Composition of topological and fractal invariants in the identification of structure

Abstract

Formulation of the problem. The processes of formal representation of the metal structure, according to the well-known hypothesis of S. Wolffrem, are described only by numerically irreducible algorithms, the results of which can not be predicted without completely completing them. In material science, such a singularity manifests itself in the identification of the structure of a metal and is explained by its sensitivity to even relatively small changes in thermodynamic characteristics. The search for a more accurate forecast of steel quality indicators led the authors to take into account the above-mentioned topological characteristics of structures, dimensional (fractal) characteristics. Results and discussion. It is proposed an efficacious method of estimation of properties of a metal using a composition of the topological and fractal approaches for the honeycomb, lamellar, granular and acicular class structures. The method is based on four new criteria for the structure estimation that are obtained by combining the above-mentioned approaches. Using this method, the metal strength estimation error is reduced by a factor 1,24…2,16 depending on the metal class. These approaches mutually complement each other, as they provide additional information on the influence of metal processing regimes on the structure, and, accordingly, on the properties. Conclusions. It is shown that the composition of topological and fractal methods gives a more accurate prediction than each of these approaches separately from each other.