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

[+] Author and Article Information
Zeev Zimerman

Homer Research Laboratories, Bethlehem Steel Corporation, Bethlehem, Pa.

Betzalel Avitzur

Department of Metallurgy and Materials Science, Lehigh University, Bethlehem, Pa.

J. Eng. Ind 92(1), 119-129 (Feb 01, 1970) (11 pages) doi:10.1115/1.3427695 History: Received May 03, 1968; Revised October 04, 1968; Online July 15, 2010


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.

Copyright © 1970 by ASME
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