Variational upper-bound approach to solution of axisymmetric rods through conical dies with discussion of interface friction and strain hardening

In this paper, a Variational Upper-Bound (VUB) approach which applies the upper-bound theorem with the variational technique is developed for the analysis of axisymmetric rod through conical dies. By using the VUB method, a set of naturally boundary conditions can be derived in addition to the kinematically boundary condition which is the only intuitively recognizable by traditional upper-bound analysis. These natural conditions which can scarcely be obtained intuitively play a key to effect of the interface friction and are physically interpreted in this paper. Also discussed in this paper include effect of processing parameters on several aspects. Effect of strain hardening on the solution is presented. The result has shown that (1) the VUB method may appropriately take account for the effect of interface friction, (2) considerations of workhardening effect are sometimes necessitated depending upon both the designated semi-cone angle and the anticipated area reduction, and (3) improvement of the calculated energy is accomplished by the present VUB method.