Metal Flow Through Conical Converging Dies—A Lower Upper Bound Approach Using Generalized Boundaries of the Plastic Zone

Abstract

The boundaries of the plastic zone in radial flow through conical converging dies are analyzed. The assumed boundaries are generalized, so that their shape and location are functions of the geometry of the process. An upper bound approach to the energy consumed is calculated. The energy is minimized with respect to the shape of the boundaries and that shape that yields minimum energy is found as a function of the reduction in area, the die semicone angle, and the friction between the die and material. The energy calculated with generalized boundaries was found to be lower than the energy calculated for spherical boundaries, and thus the assumptions in the present work yield a better upper bound.