Application of spherical indentation mechanics to reversible and irreversible contact between rough surfaces

• Published in: Wear 1977-01, Vol.45 (2), p.221-269
• Main Author: Francis, H.A.
• Format: Article
• Language: English
• ISSN: 0043-1648; 1873-2577
• DOI: 10.1016/0043-1648(77)90076-X

A probabilistic model for the deformation mechanics of the interface between randomly rough metal surfaces, which is geometrically and mechanically more realistic than previous models, is derived and numerically evaluated. The model is based on the premise that the contact of two nominally plane engineering surfaces is in general equivalent to loading their sum against a smooth plane. The “sum surface” is assumed to be Gaussian and isotropic; thus the height and curvature of its peaks are correlated random variables. By using an idealized peak shape which is paraboloidal only at its vertex, the surface height distribution of the population of peaks is also made Gaussian. The upper load limit of the model is estimated, beyond which the microcontacts can no longer be assumed to be geometrically discrete and mechanically independent. Each microcontact is assumed to grow by mutual spherical indentation, thus enabling the entire deformation range, from Hertzian elastic to fully plastic, to be described by previously determined empirical functions. A two-stage linear/power law stress-strain curve is assumed. By summing over all microcontacts the total contact area and load are obtained as functions of the separation of the mean surfaces. For elastic deformation both normal loading and sliding friction are treated. For plastic flow two cases are considered: (1) identical materials; (2) one surface remains elastic. The mechanics of unloading are also investigated. After enough microcontacts have yielded to cause significant deviation from totally elastic behavior, the contact mechanics depend principally on the strain hardening exponent, the ratio of the yield stress to the Young's modulus, and the measurable ratio of the mean peak radius to the r.m.s. height of the sum surface.