Plastic Wave Propagation in Linearly Work-Hardening Materials

Abstract

The combined longitudinal and torsional waves in a linearly work-hardening thin-walled tube are studied. Explicit solutions are obtained for the stress paths in the stress space for the simple waves. The stress paths are all “similar”, and hence a proportionality property in the solutions exists for simple waves as well as for a more general initial and boundary-value problem. The same results apply to any type of plane waves of combined stress. Thus the “linearity” in the solutions of one-dimensional plastic waves in a thin rod of a linearly work-hardening material is not completely lost in the solutions of combined stress waves. Depending on whether the plastic wave speed cp is larger, equal, or smaller than c2 , the nature of the solutions to a given combined stress wave problem can be quite different. Examples are given to illustrate this point.