Keywords: rolling contact problem, frictional heat generation, elastic graded materials, quasistatic method.

This paper is concerned with the numerical solution of the rolling contact problems including Coulomb friction, frictional heat generation across the contact surface and wear phenomenon governed by Archard's law. The elastic or thermoelastic rolling contact problems between homogeneous materials are considered by many authors. For details see references in monographs [1,2]. In the paper we consider this rolling contact problem for heterogeneous materials. We assume that the upper surface of the foundation where the contact occurs, i.e. the railhead of rail in wheel-rail contact, is coated with elastic graded material. The properties of this material depend on its depth according to the power law. Elastic graded materials [3,4] are generally two-phase composities with continuously varing volume fractions. These coatings are widely used in engineering structures where the contact problem is a major concern [3]. Moreover we assume that the heat flow is governed by the conduction equation both inside the surface graded layer and inside the rail.

In this paper, following reference [5], we take special features of this rolling contact problem and use so-called quasistatic approach to solve it numerically. In this approach the inertial term is replaced by the stationary term reflecting the dynamics of the body rather than completely neglected as in the classical quasistatic formulation [1]. After a brief introduction of the thermoelastic model of the rolling contact problem with friction and wear in the framework of two-dimensional linear elasticity theory [1], the general coupled time dependent system describing this physical phenomenon is formulated. This system is transformed into equivalent stationary system in a so-called quasistatic formulation. To solve numerically this stationary system we will decouple it into mechanical and thermal parts. Finite element method is used as a discretization method. The numerical results indicating that the elastic graded layer reduce the values of the normal contact stress and the maximal temperature in the contact zone are provided and discussed.

1

W. Han, M. Sofonea, "Quasistatic contact problems in viscoelasticity and viscoplasticity", AMS and IP, 2002.

2

W. Sextro, "Dynamical Contact Problems with Friction", Springer, Berlin, 2007.

3

M. Hiensch, P.O. Larsson, O. Nilsson, D. Levy, A. Kapoor, F. Franklin, J. Nielsen, J.W. Ringsberg, B.L. Josefson, "Two-material rail development: field test results regarding rolling contact fatigue and squeal noise behaviour", Wear, 258, 964-972, 2005. doi:10.1016/j.wear.2004.03.067

4

S. Suresh, "Graded materials for resistance to contact deformation and damage", Science, 292, 2447-2451, 2001. doi:10.1126/science.1059716

5

A. Chudzikiewicz, A. Myslinski, "Rolling contact problem with the generalized Coulomb friction", Proceedings of Applied Mathematics and Mechanics, 6, 299-300, 2006. doi:10.1002/pamm.200610131

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