ELASTIC-PLASTIC WAVES FOR COMBINED STRESSES.
Interim technical rept.,
STANFORD UNIV CALIF DEPT OF APPLIED MECHANICS
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The general case of plane wave propagation for combined stresses is considered in a half-space. The analysis is based on an elastic-plastic theory for an isotropic work-hardening material which satisfies a flow or incremental type law. The stress-strain curve is assumed concave towards the strain axis with possibly a bend at yield. The wave propagation analysis determines the motion to be governed by a system of quasi-linear hyperbolic equations of the first order. Two different types of loading are considered in this study--the coupled double shear loading and the combined pressure and shear. The loading functions are continuous and are assumed to be uniformly distributed over the surface for all t. Two distinct wave speeds are found in the plastic region for both loading types. For general loading plastic flow can propagate with each wave speed which may be as fast as the elastic wave speed. This is contrary to wave for a single stress component. This fact may have an important bearing on the interpretation of experiment, for which, in the past, propagation of plastic waves at elastic wave speed has been considered to indicate rate effects. Solutions of the problems are obtained by numerical integration along the characteristics on a step by step basis. The loading-unloading boundaries are determined in the x - t plane. For a simple case of the double shear problem when the components are in proporation, very good agreement is obtained between the numerical result and the known analytical solution. Author