Abstract
In the fractal rough surface characterized by Weierstrass-Mandelbrot function, the amount of asperities with frequency index n is γ times the amount of asperities with frequency index n-1. According to the property, the revised size distribution functions and truncated size distribution functions of asperities with frequency index n are developed for the two-dimensional and three-dimensional fractal rough surfaces, respectively. The relations between real contact area and total contact load are obtained. The comparison between predictions of present model, the revised MB model and experimental data are given. The results show these asperities whose frequency indexes range from nmin to nmin+5 are major contribution to real contact area and total contact load. For given initial frequency index and total contact load, the real contact area of present model is smaller than that of the revised MB model. With an increase in initial frequency index, the results of present model gradually approach to that of the revised MB model. When initial frequency index nmin is less than the elastic critical frequency index nec, the trends of present model are in better agreement with experiment than that of the revised MB model.
Highlights
Almost all surfaces of structures are not smooth in micro-scale, which include many asperities with different geometrical shapes, called rough surface
The contact between rough surfaces is characterized by the interaction of asperities, which leads to the real contact area being a small fraction of the apparent contact area
In 1957, Archard[1] defined that rough surface is covered by lots of overlap spherical asperities and obtained that the real contact area is proportional to the external force
Summary
Almost all surfaces of structures are not smooth in micro-scale, which include many asperities with different geometrical shapes, called rough surface. Morag and Etsion[7] developed a revised elastic plastic contact model of a single fractal asperity. The model shows the critical area of asperity is scale dependent, as the load and contact area increase the deformation of asperity takes place from elastic to plastic. Liou and Lin[8] developed an elastic plastic contact model of a single fractal asperity according to classical contact mechanics, and the total contact load and the real contact area were evaluated. The previous researches have analyzed and deduced the contact load and contact area neglecting the difference such as size and area-distribution rule among the asperities on rough surfaces, which is not in line with practical engineering surfaces. An experiment is conducted to verify the reasonability of this revised model and the result reveals the present model has a preferable accordance with practical conditions
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