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Statistical Analysis of the Parameters and Grain Size Distribution Functions of Single-Phase Polycrystalline Materials

  • STRUCTURE AND PROPERTIES RESEARCH PHYSICAL METHODS OF RESEARCH AND MONITORING
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Inorganic Materials Aims and scope

Abstract

A statistical analysis of the grain size distribution is necessary both for the construction and development of the theory of grain growth and microstructure formation and for the description of the size dependences of the characteristics of the physical and mechanical properties of polycrystalline materials. The grain size distribution is one of the most important characteristics of the uniformity of the structure and, consequently, the stability of the properties of products during operation. The results of the study of single-phase and equiaxed polycrystalline microstructure using Monte Carlo modeling of parameters and grain size distribution functions are presented. Statistical parameters (mean values, variances, and coefficients of variation) and distribution functions of characteristics of grain microstructure are given. It is found that the distribution function of effective grain sizes for the studied model of a polycrystal is most adequately described by the γ distribution. It should be used in the analysis of experimental grain size distribution functions for single-phase polycrystalline materials with equiaxed grains. It is shown that the population mean (expected value) of the effective sizes (projection diameters) of grains with the γ-distribution function can be taken as a statistically substantiated and reliable estimate of the mean grain size; the parameters of the γ-distribution function must be preliminarily determined when studying the grain structure of a polycrystalline material. The results of statistical modeling are confirmed by experimental data of metallographic analysis of microstructures of model and industrial materials with varying degrees of grain structure inhomogeneity.

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ACKNOWLEDGMENTS

We are grateful to E. E. Novosvetlova, V. V. Romashova, and E. V. Sherstneva (Chair of Physics of Metals and Materials Science, Tula State University) for their help in experimental studies.

Funding

This work was supported in part by the Russian Foundation for Basic Research, project no. 18-02-00760.

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  1. Tula State University, 300012, Tula, Russia

    S. I. Arkhangelskiy & D. M. Levin

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  1. S. I. Arkhangelskiy
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  2. D. M. Levin
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Correspondence to D. M. Levin.

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Translated by I. Obrezanova

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Arkhangelskiy, S.I., Levin, D.M. Statistical Analysis of the Parameters and Grain Size Distribution Functions of Single-Phase Polycrystalline Materials. Inorg Mater 57, 1457–1462 (2021). https://doi.org/10.1134/S0020168521150036

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