From structure to strength: A multifractal technology on chromium-nickel cast iron with flake graphite

Chromium–nickel cast iron with flake graphite is used in mechanically demanding components where hardness, toughness, and strength are strongly influenced by graphite morphology and carbide distribution. Conventional metallographic assessment based on graphite shape, size, distribution, and phase fraction provides useful classification information but does not fully capture the spatial complexity of microstructural phases. This study applies multifractal analysis to etched optical micrographs of chromium–nickel cast iron to evaluate microstructure–property correlations. Binary graphite and carbide phase masks were generated from metallographic images, and Renyi entropy-based generalized dimensions D(q) were calculated using a box-counting approach. The multifractal descriptors were compared with conventional structural parameters and correlated with Shore hardness (HSD), tensile strength, flexural strength, and impact toughness. Conventional phase-fraction and graphite-grading descriptors showed limited correlations with mechanical properties, with R² values of approximately 0.40–0.77. In contrast, multifractal descriptors showed stronger correlations, including D₀ with tensile strength (R² = 0.9558), D₁ with flexural strength (R² = 0.8374), and D₂ with Shore hardness (R² = 0.9486). These results indicate that scale-dependent distributions of graphite and carbide provide more informative descriptors than area-based measurements alone. The findings support the use of multifractal analysis as a laboratory-scale framework for microstructure–property correlation in this alloy. Future innovation should examine larger datasets, additional alloy systems, varied processing conditions, and independent validation protocols before practical use in representative foundry production environments for quality control.