Evaluation of normal versus non-normal grain size distributions

ASTM E112-13 states that it covers test methods to determine the average grain size of specimens with a uni-modal distribution of grain areas, diameters, or intercept lengths. It states that these distributions are approximately lognormal. However, it does not describe how one can determine if the specimen's grain size distribution is a uni-modal normal (Gaussian) distribution. ASTM E1181-02(2015) says it covers test methods to characterize grain size in products with any other distribution (other than a "single lognormal distribution of grain sizes"). However, the only example given in Appendix X2 shows the percentage of the number of intercept measurements in 38 length classes from 0 to 1 to 37 to 38 mm. Thirty eight classes is far too many to properly reveal the grain size distribution. This procedure revealed a log-normal distribution, but it is not in terms of ASTM grain size numbers, which makes it less useful. No guidance was given in ASTM E1181 to determine the nature of the grain size distribution. In this paper, a mathematical and graphical approach was defined. Copyright © 2016 by ASTM International, 100 Barr Harbor Drive, P.O. Box C700, West Conshohocken, PA 19428-2959.