Examination of Normal, Non-Normal and Bi-Modal Grain Size Distributions

This study was initiated due to concern over a statement in ASTM E 1181 concerning the width of a normal, or Gaussian, grain size distribution as compared to a duplex or bi-modal distribution, of which there are several types defined in E1181. Due to the influence of the sectioning plane, the metallographer does not see only the maximum grain area for each grain but a wide range of apparent areas, even if the grains in 3-D were all of uniform size and shape. Consequently, as the mean grain size becomes larger, we should observe a wider range of grain size classes over the distribution. So, one cannot use a number of ASTM grain size classes to define a normal grain size distribution, nor any type of non-normal or bi-modal distribution. Instead, it is necessary to calculate the skew and kurtosis of a distribution of grain areas (a plot of area percent per grain size class vs. ASTM grain size, G, per G class). If the kurtosis is >5, it is not a normal, Gaussian grain size distribution, but non-normal or perhaps bi-modal. Examples will be shown of normal, non-normal and bi-modal grain size distributions as a function of the mean grain area, standard deviation, skew and kurtosis.

Keywords: bi-modal, Gaussian, kurtosis, normal, skew