Fretting contact with finite friction of a functionally graded coating with arbitrarily varying elastic modulus Part 1: Normal loading

Abstract

The two-dimensional normal contact of a functionally graded coated half-space by a rigid cylindrical punch under the action of a monotonically increasing normal load is considered. Friction with a finite coefficient is assumed between the contact surfaces. The whole contact region is composed of an inner stick region and two outer slip regions. The linear multilayered model is used to model functionally graded materials (FGMs) with arbitrarily varying shear modulus and constant Poisson's ratio under plane strain deformation, i.e. the FGM is divided into several sublayers and in each sublayer the shear modulus is assumed to be a linear function while Poisson's ratio is a constant. With the use of the transfer matrix method and Fourier integral transform technique, the problem is reduced to a set of Cauchy singular integral equations. An iterative method is developed to determine the stick-slip region. Normal and tangential tractions in the whole contact region are calculated. It is found that the stick region depends on the gradient of the functionally graded coating as well as on Poisson's ratio and the friction coefficient. The results also show that appropriate gradual variation in the shear modulus can significantly alter the contact traction. This may lead to suppression of Hertzian cracking at the edges of the contact region and thus modify the contact damage. Therefore, it is believed that FGM coatings would have potential applications in improving the resistance to contact damage at the contact surfaces.