Design of Plane Strain Bending Based On Ideal Flow Theory

摘要

Numerical codes based on the ideal flow theory have been mainly developed for nonsteady sheet(membrane)metal forming processes.To account for thickness effects in sheet metal forming processes,two-and three-dimensional theories should be adopted.The simplest theory of this class is the theory of plane strain deformation.In particular,it can be applied to design sheet bending.It is known that pure bending under the plane strain condition produces redundant work in a layer near the center of the material.To exclude such redundant work,appropriate loading conditions should be chosen.One way to determine such loading conditions is to apply the ideal flow theory.In general,the ideal flow theory is restricted to perfectly plastic materials.However,in the case under consideration,viscoplastic hardening materials can be treated as well.In the present paper,a semi-analytical solution for such materials is found.An optimal initial shape is determined by adopting the criterion that the work required to transform the initial shape into the final shape attains a minimum among a class of initial shapes.The solution also gives tractions for obtaining the final shape of given geometry with no redundant work.Comparison with pure bending is made.