Technical Diagnostics and Non-Destructive Testing, 2022, №01



2022 №01 (01)

DOI of Article 10.37434/tdnk2022.01.02

2022 №01 (03)

---

Technical Diagnostics and Non-Destructive Testing #1, 2022, pp. 22-30

Application of fractal analysis in diagnostics of technical condition of metal structure elements

V.V. Usov¹, M.D. Rabkina², N.M. Shkatulyak¹, N.I. Rybak¹, O.O. Stofel³

¹1K.D. Ushinskii South-Ukraine National Pedagogical University. 26 Staroportofrankivska Str., 65020, Odessa, Ukraine. E-mail: valentinusov67@gmail.com
²E.O. Paton Electric Welding Institute of NASU. 11 Kazymyr Malevych str., 03150, Kyiv, Ukraine. E-mail: marjanara17@gmail.com
³National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute». 37 Peremohy Ave., 03056, Kyiv, Ukraine

It is shown that fractal analysis, as an additional tool of technical diagnostics and non-destructive testing, allows determination of the most important features of the state and behaviour of metal structure elements during their operation and failure. Examples of application of fractal dimension of the fractures are presented to assess the critical dimension of brittle cracks and to determine its eff ect on impact toughness, yield limit, ultimate strength, and destructive pressure at hydraulic testing, and to detect the interrelation of fractal dimension with fatigue life after low-cycle fatigue fracture of metal of pipeline welded joints. It is found that the nature of fractal dimensions of the fractures and diagrams of time dependence of the applied load at impact loading is due to the direction of cutting and temperature of testing the samples. It is shown that the main component of {001} <110> texture of low-alloyed steel promotes an increase of fractal dimension of the fractures and development of brittle fracture at impact testing. Ref. 25, Tabl. 4, Fig. 9.
Keywords: impact testing, fractal dimension, brittle crack, destruction

