Rate-dependent transient extrusion

Plane strain slip line field solutions are developed for deformation at the edge of a cylindrical billet when this is backward extruded to form a thin-walled cup. The extrusion pressure for a perfectly plastic material is then derived assuming homogeneous compression in the centre of the billet. A geometric factor, derived from the slip line field, is identified which permits the extrusion pressure to be determined for a nonlinear viscous material.Theoretical results agree well with recent experimental data on back extrusion of highly rate-sensitive superplastic alloys. It is shown that an apparent steady state exists in the process and that extrusion pressure increases with ram speed with a rate index approximately equal to that of the material. The punch profile shape has a greater effect on extrusion pressure for viscous materials than for perfectly plastic ones. The method of analysis appears to have a generality beyond the particular process considered and may be used to optimize extrusion equipment designs.