Mechanics of sliding frictional contact for a graded orthotropic half-plane

The main interest in this study is the crack initiation in graded orthotropic materials under sliding contact conditions. We consider the two-dimensional sliding contact problem between a graded orthotropic half-plane and a rigid punch with an arbitrary profile. The orthotropic graded half-plane is modeled as a linearly elastic and locally inhomogeneous orthotropic material with an exponentially varying Young’s modulus in the depth direction. The principal axes of orthotropy are assumed to be parallel and perpendicular to the contact surface. The problem is formulated under plane strain or generalized plane stress conditions. Using the standard Fourier transform, the problem is reduced to a singular integral equation, which is solved numerically using Jacobi polynomials. Extensive parametric study is done to determine the effect of the inhomogeneity parameter, β, the friction coefficient between the half-plane and the stamp, η, as well as the material orthotropic elastic parameters: the stiffness ratio, δ, the effective Poisson’s ratio, ν, and the shear parameter, κ, on the contact stress distribution and stress intensity factors at the sharp edges of the stamps that may have a bearing on the fatigue and fracture of the graded orthotropic half-plane.