Geodesic
The method of processing information about nonmetallic inclusions obtained from the investigation of the surface of finished steel samples
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 6 (2017) no. 4, pp. 5-19 Cet article a éte moissonné depuis la source Math-Net.Ru

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Nonmetallic inclusions formed in the process of steel production are microparticles of chemical reactions products and foreign impurities having dimensions of 0.1–100 microns. They concentrate stresses in finished products and impair the mechanical properties of steel. To study them, sections are made from the sample of the tested metal and microscopic sections of inclusions are observed in the microscope. However, on the section plane a researcher does not see the inclusions themselves, but only their sections, while inclusions of different sizes can give the sections of the same size and, conversely, the inclusions of the same size can produce the sections of various sizes. In this paper, we consider a method for determining the amounts and sizes of nonmetallic inclusions on the basis of this information, that is, reconstructing the volume picture of the inclusion size distribution based on еру plane distribution of their sections by a section plane. The method is based on probability theory and mathematical statistics. It is shown that the number of inclusion sections into each size interval obeys the normal law. A technique for determining the distribution function of inclusions with respect to sizes for inclusions of a spherical shape and an appropriate algorithm has been developed.
Keywords: information processing, crystallography, nonmetallic inclusions, stereology. 
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A. D. Drozin. The method of processing information about nonmetallic inclusions obtained from the investigation of the surface of finished steel samples. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 6 (2017) no. 4, pp. 5-19. http://geodesic.mathdoc.fr/item/VYURV_2017_6_4_a0/

[1] T. Lipiński, A. Wach, “Size of Non-Metallic Inclusions High-Grade Medium Carbon Steel”, Archives of Foundry Engineering, 14:4 (2012), 55–60

[2] K. Lambrighs, L. Verpoest et al., “Influence of Non-Metallic Inclusions on the Fatigue properties of Heavily Cold Drawn Steel Wires”, Procedia Engineering, 2:1 (2010), 173–181 | DOI

[3] D. Zeng, G. Tian et al., “Fatigue Strength Prediction of Drilling Materials Based on the Maximum Non-Metallic Inclusion Size”, Journal of Materials Engineering and Performance, 24:12 (2015), 4664–4672 | DOI

[4] V. E. Roshchin, A. V. Roshchin, Electrometallurgy and Metallurgy of Steel, Publishing Center of SUSU, Chelyabinsk, 2013, 571 pp.

[5] Steel. Determination of the Content of Nonmetallic Inclusions. Metallographic Method Using Reference Scales, ISO 4967:1998. Official Edition, Standartinform, Moscow, 2010, 32 pp.

[6] S. A. Saltykov, Stereometric Metallography, Metallurgy, Moscow, 1970, 376 pp.

[7] K. S. Chernyavskii, Stereology in Physical Metallurgy, Metallurgy, Moscow, 1977, 280 pp.

[8] J. Chraponski, J. Cwajna et al., “Usefulness Evaluation of the Stereological Methods Applied for Grain Size Estimation”, Acta Stereologica, 18:1 (1999), 81–88

[9] A. Davtian, U. Hahn et al., “Estimating Number Density NV — a Comparison of an Improved Saltykov Estimator and the Disector Method”, Image Analysis Stereology, 19:3 (2000), 209–214 | DOI

[10] R. Anderssen, A. Jakeman, “Computational Methods in Stereology”, Proceedings of the Fourth International Congress for Stereology (Gaithersburg, Maryland, USA. September 4–9, 1975), National Bureau of Standards. U.S. government printing office., Washington, 1976, 13–18

[11] A. Jakeman, R. Anderssen, “On Optimal Forms for Stereological Data”, Proceedings of the Fourth International Congress for Stereology (Gaithersburg, Maryland, USA. September 4–9, 1975), National Bureau of Standards. U.S. government printing office, Washington, 1976, 69–74

[12] W. Nicholson, “Estimation of Linear Functionals by Maximum Likelihood”, Proceedings of the Fourth International Congress for Stereology (Gaithersburg, Maryland, USA. September 4-9, 1975), National Bureau of Standards. U.S. government printing office, Washington, 1976, 19–24

[13] A. D. Drozin, “Calculating of the True Sizes and the Numbers of Spherical Inclusions in Metal”, Metallography, Microstructure, and Analysi, 6:3 (2017), 240–246 | DOI

[14] W. Feller, An Introduction to Probability Theory and its Applications, v. 2, John Wiley Sons Inc, New York, London, Sydney, 1968, 754 pp.