Determination of processing power and optimum billet radius of modified backward extrusion by upper bound approach

A recently developed backward extrusion method entitled "modified backward extrusion" was presented using an upper bound analysis. For this purpose deformation area was divided into four distinct zones and a kinematically admissible velocity field for each of them was suggested. Total dissipated power was calculated for the deformation zones and the extrusion power was computed. The correlations of important geometrical parameters with extrusion force and dissipated powers were shown. Finding the initial billet size, a challenging area in the modified backward extrusion method, was discussed and the optimum billet radius was obtained, considering the minimum relative extrusion pressure. Finite element analyses were conducted and the results were compared with the upper bound analysis. Finally, experiments were executed on commercially pure aluminium and a good agreement between upper bound and finite element analyses with experimental values was observed.