an investigation in the deformation zone of the ecae process by the upper bound theorem

in the present paper, the deformation zone of the ecae (equal channel angular extrusion) process was investigated using the upper bound theorem. for this purpose, the shape of the streamlines in the deformation zone was assumed to be cubic bezier curves. then, the force required for the ecae process was optimized with regard to the parameters defining the shape of streamlines by the upper bound theorem. by using of these streamlines, equivalent stain induced through one pass of the ecae was calculated and the shape of the dead metal zone was determined. the influence of different friction conditions on the deformation field was studied. the force applied through the process was determined by optimizing an upper bound solution and was compared with other works including experimental and theoretical data. also using this comparison, it was seen that the difference between the theoretical and experimental value for the force was reduced in the present method.