A general expression for plasticity index

The well-known plasticity index ψ has been widely applied in studying the contact of rough surfaces since 1966, when it was postulated by Greenwood and Williamson. Because the plasticity index ψ was derived under the implicit hypothesis that the surfaces in contact were isotropic, it was limited in application and there was some confusion over its use. A general expression for the plasticity index Ω, suitable for both isotropic and anisotropic rough surfaces, is introduced in this paper. According to the experiments, it is found that the contacts of asperities are, on the whole, elastic when Ω is smaller than about 0.6 and plastic when it is greater than about unity. The contact behaviour is relatively complicated when it is between 0.6 and unity. These results are reasonably consistent with the conclusions drawn from isotropic surfaces by Greenwood and Williamson.