A New Method of Solving Plane Strain Boundary Value Problems for the Double Slip and Rotation Model

A method of solving plane-strain boundary value problems for a reduced version of the double slip and rotation model is developed. It is assumed that the intrinsic spin vanishes. Elastic strains are neglected. The Mohr-Coulomb yield criterion is adopted. An analogy between the solutions for this model and classical rigid plastic solutions of pressure-independent plasticity is revealed. The method is based on introducing auxiliary variables that satisfy the equation of telegraphy in regions where both families of characteristics are curved. Therefore, Riemann's method can conveniently be applied to solving boundary value problems. The method is employed for analyzing the processes of plane strain drawing and extrusion through a wedge-shaped die. Friction is neglected. The solution is given in terms of ordinary integrals. The effect of the angle of internal friction on processes' parameters is revealed. The solution reduces to available solutions of pressure-independent plasticity if the angle of internal friction vanishes.