Two-parameter Rigid Block Approach to Upper Bound Analysis of Equal Channel Angular Extrusion Through a Segal 2θ-die

This article deals with a phenomenological description of experimentally determined complex geometric shape of material dead zone during Equal Channel Angular Extrusion (ECAE) through a Segal 2 theta-die with a channel intersection angle of 2 theta>0 degrees and 2 theta<180 degrees. Taking into account the complex dead zone geometry in a 2 theta-die, a two-parameter Rigid Block Method (RBM) approach to a two-parameter Upper Bound Method (UBM) has been introduced with Discontinuous Velocity Field (DVF) for planar flow of plastic incompressible continua. The two-parameter UBM has allowed us to derive the numerical estimations for such energy-power parameters of ECAE as punching pressure and accumulated plastic strain for 2 theta-dies. The obtained computational data have been compared with the one-parameter analytic UBM solution. Good agreement between the two computational results has been found.