Thermal stresses due to spheroidal inclusions

Thermal stresses due to a spheroidal inclusion were investigated using the equivalent inclusion approach proposed by Eshelby. The temperature inside t he spheroid is maintained constant and different from that of the surroundi ng matrix of an infinite extent. A new relation between the Cartesian coord inates and spheroidal coordinates was established. Based on this relation, the solution for a prolate spheroidal inclusion was readily obtained from t hat for an oblate spheroidal inclusion. The principal stress inside the sph eroid increases with decreasing m, the ratio of shear moduli of the spheroi d and matrix. The value of sigma(1)(11) inside the spheroid increases with increasing k, the aspect ratio, but the trend for sigma(33)(I) is opposite. The stress components, sigma(11), along the x(1) axis and, sigma(33), alon g the x(3) axis in the matrix decrease with increasing distance away from t he inclusion. For given combinations of m and k, the maximum stress compone nts, sigma(22) and sigma(33), along the x(1) axis and all (= sigma(22)) alo ng the x(3) axis in the matrix are located at certain distances away from t he interface. Among all principal stresses, the maximum tensile stress is l ocated at the interface between the inclusion and matrix. The numerical res ults are in agreement with those reported in the literature. (C) 1999 Elsev ier Science S.A. All rights reserved.