Upper-bound analysis of square-die forward extrusion

The present study is the preliminary research for the derivation of the generalized velocity field in three-dimensional square-die forward extrusion. As a fundamental model, the square-die forward extrusion of circular-shaped bars from regular polygonal billets is chosen and a simple kinematically-admissible velocity field is proposed. From the proposed velocity field, the upper-bound extrusion load, the velocity distribution and the average length of the extruded billets are determined by minimizing the total power consumption with respect to chosen parameters. Experiments have been carried out with hard-solder billets at room temperature. The theoretical predictions of the extrusion load are in good agreement with the experimental results and there is also a reasonable agreement in the average extruded length between theory and experiment.