Contact mechanics of two deformable elastic solids with graded coatings

The contact problem for two deformable solids with FGM coatings is considered. The problem is considered under the assumption of plane strain, Coulomb friction and linear nonhomogeneous elasticity. The variation of the elastic modulus in the FGM coatings are exponential. It is assumed that the contact area is small compared to radii of curvatures of the cylinders. Thus the standard Hertzian assumption may be used. After solving the half space problem the Green’s functions necessary for deriving the integral equations of the contact problem are obtained. The resulting integral equations are solved to obtain a series of analytical benchmark results for examining the influence of such factors as material inhomogeneity constants, the coefficient of friction, and various length parameters on the critical stresses that may have a bearing on the fatigue and fracture of the components with FGM coatings. The results regarding the contact stresses, the in-plane component of the surface stress and the contact length versus the applied load relationship are presented.