From Micrograph to Grain-Size Distribution with Ultrasonic Applications

A matrix inversion procedure is presented for the computation of the grain-size distribution NV of a solid volume from the image-size distribution on a photomicrograph of its surface. Averages over the distribution NV are taken to find the average volume to use in ultrasonic scattering formulas. For several metals, NV is adequately expressed in terms of the grain radius R as NV=A (R−R0) exp (−aR) where R0, A, and a are constants for a specimen. NV is zero for RR0. Relationships are developed between the average volume and the sizes of the images on a photomicrograph, as well as between the average radius Rav of the grains and the average radius rav of the images. The results of ultrasonic attenuation experiments agree well with theoretical predictions when the average scattering volume is computed from the grain-size distribution. Agreement is especially good when the metal grains are single crystals. The martensitic transformation lowers the experimental attenuation by a factor of about 10; the process is thought to be a lowering of the anisotropy of the grain through averaging over all the platelets. Pearlitic steel, on the other hand, has higher attenuation than theory predicts. The grain-size distribution will be useful in other problems involving average sizes of grains.