Radical Voronoï tessellation from random pack of polydisperse spheres: Prediction of the cells’ size distribution

Abstract

This paper investigates the relevance of the representation of polycrystalline aggregates using Radical Voronoï (RV) tessellation, computed from Random Close Packs (RCP) of spheres with radius distribution following a lognormal distribution. A continuous relationship between the distribution of sphere radii with that of RV cell volumes is proposed. The stereology problem (deriving the 3D grain size distributions from 2D sections) is also investigated: two statistical methods are proposed, giving analytical continuous relationships between the apparent grain size distribution and the sphere radius distribution. In order to assess the proposed methods, a 3D aggregate has been generated based on a EBSD map of a real polycrystalline microstructure.

Resolution of the Wicksell's equation by Minimum Distance Estimation

“…Uranium dioxide (UO 2 ), introduced in a previous paper (Depriester and Kubler, 2019), has been used as a test material. Its microstructure was imaged by Electron Backscattered Diffraction (EBSD) mapping and the EBSD data were processed to reconstruct the grains using of misorientation threshold of 5 • .…”

“…The results from MDE can be compared with those from other stereology techniques, namely the Saltikov method (Saltikov, 1967), the two-step method (Lopez-Sanchez and Llana-Fúnez, 2016) and the threestep method (Depriester and Kubler, 2019). Fig.…”

“…9. Result of MDE performed using the lognormal distribution, compared to that obtained thanks to the two-step method (Lopez-Sanchez and Llana-Fúnez, 2016) and the three-step method (Depriester and Kubler, 2019).…”

“…3). Then, the proposed algorithm is applied on an experimental set, provided by a previous work (Depriester and Kubler, 2019), investigating some well-known distributions (monodisperse, uniform, normal, lognormal etc.). Finally, the results are discussed.…”

“…In a previous work (Depriester and Kubler, 2019), the present authors have numerically generated 3D radical-Voronoï tessellations (Okabe et al, 2009) based on random packs of spheres whose radii follow lognormal distributions. Then, they have characterized the 2D sections in order to evaluate the ability of the two-step method to unfold the 3D distribution.…”