A Theory on the Mechanics of Axisymmetric Extrusion through Conical Dies

Abstract

For axisymmetric extrusion through conical dies, an admissible velocity field without discontinuities was obtained by superposition of basic flow patterns. Based on this velocity field, the upper bound to the average forming pressure and the detailed mechanics were calculated for the extrusion of a rod with a semi-cone angle of 45° and a reduction of 75 per cent in area. Three different friction conditions along the die were considered and their influence on the deformation characteristics was discussed. Flow lines, velocity components, grid distortion, strain-rate components, effective strain rate, effective strain, and stress components were plotted. A comparison of the present results with those obtained experimentally (visioplasticity) shows good agreement.