A Fractal Theory of the Interfacial Temperature Distribution in the Slow Sliding Regime: Part II—Multiple Domains, Elastoplastic Contacts and Applications

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Abstract
The limitation of the fractal theory as applied to real surfaces is interpreted, and engineering surfaces are considered as a superimposition of fractal structures on macroscopic regular shapes by introducing the concepts of fractal-regular surfaces and multiple fractal domains. The effects of frictional heating at neighboring microcontacts are analyzed, and a simple solution of the temperature distribution is obtained for contact regions that are appreciably larger than a fractal domain. It is shown that the temperature rise at an elastoplastic microcontact does not differ significantly from that at an elastic microcontact of a similar geometry under the same load. The fractional real contact area subjected to temperature rises greater than any given value is represented by a complementary cumulative distribution function. The analysis yields that the average value and standard deviation of the temperature rise at the real contact area are 0.4 and 0.24 times the maximum temperature rise, respectively. The implications of the theory in boundary lubrication are demonstrated in light of results for ceramic materials.

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