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

摘要

This study formulates a universal velocity field thatis kinematically aditussible for application in the extrusion ofnon-axisymmetric rods. Then upper bound theorem dictates that abetter upper bound solution heavily depends on the preciseconformity of the velocity field postulated. However, acompromise must frequently be made, since the formulation is ingeneral rather complicated. The kinematically admissible velocityfield proposed herein has the following features: (a) it is three-dimensional, (b) it is non-uniformally distributed in die axialdirection, and (c) the formulation is straight-forward once theboundary of the deformation zone is specified. In addition, thevelocity field is applied to the extrusion of rectangular, hexagonal,and octagonal rods from round billets. Moreover, the extrusionloads are calculated against process variables such as the semi-dieangle, the percentage reduction of area, and the friction factor.Furthermore, the velocity field is compared with results from theliterature, indicating that the present results render a better upperbound solution for application in extrusion than do previousresults. 2000 Published by Elsevier Science S.A. All rights reserved.