Determination of spatial grain size with the area-weighted grain area distribution of the planar sections in polycrystal
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NTRODUCTION
GRAIN size is the dominant microstructure feature of polycrystalline materials and influences considerably the mechanical properties of the materials. The planimetric method and intercept count method are defined to obtain the average grain size in ASTM E112-82, based on the counting of grain number in a defined area and intercept lengths of grain boundaries on a defined line in planar sections, respectively. Crystal grains are three-dimensional objects and they have specific three-dimensional shapes (spatial grain shape), and in a real crystalline material, the volumes of the grains are different from each other and show a specific distribution feature (spatial grain size distribution). Grain size can be described by length dimension, area dimension, and volume (or weight) dimension depending on the measurement methods, and the grain volume indicates the real grain size and has been called spatial grain size. Without specific definition, grain size distribution means the number fraction distribution of the varied grain sizes, i.e., the number-weighted grain size distribution. In contrast, area-weighted and volume-weighted grain size distribution indicate the changes of the product value of the number and grain area or grain volume at each grain size class with the varied grain sizes. Both spatial grain shape and the spatial grain size distribution extensively FUXING YIN, Senior Researcher, and ATSUKO SAKURAI, Assistant Researcher, are with the Innovative Materials Engineering Laboratory, National Institute for Materials Science, Tsukuba 305-0047, Japan. Contact e-mail: [email protected] XIAOYAN SONG, Professor, is with the Material Science and Engineering School, Beijing University of Technology, Beijing 100022, P.R. China. Manuscript submitted June 11, 2006. METALLURGICAL AND MATERIALS TRANSACTIONS A
influence the correspondence between the mean grain size measured on planar sections and the mean spatial grain size, the latter being the intrinsic one for the target material. It was indicated that the spatial grain size distribution has the larger impact on that correspondence than the spatial grain shape.[1] Meanwhile, the fabrication process and mechanical properties of ultrafine microstructure in structural materials have been extensively investigated.[2,3] It is found that the Hall–Petch relation between grain size and yield strength is valid also for the ultrafine ferrite microstructure in the nominal grain size range of 50 to 0.2 mm.[4] However, according to the Hall–Petch relation, grain size deviation for 1-mm microstructure may cause a deviation in yield strength of above 30 times larger than that for the 10-mm microstructure. It is shown that grain size distribution becomes more important as a microstructure feature that influences the reliability of mechanical properties, especially for the ultrafine microstructures. Since the late 1960s, extensive studies of topological properties and size distribution of grains have been conducted, employing either serial sectioning or grain separation methods.[5]
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