Initiation of spherical elastic-plastic boundaries due to loading at a spherical cavity

Abstract

The spherical waves in an elastic-plastic, isotropically work-hardening medium generated by radial stress uniformly applied at a spherical cavity r= r 0 are studied ( r denoting radial distance). The radial stress and its time derivative at the cavity may be discontinuous at time t= t 0. If the applied radial stress is continuous while its time derivative is not, the discontinuity at ( r 0, t 0) propagates into r > r 0 along the characteristics and/or the elastic-plastic boundaries. If the applied radial stress itself is discontinuous, the discontinuity may propagate into r > r 0 in the form of a shock wave, or a centered simple-wave, or a combination of both. In any case, the solutions in the neighborhood of ( r 0, t 0) are obtained for all possible combinations of discontinuous loadings applied at r= r 0. This is a systematic study on the nature of the solution near ( r 0, t 0) where the applied load is discontinuous. Solutions for special materials, such as linearly work-hardening or ideally-plastic ones, and for special applied loadings at the cavity obtained by other workers, in which the nature of the solutions near ( r 0, t 0) are assumed a priori rather than determined, are compared with the results obtained here. Some of the solutions are found to be in error because of incorrect a priori assumptions.