Invariance of plastic strains with respect to imposed rate at boundary

The concept of material "formability" is often related to imposed boundary velocity in the literature and in discussions of practical forming operations. While material strain-rate sensitivity is frequently cited, without proof, as the source of this dependence, other factors may contribute, including contact and friction conditions, temperature changes, and inertial forces in the workpiece and tooling, all of which may depend on boundary velocity. The authors showed in 1986 that strain localization in a tensile test (and other operations not involving friction and contact) was theoretically independent of boundary velocity (and material strength) for certain rate-sensitive constitutive equations, contrary to the common perception [1]. In the present paper, we generalize the principle of invariance to operations involving contact and friction and state the conditions under which the invariance is valid. These conditions are closely met for many forming operations. This expands the usefulness of the idea, which can therefore help interpretation of the role of imposed boundary velocity (and material strength) in altering material formability. The generalized principle is presented and proven using a variational formulation for rigid plasticity and the principle is discussed with respect to several analyses of common forming operations.