Thermally loaded functionally graded materials with embedded defects

The material properties of a functionally graded material (FGM) may be very complicated functions of spatial position. Therefore, the development of a fracture mechanics analysis model for FGMs with arbitrarily distributed properties is essential. This article investigates the penny-shaped crack problem in FGMs with properties that are arbitrary functions of the axial coordinate. In the analysis, the graded region is modeled by a large number of layers stacked along the axial direction with each layer having different material properties. By utilizing the Hankel transform technique, dual integral equations for the entire elastic region are obtained. Thermal stresses and thermally induced crack deformations are computed by solving the dual integral equations numerically. As a numerical illustration, crack-tip fields for a metal substrate coated with an FGM subjected to an axial thermal flux are presented for different material nonhomogeneity parameters and coating thickness. It is found that the fracture strength of an FGM coating is much higher than that of a pure ceramic coating.