Analysis of three-dimensional extrusion of arbitrarily shaped tubes

Abstract

In cold lubricated tube extrusion of arbitrarily shaped sections, the material properties and surface quality of the extruded products are influenced by the die profile. In the present analysis the axial velocity component on the intermediate cross-section in the plastically deforming region is expressed as a general function of the coordinates and this allows the description of complete three-dimensional distortion or flow rendering more realistic flow patterns. From the derived kinematically admissible velocity field, the corresponding upper-bound extrusion pressure is then obtained by optimizing the pressure with respect to the given parameters. The grid distortion is computed by tracing the metal flow along the streamlines. The effective strains are computed in order to study the work-hardening pattern of the extruded products. Experiments have been carried using A12024 as the working material. In the computation, three product shapes namely clover, trocoidal gear and ellipse are chosen. The effects of area reduction, die length, product shape complexity and frictional condition on the extrusion pressure, the metal flow and distribution of the final effective strain have been studied extensively. The theoretical predictions both in extrusion load and metal flow are in good agreement with the experimental results.