FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODES
Abstract
The paper considers a model of damage accumulation in parts of machines and structures which is based on a theory of fractals. Hidden process of destruction prior to the formation of macroscopic cracks is usually associated with the accumulation of micro-damages. Various models of damage accumulation and crack growth under the influence of power and thermal loads. However, models describing the accumulation process of micro-damages and their outgrowth into macro-crack are practically non-existent. Fractal structures with self-similarity are an adequate model of the fracture process. The MacDonald correlation function describing the medium structure allows to present the self-similarity of structures within a certain range of scales.
The paper reviews models of damage accumulation near an opening in a composite medium and at layer boundaries. The Cantor model in a forward algorithm and a backward algorithm have been used in order to describe the model of damage accumulation. As it is known, the Cantor fractal (Cantor dust) is obtained by using a recursive algorithm being applied to fracture mechanics can be regarded as a model of stepwise formation of dispersed micro-damages. The process of damage accumulation (latent destruction phase) and its transition in the formation process of macro-cracks and their unification in a through-thickness crack can be described, for example, by the Paris' law.
About the Authors
Alim. Abed Al-Zobaede
Belarusian National Technical University
Yu. V. Chigareva
Belarusian National Technical University
References
1. Vstavsky, G. V. (1992) Model of Fractal Fatigue Crack Profile. Prikladnaia Mekhanika i Tekhnicheskaia Fizika [Applied Mechanics and Technical Physics], 2, 130-137 (in Russian).
2. Louis, E., Ginza, F., Flores, F. (1985) Fractal Nature of Cracks, Fractals in Physics. Proceedings of VI-th International Symposium on Fractals in Physics. International Centre for Theoretical Physics. Trieste, Italy, 9-12 Yuly 1985 (Edited by L. Pietronero and E. Tosatti). Elsevier, 487-497.
3. Mandelbrot, B. B. (1983) The Fractal Geometry of Nature. Freeman: San Francisco. 287 r.
4. Morozov, A. D. (2002) Introduction in Theory of Fractals. Moscow; Izhevsk: Institute of Computer Research. 160 p. (in Russian).
5. Zosimov, V. V., Liamshev, L. M. (1994) Fractals and Scaling in Acoustics. Akusticheskii Zhurnal [Acoustics journal], 40 (5), 709-737 (in Russian).
6. Lysanov, Yu. P., Liamshev, L. M. (1999) On Fractal Nature of Low-Frequency Sound Attenuation in the Ocean. Doklady Akademii Nauk [Reports of Academy of Sciences. Physics], 366 (1), 36-38 (in Russian).
7. Kozlov, G. V., Buria, A. I., Sviridenok, A. I., Zaikov, G. E. (2003) Application of Autocorrelation Function Method for Structural Analysis of Glass-Like Polycarbonate. Doklady Natsyonal'noi Akademii Nauk Belarusi (Doklady of the Natinal Academy of Sciences of Belarus), 47 (4), 51-54 (in Russian).
8. Schefer, D., Kefer, K. (1988) Structure of Accidental Silicate: Polymer, Colloid and Porous Solid Bodies. Fraktaly v Fizike. Trudy VI Mezhdunarodnogo Simpoziuma po Fraktalam V Fizike [Fractals in Physics Proceedings of VI-th International Symposium on Fractals in Physics. International Centre for Theoretical Physics. Trieste, Italy, 9-12 Yuly 1985 (Edited by L. Pietronero and E. Tosatti)]. Moscow, Mir, 62-71 (in Russian).
9. Vladimirov, V. S. (1979) Generalized Functions in Mathematical Physics. Moscow, Nauka. 318 p. (in Russian).
10. Shermergor, T. D. (1977) Elasticity Theory of Micro Heterogeneous Media. Moscow, Nauka. 400 p. (in Russian).
11. Ernst, M. (1989) Kinetics of Cluster Formation During Irreversible Aggregation. Fractals in Physics. Fraktaly v Fizike. Trudy VI Mezhdunarodnogo Simpoziuma po Fraktalam v Fizike [Fractals in Physics Proceedings of VI-th International Symposium on Fractals in Physics. International Centre for Theoretical Physics. Trieste, Italy, 9-12 Yuly 1985 (Edited by L. Pietronero and E. Tosatti)]. Moscow, Mir, 399-429 (in Russian).
12. Ishimaru, I. (1979) Distribution and Dispersion of Waves in Accidentally Heterogeneous Media. Vol. 2. Moscow, Mir. 343 p. (in Russian).
13. Kulak, M. I. (2002) Fractal Material Mechanics. Minsk: Vysheishaya Shkola. 304 p. (in Russian).
Review
For citations:
Al-Zobaede A., Chigareva Yu.V. FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODES. Science & Technique. 2014;(6):42-48. (In Russ.)
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