Study of the effect of carbon on the fractal dimension of steel
DOI:
https://doi.org/10.30838/J.PMHTM.2413.241120.38.689Keywords:
martensite, fractal dimension, scoring, methodology, regression modelAbstract
Introduction.The martensitic structure of steels arising by the mechanism of atomic lattice shift due to rapid cooling in various media has a complex shape at various scale levels of its representation. Traditionally, the analysis of the martensitic structure at the microstructural level is carried out using a point scale, which is a semi-quantitative characteristic. However, this approach does not always satisfy the results of a quantitative assessment of the martensitic structure of steels and the prediction of their service characteristics, in particular, mechanical ones. A fractal approach was used to quantify the martensitic structure of steels. Materials and methods. The work investigated the point scale of the martensitic structure (point grade 1−10) according to ГОСT 8233 using fractal formalism. The method for determining the fractal dimension is based on a patented technique, including the search for the convergence of the values of the fractal cell and point dimensions. The applied technique increases the adequacy of the obtained values of the fractal dimension of the structure of the material under study. Experiment Results. By determining the dimension of the point martensite structure, it was established that it is fractional, that is, it is fractal. An increase in the fractal dimension of martensite needles with an increase in their score was recorded. A similar trend is also observed for the fractal dimension of the grain boundaries (needles) of martensite, which increases with an increase in the score. An increase in the fractal dimension of martensite may be due to a change in its morphology from latent-acicular to coarse-acicular. Conclusions. The analysis of the point martensite structure is carried out in accordance with the normative documents. Regression models for evaluating the martensitic structure in terms of its fractal dimension (R2 = 0,81) and grain boundaries (R2 = 0,67) are obtained. This indicates the possibility of using the fractal approach, as an alternative, when controlling the structure of martensite after different modes of heat treatment.
References
Dubrov Yu., Bolshakov V. and Volchuk V. Puti identifikatsii periodicheskikh mnogokriterial'nykh tekhnologiy [Road periodic identification of multi-criteria Technology]. Saarbrucken : Palmarium Academic Publishing, 2015,
236 p. (in Russian).
Bolshakov V.I., Volchuk V.N. and Dubrov Yu.I. Identifikatsiya mnogoparametricheskikh, mnogokriterial'nykh tekhnologiy i puti ikh prakticheskoy realizatsii [Multiparameter identification, multicriteria techniques and ways of their implementation]. Metaloznavstvo ta termichna obrobka metaliv [Metall Science and Heat Treatment of Metals]. 2013, no. 4, pp. 5–11. (in Russian).
Bolshakov V.I., Volchuk V.M. and Dubrov Yu.I. Osnovy organizatsii fraktal'nogo modelirovaniya [Fundamentals of fractal modeling]. Kyiv : Akademperiodika, 2017, 170 p. (in Russian).
Volchuk V.N. O primenenii veyvletno-mul'tifraktal'nogo analiza v zadache otsenki struktury metalla [The application of wavelet-multifractal analysis in problems of metal structure]. Visnyk Prydniprovs’koyi derzhavnoyi akademiyi budivnytstva ta arkhitektury [Bulletin of Prydniprovs’ka State Academy of Civil Engineering and Architecture]. 2015, no. 9, pp. 24–30. (in Russian).
Volchuk V.N. Primeneniye rezul'tatov veyvletno-mul'tifraktal'nogo analiza struktury metalla dlya prognoza yego kachestva [Application of results of wavelet and multifractal analysis of metal structure for prognosis of its quality]. Visnyk Prydniprovs’koyi derzhavnoyi akademiyi budivnytstva ta arkhitektury [Bulletin of Prydniprovs’ka State Academy of Civil Engineering and Architecture]. 2015, no. 10, pp. 16–20. (in Russian).
Volchuk V., Klymenko I., Kroviakov S. and Orešković M. Method of material quality estimation with usage of multifractal formalism. Tehnički glasnik − Technical Journal. 2018, vol. 12, no. 2, рр. 93−97.
Bol’shakov V., Volchuk V. and Dubrov Yu. Fractals and properties of materials. Saarbrucken : Lambert Academic Publishing, 2016, 140 p.
Bol’shakov V.I., Volchuk V.N. and Dubrov Yu.I. Materialovedcheskiye aspekty primeneniya chastichnoy kompensatsii nepolnoty formal'noy aksiomatiki [Material aspects of use of partial compensation of incompleteness of formal axiomatics]. Visnyk Prydniprovs’koyi derzhavnoyi akademiyi budivnytstva ta arkhitektury [Bulletin of Prydniprovs’ka State Academy of Civil Engineering and Architecture]. 2015, no. 5, pp. 10–16. (in Russian).
Mandelbrot B. B. The Fractal Geometry of Nature. New-York, San Francisco : Freeman, 1982, 480 p.
Zhuravel' I. M. and Svirs'ka L.M. Measurement of the mean grain size in a metal by using fractal dimensions. Materials Science. 2015, vol. 46, no 3,рp. 418−420.
Bolshakov V.I., Volchuk V.N. and Dubrov Yu.I. Osobennosti primeneniya mul'tifraktal'nogo formalizma v materialovedenii [Features of the multifractal formalism in materials]. Dopovidi Natsionalnoi akademii nauk Ukrainy [Reports of the National Academy of Sciences of Ukraine]. 2008, no. 11, pp. 99−107. (in Russian).
