Analysis of the point ferrite-perlite structure

Abstract

Abstract. Introduction . Steel with ferrite-perlite structure is widely used in various areas of the national economy. To assess the quality control of such steels, various methods of structural analysis are used: optical and electron microscopy, X-ray analysis, ultrasound diagnostics, magnetic resonance, and others. The use of mathematical methods allows us to establish a relationship between the structure and properties of the metal. The ratio between ferrite and perlite is fixed by scoring and is used in metallographic methods of quality control of manufactured metal products. However, the incompleteness of formal axiomatics arising from the identification of certain perlite structures of steels and cast irons, according to Godel, initiates a search for various approaches to their evaluation. To fix changes in the configuration of the grain structure of perlite and ferrite, it is suggested that the theory of fractals should be applied. Materials and methods. The point scale of ferrite-perlite structures from 1 to 10 according to GOST 8233 was investigated by calculating the fractal dimension of ferrite and perlite. Results of the experiment. An additional method for estimating the ferrite-perlite structure is suggested, it is based on a fractal analysis of their point scale. It is found that the fractal dimension of both the ferrite and perlite grains on the plane increases with an increase in their percentage from 1.45 to 1.98. This fact is explained by the sensitivity of the fractal dimension to occupancy of the space of one or another structural component. Conclusions. The results obtained in the fractal analysis of the scale 7 of the ratio of ferrite and perlite according to GOST 8233 indicate the possibility of using their fractal dimension as an indicator of changes in the structure. A similar approach can be applied in the acceptance work of steels with a ferrite-perlite structure.