TY - JOUR

T1 - Accurate representation of the distributions of the 3D Poisson-Voronoi typical cell geometrical features

AU - Vittorietti, Martina

AU - Kok, Piet J.J.

AU - Sietsma, Jilt

AU - Jongbloed, Geurt

N1 - Accepted author manuscript

PY - 2019

Y1 - 2019

N2 - Understanding the intricate and complex materials microstructure and how it is related to materials properties is an important problem in the Materials Science field. For a full comprehension of this relation, it is fundamental to be able to describe the main characteristics of the 3-dimensional microstructure. The most basic model used for approximating steel microstructure is the Poisson-Voronoi diagram. Poisson-Voronoi diagrams have interesting mathematical properties, and they are used as a good model for single-phase materials. In this paper we exploit the scaling property of the underlying Poisson process to derive the distribution of the main geometrical features of the grains for every value of the intensity parameter. Moreover, we use a sophisticated simulation program to construct a close Monte Carlo based approximation for the distributions of interest. Using this, we determine the closest approximating distributions within the mentioned frequently used parametric classes of distributions and conclude that these representations can be quite accurate. Finally we consider a 3D volume dataset and compare the real volume distribution to what is to be expected under the Poisson-Voronoi model.

AB - Understanding the intricate and complex materials microstructure and how it is related to materials properties is an important problem in the Materials Science field. For a full comprehension of this relation, it is fundamental to be able to describe the main characteristics of the 3-dimensional microstructure. The most basic model used for approximating steel microstructure is the Poisson-Voronoi diagram. Poisson-Voronoi diagrams have interesting mathematical properties, and they are used as a good model for single-phase materials. In this paper we exploit the scaling property of the underlying Poisson process to derive the distribution of the main geometrical features of the grains for every value of the intensity parameter. Moreover, we use a sophisticated simulation program to construct a close Monte Carlo based approximation for the distributions of interest. Using this, we determine the closest approximating distributions within the mentioned frequently used parametric classes of distributions and conclude that these representations can be quite accurate. Finally we consider a 3D volume dataset and compare the real volume distribution to what is to be expected under the Poisson-Voronoi model.

KW - 3D grain size

KW - Parametric representation

KW - Poisson-Voronoi diagrams

KW - Voronoi

UR - http://www.scopus.com/inward/record.url?scp=85065100386&partnerID=8YFLogxK

U2 - 10.1016/j.commatsci.2019.04.054

DO - 10.1016/j.commatsci.2019.04.054

M3 - Article

AN - SCOPUS:85065100386

VL - 166

SP - 111

EP - 118

JO - Computational Materials Science

JF - Computational Materials Science

SN - 0927-0256

ER -