Funct. Mater. 2024; 31 (3): 391-395.

doi:https://doi.org/10.15407/fm31.03.391

Mathematical modeling of the structure and properties of low-carbon alloys

D.B. Hlushkova1, V.M. Volchuk 2

1Kharkiv National Automobile and Highway University, 25 Yaroslava Mudrogo Str., 61002 Kharkiv, Ukraine
2Prydniprovska State Academy of Civil Engineering and Architecture, 24a Architect Oleh Petrov Str., 49000 Dnipro, Ukraine

Abstract: 

Issues related to the determination of the numerical values of the qualitative characteristics of Fe-C alloys by interpreting the spectrum of elements of its structure by the spectrum of fractal dimensions are considered. This is due to the fact that the geometric configuration of many elements of iron-carbon alloys is complex, and it is not enough to use Euclidean geometry for its identification. Therefore, the fractal theory was applied to estimate the structure of Fe-C alloys. The results of experimental studies are presented, where it was found that the most sensitive to the fractal dimension of pearlite are the indicators of strength and hardness, which is confirmed by their physical-mechanical interaction and the obtained mathematical models. The indicators of plasticity were most sensitive to the fractal dimension of ferrite and grain boundaries, which is also consistent with the main provisions of their structure formation processes and is confirmed by the corresponding models. The obtained results can be interpreted as a technique for evaluating the quality criteria of the Fe-C alloy based on the analysis of the fractal dimension of its microstructure.

Keywords: 
Fe-C alloy, fractal, ferrite, pearlite, grain boundaries, quality criteria.

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