Determination of spatial grain size with the area-weighted grain area distribution of the planar sections in polycrystalline materials

Abstract

The electron backscattering diffraction (EBSD) technique has made it quite easy to obtain the grain area distribution in a planar section of the polycrystalline materials. Usually, area-weighted grain area and number-weighted grain area show completely different distribution profiles. Instead of the nominal average grain size calculated from the grain area distribution results, the spatial grain size and its distribution character reflect the real features of the materials and those parameters are expected through a simple measurement on the planar sections. In the present work, the section area distribution model of a randomly sliced truncated octahedron is used to relate the lognormally distributed spatial grain size to the area-weighted grain size distribution features. Based on the truncated octahedron grain shape model, area-weighted grain area distribution is derived by convoluting the lognormal distribution of the area of the section with the maximum section area (SMSA) in each grain and the area-weighted section area distribution of the sliced truncated octahedron. It is found that area-weighted grain area distribution on a planar section shows also the lognormal distribution character when the spatial grain size has the lognormal distribution character. Meanwhile, the variance parameter, τ(ins), and the mean value of grain area, \(X_s^{mean} \), obtained by fitting the area-weighted grain area distribution, have also been related to the lognormal distribution characters of the spatial grain size, i.e., A and \(\overline \nu _n \). The simulation results are then experimentally checked on a polygonal grain structure of hot-rolled low-carbon steel by applying the point-sampling method to obtain the spatial grain size distribution features.