An upper-bound analysis of the geometric shape of the deformation zone in rod extrusion

Abstract

The subject of this paper is an analysis of the geometric shape of the deformation zone in rod extrusion by an upper-bound analysis. In this analysis the boundary at the entrance into the deformation zone is assumed to be an arbitrarily curved surface, convex or concave, whilst the boundary at the exit is assumed to be a spherical surface. The shape of the boundary at the entrance is determined by minimizing the energy dissipation during the extrusion process. It is shown here that the boundary at the entrance of the deformation zone is generally a concave ellipsoidal surface, the concavity decreasing with increasing extrusion ratio and friction factor and decreasing die angle. The tendency to central cracking in the rod extrusion process increases with increasing concavity of the boundary at the entrance and decreasing extrusion ratio.