Frictional Dynamics in a Two Dimensional Frenkel-Kontorova Model with Square Lattice Symmetry

Abstract

A two-dimensional (2D) Frenkel-Kontorova (FK) model with a square symmetry substrate potential for a square lattice layer driven by an external driving force with an arbitrary direction α and an arbitrary misfit angle θ between upper and lower layers is presented. Both the theoretical and the numerical study of the lock-to-sliding transition for this 2D FK model are given. The results show that both the misfit angle θ and the direction (cosα, sinα) of the external driving force play crucial roles in the scenario of the lock-to-sliding transition and the determination of the structure of the sliding state. The effects of the system parameters such as the magnitude of the adhesive force between the two layers, the stiffness of the interatomic bonds, and the viscous damping constant to the lock-to-sliding transition have also been investigated. The application of our results to the tribology is discussed and the dependence of the static friction force on the system parameters is studied. It is noted that the parameters of both θ and α play important roles in the magnitude of the static friction force Fs. The numerical results show that the possibility to obtain superlubricity is larger between two same material layers than that for different materials. How to make the material with superlubricity is suggested.