This paper shows that the Mindlin problem involving two spheres in contact under the action of oscillating tangential force can lead to the account of static-kinetic friction transition. In Mindlin’s problem two spheres experience partial slip as a result of application of oscillating tangential load. When the problem is extended to multi-sphere contact, i.e. two rough surfaces, the application of tangential oscillating load results in partial slip for some asperity contacts while others experience full slip. Increase in the amplitude of the oscillating tangential force results in more contacts experiencing full slip, thereby decreasing the number of contacts in parial slip. Constitutive relation proposed by Mindlin at small scale, governing asperity interaction, is used to obtain the large scale slip function through a statistical summation of asperity scale events. The slip function establishes the fraction of asperity contact in full slip. The complement of the slip parameter is a fraction of asperities in partial slip. Through slip function it is shown that it is possible to define a slip condition for the entire surface. The derivation of the slip function allows the account of transition between static friction and kinetic friction.
On the Static-Kinetic Friction Transition in Dry Contact of Rough Surfaces
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Farhang, K, Segalman, D, & Starr, M. "On the Static-Kinetic Friction Transition in Dry Contact of Rough Surfaces." Proceedings of the ASME/STLE 2011 International Joint Tribology Conference. ASME/STLE 2011 Joint Tribology Conference. Los Angeles, California, USA. October 24–26, 2011. pp. 281-283. ASME. https://doi.org/10.1115/IJTC2011-61098
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