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.