On the computer aided description of grain size distribution in polycrystalline materials
Abstract
Population of grains in polycrystals is characterized by the distribution functions of their size and shape. The volume of grain is a desired parameter to describe its size, because grain is a 3-D object. Commonly available experimental techniques can be used to measure only 2-D and 1-D parameters of grain size. Stereological computer aided method to describe grain volume distribution parameters on the basis of grain section area measurement is presented in this work. This method is designed especially for computerized image analysis system. The developed method is based on interactive, computer aided modelling of polycrystalline aggregate. The method uses non-standard approach to reconstruction of 3-D parameters of polycrystal microstructure. Algorithm consisting of modelling 3-D grain structure, and modelling preparation process of 2-D section is used in presented method. The modelled section is then compared with section of real sample by means of comparison of 2-D size and shape distributions. The method takes into account resolution limit that result in small sections of grains not to be revealed on 2-D images. This factor, if not considered, can lead to significant errors in 3-D size parameters estimation. Using proposed method one can obtain such parameters describing grain size inhomogeneity as coefficient of variation, skewness or kurtosis of grain volume distribution function.