Application of the method of fractal analysis to the study of metal structure

Abstract

The traditional methods for geometric estimation of the shape of various objects, including materials science, based on approximate approximation of the structure of the object under study by geometric figures, for example, lines, segments, planes, polygons, polyhedra, spheres. All these techniques are based on a classical Euclidean geometry with an integer topological dimension. For a quantitative description of fractals, one quantity is enough - the fractal dimension or a some parameter that describes the invariability of statistical characteristics when the scale changes.
An analysis of traditional methods for studying the structure of metals – optical microscopy, in particular, quantitative metallography, electronic microstructure, and crystallographic texture by structural analysis, indicates that none of them can be universal and suitable for solving the full scope of the tasks of identifying quantitative characteristics of a metal by analysis its structure.
In a metallography, fractal analysis refers to the microscopic images of the surfaces of materials. In this case, using fractal characteristics, one can describe the structure and mechanical properties of materials, like the degree of surface roughness, chemical surface changes, deformation of materials, etc.
This article describes the application of the fractal analysis method to the general concept of the metal structure described by GOST 5639-82 and 8233-56. With the help of a software tool written by the author that allows you to quickly calculate the fractal dimension, the calculated fractal dimension of the metal structure about various magnifications and various balls of grains. The described algorithm for searching for fractal dimension and an example of the use of software for quick search of fractal dimension. The analysis of the influence of structural parameters on the value of fractal dimension is carried out. The choice of ferrite-pearlite steels is reasoned and it is analyzed which metal structures it is possible to further apply the fractal analysis method and look for correlations with physicomechanical properties.