Noise Effect on Ice Surface Softening During Friction

The ice surface softening by friction is investigated considering the additive non-correlated fluctuations of the shear strain and stress, and the temperature. The premelting is construed by the Kelvin–Voigt equation for shear strain and by the relaxation equations of Landau–Khalatnikov type for shear stress and temperature. Taking into account the noises in these equations, the Langevin and Fokker–Planck equations are derived. Their analysis is based on the investigation of extrema of the distribution function, i.e., steady-state values of the shear strain using the Stratonovich interpretation. The phase diagrams are constructed, where the noises intensities and thermostat temperature determine the regions of ice, softened ice and their mixture (stick–slip rubbing). We present that domain of ice friction is bounded by relatively small background sliding block temperatures and fluctuation intensities of the stress and temperature. The ice film softens with growth of the stress noise intensity even at small thermostat temperatures. The friction force time series for all rubbing modes are calculated and compared with experimentally observed ones.