AN UPPER-BOUND ANALYSIS OF THE BACKWARD EXTRUSION OF INTERNALLY ELLIPTIC-SHAPED TUBES FROM ROUND BILLETS

Abstract

An upper-bound method is applied to determine the final-stage extrusion load and the deformed configuration for the three-dimensional backward extrusion of internally elliptic-shaped tubes from round billets. A simple kinematically admissible velocity field for the three-dimensional deformation is proposed, from which the upper-bound extrusion load, the velocity distribution, and the configuration of the extruded billet are determined by minimizing the total power consumption with respect to chosen parameters. Experiments have been carried out with fully-annealed commercial aluminum alloy billets at room temperature, using different sizes of elliptic punches. The theoretical predictions both for extrusion load and deformed configuration are in good agreement with the experimental results.