Frictionless contact mechanics of an orthotropic coating/isotropic substrate system

This study has been performed to investigate the receding contact problem of a homogeneous orthotropic coating that is not bonded to a homogeneous isotropic substrate without any interfacial defects. The isotropic substrate is supported on a Winkler foundation. The problem is solved assuming that the contact between the rigid punch and orthotropic coating, and that between the orthotropic coating and isotropic substrate, are frictionless. Additionally, the effect of the body forces is neglected, and only compressive normal tractions can be transmitted through the interfaces. The contact analysis of the orthotropic coating, which is subjected to a contact load using a rigid cylindrical punch, is performed under plane strain conditions. The governing equations are analytically found using the theory of elasticity and Fourier integral transformation techniques. Subsequently, the governing equations are reduced to a system of two singular equations, wherein the unknowns are the contact stresses and contact widths. To numerically solve the resulting singular integral equations, Gauss-Chebyshev integration formulas are employed. It is analyzed the influence of the following parameters on the contact stresses and contact widths: orthotropic-material properties, punch radius, load ratio, Winkler foundation stiffness.