Power-Formula Viscoplasticity, Its Modification and Some Applications

Abstract

A power viscoplastic constitutive equation was first proposed by Bodner and Partom in 1972. This specific formula has its origin in the physical phenomenon of dislocation dynamics and due to the simplicity of its mathematical form, it is a useful constitutive equation in solving boundary value problems. In this paper a brief review of the basic relation is given, followed by discussion of some relatively less known features of this formula. The body of the paper deals with the modification of the equation to explore its potential in several directions. The first modification consists of making the “threshold stress” strain rate dependent. The second modification aims of modeling strain rate history dependency. Due to space the formulation of the boundary value problems of uniaxial testing and its implementation through finite element programs will not be reported here. Results demonstrating the effect of strain rate and strain-rate history are presented. They are in good qualitative agreement with available experimental data.