The Upper Bound Approach to Plane Strain Problems Using Linear and Rotational Velocity Fields—Part II: Applications

[+] Author and Article Information
Betzalel Avitzur

Institute for Metal Forming, Department of Metallurgy and Materials Engineering, Lehigh University, Bethlehem, Pa. 18015

Waclaw Pachla

High Pressure Research Center, Polish Academy of Sciences, “Unipress,” Warszawa, Poland

J. Eng. Ind 108(4), 307-316 (Nov 01, 1986) (10 pages) doi:10.1115/1.3187081 History: Received May 10, 1985; Online July 30, 2009


Following Part I which investigated an upper bound approach to plane strain deformation of a rigid, perfectly plastic material, this Part II considers the same approach as applied to actual forming operations. The processes of drawing and extrusion, of metal cutting and of rolling are analyzed, and explicit equations are developed to calculate the surfaces of velocity discontinuity (shear boundaries), velocity discontinuities, and the upper bound on power for these processes. Both the simple, unielement velocity fields as well as the more complex multielement fields are explored. The upper bound solution is shown to be a function of the independent (input) and pseudoindependent (assumed) process parameters as minimized by an optimization procedure. Rules concerning the assumption of pseudoindependent parameters are presented and the optimization procedure is discussed. Final conclusions lead the way for the application of upper bound analyses to such industrial processes as sheet and strip drawing, extrusion, forging, rolling, leveling, ironing and machining, and to the investigation of such flow failure modes as central bursting, piping and end splitting (alligatoring).

Copyright © 1986 by ASME
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