Analysis of the Thermal Stress-Focusing Effect in a Spherical Inclusion Embedded in an Infinite Elastic Medium.

Abstract

When an infinite elastic medium with a spherical inclusion is suddenly subjected to a uniform temperature rise, stress waves occur at the interface of spherical inclusion the moment thermal impact is applied. The stress wave in an inclusion proceeds radially inward to the center of the inclusion. The wave may accumulate at the center and cause very large stress magnitudes, even though the initial thermal stress should be relatively small. This phenomenon is called the stress-focusing effect. The stress wave in an infinite medium proceeds radially to infinity. This paper analyzes, in an exact manner, the effects of these waves using the ray integrals. The results give a clear indication of the mechanism of stress-focusing effect in an inclusion embedded in the infinite elastic medium. In the special case, if the elastic compliances of the spherical inclusion tend to be zero, the problem becomes the problem of wave motion in the infinite medium with a spherical cavity.