Bol’shakov V., Volchuk V. and Dubrov Yu. Puti primeneniya teorii fraktalov [Ways of applying the theory of fractals]. Saarbrucken : Palmarium Academic Publishing, 2016, 146 p. (in Russian).
Volchuk V.M. Opredeleniye chuvstvitel'nosti mul'tifraktal'nykh kharakteristik metalla[Determining the sensitivity of the multifractal characteristics of metals]. Visnyk Prydniprovs'koyi derzhavnoyi akademiyi budivnytstva ta arkhitektury [Bulletin of Prydniprovs’ka State Academy of Civil Engineering and Architecture]. 2015, no. 12,
pp. 10–14. (in Russian).
Bolshakov V.I., Volchuk V.M. and Parhomenko O.F. Evaluation of High Strength Steel Fatigue. UDCS'19: Fourth International Iron and Steel Symposium, April 4−6, 2019, Karabuk University, Karabuk, Turkey, 2019, vol. 4, рр. 415−417.
Volchuk V.M. Primeneniye kontseptsii mul’tifractalov dlya kontrolya kachestva nizkolegirovannoy stali [Application of the concept of multifractal to control the quality of low-alloy steel]. Metallovedenie i termicheskaya obrabotka metallov [Physical Metallurgy and Heat Treatment of Metals]. 2018, no. 3, pp. 20–27. (in Russian).
Bolshakov V.I., Volchuk V.M. and Dubrov Yu.I. Regularization of One Conditionally Ill-Posed Problem of Extractive Metallurgy. Metallofizika i Noveishie Tekhnologii. 2018, vol. 40, no. 9, pр. 1165−1171. URL : https://DOI: 10.15407/mfint.40.09.1165
Volchuk V.M. Modelʹ otsinyuvannya tverdosti chavunnykh valkiv СПХН-43 ta СШХНФ-47 [Model of assessment of the hardness of the iron rollers СПХН-43 and СШХНФ-47]. Metallovedenie i termicheskaya obrabotka metallov [Physical Metallurgy and Heat Treatment of Metals]. 2019, no. 4, pp. 22–35. (in Ukrainian).
Volchuk V.M. Fraktal'nyy analiz ballovoy sistemy [Fractal analysis of the point system]. Visnyk Prydniprovs’koyi derzhavnoyi akademiyi budivnytstva ta arkhitektury [Bulletin of Prydniprovs’ka State Academy of Civil Engineering and Architecture]. 2018, no. 5, pp. 47–53. (in Russian).
Volchuk V. M. K primeneniyu fraktal'nogo formalizma pri ranzhirovanii kriteriyev kachestva mnogoparametricheskikh tekhnologiy [On the Application of Fractal Formalism for Ranging Criteria of Quality of Multiparametric Technologies ]. Metallofizika i noveyshiye tekhnologii [Metal Physics and Advanced Technologies]. 2017, vol. 39, no 3,рp. 949−957.URL : http://mfint.imp.kiev.ua/ru/abstract/v39/i07/0949.html. (in Russian).
Kroviakov S., Volchuk V., Zavoloka M., and Kryzhanovskyi V. Search for Ranking Approaches of Expanded Clay Concrete Quality Criteria. In: Materials Science Forum. Trans Tech Publications Ltd, 2019, vol. 968, pp. 20−25.
Volchuk V.M. Doslidzhennya vplyvu vuhletsyu na fraktalʹnu rozmirnistʹ stali [Study of the effect of carbon on the fractal dimension of steel]. Visnyk Prydniprovs’koyi derzhavnoyi akademiyi budivnytstva ta arkhitektury [Bulletin of Prydniprovs’ka State Academy of Civil Engineering and Architecture]. 2020, no. 3, pp. 31–39. (in Russian).
Bol’shakov V.I., Dubrov Yu.I., Kryulin F.V. and Volchuk V.N. Sposib vyznachennya fraktal’noyi rozmirnosti zobrazhennya [Method for Determining the Dimensionality of Images]. Patent product no. 51439А, UA. MPK 7 G06K9/00, bulletin no. 11, 2002. (in Ukrainian).
Volchuk V.M. and Parhomenko O.F. Fractal approach in assessing the quality of steel 20. Innovative Lifecycle Technologies of Housing, Industrial and Transportation Objects : collective monograph; under the general editorship Savytskyi M. Dnipro : SHEE “Prydniprovska State Academy of Civil Engineering and Architecture”; Bratislava : Slovac University of Technology in Bratislava, 2018, pp. 48−53.
Volchuk V.M. Modelyuvannya vlastivostej konstrukcіjnih materіalіv[Modeling properties of structural materials]. Metallovedenie i termicheskaya obrabotka metallov [Physical Metallurgy and Heat Treatment of Metals]. 2020, no. 1, pp. 21–35. (in Ukrainian).
Bol’shakov V.I., Volchuk V.N. and Dubrov Yu.I. K opredeleniyu metriki ob"yekta identifikatsii [To the definition of the identity metric]. Metaloznavstvo ta termіchna obrobka metalіv [Metall Science and Heat Treatment of Metals]. 2016, no. 4, pp. 10–14. (in Ukrainian).
Downloads
Issue
Section
License
Authors that are published in this journal agree to follow the conditions:
Authors reserve the right to the authorship of his work and cede the right to the journal of first publication of this work on conditions of the license under the Creative Commons Attribution License, which allows others to distribute it freely with the obligatory reference to the author of the original work and the first publication of the work in this journal.
