The Elliptical Elastic-Plastic Microcontact Analysis

Abstract

The elastic-plastic contact of a flat and an asperity which shape is a sphere or an ellipsoid is a fundamental problem in contact mechanics. It is applicable in tribological problems arising from the points of contact between two rough surfaces, such as gear teeth, cam and follower and micro-switches etc. Indeed, numerous works on the contact of rough surfaces were published so far (see review by Liu et al.). Many of these works are based on modeling the contact behavior of a single spherical asperity, which is then incorporated in a statistical model of multiple asperity contact. Based on the Hertz theory, the pioneering work on contact models of pure elastic sphere was developed by Greenwood and Williamson (GW) . The GW model used the solution of the frictionless contact of an elastic hemisphere and a rigid flat to model an entire contacting surface of asperities with a postulated Gaussian height distribution. The basic GW model had been extended to include such aspects as curved surfaces (by Greenwood and Tripp), two rough surfaces with misaligned asperities (by Greenwood and Tripp) and non-uniform radii of curvature of asperity peaks (by Hisakado). Abbott and Firestone introduced the basic plastic contact model, which was known as surface micro-geometry model. In this model the contact area of a rough surface is equal to the geometrical intersection of the original undeformed profile with the flat. Based on the experimental results, Pullen and Williamson proposed a volume conservation model for the fully plastic contact of a rough surface. The works on the above two models are suitable for the pure elastic or pure plastic deformation of contacting spheres. In order to bridge the two extreme models, elastic and fully plastic, Chang et al. (CEB model) extended the GW model by developing an elasticplastic contact model that incorporated the effect of volume conservation of a sphere tip above the critical interference. Numerical results obtained from the CEB model are compared with the other existing models. In the CEB model, there is no transition regime from the elastic deformation to the fully plastic deformation regime. These deficiencies triggered several modifications by other researchers. Zhao et al. (the ZMC model) used mathematical smoothing expressions to incorporate the transition of the contact load and contact area expression between the elastic and fully plastic deformation regions. Kogut and Etsion (KE model) performed a finite element analysis on the elastic-plastic contact of a deformable sphere and a rigid flat by using constitutive laws appropriate to any mode of deformations. It offered a general dimensionless relation for the contact load, contact area