found out whether the slab broadening exists and the approximate range of

CompanyA Company B Company C Company D Company E Handbook

RAS (%) 0.47~0.54 1.81 1.93~2.16 1.70~1.90 1.10 ~2.11 2.1 RUB (%) 1.96~2.03 0.69 0.34~0.57 0.60~0.80 0.39~1.40 0.4

The data show that slab broadening is common in continuous casting. The slab width is the result of shrinkage and broadening. The linear shrinkage of a carbon steel is about 2.5%,

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,

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**Table 1.** RAS and RUB values at various manufactures (FU JianXun et al. 2010(a))

which is slightly larger than the slab broadening.

determine the degree of slab broadening.

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

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

**2.3. RAS and RUB investigation** 

it could also be derived.

certain operating conditions for some particular grades of steel.

$$\text{RUB} = \left(\text{S} / \text{T} - 1\right) \times 100\% \tag{2}$$

where:

U is size of mold on the top entrance (mm); W is the measured width of the slab (mm); T is the ultimate width of the slab (in mm); S is the width of the slab (in mm).

The value of the RAS, which denotes the degree of mold shrinkage, is positive when the top width exceeds the slab width. This index can be used to set the mold size. The value of the RUB, which denotes the degree of broadening, is positive when the slab width exceeds the ultimate width.
