Discrete dislocation plasticity analysis of loading rate-dependent static friction

• Published in: Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 472; no. 2192; p. 20150877
• Main Authors: Song, H., Deshpande, V. S., Van der Giessen, E.
• Format: Journal Article
• Language: English
• Published: England The Royal Society Publishing 01.08.2016
• Subjects: Adhesion; Contact; Discrete Dislocation Plasticity; Dislocations; Formulas (mathematics); Friction; Friction Strength; Loading Rate; Mathematical models; Plasticity; Strength; discrete dislocation plasticity; friction strength; loading rate; adhesion
• ISSN: 1364-5021; 1471-2946
• DOI: 10.1098/rspa.2015.0877

From a microscopic point of view, the frictional force associated with the relative sliding of rough surfaces originates from deformation of the material in contact, by adhesion in the contact interface or both. We know that plastic deformation at the size scale of micrometres is not only dependent on the size of the contact, but also on the rate of deformation. Moreover, depending on its physical origin, adhesion can also be size and rate dependent, albeit different from plasticity. We present a two-dimensional model that incorporates both discrete dislocation plasticity inside a face-centred cubic crystal and adhesion in the interface to understand the rate dependence of friction caused by micrometre-size asperities. The friction strength is the outcome of the competition between adhesion and discrete dislocation plasticity. As a function of contact size, the friction strength contains two plateaus: at small contact length (≲0.6 μm), the onset of sliding is fully controlled by adhesion while for large contact length (≳10 μm), the friction strength approaches the size-independent plastic shear yield strength. The transition regime at intermediate contact size is a result of partial de-cohesion and size-dependent dislocation plasticity, and is determined by dislocation properties, interfacial properties as well as by the loading rate.