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The stereological method for studying grain structures is presented, it determines the interrelation between the size distributions of three-dimensional grains and their planar and linear sections. Method is applicable for both reconstruction and simulation of the 3D structures. The polyhedral shape of the grains is taken into account by means of the shape factors established for them. An original method to determine the distribution of plane sections from the certain grain-polyhedron to calculate the shape factors is presented. This method can be used to describe the shape of different structural components in many materials: steels, cast irons, concretes, rocks, ceramics, open-porosity materials, biofilms, foams, etc. The stereological method is also applicable to structures with spherical particles, for which the shape factors are equal to unity. The method makes it possible to create the standards of plane sections of grain structures and other structures with a previously known size distribution of 3D grains or particles.

Method for the simulation and reconstruction of 3D particle size distributions in metal structures