Fractal characterisation of the anisotropy of rough surfaces

Abstract

Existing techniques for measuring and characterising anisotropy are discussed. The advantages are suggested in treating anisotropic surfaces as self-affine fractals, characterised by two parameters, the fractal dimension and the topothesy. These parameters are conveniently determined experimentally by measuring the slope and intercept of a logarithmic plot of the structure function. A 3D version of the structure function is presented, any section for which is equivalent to an ensemble average of profile structure functions. The angular variation of topothesy and fractal dimension obtained from such sections describes the anisotropy of the parent surface. Also, a bifractal structure function, typical of surfaces with stratified textures, may be split into its component straight lines by fitting with a hyperbola. The intersection of the asymptotes then defines the so-called “corner frequency” between the two fractals. The 3D height measurements were made on a grit-blasted, a ground and a plateau-honed surface with a scanning white-light interferometer and a stylus instrument. On the isotropic grit-blasted surface, fractal parameters did not vary with direction. On the strongly anisotropic ground surface, the fractal dimension varied only parallel to the lay, as predicted, but the topothesy varied by some orders of magnitude. On the stratified plateau-honed surface, the only true bifractal, fractal parameters were found to be sensitive to the direction of honing scratches.