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.

In this paper, the frictional contact problem of a homogeneous orthotropic material in contact with a wedge-shaped punch is considered. Materials can behave anisotropically depending on the nature of the processing techniques; hence it is necessary to develop an efficient method to solve the contact problems for orthotropic materials. The aim of this work is to develop a solution method for the contact mechanics problems arising from a rigid wedge-shaped punch sliding over a homogeneous orthotropic half-plane. In the formulation of the plane contact problem, it is assumed that the principal axes of orthotropy are parallel and perpendicular to the contact. Four independent engineering constants , , , are replaced by a stiffness parameter, , a stiffness ratio, a shear parameter, , and an effective Poisson’s ratio, . The corresponding mixed boundary problem is reduced to a singular integral equation using Fourier transform and solved analytically. In the parametric analysis, the effects of the material orthotropy parameters and the coefficient of friction on the contact stress distributions are investigated.

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In this study, the contact problem for a graded elastic half-plane in frictional contact with a rigid stamp is considered. The plane contact problem is assumed to be linear elastic and the Poisson's ratio is assumed to be constant. Analytical formulation of the study includes Fourier transforms of the governing equations and boundary conditions. The resulting integral equation is solved numerically. Contact pressure, in-plane stress and the stress intensity factor at the sharp edges of the contact are evaluated and demonstrated for various stamp profiles. The results are compared with a closed form solution for homogeneous isotropic half-plane indented by rigid stamps. The effects of the nonhomogeneity parameter, coefficient of friction and stamp profiles on the contact and in-plane stresses are analyzed in detail.