Oblique surface cracking and crack closure in an orthotropic medium under contact loading

Abstract

This article presents analytical methods for analysis of an inclined surface crack in an orthotropic medium subjected to contact loading. Governing partial differential equations are derived in accordance with plane theory of orthotropic elasticity. Contact and crack problems are formulated separately utilizing Fourier transformation techniques. The contact problem consists of a rigid flat punch pressing upon an orthotropic half-plane, and is reduced to a singular integral equation of the second kind. The surface crack is assumed to be tilted at an arbitrary angle with respect to the normal of the half-plane surface. Three different crack configurations are considered, which are completely closed, partially-closed, and fully-open cracks. Frictional contact between the crack faces is implemented in the cases of completely closed, and partially-closed cracks. A single singular integral equation is derived for the completely closed crack, whereas each of the problems of partially- and fully-open cracks requires derivation of a set of two singular integral equations. The contact problem and each of the crack problems are solved numerically by means of the expansion-collocation technique. A flowchart is developed and implemented to detect the type of crack closure configuration under a given contact loading. The parametric analyses carried out illustrate the influences of factors such as crack inclination angle, crack face and contact surface friction coefficients, material orthotropy, and relative punch location on crack face contact stresses, degree of crack closure, and mode I and II stress intensity factors.