Stationary axisymmetric ideal plastic flows in pressure-dependent plasticity

Previous work has developed the ideal flow theory and established that axisymmetric ideal frictionless drawing and extrusion dies can be shaped such that the principal stress trajectories are everywhere coincident with streamlines for Tresca's solids (i.e., the constitutive equations are Tresca's yield criterion and its associated flow rule). This design increases these processes’ efficiency and the final product's strain uniformity. The present work shows that a large class of stationary axisymmetric deformation processes in which the principal stress trajectories are everywhere coincident with streamlines exists for a special case of the double slip and rotation model based on the Mohr-Coulomb yield criterion, extending the ideal flow theory to these constitutive equations. Two equation systems in the form ready for applying the finite-difference method in characteristic space are derived. One of these systems is adopted to calculate the shape of the ideal drawing die for the constitutive equations considered. The effect of the reduction and the internal friction angle on the die's shape and the drawing stress is illustrated.