Finite element analysis of the plastic deformation zone and working load in equal channel angular extrusion

A comprehensive finite element (FE) study is conducted to analyze the formation of the plastic deformation zone (PDZ) and evolution of the working load with ram displacement during a single pass of equal channel angular extrusion (ECAE) with intersection angle 90°. This study explores systematically the coupled effects of material response, outer corner angle (Ψ = 0°, 45°, or 90°), and friction on ECAE deformation, which can be effectively analyzed through two key characteristics of the PDZ alone. These characteristics, the morphology and strain-rate distribution within the PDZ, are largely responsible for the heterogeneity in strain that develops in the sample at the end of a single pass. Strain hardening, Ψ, and friction were all found to have some effect on the PDZ, though under their combined influence, one tends to dominate over the others. Strain hardening tends to produce asymmetry in the strain-rate distribution within the PDZ, resulting in corner gaps and a more heterogeneous strain distribution than an ideal perfectly plastic material. In cases in which the material fills the die, the PDZ shape is largely governed by the die geometry, i.e. Ψ, independent of material response and friction. In this respect, friction does however help to reduce the free surface gaps that form between a strain hardening material and the die, but to further increase the degree of heterogeneity. The distinct stages that are present in the load versus displacement curves are defined and associated with those in sample deformation, some of which depend on Ψ and others on material properties. Effective strain calculations are compared with various analytical models and the one that directly accounts for the PDZ tends to perform better. To date, most of the cases studied here have not been modeled analytically; however, a stronger connection between analytical modeling and actual ECAE deformation can be made by the guidance of these FE studies on the interactive influence of processing and material variables.