© 1962 by Oxford University Press
PROPAGATION OF SPHERICAL PLASTIC-ELASTIC DISTURBANCES FROM AN EXPANDED CAVITY
( Department of Applied Mathematics, Sheffield University )
An infinite medium of elastic-perfectly plastic material contains a single spherical cavity and is initially subject to a uniform hydrostatic pressure. By the quasi-static application of an additional uniform pressure to the wall of the cavity, the medium is then placed in an expanded state in which the cavity is surrounded by a zone within which plastic flow has occurred. A detailed study of this expanded state has been made in an earlier paper (1) in the case of a homogeneous, isotropic material which obeys the generalized Hooke's law when undergoing elastic deformation and Coulomb's law of failure with its associated flow rule during plastic deformation. The present paper is concerned with the propagation of stress waves through the medium by the application of an additional uniform, time-dependent pressure a(t) to the face of the expanded cavity, the additional straining produced by this pulse being assumed to be universally small.
When a < 0 for all t, the material in the plastic zone is subjected to further loading and a plastic wave is formed in this region which is successively reflected at the plastic-elastic interface and at the cavity wall, each reflection at the interface resulting in the initiation of an outgoing elastic wave. The bulk of the paper is devoted to a discussion of this plastic-elastic wave system.
When a < 0 for all t, the plastically deformed material unloads and the motion of the medium consists of a single diverging elastic wave. In materials which are free from internal friction (e.g. ductile metals) this disturbance is unaffected by the preloading of the medium, but as the internal friction parameter increases so does the extent to which the form of the unloading wave may be modified by the pre-existing state of stress.