Abstract
A method has been proposed to estimate the grain size, which is defined as the grain size distribution in three dimensions, from the measured distribution of linear intercept length. The method is developed on the assumption that the grain size distribution is log normal in three dimensions. The three-dimensional grain size distribution is expressed as that of the “grain diameter” D defined as the equivalent volume diameter; the distribution of D is estimated from ln Dg and ln σg (where Dg is the geometric mean of D and σg is the geometric standard deviation for D). The estimation is based upon the theoretical distribution of linear intercept length calculated numerically from a tetrakaidecahedron grain structure model with log-normal distribution of grain diameter. The values of Dg and ln σg are determined by applying the ‘discrete’ least squares method to the measured linear intercept length distribution on the basis of the calculated results. The present method has made it possible to evaluate the fundamental parameters of Dg and ln σg defining three-dimensional distribution of grain size from measurements on the cross-sectional structure. Futher, the influence of grain size distribution on the estimation of mean grain sizes by the two representative methods, the intercept method and the planimetric method, has been discussed from the calculation in the above model and the analysis of the experimental results. As a result, it has been concluded that the grain size distribution has a significant effect on the estimation of the mean grain size.
