A surface crack in a graded coating subjected to sliding frictional contact

Abstract

This article presents an analytical method developed to conduct fracture analysis of functionally graded coatings that are under the effect of contact stresses. The geometric model considered comprises a functionally graded coating, which possesses a surface crack and is perfectly bonded to a homogeneous half-plane. A two-step solution procedure is put forward in which the contact and crack problems are treated separately. First, the graded coating is assumed to be in sliding frictional contact with a rigid flat punch and the contact stresses are computed. These stresses are then used as inputs for the crack problem and the mode I and II stress intensity factors are evaluated. Governing partial differential equations for the contact and crack problems are derived by using the theory of plane elasticity and solved by utilizing Fourier transformation techniques. The derivations lead to a single singular integral equation in the case of the contact problem, and two uncoupled singular integral equations in the case of the crack problem. An expansion–collocation approach is adopted for the numerical solutions of the integral equations. Comparisons of the results generated for the contact and crack problems to those available in the literature demonstrate the high levels of accuracy attained by the proposed solution techniques. Further numerical results are presented so as to illustrate the influences of material nonhomogeneity and coefficient of friction on the contact stresses and the mode I and II stress intensity factors.