If the real area of contact between surfaces is determined by ideal plastic flow of the microcontacts, then the proportionality between the area of contact and the load follows immediately. If the deformation mode is elastic, or elastic-plastic, or plastic with work-hardening, which will be the usual cases, then the proportionality is harder to explain. However, by considering the statistical distribution of heights of the surface asperities, it can be shown that the average size of a microcontact is almost constant, independent of load; consequently, the fact that the contact pressure at a single micro-contact may vary with contact size becomes irrelevant. If the real origin of the laws of friction is in the statistics of surface roughness and not in a particular mode of deformation, the applicability of the Bowden and Tabor theory of friction to plastics and other nonmetals becomes more readily understandable.
The Area of Contact Between Rough Surfaces and Flats
J. A. Greenwood
Burndy Corporation, Norwalk, Conn.
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Greenwood, J. A. (January 1, 1967). "The Area of Contact Between Rough Surfaces and Flats." ASME. J. of Lubrication Tech. January 1967; 89(1): 81–87. https://doi.org/10.1115/1.3616906
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