Fractal Modeling of Microstructure and Mechanical Properties of Medium-Carbon Steel St6 Based on Fractal Dimension

This study examines the relationship between cooling conditions after austenitisation and the resulting microstructure and mechanical properties of medium-carbon steel St6. Samples were cooled in air, oil, Water-Polymer Solution (WPS) medium, and water following heating at 830 °C for 10 minutes. The Hausdorff (fractal) dimension of the obtained ferrito-pearlitic, bainitic, and martensitic structures was determined from optical micrographs at ×1000 magnification. Significant correlations were identified between the fractal dimension and hardness (HRB), ultimate tensile strength (s B ), and yield strength (s T ). Regression equations were developed that allow accurate prediction of the steel’s mechanical characteristics directly from the fractal dimension of its microstructure. The results indicate that a reduction in fractal dimension, which reflects increased structural ordering, leads to substantial improvements in strength and hardness. The fractal approach offers a promising non-destructive method for evaluating and optimizing heat treatment processes in structural steels.