Thermal stresses near a penny-shaped crack in an elastic sphere embedded in an infinite elastic space

This paper gives an analysis of the distribution of thermal stresses in a sphere which is bonded to an infinite elastic medium. The thermal and the elastic properties of the sphere and the elastic infinite medium are assumed to be different. The penny-shaped crack lies on the diametral plane of the sphere and the centre of the crack is the centre of the sphere. By making a suitable representation of the temperature function, the heat conduction problem is reduced to the solution of a Fredholm integral equation of the second kind. Using suitable solution of the thermoelastic displacement differential equation, the problem is then reduced to the solution of a Fredholm integral equation, in which the solution of the earlier integral equation arising from heat conduction problem occurs as a known function. Numerical solutions of these two Fredholm integral equations are obtained. These solutions are used to evaluate numerical values for the stress intensity factors. These values are displayed graphically.