Estimation of 3D grain size distributions from 2D sections in real and simulated microstructures

Obtaining information about the 3D grain size distribution of metallic microstructures is crucial for understanding the mechanical behavior of metals. This paper addresses the problem of estimating the 3D grain size distribution from 2D cross sections. This is a well-known stereological problem and different estimators have been proposed in the literature. We propose a statistical estimation procedure that provides consistent estimates without relying on arbitrary binning choices. When applying this procedure to space filling structures, we investigate the impact of the choice of grain shape and propose a heuristic to choose the best grain shape. To validate our approach, we employ simulations using Laguerre–Voronoi diagrams and apply our methodology to a sample of Interstitial-Free steel, obtained via EBSD. • We estimate the 3D grain size distribution using a novel statistical procedure. • We study the influence of assumed grain shapes on grain size distribution estimates. • Extensive simulations using 2D sections of 3D (Laguerre)–Voronoi microstructures. • Promising results are obtained applying the new estimation procedure to real data.