In order to solve the nonlinear integral difficulty of the Mises yield criterion, a linear yield criterion, called the collaborative approximation (CA) yield criterion, is proposed by the collaborative control method. According to the approximation method, the mathematical expression of the CA yield criterion is derived as a linear function of the three principal stresses. The theoretical results based on the yield criterion in the form of the Lode parameter are verified with the classical test data, and a good agreement is found. Meanwhile, for the purpose of proving the effectiveness of the yield criterion, its specific plastic power is derived and applied to establish the rolling force model of an extra-thick plate. In the modeling, the internal power of plastic deformation is obtained by using the derived specific plastic power, while the shear power dissipation and the frictional power dissipation are obtained by using the methods of strain vector inner product and average velocity integration. Then, the analytical solution of the rolling force is obtained and then extended to the one accounting for the temperature rise. The maximum errors of the predicted rolling torque and rolling force without considering the temperature rise are 12.72% and 11.78%, respectively, while those considering the temperature rise decrease to 3.54% and 5.23%, respectively. Moreover, the influence of relative reduction, friction factor, surface temperature, and the temperature rise of the workpiece on the theoretical results is discussed.
Optimization solution of vertical rolling force using unified yield criterion
