On the fractal dimension of rough surfaces

Abstract

Most natural surfaces and surfaces of engineering interest, e.g., polished or sand blasted surfaces, are self affine fractal over a wide range of length scales, with the fractal dimension Df = 2.15 ± 0.15. We give several examples which illustrate this and a simple argument, based on surface fragility, for why the fractal dimension usually is <2.3. A kinetic model of sand blasting is presented, which gives surface topographies and surface roughness power spectra in good agreement with experiments.