A Model for Fractal Dimension of Rough Surfaces

We report a model for the fractal dimension D_s of rough surfaces based on the fractal distribution of roughness elements on surfaces and the fractal character of surface profiles. The proposed model for the fractal dimension D_s is expressed as a function of the fractal dimensions D for conic roughness diameter/height and D_p for surface profile, maximum roughness base diameter λ_max, the ratio β of conic roughness height to its base radius as well as the ratio λ_min/λ_max of the minimum to the maximal base diameter.