One-Dimensional Theory of Stress Waves of Solids in Uniaxial Stress State.

Abstract

Using an elastic-plastic-viscoplastic constitutive equation, an equation relating stress wave speed, particle velocity and strain is derived. The derived equation is of the same form as that of the theory of the elastic-plastic stress wave (Karman's theory). However, contents of both equations are different because the former takes into account the viscoplastic strain and the latter does not. It is shown from numerical values for the derived equations that the stress wave speed decreases with increasing particle velocity and the stress wave speed corresponding to particle velocity increases with increasing strain rate. Also, it is shown that the propagation speed corresponding to particle velocity agrees qualitatively with the experimental results. Moreover, every equation of existing theories of the elastic-plastic, elastic-viscoplastic and longitudinal elastic stress waves is derived in consistent mathematical form from the theory of elastic-plastic-viscoplastic stress waves.