Analysis of orientation clustering in a directionally solidified nickel-based ingot
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I.
INTRODUCTION
THE properties of polycrystalline materials often have been correlated with average grain size. However, the hypothesis that some mechanical and electrical properties depend on length scales different than the grain diameter has recently been explored.[1,2] In particular, it is now evident that the length scale for some constitutive relations is generally larger than the average grain diameter and is associated with clusters of grains sharing low-angle or special boundaries, rather than with individual grains. Thus, some properties of polycrystals are now believed to depend not only on the size and shape of the grains, but to a more accurate degree on the spatial arrangement of these grains in the microstructure and on the type of boundaries they share with their neighbors. For example in Reference 1, polycrystalline superconducting films were modeled as two-dimensional (2-D) arrays of Josephson junctions. Critical currents in the arrays were found to depend on a cluster length scale which is larger than the average grain diameter. This length scale is determined by the cooperative behavior of the grains and their connectivity. In Reference 2, the following relationships between material properties and cluster length scales are suggested where the properties are known to depend on grain-boundary misorientation: (a) electrical resistivity of high-purity metallic polycrystals at cryogenic temperatures, where scattering processes are dominated by structural defects such as grain boundaries, is dependent on the average distance between strongly scattering boundaries; (b) in NaDAVID A. WEST, Doctoral Candidate, formerly with the Department of Manufacturing Engineering and Engineering Technology, Brigham Young University, Provo, UT 84602, is with the Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616. BRENT L. ADAMS, Professor, is with the Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15212-3890. Manuscript submitted September 8, 1995. METALLURGICAL AND MATERIALS TRANSACTIONS A
barro–Herring creep, where low-angle boundaries may be considered as poor sources and sinks for vacancies, the creep rate would be driven by vacancy concentration gradients existing over a distance defined by the maximum distance between two grains in the same cluster; (c) similarly, in Coble creep, where vacancies diffuse along grain boundaries, the natural length scale would be associated with the perimeter of the clusters; and (d) finally, in the fracture of brittle polycrystalline materials, dominant flaw sizes, slip-line lengths initiating a flaw, and average bridge spacing are all suggested to be closely related to cluster dimensions. The clustering that has been analyzed previously in simulated 2-D fiber textures has now been observed experimentally in a directionally solidified (DS)[3] nickel-based alloy ingot. Because this clustering cannot be reliably studied by ordinary microscopy, it is necessary to employ experimental tech
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