Real Contact Area of Fractal-Regular Surfaces and Its Implications in the Law of Friction

The concept of a fractal-regular surface, with a dual-section power spectrum, has been implemented in an elastic-plastic contact analysis. Under certain assumptions, the analysis of individual fractal domains can be decoupled from that of the macroscopic shape. Due to the increase in the number of contacting fractal domains associated with a macroscopic contact expansion, the contact area-load relationship for fractal-regular surfaces is nearly linear, with a load exponent of 1-1.11, in contrast to 1-1.33 for fractal surfaces. Thus, the Amontons law of friction can be reasonably explained with fractal-regular surfaces under the assumption of a linear friction-area relationship. The distribution of the local real-to-apparent contact ratio in a nominally Hertzian contact was found to vary with the fractal dimension. The plastic contact ratio tends to be more uniformly distributed as the fractal dimension approaches unity.