Fractal structure of cast iron and its strength characteristics

The object of research is the structure and hardness of cast iron rolls used in section rolling mills. The study focuses on the use of multifractal analysis to assess the microstructural features of cast iron and their correlation with hardness. Method. Quantitative metallography methods and a multifractal approach were employed to analyze the microstructure of cast iron. Statistical characteristics of the microstructure were calculated using Rényi's formula. Hardness measurements were conducted on rolls made from SPHN and SSHNF grades of cast iron at three equidistant points along the barrel. Correlation coefficients were computed to evaluate the relationship between hardness and both traditional structural characteristics (length, diameter, area) and multifractal parameters. Results. The analysis revealed the significant influence of statistical fractal dimensions and the morphology of carbides and graphite (lamellar and spheroidal) on the hardness of cast iron rolls. Correlation coefficients for hardness prediction based on traditional structural features ranged from , while prediction using multifractal characteristics showed higher coefficients:  to  for SPHN rolls and  to  for SSHNF rolls. These results demonstrate the effectiveness of multifractal analysis in assessing the quality of cast iron rolls. A novel approach for evaluating the hardness of SPHN and SSHNF rolls is proposed. It includes the calculation of the statistical dimension spectrum of cast iron structural elements, determination of sensitivity coefficients of hardness to the spectrum, and the development of a mathematical model for hardness prediction. This method offers an alternative framework for assessing the quality of cast irons by analyzing their structural characteristics.