Mechanical properties of construction steel under rapid assessment

The object of research is the fractal modeling methodology applied to the structure and properties of materials, specifically metals. The study explores the relationship between the fractal (fractional) dimensions of structural elements and the physical and mechanical properties of materials, such as steel and cast iron. This work aims to analyze and refine the stages of fractal modeling to improve the prediction of material quality criteria. Method. The study employs a systematic fractal modeling approach, which includes the following steps: calculating the fractal dimension  using Hausdorff’s formula, determining self-similarity and scale invariance, assessing sensitivity conditions, selecting a target function and variables, and formalizing results through appropriate modeling. The heterogeneity of fractal objects is evaluated using Rényi’s formula to detect multifractality, and the results are interpreted in the context of material structure-property relationships. Examples of algorithm implementation and its augmentation with fractal formalism for ranking quality criteria are provided. Results. The analysis demonstrates that the proposed algorithm improves the prediction of material properties based on structural and macrostructural analysis. It highlights the importance of correlating fractal dimensions with mechanical properties and emphasizes sensitivity assessments. The findings confirm that applying fractal modeling allows the ranking of quality criteria for materials, thereby establishing new structure-property relationships. Suggestions for algorithm enhancements include integrating advanced methods to evaluate sensitivity and quality metrics within specific operational ranges.