Fractal analysis of the point system

Introduction. The point estimate of the structure of metals is used in the control of their quality. However, it is a semi-quantitative estimate. The work is devoted to the search for alternative methods for assessing the grain structures of metals. Materials and methods. The scoring scale of the grain structures of metals according to ГОСТ 5639 using the fractal formalism was investigated. Results of the experiment. An increase in the fractal dimension of the grain boundaries with decreasing grain sizes (score 1 -10 for the main scale) was established. This is due to the increase in the total length of the grain boundaries, which is more fine-grained steel than coarse-grained steel, and hence the occupancy of space by grain boundaries is greater, which leads to an increase in their fractal dimension up to the topological dimension of the plane 2. Conclusions. The analysis of the scoring system of the metal grain structures according to GOST 5639 has been carried out. The change in the fractal dimension depending on the grain score indicates their sensitivity and provides an opportunity to use the fractal dimension as a quantitative assessment of the metal structure while controlling its quality.