Adhesive rough contacts near complete contact

Classical asperity theories predict, in qualitative agreement with experimental observations, that adhesion is always destroyed by roughness except if the roughness amplitude is extremely small, and the materials are particularly soft. This happens for all fractal dimensions. However, these theories are limited due to the geometrical simplification, which may be particularly strong in conditions near full contact. We therefore introduce a simple model for adhesion which aims at being rigorous near full contact, where we postulate there are only small isolated gaps between the two bodies, as an extension of the adhesive-less solution proposed recently by Xu, Jackson, and Marghitu (XJM model) (Xu et al., 2014) [1], using the JKR theory for each gap. The results confirm recent theories in that we find an important effect of the fractal dimension. For D<2.5, the case which includes the vast majority of natural surfaces, there is an expected strong effect of adhesion. Only for large fractal dimensions, D>2.5, it seems that for large enough magnifications a full fractal roughness completely destroys adhesion. These results are partly paradoxical since strong adhesion is not observed in nature except in special cases