Strongly Different Adhesion Reduction for 1D or 2D Random Fractal Roughness, and an Extension of the BAM Model to Anisotropic Surfaces

The influence of roughness on adhesion has been studied since the time of Fuller and Tabor, but recently there has been debate about how roughness exactly seems to kill (but sometimes enhance!) adhesion, particularly with reference to the accepted model of fractal roughness. We show that the Persson–Tosatti criterion does not depend on anisotropy of the surface for a typical power law PSD if written in terms of rms roughness and magnification. Instead, a very simple extension of the Bearing Area Model (BAM) of Ciavarella to anisotropic fractal surface shows a weak but clear dependence on the anisotropy, with higher adhesion in the 1D case, showing better agreement than the Persson–Tosatti criterion to actual numerical results of Afferrante Violano and Dini. However, neither of the two models permit to capture the strong hysteresis found in experiments between loading and unloading, which is very likely to enhance adhesion more as we move from the isotropic to the full 1D case. This suggests the mechanism of load amplification along contact lines and the associated elastic instabilities, is not captured by either the Persson–Tosatti or the BAM model applied to anisotropic surfaces.