Statistical Models of Nominally Flat Rough Surface Contact

Abstract

In this dissertation, the linear elastic contact between a nominally-flat rough surface and a rigid flat is studied analytically and numerically. When the roughness is excluded from the surface, the corresponding contact area is referred to as the nominal contact area and it is larger than the real area of contact when the roughness is included. At the stage of early contact, where the real area of contact is nearly vanishing, the historical development of the corresponding statistical models is studied systematically based on the various combinations of the different forms of the asperity contact model and the probability density function. At the stage of nearly complete contact, where the real area of contact almost reaches the nominal contact area, various statistical models are proposed under the framework of the statistical model at the stage of early contact. At this stage, the non-contact area (the complementary of the real area of contact) consists of multiple non-contact regions which can be considered by pressurized cracks. Through the study of the area and the trapped volume of each pressurized crack, the (non-)contact ratio and the average interfacial gap can be formulated following the statistical approach.

For the purpose of validation, the boundary element method (Polonsky and Keer model) is adapted for the periodic nominally-flat rough surface contact problem. A new surface generation algorithm is developed to generate a rough surface which is isotropic, Gaussian and fractal. Multiple surface groups are generated numerically associated with different parameters (i.e., the lower/upper cut-off wavenumber and Hurst dimension) and each group contains 50 generated surfaces. The statistical models at the stage of early contact and the nearly complete contact are validated by the solutions solved by the boundary element method. Finally, an empirical model is found through a curve-fit based on the statistical model of nearly complete contact and the boundary element method results.