Effect of Constitutive Laws on Plane Strain Ideal Flow Design: an Analytical Example

The major objective of this paper is to clarify the effect of constitutive laws on bulk forming design based on the ideal flow theory. The latter theory is in general applicable for perfectly/plastic materials. However, its kinematics equations constitute a closed-form system, which are valid for any incompressible materials, therefore enabling us to extend design solutions based on the perfectly/plastic constitutive law to more realistic laws with rate sensitive hardening behavior. In the present paper, several constitutive laws commonly accepted for the modeling of cold and hot metal forming processes are considered and the effect of these laws on one particular plane strain design is demonstrated. The closed form solution obtained describes a nontrivial nonsteady ideal process. The design solutions based on the ideal flow theory are not unique. To achieve the uniqueness, the criterion that the plastic work required to deform the initial shape of a given class of shapes into a prescribed final shape attains its minimum is adopted. Comparison with a non-ideal process is also made