Effect of Finite Velocity of Thermal Wave on Stress Focusing Phenomena

Abstract

When an isotropic and homogeneous solid sphere and/or infinitely long solid cylinder are suddenly subjected to an instantaneous uniform heating, a stress wave occurs at the moment thermal impact is applied. The stress wave proceeds radially inward to the center of a sphere and/or cylinder. The wave may accumulate at the center and give rise to very large stress magnitudes, even though the initial thermal stress is relatively small. This phenomenon is called the stress-focusing effect. In this study, the stress focusing effect in a solid sphere and solid cylinder under instantaneous uniform heating at the free surface is studied on the basis of the generalized thermoelastic theories, that is, the Lord-Shulman (L-S) and the Green-Lindsay (G-L) theories. The combined governing equations of both theories are solved by the numerical inversion of Laplace transform. Calculations have been performed to exhibit the radial distributions and time variations of the radial and hoop thermal stresses on the basis of the L-S theory. The effects of the thermomechanical coupling and the relaxation time on the stress focusing phenomena as well as the singularity of stresses are discussed.