Abstract
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.
Highlights
The surface of the mechanical structure is rugged at a microscopic scale, and consists of numerous asperities of different sizes
The relations between total real contact area and total contact load for 3D fractal rough surfaces are presented
With an increase in contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. These results are in accord with classical contact mechanics
Summary
May undergo plastic deformation during loading and unloading, resulting in residual strain and the change of asperity height distribution function. Yan and Komvopoulos[14] extended it to three-dimensional rough surface by using a modified Weierstrass-Mandelbrot function In these two models, the mechanism of a single asperity occurring elastic, completely plastic deformation was established, and the relationship between the real contact area and the contact load was obtained by using the asperity size distribution function. The mechanism of a single asperity occurring elastic, completely plastic deformation was established, and the relationship between the real contact area and the contact load was obtained by using the asperity size distribution function According to these two fractal models, scholars have proposed many fractal models to obtain more accurate rough surface contact mechanics recently. The relation between the total contact load and the total contact area on the entire rough surface is given
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