Analysis of Axisymmetric Extrusion Process through Dies of any Shape with General Shear Boundaries

In this paper, a generalized expression for the flow field in axisymmetric extrusion process is suggested to be valid for any dies and the boundary shapes of the plastic deformation zone. The general power terms are derived and the extrusion force is calculated by applying upper bound technique for a streamlined die shape and exponential functions for shear boundaries. It is shown that assuming exponential boundaries for deformation zone yields a die shape with smaller extrusion force than that of by assuming spherical shape boundaries is in agreement with the results obtained by the finite element method.