ABSTRACT CONTACT MECHANICS OF GRADED MATERIALS WITH TWODIMENSIONAL MATERIAL PROPERTY VARIATIONS G&ouml / kay, Kemal M.S., Department of Mechanical Engineering Supervisor: Asst. Prof. Dr. Serkan Dag September 2005, 62 pages Ceramic layers used as protective coatings in tribological applications are known to be prone to cracking and debonding due to their brittle nature. Recent experiments with functionally graded ceramics however show that these material systems are particularly useful in enhancing the resistance of a surface to tribological damage. This improved behavior is attributed to the influence of the material property gradation on the stress distribution that develops at the contacting surfaces. The main interest in the present study is in the contact mechanics of a functionally graded surface with a two &ndash / dimensional spatial variation in the modulus of elasticity. Poisson&rsquo / s ratio is assumed to be constant due to its insignificant effect on the contact stress distribution [30]. In the formulation of the problem it is assumed that the functionally graded surface is in frictional sliding contact with a rigid flat stamp. Using elasticity theory and semi-infinite plane approximation for the graded medium, the problem is reduced to a singular integral equation of the second kind. Integral equation is solved numerically by expanding the unknown contact stress distribution into a series of Jacobi polynomials and using suitable collocation points. The developed method is validated by providing comparisons to a closed form solution derived for homogeneous materials. Main numerical results consist of the effects of the material nonhomogeneity parameters, coefficient of friction and stamp size and location on the contact stress distribution.