A study of cup-cup axisymmetric combined extrusion by the upper-bound approach I. Upper-bound solutions for the deformation force

Abstract

In this paper, several kinematically admissible velocity fields for cup-cup axisymmetric combined extrusion are advanced. On the basis of these velocity fields, the upper-bound approach is applied to analyze the process of combined extrusion and to estimate the average uppper-arm pressures at different stages of deformation. It is found that the average upper-ram pressure varies with the reduction in area of the backward-extrusion part in a manner somewhat similar to a parabolic function, and that it varies monotonously with the reduction in area of the forward-extrusion part. During the extrusion process, with progressive penetration of the upper ram, the deformation flow may change from steady flow in the early stages into non-steady flow in the final stages. Moreover, both in the early stages and in the final stages, there are three possible flow patterns: simple forward extrusion; simple backward extrusion; and forward-backward extrusion. Good correlation is found between the theorical and experimental results. The results presented in the paper can be used for process design.