A universal velocity ®eld for the extrusion of non-axisymmetric rods with non-uniform velocity distribution in the extrusion direction

This study formulates a universal velocity ®eld that is kinematically admissible for application in the extrusion of non-axisymmetric rods. Then upper bound theorem dictates that a better upper bound solution heavily depends on the precise conformity of the velocity ®eld postulated. However, a compromise must frequently be made, since the formulation is in general rather complicated. The kinematically admissible velocity ®eld proposed herein has the following features: (a) it is three-dimensional, (b) it is non-uniformally distributed in the axial direction, and (c) the formulation is straight-forward once the boundary of the deformation zone is speci®ed. In addition, the velocity ®eld is applied to the extrusion of rectangular, hexagonal, and octagonal rods from round billets. Moreover, the extrusion loads are calculated against process variables such as the semi-die angle, the percentage reduction of area, and the friction factor. Furthermore, the velocity ®eld is compared with results from the literature, indicating that the present results render a better upper bound solution for application in extrusion than do previous results. # 2000 Published by Elsevier Science S.A. All rights reserved.