Relationship between contact size and static friction: An approach for rigid crystalline surfaces

Relationship between contact size (A) and static friction (f) has been studied for rigid crystalline systems. We built a series of systems with two identical surfaces but different orientations and investigated the effects of the size and shape of the contact area on static friction. In these systems, there are numerous nontrivial commensurate contacts. Our results confirmed that the relationship betweenAandfwas determined by both commensurability and shape of the contact. For commensurate contacts,f proportional to Aindependent of the shape. For incommensurate contacts, generallyf proportional to A(0)for regular shapes orf proportional to A(1/4)for irregular shapes; however, in very few cases of regular shapes,f proportional to A(1/2). Moreover, in above systems, commensurability of a contact can be easily changed by a perturbation of the misfit angle. Therefore, if the perturbation caused by the lateral force and the deformation of the surface are considered (as is the case in real systems), further research is necessary.

Automated summary

The relationship between contact size (A) and static friction (f) in rigid crystalline systems is determined by both commensurability and contact shape. For commensurate contacts, f is proportional to A and independent of shape, while for incommensurate contacts, the relationship between f and A varies depending on the shape, with different exponents ranging from 0 to 1/2. The commensurability of a contact can be easily changed by perturbation of the misfit angle, which suggests further research is necessary when considering lateral forces and surface deformations in real systems.