Study of the ECAE process by the upper bound method considering the correct die design

Equal channel angular extrusion or pressing (ECAE or ECAP) is a process used to introduce severe plastic deformations (SPD) to processed materials with the aim of improving their mechanical properties by reducing the grain size. In this work a study of the required force for performing the ECAE process, which takes into account the ECAE dies proposed by Luis [Luis, C.J., 2004a. On the correct selection of the channel die in equal channel angular extrusion processes. Scripta Mater. 50, 387–393] is developed. These die geometries improve the deformations attained in the traditional ECAE dies and they allow a correct flow of the material, a complete filling of the channels and reduce the damage introduced inside the part, increasing the attained strain. By using the upper bound method the required force for performing the ECAE process in function of all the geometric parameters is determined. Although some works exist that have applied the upper bound method to analyse the ECAE process, they consider plane strain conditions. This works presents an analysis of required forces in the ECAE process considering a three dimensional geometry and hence attained results are more reliable than those obtained by assuming plane strain conditions.