Mathematical modeling of closure behavior for a centrally elliptical void in thick slab

Abstract To investigate the evolution behavior of a centrally elliptical void in thick slab during rolling, a critical criterion for closing a central elliptical void is established through the energy analysis. According to the condition of volume constancy, a triangular velocity field embedding an elliptical void is established. Based on the velocity field, the minimum value of rolling energy rate, composed of shear energy rate and cracking energy rate, is calculated. According to the balance principle of energy rate, the expression of relative stress factor is obtained. Then, a mechanical criterion for void closure is derived from the basis of extreme condition, and the effects of void size, aspect ratio, geometrical shape parameter, thickness-to-radius ratio, and the relative reduction on the void closure are analyzed. Several rolling processes with different elliptical voids under seven aspect ratios are simulated by the finite element method (FEM), and the evolution characteristic of the void is revealed. The analytical results based on the mechanical criterion and those by the FEM are compared. It is shown that the two prediction results are in good agreement, and a flat void is easier to be closed than a sharp one. Also, the simulated rolling force and torque are obtained through the FEM model, and the comparison result confirms the validity of the upper bound solution. Finally, a rolling experiment with a prefabricated void is carried out to check the reliability of the closure criterion, and a good consistence is also found. In addition, the shortage of the present investigation based on 2D simulation for assessing the mechanical criterion is discussed as a prospect of the future research.