Shape distortion and air gap formation during continuous casting.

A theoretical model has been developed which relates the build-up of stresses in the thin shell of steel solidifying in a continuously casting mould, to the shape distortion and the formation of an air gap. The work postulates that the behaviour of this shell can be analysed as that of a flexible structure formed by four elasto-perfectly plastic beams linked by rigid comers. This "box" represents the whole section of solidified shell at a given metallurgical height only if the section is totally detached from the mould. In general, it represents the detached corner portions alone. The rest of the shell is assumed to remain clamped against the mould wall by the metallostatic pressure. The thermal contraction of the neutral axis "filament" along the whole shell determines the amount of room which is available for the detached corner portion to distort, and thus also the size of the detached lengths of shell. The mechanical equilibrium of the structure is determined by the combined effect of temperature gradients and metallostatic pressure, by the rigidity condition imposed at the corner and by the flexural characteristics of the shell. The yield stress of the steel is assumed linearly dependent on temperature.The analysis of the shape distortion and air gap formation was initially informed by the observed behaviour of a partial physical analogue constructed from bi-metallic strips linked by rigid corners. Thermal moments were induced by immersing this analogue in a water bath at controlled temperatures, and distributed loads were imposed through a system of pulleys. The elastic behaviour of this physical analogue was predicted using basic beam theory.For the analysis of the deformation of a continuously cast structure, mathematical equations were derived which describe the overall moment and force equilibrium; the elastic and plastic stress distribution across the thickness of the shell; and the force and moment equilibrium within the cross-section of the shell. An equation was derived relating the curvature at any point along the shell to the moment at the corner of the structure. An iterative procedure was developed to determine the moment at the corner and a Runge-Kutta algorithm was incorporated to integrate the curvature equation. Further equations were derived which relate the deflection at the corner and the detached length on one side of the section, to the total length of the other side of the section. Recent high temperature studies of the mechanical behaviour of steels have been analysed in terms of the theoretical model developed. The model is able to predict the extent and thickness of the air gaps forming in the corner regions during the casting of billets and slabs and also provides explanation for the formation of both internal and external off-corner cracks. It also demonstrates the theoretical basis behind the practically observed relationship between casting speed and crack formation.