Received: 16.12.2021

References

1. Usov V.V., Girenko V.S., Rabkina M. D. et al. (1993) Effect of the crystallographic texture on the anisotropy of fracture characteristics of control-rolled low-alloy steel. Materials Science, 29 (2) 146-150. http://lib.gen.in/d55dae53541a8dc954b7f4d30d0a34cf.pdf https://doi.org/10.1007/BF00558813
2. Lyakishev, N.P.,Egiz, I.V., Shamraj, V.M. (2000) Texture and crystallographic peculiarities of fracture of steel X70 pipe material. Metally, 2, 68-72 [in Russian]. http://www.imet.ac.ru/metally/nambers.htm
3. Ivanova, V.S., Balankin, A.S., Bunin, I.Zh., Oksagoev, A.A. (1994) Synergy and fractals in materials science. Moscow, Nauka [in Russian]. https://www.researchgate. net/publication/268999858_Sinergetika_i_fraktaly_v_materialovedenii
4. Mandelbrot, B. (2002) Fractal geometry of nature. Moscow, Institute for Computer Research. https://ruwapa.net/book/benua-mandelbrot-fraktalnaya-geometriya-prirody/
5. Watanabe, T., Tsurekawa, S. (2004) Toughening of brittle materials by grain boundary engineering. Mater. Sci. Engng. A., 387-389, 447-455. https://www.researchgate.net/publication/222146139_Toughening_of_Brittle_Materials_by_Grain_Boundary_Engineering https://doi.org/10.1016/S0921-5093(04)00653-7
6. Vitek, V., Chen, S.P., Voter, A.F. et al. (1989) Grain boundary structure and intergranular fracture in L12 ordered alloys. Mater. Sci. Forum, 46, 237-252. https://www.scientific.net/ MSF.46.23 https://doi.org/10.4028/www.scientific.net/MSF.46.237
7. Watanabe, T. (1993) Grain boundary design and control for high temperature materials. Mater. Sci. Engng. A., 166, 11-28. https://www.sciencedirect.com/science/article/abs/pii/092150939390306Y https://doi.org/10.1016/0921-5093(93)90306-Y
8. Zhou, H.W., Xie, H. (2003) Direct estimation of the fractal dimensions of a fracture surface of rock. Surface Review and Letters, 10(5), 751-762. https://paperzz.com/doc/9119828/direct-estimation-of-the-fractal-dimensions-of-a https://doi.org/10.1142/S0218625X03005591
9. Lucas, M.A. (2012) Foundations of Measurement Fractal Theory for the Fracture Mechanics Applied. In Fracture Mechanics, Edited by Alexander Belov. https://www.intechopen.com/chapters/41469
10. Harfa: download. http://www.fch.vut.cz/lectures/imagesci/includes/harfa_download.inc.php
11. ACDSee Professional 2019. https://www.acdsee.com/en/products/photo-studio-professional
12. Usov, V.V., Shkatulyak, N.M. (2005) Fractal Nature of the Brittle Fracture Surfaces of Metal. Materials Science, 41(1), 62-66. https://www.researchgate.net/publication/226818869_Fractal_Nature_of_the_Brittle_Fracture_Surfaces_of_Metal https://doi.org/10.1007/s11003-005-0132-8
13. Mosolov, A.B. (1991) Fractal Griffi th crack. Zhurn. Tekh. Fiz., 64, (7), 57-60 [in Russian]. http://journals.ioff e.ru/articles/viewPDF/24666
14. Honeycomb, R. (1962) Plastic deformation of metals. Moscow, IL [in Russian]. https://ua1lib.org/book/2433166/2721d7
15. Bernshtejn, M.L., Zajmovsky, M.A. (1979) Mechanical properties of metals. Moscow, Metallurgiya [in Russian]. https://ua1lib.org/book/2720875/410310
16. Usov, V.V., Rabkina, M.D., Shkatulyak, N.M., Cherneva, T.S. (2015) Fractal dimension of grain boundaries and mechanical properties of the metal of oxygen cylinder. Material science, 50(4), 612-620. https://www.researchgate.net/publication/276456141_Fractal_Dimension_of_Grain_Boundaries_and_Mechanical_Properties_of_the_Metal_of_Oxygen_Cylinders https://doi.org/10.1007/s11003-015-9761-8
17. Usov, V.V., Gopkalo, E.E., Shkatulyak, N.M. et al. (2015) Texture, Microstructure, and Fractal Features of the Low Cycle Fatigue Failure of the Metal in Pipeline Welded Joints. Russian Metallurgy (Metally), 9, 759-770. https://www.researchgate.net/publication/289569432_Texture_microstructure_and_fractal_features_of_the_low-cycle_fatigue_failure_of_the_metal_in_pipeline_welded_joints https://doi.org/10.1134/S0036029515090128
18. Carney, L.R., Mecholsky, J.J. (2013) Relationship between fracture toughness and fracture surface fractal dimension in AISI 4340 steel. Mater. Sci. Applicat., 4(4), 258-267. https://doi.org/10.4236/msa.2013.44032
19. Glushkov, A., Khetselius, O., Brusentseva, S., Duborez, A. (2014) Modeling chaotic dynamics of complex systems with using chaos theory, geometric attractors, quantum neural networks. Proc Int. Geom. Center, 7(3), 87-94, http://eprints.library.odeku.edu.ua/id/eprint/2938/1/%D0%93%D0%BB%D1%83%D0%A5%D0%B5%D1%86%D0%91%D1%80%D1%83%D0%94%D1%83%D0%B1Pmgc_2014_7_3_13%20(1).pdf
20. Glushkov, A.V., Buyadzhi, V.V., Ternovsky, V.B. et al. (2018) A chaos-dynamical approach to analysis, processing and forecasting measurements data of the chaotic quantum and laser systems and sensors. Sensor Electronics and Мicrosystem Technologies, 15(4) 41-49, http://eprints.library.odeku.edu.ua/id/eprint/4481/1/2018%20T15%20%234%20CEMST.pdf https://doi.org/10.18524/1815-7459.2018.4.150497
21. Usov, V., Rabkina, M., Shkatulyak, N. et al. (2020) Anisotropy of Fractal Dimensions of Fractures and Loading Curves of Steel Samples During Impact Bending. Material Science, 17(4), 142-151. http://ijmse.iust.ac.ir/article-1-1680-en.pdf
22. Kondryakov, E.A., Zhmaka, V.N., Kharchenko, V.V. et al. (2005) System of Strain and Load Measurement in Dynamic Testing of Materials. Strength Mater, 37, 331-335. https://doi.org/10.1007/s11223-005-0046-6
23. Steel. Charpy impact V-notch test. Instrumental test method [in Russian]. http://rossert.narod.ru/alldoc/info/2z77/g39315.html
24. Winston, R. (Editor) (2015) Oil and Gas Pipelines: Integrity and Safety, Handbook. https://www.worldcat.org/title/oil-and-gas-pipelines-integrity-and-safety-handbook/oclc/904715784
25. Pineau, A., Benzerga, A.A., Pardoen, T. (2016) Failure of metals I: Brittle and ductile fracture. Acta Materialia, 107, 424-483. https://par.nsf.gov/servlets/purl/10019128Pineau https://doi.org/10.1016/j.actamat.2015.12.034

---

Advertising in this issue:

---