A new generalized upper-bound solution for the ECAE process

A new generalized upper-bound solution for the equal-channel angular extrusion (ECAE) process is presented in this paper. Using mathematical definition of Bezier curves, a streamline was formulated to define a generalized deforming region. Based on this deforming region, a kinematically admissible velocity field was obtained from which upper-bound solutions were computed. By changing the parameters defining the Bezier-shaped streamline which in turn defines the deforming region, the optimization of the upper-bound solution was carried out. Equal-channel angular extrusion through a 90° bend was considered. Using the formulation presented in here, it was possible to predict the shape of the dead metal zone and its variation with frictional conditions. Unlike previous work in which a fixed circular shape had been assumed for the dead metal zone, in this paper, a generalized shaped Bezier curve was used. The optimum value of the extrusion pressure for ECAE was obtained and compared with both experimental and theoretical data from previous works. It was concluded that the present solution gave an improvement over all previous works and the authors’ results were closer to experimental data.