Stress wave propagation in rods of elastic-viscoplastic material

Abstract

A number of uniaxial stress wave propagation problems are solved based on the unified, multi-dimensional, elastic-viscoplastic constitutive equations of Bodner-Partom and a finite difference numerical procedure. Solutions are obtained for cases of a velocity imposed for a time period or indefinitely at the end of a semi-infinite bar, and for the condition of a finite bar subjected to a high velocity superimposed on an applied low velocity after a time interval. Work-hardening is taken to be isotropic for stress of constant sign, while an isochoric, anisotropic work-hardening formulation is employed for problems involving stresses of reversed sign due to unloading or reflections. The numerical exercises are based on constants for a strongly strain rate sensitive material, titanium, and the results indicate good qualitative agreement with a wide range of experimental observations.