Is There Possible Bias in ASTM E112 Planimetric Grain Size Measurements?

The claim made by Li in 1995 and 2011 publications that the Jeffries planimetric method of determining grain size presented in ASTM E112, as well as in DIN 50601 (it is the standard for every national and international grain size test method and is described in every textbook on quantitative metallography), is wrong and produces biased grain size ratings when the counts are low is incorrect. Li based this statement upon theoretical considerations described by Saltykov, who proposed using rectangles for the planimetric method, rather than circles, to minimize bias at low counts of the number of grains inside the circle. Saltykov, however, did not publish actual test data to back up this proposition. The count levels mentioned are far below those recommended by ASTM E112 for these methods, but they could be encountered in manual measurements of the size of very coarse grains (which might be performed but is rarely done). Actual grain size measurements using both test circles and rectangles, with a very wide range of grains within the test figures and intersecting their borders, showed that the ASTM Jeffries planimetric and Hilliard single-circle intercept methods produced statistically identical measures of the ASTM grain size G down to count levels far below what is recommended—down to 30 for (n_inside + 0.5n_intercepted) for the planimetric method and down to 20 grain boundary intersections (P_{intersections}) for the intercept method (well below the recommended minimums of 50 and 35, respectively). At levels below these limits, bias was small—mainly data scatter was observed at counts less than 10 for both methods. The Saltykov planimetric method using rectangles gave the best data, identical to the ASTM E112 data, with statistically identical grain size values down to 10, and it was bias free, but it also exhibited data scatter at counts less than 10. Li's counting method, however, produced more bias at low counts than any other method. His claims have no validity. His model did not evaluate the effect of varying the counting conditions, which was the basis of his claim about the creation of bias. Also, he did not do actual tests to prove that his model was valid and that his claim was correct. Models do not have any validity if they do not test the actual conditions and are not verified by actual experimental data.