Multifractal Analysis of Fatigue Failure in Friction

Abstract The paper explains the need to combine synergetics and fractal analysis to study the contacting elements in friction and wear, as part of self-organizing into open systems dissipative structures known as a fractal behavior. The concept of multifractal analysis introduces the new quantitative parameters for the structures, characterized by a spectrum of generalized fractal dimensions and reflected by the degree of randomness. In accordance with the diversity of types of tribological process, various scenarios of system evolution seem possible. The most adequate description of these scenarios is achieved not in real physical space, but in a hypothetical space with ultrametric topology. Different levels of structures (micro, mesa, and macro scale) are described in the framework of multifractal analysis. It has been established that the frictional contact under study is a non-uniform fractal, that is, a multifractal. The procedure for calculating the multifractal dimension of this structure and the results of numerical calculations are presented, which confirm that the analyzed friction unit is a non-uniform fractal, i.e., a multifractal.