Application of Generalized Pareto Distribution to Determine the Structural Graphite Parameters in Cast Iron

Abstract

The power-law distribution of probability density (SSRV) sizes of graphite inclusions in the plane of the thin section is established in the work. The possibilities of structures parameterization of cast iron are shown: with flake graphite such as PG 10; vermicular graphite such as SHG10-VG85; spheroidal graphite such as SHG12. It is proposed to use the SSRV index of the sizes of graphite inclusions in cast iron for classification of cast iron structures that takes a value 0 < a < 1 and characterizing the risk and accident assessment of structures. The nature of power-law distribution of sizes of graphite inclusions occurs because of the fractality of graphitization processes and the graphite structure. It is shown that SSRW is modified into a generalized Pareto distribution (GP) which has all finite moments that allows the distribution function of the graphite cross-sections of random plane to move to the distribution of their sizes in volume. The generalized Pareto distribution of dimensions of flat inclusions of graphite allows for analyzing the specific scale <d> and structural parameters a and b of graphite in cast iron. There is a possibility of cast iron classification for platelet-shaped graphite such as PG 10 b = (0.39-0.56), for spherical shape graphite such as SHG12 b = (1.05-1.06), and for vermicular graphite such as SHG10-VG85 b = 0.66. The distribution function of graphite inclusions by diameters of balls opens up new possibilities of quantitative analysis of the “structure-properties” connections, for forecasting and modeling of high-strength cast iron with spheroidal graphite.