A size-dependent closure criterion for slab corner defects during vertical rolling process based on mathematical method

Abstract

The compression behaviour of slab corner defect in vertical rolling process is studied theoretically. In order to analyse the initial corner defect, a gamma distribution-cubic function edge deformation model is put forward. The plastic flow is analysed according to the properties of stream function and the principle of volume invariant. By using geometrical approximation yield criterion and Pavlov projection principle, the plastic deformation power, shear power, friction power and cracking power are derived. The numerical solution is obtained by minimising the total power functional, and a closure criterion of corner defect is obtained. The accuracy is well verified by comparing with experiments and FEM. Taking the typical triangular prism defect as an example, the influences of defect size on edge deformation, rolling force and critical cracking parameters are discussed. With the defect size increasing, the dog-bone peak moves outwards, the peak height increases, and the rolling force decreases. The ratio of shear power slightly decreases while the ratio of the other three types of power increases. As the defect size increases, the critical width reduction decreases, the critical radius increases, and the critical friction factor reduces. The proposed method can be helpful for improving the edge quality of steel slab and optimising hot rolling process.