Analysis of Combined Backward-Forward Extrusion

The upper bound approach is used to analyze combined backward-forward extrusion. The deformation region is divided into five zones separated by planer and cylindrical surfaces of velocity discontinuities. The internal power of deformation and shear and friction losses are computed individually and summed. The pseudo-independent process parameter is the backward rate of flow with respect to which the total power of deformation is optimized. The optimal backward rate of flow is assumed to be the actual one. Thus, the backward rate of flow becomes a dependent parameter to be studied through this analysis. Conditions covering backward rates of flow from zero to maximum are demonstrated graphically. Examples are given for which combined flow results and for which either only forward flow or only backward flow occur.