A novel yield criterion and its application to calculate the rolling force of a thick plate during hot rolling

In order to solve the problem of establishing the rolling force model, which is caused by the nonlinear Mises specific plastic power, a novel yield criterion, called mean slope yield criterion, is constructed by averaging the slopes of yield loci of the Tresca criterion and Mises criterion. The yield criterion is a linear combination of the principal stress components, and its locus on the π-plane is an irregular dodecagon which intersects the Mises circle. For verification, the yield criterion was rewritten by introducing the Lode stress parameter and compared with the experimental data, and a good consistency is achieved. Meanwhile, a three-dimensional velocity field whose horizontal component satisfies the elliptic distribution from the entrance to the exit is proposed. Based on these achievements, the energy analysis of the velocity field is carried out with the derived yield criterion, and the expression of the internal deformation power is derived. Also, the friction power and shear power are derived in terms of the velocity field. Ultimately, the analytical solutions of rolling torque, rolling force, and the stress state coefficient are obtained through the minimization of the total power. By comparison, it is shown that the theoretical rolling torques and rolling forces coincide well with the measured ones since both the maximum errors are only 13.77%.