Multifractal Analysis of Fatigue Failure in Friction

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.

1. Janahmadov A.Kh. and Javadov M.Y. Synergetics and Fractals in Tribology. — USA: Springer. — 2016

2. Panin V.E., Lihachev V.A., Grinjaev Ju.V. Strukturnye urovni deformacii tverdyh tel. — Novosibirsk: Nauka. Sib. otd-nie. — 1985 (in Russian)

3. Sinergetika i ustalostnoe razrushenie metallov. — M.: Nauka. — 1989. (in Russian)

4. Janahmadov A.Kh. Mezomehanika frikcionnogo kontakta v uslovijah malociklovoj ustalosti // Trenie i iznos. — 2022 (43), № 3, 310—317 (in Russian)

5. Olemskoj A.I., Kacnelson A.A. Sinergetika kondensirovannoj sredy. Izd. 2-e. — M.: Editorial URSS. — 2010 (in Russian)

6. Rumer Ju.B., Rybkin M.Sh. Termodinamika, statisticheskaja fizika i kinetika. — Novosibirsk: Izdvo Novosib. un-ta: Sib. univ. Izd-vo. — 2001 (in Russian)

7. Romaniv O.N., Kryskiv A.S. Ispolzovanie kriteriev mehaniki razrushenija dlja ocenki hladnolomkosti stalej // Fiz.-him. Mehanika materialov. — 1981, № 5, 40—51 (in Russian)

8. Medovar B.I., Gladshtejn L.I., Saenko V.Ja. i dr. Vjazkost razrushenija stali 16G2AF elektroshnakovogo pereplava // Probl. spec. elektrometallurgii. — 1983, № 19, 32—35 (in Russian)

9. Janahmadov A.Kh. Tribotekhnicheskie problemy v neftegazovom oborudovanii. — Baku: ELM. — 1998 (in Russian)