Effects of graded layering on the tip behavior of a vertical crack in a substrate under frictional Hertzian contact

Abstract

An analysis of a crack in a substrate overlaid with a functionally graded material subjected to frictional contact loading is performed, within the linear plane elasticity framework. The graded material exists as an interlayer between the dissimilar phases of the coating/substrate system or as a graded coating deposited on the substrate. The crack in the underlying substrate is oriented perpendicular to the boundary of the coated medium. The contact pressure is assumed to be Hertzian and the resulting normal and friction-induced tangential tractions acting on the boundary of the medium give rise to the mixed-mode behavior at the crack tips. Formulation of the problem is reduced to solving a set of singular integral equations. In the numerical results, the emphasis is given to the effects of material, geometric, and loading parameters on the values of the stress intensity factors. Further addressed are the correlations of such parameters to the crack growth mechanisms in terms of the probable cleavage angles at the crack tips, the effective tensile mode stress intensity factors, and the ranges of stress intensity factors. In the present analysis, the contact between the crack faces is not taken into account so that the influence of crack-face friction is neglected.