A dynamic closure criterion for central defects in heavy plate during hot rolling

A new continuous velocity field used to analyze central defect closure for heavy plate rolling is proposed by modifying a two-dimensional velocity field. By using the proposed velocity field and mean yield criterion (or called MY criterion for short), the internal deformation energy rate is obtained. With co-line vector inner-product method, the frictional energy rate is then integrated. Ultimately, an analytical solution of the rolling torque and rolling force is obtained by minimizing the total energy rate with respect to neutral angle. Based on the assumption that when a central defect tends to be closed the stress state coefficient will obtain its critical value, a mathematical expression of critical shape factor together with a dynamic closure criterion for rectangular shape defects are derived. It is found that the critical shape factor is a function of initial plate thickness, relative reduction, work roll radius, and friction factor. The effects of independent rolling parameters such as plate thickness, relative reduction, work roll radius, and friction factor on the critical shape factor are discussed systematically. The results show that the increases in relative reduction, work roll radius and friction factor benefit defect closure, while a large value of initial plate thickness induces central burst formation. In addition, the proposed criterion is validated by comparison with available theoretical results and very good agreement is found.