THE MECHANICS OF IDEAL FORMING

In this paper, the mechanics of ideal forming theory are summarized fo r general, three-dimensional, nonsteady processes. This theory has bee n 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 def orm along minimum plastic work paths, assuming that the materials have optimum formabilities in such paths. Then, the ideal forming processe s are obtained so as to have the most uniform strain distributions in final products without shear tractions. As solutions, the theory provi des the evolution of intermediate shapes of products and external forc es as well as optimum strain distributions. Since the requirement of i deal forming to follow minimum work paths involves an over determinati on of the field equations, the theory places constraints on constituti ve and boundary conditions. For example, tool interfaces must be frict ionless and yield conditions must have vertices to achieve self-equili brating three-dimensional deformations in most cases. Despite these co nstraints, the theory is believed to provide a useful starting point f or deformation process design.