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Roughness measurements by optical interferometry and scanning tunneling microscopy on a magnetic thin-film rigid disk surface have shown that its surface is fractal in nature. This leads to a scale-dependence of statistical parameters such as r.m.s height, slope and curvature, which are extensively used in classical models of contact between rough surfaces. Based on the scale-independent fractal roughness parameters, a new model of contact between isotropic rough surfaces is developed. The model predicts that all contact spots of area smaller than a critical area are in plastic contact. When the load is increased, these plastically deformed spots join to form elastic spots. Using a power-law relation for the fractal size-distribution of contact spots, the model shows that for elastic deformation, the load P and the real area of contact Ar are related as P~Ar(3−D)/2, where D is the fractal dimension of a surface profile which lies between 1 and 2. This result explains the origins of the area exponent which has been the focus of a number of experimental and theoretical studies. For plastic loading, the load and area are linearly related. The size-distribution of spots also suggests that the number of contact spots contributing to a certain fraction of the real area of contact remains independent of load although the spot sizes increase with load. The model shows that the load-area relation and the fraction of the real area of contact in elastic and plastic deformation are quite sensitive to the fractal roughness parameters.
Majumdar et al. (Tue,) studied this question.