Analysis of thermal stresses in FGM-matrix media induced by a constant heat generation

Abstract

The three-dimensional thermal stress field is derived for an elastic medium that contains a spherical inclusion made of an functionally graded material (FGM) embedded in a matrix phase. The material properties in the inclusion phase are assumed to vary linearly while the material properties in the matrix phase are uniform. The presence of a uniform heat source in the inclusion introduces the temperature distribution which generates thermal stresses. The temperature distribution is derived analytically by solving the heat conduction equation. Based on the temperature distribution, the differential equations for the displacement field are derived for both the inclusion and matrix phases. The displacement for the matrix phase is solved analytically while the displacement for the FGM inclusion phase is solved semi-analytically using the method of weighted residuals. Only a single differential equation needs to be solved. To the authors’ best knowledge, this is the first attempt to express the thermal stress field semi-analytically. Unlike the conventional two-phase composite materials in which the von Mises stress is discontinuous at the interface of the inclusion and the matrix, the von Mises stress in this model shows continuity at the interface.