The General Fracture Problem of a Functionally Graded Thermal Barrier Coating (TBC) Bonded to a Substrate

Abstract

In this paper we consider the general fracture problem of a functionally graded thermal barrier coating (TBC) bonded to a substrate. Functionally Graded Materials (FGMs) used in TBCs are usually made from ceramics and metals. Ceramics provide thermal and corrosion resistance while metals provide the necessary fracture toughness and heat conductivity. The volume fractions of the constituents will usually vary from 100% ceramic at the surface to 0% at the interface continuously providing seamless bonding with the metal substrate. To study the general fracture problem in the TBC we consider an arbitrarily oriented crack in an FGM layer bonded to a half plane. The elastic properties of the FGM layer are assumed to vary exponentially, while those of the half plane are homogeneous. The elastic properties are continuous at the interface. As shown in [1], then the governing elasticity equations become partial differential equations with constant coefficients. Using the transform technique, and defining the crack surface displacement derivatives as the unknown auxiliary functions, the mixed-mode crack problem is reduced to a system of Cauchy type singular integral equations. It is shown that at the crack tips the stresses still possess the regular square-root singularity, making it possible to use the classical definition of stress intensity factors. The singular integral equations are solved numerically using a Gaussian type quadrature and the mode I and mode II stress intensity factors are calculated for various crack lengths and crack orientations. Also the crack surface displacements are computed for different crack inclinations. It is observed that the crack orientation, crack length and the nonhomogeneity parameter affect the stress intensity factors significantly.