Thermal Shock in a Hollow Sphere Caused by Rapid Uniform Heating

Abstract

This paper is concerned with a method for calculating the dynamic stress distribution in a hollow sphere. Adopting the Goodier’s concept, the dynamic thermoelastic problem in a sphere is decomposed into a particular form of dynamic stress problem corresponding to the thermoelastic displacement potential and the homogeneous form of dynamic stress problem corresponding to the stress functions. Applying the ray theory to the homogeneous form, we obtain the general solution for transient waves induced by sudden heating. When a hollow sphere is subjected suddenly to a uniform temperature rise throughout the sphere, stress waves occur at the internal and external surfaces the moment thermal impact is applied. During instantaneous heating, the interfering effects of these waves can cause a very high dynamic stress at the internal surface of a sphere. The numerical results show that, as the ratio of the internal radius to the external one increases, the tangential stress on the internal surface becomes higher.