In this short note we remark that, at least for the theory of Fuller & Tabor for the adhesive contact of rough random surfaces, fractal surfaces have a limiting zero pull-off force, for all fractal dimensions or amplitudes of roughness. This paradoxical result raises some questions. I ask the iMechanica community for opinions, comparisons of experiments, etc.

J.R.Barber The contact of rough surfaces Surfaces are rough on the microscopic scale, so contact is restricted to a few `actual contact areas'. If a current flows between two contacting bodies, it has to pass through these areas, causing an electrical contact resistance. The problem can be seen as analogous to a large number of people trying to get out of a hall through a small number of doors.

Classical treatments of the problem are mostly based on the approximation of the surfaces as a set of `asperities' of idealized shape. The real surfaces are represented as a statistical distribution of such asperities with height above some datum surface. However, modern measurement techniques have shown surfaces have multiscale, quasi-fractal characteristics over a wide range of length scales. This makes it difficult to decide on what scale to define the asperities.