An upper-bound solution for axisymmetric extrusion of composite rods through curved dies

Abstract

The study is concerned with an analysis of forward extrusion of composite rods through curved dies. A kinematically admissible velocity field is derived by assuming proper streamlines and applying the flow function concept to each material region of plastic deformation. Two kinds of flow functions are chosen in order to compare the effect of the choice of the flow functions. The effect of work-hardening is incorporated approximately by calculating the strains at the exit of both materials. The upper-bound method is then employed to determine the extrusion pressure for various process variables. The experiments are carried out with commercially pure aluminum and copper billets for various reductions of area and cone angles at room temperature. The experimental results are then compared with the theoretical calculations. The comparison shows that the second-order flow function is in better agreement with the experimental observation both in extrusion loads and in deforming regions.