Mixed-Mode Fracture Analysis of a Functionally Graded Layer with Clamped Longitudinal Edges

Abstract

Properties of functionally graded materials as nonhomogeneous solids with gradually varied composition make them suitable for many applications, such as coating in interfacial zones. The present study investigates the plane elasticity problem for an isotropic functionally graded material layer containing multiple cracks using the distributed dislocation technique. The layer has a finite thickness and infinite length where it’s top and bottom surfaces are fixed. The elastic modulus of the medium is assumed to vary exponentially in the thickness direction. The Fourier integral transform method is used to obtain the stress fields caused by an edge dislocation in the layer. The stress components exhibit familiar Cauchy as well as logarithmic singularity at the dislocation position. In fact, the dislocation solution in this study is primarily employed to derive a set of integral equations to analyze cracks with arbitrary configuration. The numerical solution of these equations yields dislocation densities on a crack surface which is used to compute the crack stress intensity factors.Then after validating the formulation for homogenous case, several configurations of embedded cracks such as a rotating crack, a stationary horizontal and a rotating crack, two fixed vertical and a horizontal crack with variable location are investigated. Moreover, effects of important parameters on stress intensity factors such as crack geometries, material non-homogeneity and boundary condition are studied.