Reliability of Inclusion Statistics in Steel by Stereological Methods

Abstract

In this paper, we investigate the reliability of estimating of inclusion size distribution and number density in steel by using stereological methods. The magnitude of the inclusion concentration in steel is evaluated by the total oxygen and the assumed average inclusion sizes. The principles of Schwartz-Saltykov (SS) and modified SS (MSS) methods are introduced. A simulation model is developed to disperse particles with a predefined particle size distribution (PSD) randomly into a three dimensional (3D) space. A series of test planes are generate to measure the two dimensional (2D) PSD and particle number density (PND) on the cross-sections (CS). The SS and MSS methods are applied to investigate the reliability of the translation between the 3D and 2D information of the system, such as the 2D and 3D PSD and PND. The influence of predefined 3D PSD on the reliability of the stereological methods are studied, such as mono sized, lognormal and normal distributions. The effect of the representative group diameters in the discretized groups for SS and MSS methods is investigated as well.

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

“…The analysis of the planar section which bases on the direct Wickesell equation (2) has been used for the volume size distribution of the spheroidal particles by Scheil [4], Schwartz [5], Saltykov [6,7], Li at al. [8]. A similar solution to the mineralogy task has been presented in [9].…”

“…(2) is usually used not for the designation of the PDF 3 form, but for the examination of matching the empirical function and one of the selected statistical distribution law, e.g. normal, log-normal, Weibull or uniform-sized [3,8,12].…”

Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

“…The set C3 contains these nodules that have their radii in the range from r 3 to r 3 + dr 3 . The count of the particles belonging to this set can be calculated by Equation (13). If we place a random secant in the sample space (Fig.…”

“…Another fact is that it also contains an additional unknown parameter which is the expected value E[r 3 ]. Generally, this equation is well known and has been used and analysed many times by various authors in papers [13,14]. In [14] there are presented, in a form of a short description, methods used for solving this equation and how to estimate the value of…”

Three-dimensional Observation of Nonmetallic Inclusion Clusters in Solid Metal by X-ray Micro-CT

“…Tao LI, 1,2) * Shin-ichi SHIMASAKI, 1,3) Shoji TANIGUCHI, 1) Shunsuke NARITA 1,4) and Kentaro UESUGI 5) 1) Graduate School of Environmental Studies, Tohoku University, 6-6-20 Aoba-yama, Aoba-ku, Sendai, 980-8579 Japan.…”