Funct. Mater. 2025; 32 (3): 411-417.
From microstructure to properties: fractal patterns in carbon steels
1 Kharkiv National Automobile and Highway University, 25 Yaroslava Mudrogo Str., 61002 Kharkiv, Ukraine
2 Prydniprovska State Academy of Civil Engineering and Architecture, 24a Architect Oleh Petrov Str., 49000 Dnipro, Ukraine
3 Kremenchuk Mykhailo Ostrohradskyi National University 20 University Str., 39600 Kremenchuk, Ukraine
Using multifractal analysis, the microstructural homogeneity in carbon alloys after different heat treatment regimes was quantitatively assessed. The sizes of the regions within which the fractal dimension of individual structural elements does not change are established: for lamellar pearlite – 5.3×5.3 μm, for pearlite and residual austenite – 6.2×6.2 μm, for martensite – 4.4×4.4 μm. The homogeneity is expressed through the fractal dimension of each structural component and hardness (HRC). Comparison of the results obtained by traditional metallography and multifractal analysis methods confirmed the complementarity of the approaches and showed the high sensitivity of multifractal analysis to structural changes in the material. The use of digital methods of multifractal analysis opens up prospects for optimizing heat treatment modes and predicting the mechanical properties of carbon alloys.