Nonlinear Model of Ice Surface Softening during Friction Taking into Account Spatial Heterogeneity of Temperature

Authors A.V. Khomenko , D.T. Logvinenko, Ya.V. Khyzhnya

Sumy State University, 2, Rymsky-Korsakov St., 40007 Sumy, Ukraine

Issue Volume 12, Year 2020, Number 4
Dates Received 18 June 2020; revised manuscript received 15 August 2020; published online 25 August 2020
Citation A.V. Khomenko, D.T. Logvinenko, Ya.V. Khyzhnya, J. Nano- Electron. Phys. 12 No 4, 04002 (2020)
PACS Number(s) 05.65. + b, 05.70.Ln, 46.55. + d, 62.20.F –, 64.60. – i, 81.40.Pq
Keywords Ice friction, Phase transition (6) , Rheology, Plasticity, Friction force, Shear strain and stress.

A nonlinear model of a viscoelastic medium is proposed, which describes softening of a thin layer of the ice surface during friction. The description of this transformation is based on the three following basic equations: the Kelvin-Voigt equation for a viscoelastic medium, the relaxation equations of Landau-Khalatnikov-type and for heat conductivity. It is revealed that mentioned equations coincide formally with the synergetic Lorenz system, where the order parameter is reduced to the shear strain, the stress acts as the conjugate field, and the temperature plays the role of the control parameter. The work further develops a nonlinear model of ice surface softening during friction, taking into account the spatial inhomogeneity of temperature in the equation of heat conductivity. In the framework of one-mode and adiabatic approximations an analytical soliton solution of a one-dimensional parabolic equation for the spatial normal distribution of shear strain to the ice surface is found. Due to the numerical solution of the one-dimensional Ginzburg-Landau differential equation, the distribution of friction force over the softened surface layer of ice is obtained and described. Two physical situations are considered: 1) the upper and lower surfaces move with equal velocities in opposite directions; 2) the upper surface is sheared along the fixed lower one. The coordinate dependencies of the friction force at different times are constructed and the evolution of the system to a stationary state is described. It is shown that the growth of time and background ice temperature leads to a sharper change of the friction force along the thickness of the premelted surface layer of ice, i.e. the relative shear velocity of the rubbing surfaces increases.

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