Thermal shock in a transversely isotropic cylinder containing an annular crack

Abstract

The present paper is concerned with a thermal shock problem in a transversely isotropic cylinder containing an annular crack. In analysing this problem, we propose a simple solution technique for transient thermoelastic problems in transversely isotropic solids. This problem can be formulated in terms of a triple-series equation by means of the method of successive approximation as well as the Fourier integral and Bessel series. The triple-series equation is reduced to a simultaneous algebraic equation by the application of Fourier and Neumann series. The stress intensity factors at the inner and outer crack tips are derived from the axial displacement. Numerical calculations of the stress intensity factors which are carried out for graphites and ceramics are compared with one another. Finally, we propose simple formulations expressing the maximum stress intensity factors as a function of Biot's number and crack length.