Theoretical Approach to the Measuring Method for Grain Size Distribution of Metal Microstructure

摘要

A basic theory for the estimation of grain sizedistribution from a microstructure image of metals is discussedin this paper. In the theory it is assumed that grains are spherical,and that many grains of various diameters are randomlydistributed in a 3-dimensional material model. A relationshipbased on geometric theory between the true grain sizedistribution and the frequency of the scanline intercept lengthdivided by grain boundaries, which is measured on a cut planeof a specimen, is derived. A relationship between the true grainsize distribution and frequency of the grain cross section is alsoderived. Then, relationships between the average values; i.e.,true average grain size, the average scanline intercept length andthe average diameter of a grain cross section, are discussed.Volume fractions are also discussed, and it is proven that thearea ratio of a texture measured from a microstructure imagecorresponds with the true volume fraction, independent of grainsize distribution.