Loading-unloading contact model between three-dimensional fractal rough surfaces

Based on fractal theory, a loading-unloading contact model between three-dimensional rough surfaces has been developed. The critical contact areas of a single asperity are scale dependent. The expressions between contact area and contact load for a single asperity in loading and unloading processes are obtained. The truncated asperity size distribution functions of different frequency indexes in loading and unloading processes are deduced. The dimensionless relation between the total contact load and the total real contact area is obtained in loading and unloading processes. When 3D fractal rough surface is in elastic deformation, the dimensionless load-area relations of loading and unloading processes are identical. When 3D fractal rough surface is in inelastic deformation, the dimensionless total real area in unloading process is greater than the dimensionless total real area in loading process for a given contact load. For a given load, the differences in total real contact area between loading and unloading processes decrease with an increase in fractal dimension. (c) 2018 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license.