A kinematic analysis of the angular extrusion (AE) operations

Detailed deformation analysis of the AE process is presented, based on a finite-deformation formulation. The two basic assumptions used in the analysis are that (1) the material is incompressible, and (2) the material flow is steady state in both the incoming channel and the outgoing channel. The main objective of this study is to identify the parameters, which are consistent with finite-deformation formulation, that appropriately characterize the extrusion process and can be observed and measured through experiments. These parameters are the maximum principal stretch and its orientation angle, or equivalently, the maximum amount of shear and its orientation. The expressions of these parameters as functions of the geometry of the angular extrusion setup are given in closed forms for angular extrusions with either sharp transitions or circular transitions. Finally, we also analyze the deformation of multiple-extrusion operations. Through a specific example, we illustrate that the final deformation is not simply the summation of the deformation associated with each individual step, as suggested by the infinitesimal deformation theory.