Surface cracking in an orthotropic medium subjected to frictional contact

Abstract

This article presents an analytical method capable of resolving the coupled problem of surface cracking in an orthotropic elastic medium subjected to frictional contact by a rigid flat punch. Reciprocal influences between the surface crack and the flat punch are accounted for by establishing a fully coupled formulation. Governing partial differential equations involving the displacement components are derived in accordance with plane theory of orthotropic elasticity. General solutions corresponding to mode I and II crack problems and contact problem are obtained employing Fourier transformation techniques. These separate solutions are then reconciled; and three coupled singular integral equations are developed by applying crack surface and contact zone conditions. Singular integral equations are solved numerically through an expansion–collocation method in which the primary unknowns are expanded into series in terms of Jacobi polynomials. Comparisons to the results available in the literature for certain special cases do verify the proposed procedures. Further numerical results are presented to be able to demonstrate the influences of material orthotropy, coefficient of friction, and geometric parameters upon the mixed-mode stress intensity factors and the contact stress.