Electrical Contact Resistance of Fractal Rough Surfaces
The presence of roughness at electrical contacts tends to involve contacting asperities across multiple scales. Depending on the nature of the contact between asperities on opposing surfaces, different conduction mechanisms take place. This is shown in the figure here.
Contact stiffness of multiscale surfaces by truncation analysis
In this concise piece of work, an effective method is shown to gain new understandings into the role of surface structure in the field of contact mechanics. In particular, normal contact stiffness is correlated to parameters of surfaces' fractal dimension and amplitude.
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.
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.
