A simplified elliptic model of rough surface contact

Nayak's analysis of isotropic surface roughness as a random field has been extended to show that most summits are only mildly ell, the most common ratio of principal summit curvatures being near 2:1. Also from Nayak's theory, the distribution of the geometric-mean summit curvature with height has been obtained. By using an approximate solution for elliptical Hertzian contacts based on the geometric-mean summit curvature, the full elliptical solution of Bush, Gibson and Thomas can be reproduced more conveniently. Their values for the area of contact are accurately reproduced, and it is argued that the present values for load and contact pressure are more plausible: unlike the original numerical values, the present values converge smoothly to the BGT asymptote p¯∼Ω≡E∗m2/π. Once again, it is found that elastic contact models can explain the proportionality between contact area and load, although at realistic loads the proportionality is merely very good, not exact. The model shows that a plasticity index ψm≡(E*/H)σmψm≡(E*/H)σm (closely related to Mikic's index) can be used to predict the behaviour of surfaces in contact.