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Adhesive rough contacts near complete contact

Recently, there has been some debate over the effect of adhesion on the contact of rough surfaces. Classical asperity theories predict, in agreement with experimental observations, that adhesion is always destroyed by roughness except if the amplitude of the same 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 introduce therefore 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. The gaps can be considered as "pressurized cracks" by using Ken Johnson's idea of searching a corrective solution to the full contact solution. The solution is an extension of the adhesive-less solution proposed recently by Xu, Jackson, and Marghitu (XJM model) (2014). This process seems to confirm recent theories using the JKR theory, namely that the effect of adhesion depends critically on 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, seems for large enough magnifications that a full fractal roughness completely destroys adhesion. These results are partly paradoxical since strong adhesion is not observed in nature except in special cases. A possible way out of the paradox may be that the conclusion is relevant for the near full contact regime, where the strong role of flaws at the interfaces, and of gaps full of contaminant, trapped air or liquid in pressure, needs to be further explored. If conditions near full contact are not achieved on loading, probably the conclusions of classical asperity theories may be confirmed.