The Mechanics of Ideal Forming

Abstract

In this paper, the mechanics of ideal forming theory are summarized for general, three-dimensional, nonsteady processes. This theory has been developed for the initial stages of designing deformation processes. The objectives is to directly determine configurations, both initial and intermediate, that are required to ideally form a specified final shape. In the proposed theory, material elements are prescribed to deform along minimum plastic work paths, assuming that the materials have optimum formabilities in such paths. Then, the ideal forming processes are obtained so as to have the most uniform strain distributions in final products without shear tractions. As solutions, the theory provides the evolution of intermediate shapes of products and external forces as well as optimum strain distributions. Since the requirement of ideal forming to follow minimum work paths involves an over determination of the field equations, the theory places constraints on constitutive and boundary conditions. For example, tool interfaces must be frictionless and yield conditions must have vertices to achieve self-equilibrating three-dimensional deformations in most cases. Despite these constraints, the theory is believed to provide a useful starting point for deformation process design.