Abstract
The behavior of a thin lubrication layer is described in a model combining the Landau theory of phase transformations and the Frenkel–Kontorova model. The kinetic equation for the shear modulus is obtained and solved together with the equation of overdamped motion of the layer. The maximum static and the minimum kinetic friction stresses as well as the dependence of kinetic friction stress on sliding velocity are calculated analytically. The state of the layer during sliding is determined by a dimensionless parameter κ. At small values of κ shearing of the layer causes its melting. For large values of κ no shear melting occurs: the stable state is that of solid-state sliding. The transition from the static to the kinetic friction occurs in an interval of extremely small velocities defined as a ratio of the lattice parameter to the relaxation time of the shear modulus.
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