Abstract
Thermal stresses due to a spheroidal inclusion were investigated using the equivalent inclusion approach proposed by Eshelby. The temperature inside the spheroid is maintained constant and different from that of the surrounding matrix of an infinite extent. A new relation between the Cartesian coordinates and spheroidal coordinates was established. Based on this relation, the solution for a prolate spheroidal inclusion was readily obtained from that for an oblate spheroidal inclusion. The principal stress inside the spheroid increases with decreasing m, the ratio of shear moduli of the spheroid and matrix. The value of σ 11 I inside the spheroid increases with increasing k, the aspect ratio, but the trend for σ 33 I is opposite. The stress components, σ 11 , along the x 1 axis and, σ 33 , along the x 3 axis in the matrix decrease with increasing distance away from the inclusion. For given combinations of m and k, the maximum stress components, σ 22 and σ 33 , along the x 1 axis and σ 11 (= σ 22 ) along the x 3 axis in the matrix are located at certain distances away from the interface. Among all principal stresses, the maximum tensile stress is located at the interface between the inclusion and matrix. The numerical results are in agreement with those reported in the literature.