Estimation of Three-dimensional Grain Size Distribution in Polycrystalline Material

A new method has been proposed for the estimation of the three-dimensional grain size distribution from the two-dimensional distribution measured on the cross section of polycrystalline material. In this method, twelve types of polyhedra were employed as the grain models. The distributions of the cross-sectional diameters of the individual polyhedra were expressed as probability density functions. On the basis of the functions for each polyhedron, the supposed grain size distribution on the cross section of the material was calculated, and it was compared with the measured one. The comparison was repeated until the agreement between the both distributions. By operating this two-dimensional distribution reversely, the three-dimensional grain size distribution was estimated. The distribution of the vertex number of polygon-shaped grains on the cross section and that of the face number of polyhedron-shaped grains in three dimensions were calculated from the obtained results and were compared with the measured distributions. There was a good agreement between these distributions.