An approximate method for residual stress calculation in functionally graded materials

Thermal residual stresses in functionally graded materials (FGMs) arise primarily from nonlinear spatial variations in the thermal expansion coefficient, but can be significantly adjusted by variations in modulus. Thermoelastic analysis of FGMs is complicated by such modulus gradients. A class of problems for which thermal stress solutions for materials with constant modulus can be used as a basis for approximations for FGMs is discussed. The size of the error in this approximation due to gradients in elastic modulus is investigated. Analytical and finite element solutions for the thermal stresses in various FGM geometries are compared to results from this approximate method. In a geometry of practical interest, a right cylinder graded along the z-axis, the error for a Ni–Al 2O 3 FGM was found to be within 15% for all gradients considered. The form of the approximation makes it easier to identify desirable types of spatial nonlinearity in expansion coefficient and variations in modulus; this would allow the manipulation of the location of compressive stresses.