Bashkov A.A., Anosov M.S., Ivanov S.V., Bazhenov E.O., Akulova A.A., Chichevatov A.V. Methods for Calculating Fractal Dimension from Digital Microstructure Images for Quantitative Metallography

DOI: 10.18503/1995-2732-2026-24-3-82-92

Abstract

In modern quantitative metallography, the development of objective methods for assessing the complexity and morphology of the microstructure of metallic materials based on digital image analysis is an important task. Traditional methods of visual analysis largely depend on the subjective interpretation of the researcher, which limits the reproducibility of the results. In this regard, the application of fractal analysis methods is a promising approach, as they make it possible to describe the geometric complexity of microstructural elements using quantitative parameters. The aim of this study is to investigate the potential of fractal dimension for the quantitative characterization of the microstructure of various steel grades using digital micrographs. The materials investigated are steels 20Kh13, U10A, 50, and 12Kh18N10T. Image processing and fractal dimension calculations have been performed using fractal analysis methods, including the differential box-counting method implemented in the developed software (Computer Program Registration Certificate No. RU 2024660065), as well as the classical box-counting algorithm implemented in MATLAB R2021b. The scientific novelty of the study lies in the comparative application of different algorithms for calculating fractal dimension to digital images of steel microstructures and in the interpretation of the obtained values from the perspective of the physics of metals. It has been shown that the fractal dimension values reflect the morphological features of microstructural elements, including grain boundaries, carbide precipitates, and martensitic structures. The results demonstrate the feasibility of using fractal analysis to move from qualitative descriptions of microstructure to quantitative parameters. The practical significance of the study lies in the potential application of the proposed approaches to the automation of metallographic analysis, quality control of materials, and investigation of structure-property relationships.

Keywords

fractal dimension, steel microstructure, digital metallography, differential box-counting method, quantitative image analysis, metals science, physics of metals.

For citation

Bashkov A.A., Anosov M.S., Ivanov S.V., Bazhenov E.O., Akulova A.A., Chichevatov A.V. Methods for Calculating Fractal Dimension from Digital Microstructure Images for Quantitative Metallography. Vestnik Magnitogorskogo Gosudarstvennogo Tekhnicheskogo Universiteta im. G.I. Nosova [Vestnik of Nosov Magnitogorsk State Technical University]. 2026, vol. 24, no. 3, pp. 82-92. https://doi.org/10.18503/1995-2732-2026-24-3-82-92

Andrey A. Bashkov – Senior Lecturer at the Department of Technology and Equipment of Mechanical Engineering, Nizhny Novgorod State Technical University named after R.E. Alekseev, Nizhny Novgorod, Russia. Email: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID 0000-0002-6658-0197.

Maxim S. Anosov – PhD (Eng.), Associate Professor of the Department of Technology and Equipment of Mechanical Engineering, Nizhny Novgorod State Technical University named after R.E. Alekseev, Nizhny Novgorod, Russia. Email: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID 0000-0001-8150-9332.

Sergey V. Ivanov – Engineer at the Information and Educational Center of the Institute of Industrial Engineering Technologies, Nizhny Novgorod State Technical University named after R.E. Alekseev, Nizhny Novgorod, Russia. Email: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID: 0009-0009-5614-4656

Evgeny O. Bazhenov – Senior Lecturer at the Department of Mechanical Engineering Technological Complexes, Nizhny Novgorod State Technical University named after R.E. Alekseev, Nizhny Novgorod, Russia. Email: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID: 0000-0003-0193-6065.

Anna A. Akulova – Engineer of the Institute of Industrial Engineering Technologies, Nizhny Novgorod State Technical University named after R.E. Alekseev, Nizhny Novgorod, Russia. Email: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID: 0009-0002-6553-3433.

Alexey V. Chichevatov – Research Engineer, Y.E. Sedakov Research Institute of Measuring Systems, a branch of the Russian Federal Nuclear Center, All-Russian Research Institute of Experimental Physics, Nizhny Novgorod, Russia. Email: This email address is being protected from spambots. You need JavaScript enabled to view it..

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