Stereological Analysis of the Statistical Distribution of the Size of Graphite Nodules in DI

Abstract:

The estimate of a distribution law of the nodule diameters in a volume of cast iron provides information about the graphite nucleation kinetics, and also about the crystallization kinetics. This information is essential for building more accurate mathematical models of the alloy crystallization. The mapping of a Cumulative Distribution Function (CDF₃) of radii for graphite nodules in ductile iron is presented on the base of a Probability Density Function (PDF₁) of the chord length distribution for random sections of the sample at the planar cross-section.

• Periodical: Materials Science Forum (Volume 925)
• Pages: 98-103
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.925.98
• Online since: June 2018
• Authors: Andriy A. Burbelko*, Daniel Gurgul, Edward Guzik, Wojciech Kapturkiewicz
• Keywords: Chord Length, Ductile Iron, Graphite Nodules, Graphite Size Distribution, Stereological Analysis

References

[1] Y. Yin, Z. Tu, J. Zhou, D. Zhang, M. Wang, Z. Guo, C. Liu, X. Chen, 3D Quantitative Analysis of Graphite Morphology in Ductile Cast Iron by X-ray Microtomography, Metall. and Mater. Trans. A, 48 (2017) 3794-3803.

DOI: 10.1007/s11661-017-4130-x

[2] R.E. Ruxanda, D.M. Stefanescu, T.S. Piwonka, Microstructure Characterization of Ductile Thin Wall Iron Castings, AFS Trans., 2 (2002) 1131-1148.

[3] K. Wiencek, T. Skowronek, B. Khatemi, Graphite Particle Size Distribution in Nodular Cast Iron, Metallurgy and Foundry Eng., 31 (2005) 167-174.

[4] S.D. Wicksell, The Corpuscle Problem: A Mathematical Study of a Biometric Problem. Biometrika, 17 (No. ½) (1925), 84-99.

DOI: 10.1093/biomet/17.1-2.84

[5] E. Sheil: Statistische Gefügeuntersuchungen I. Z. Metallk., 27 (1935) 199-208.

[6] H.A. Schwartz: The Metallographie Determination of the Size Distribution of Temper Carbon Nodules, Metals and Alloys, 5 (1934) 139-140.

[7] S.A. Saltykov: Stereometric Metallurgy, Metallurgizdat, Moscow, (1952).

[8] S.A. Saltykov: The determination of the size distribution of particles in an opaque material from the measurement of the size distribution of their sections. Stereology. Berlin, Heidelberg, Springer, 1967, 163−173.

DOI: 10.1007/978-3-642-88260-9_31

[9] T. Li, S.-I. Shimasaki, Sh. Taniguchi, Sh. Narita: Reliability of Inclusion Statistics in Steel Stereological Methods. ISIJ International, 56 (No. 9) (2016) 1625-1633.

DOI: 10.2355/isijinternational.isijint-2016-269

[10] M. Kong, R.N. Bhattacharya, C. James, A. Basu: A statistical approach to estimate the 3D size distribution of spheres from 2D size distributions. GSA Bulletin, 117 (No. 1/2) (2005), 244–249.

DOI: 10.1130/b25000.1

[11] A.J. Jakeman, R.S. Anderssen: Abel type integral equations in stereology. I. General discussion, Journal of Microscopy. 105 (1975), 121–133.

DOI: 10.1111/j.1365-2818.1975.tb04045.x

[12] J. Ohser, K. Sandau: Considerations About the Estimation of the Size Distribution in Wicksell's Corpuscle Problem, Lecture Notes in Physics, 554 (2000) 185–202.

DOI: 10.1007/3-540-45043-2_7

[13] A. Burbelko, D. Gurgul, T. Wiktor: Stereological Analysis of Spherical Particles Size Distribution – Theoretical Basis, Accepted for print in Archives of Foundry Engineering, 18 (2018).

DOI: 10.1515/afe-2017-0132

[14] J. W. Cahn, R. L. Fullman: On the Use of Lineal Analysis for Obtaining Particle-Size Distribution Functions in Opaque Samples, Trans. AIME, J. Metals, 206 (1956) 610-612.

DOI: 10.1007/bf03377741

[15] C.W. Lord, T.F. Willis: Calculation of air bubble distribution from results of a Rosiwal traverse of aerated concrete, A.S.T.M. Bull., 177 (1951) 177-187.

[16] A.G. Spektor: Analysis of distribution of spherical particles in non-transparent structures, Zavodsk. Lab., 16 (1950) 173-177.

[17] A. Burbelko, D. Gurgul, T. Wiktor: Stereological Analysis of Spherical Particles Size Distribution – Validation, Archives of Foundry Engineering, 17 (2017), 67-72.

DOI: 10.1515/afe-2017-0132