Theory of the Stereological Analysis of Spheroid Size Distribution – Validation of the Equations

• Autorzy: Gurgul D. , Burbelko A. , Wiktor T.

Identyfikatory

DOI

10.1515/afe-2017-0132

• Języki publikacji: EN

Abstrakty

EN

The paper presents validation tests for method which is used for the evaluation of the statistical distribution parameters for 3D particles’ diameters. The tested method, as source data, uses chord sets which are registered from a random cutting plane placed inside a sample space. In the sample space, there were individually generated three sets containing 3D virtual spheres. Each set had different Cumulative Distribution Function (CDF₃) of the sphere diameters, namely: constant radius, normal distribution and bimodal distribution as a superposition of two normal distributions. It has been shown that having only a chord set it is possible, by using the tested method, to calculate the mean value of the outer sphere areas. For the sets of data, a chord method generates quite large errors for around 10% of the smallest nodules in the analysed population. With the increase of the nodule radii, the estimation errors decrease. The tested method may be applied to foundry issues e.g. for the estimation of gas pore sizes in castings or for the estimation of nodule graphite sizes in ductile cast iron.

Słowa kluczowe

EN

stereological analysis; linear analysis; nodule size distribution

PL

analiza stereologiczna; analiza liniowa; rozkład wielkości

• Wydawca: Komisja Odlewnictwa Polskiej Akademii Nauk Oddział w Katowicach
• Czasopismo: Archives of Foundry Engineering
• Rocznik: 2017
• Tom: Vol. 17, iss. 4
• Strony: 67--72
• Opis fizyczny: Bibliogr. 18 poz., rys., wykr.

Twórcy

autor

Gurgul D.

• AGH University of Science and Technology, 23 Reymonta Str., 30-059 Krakow, Poland

autor

Burbelko A.

• AGH University of Science and Technology, 23 Reymonta Str., 30-059 Krakow, Poland

autor

Wiktor T.

• AGH University of Science and Technology, 23 Reymonta Str., 30-059 Krakow, Poland

Bibliografia

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• [3] Więcek, K., Skowronek, K. & Khatemi, B. (2005). Graphite particles size distribution in nodular cast iron. Metallurgy and Foundry Engineering. 31(2), 167-173.
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• [10] Jakeman, A.J. & Anderssen, R.S. (1975). Abel type integral equations in stereology. I. General discussion. Journal of Microscopy. 105, Pt. 2, 121–133.
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• [13] Cahn, J.W. & Fullman, R.L. (1956). On the Use of Lineal Analysis for Obtaining Particle-Size Distribution Functions in Opaque Samples. Trans. AIME, J. Metals. 206, 610-12.
• [14] Lord, C.W. & Willis, T.F. (1951). Calculation of air bubble distribution from results of a Rosiwal traverse of aerated concrete. A.S.T.M. Bull. 177, 177-187.
• [15] Spektor, A.G. (1950). Analysis of distribution of spherical particles in non-transparent structures. Zavodsk. Lab., 16, 173-177.
• [16] Bockstiegel, G. (1966). The Porosity-Pressure Curve and its Relation to the Pore-Size Distribution in Iron Powder Compacts. in.: Modern Developments in Powder Metallurgy. H.H. Hausner (ed.), Metal Powder Industries Federation and The Metallurgical Society of AIME. pp. 155-187.
• [17] Burbelko, A., Gurgul, D. & Wiktor, T. Theory of the Stereological Analysis of Spheroid Size Distribution – on a Theoretical Basis. Archives of Foundry Engineering (under review).
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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).