Papers by Author: Martin E. Glicksman

Abstract: The theoretical description of grain growth was based for many years on the so-calledspherical model. The spherical model represents a polyhedral grain with N faces and a volume, V ,by a sphere with an equal volume having the equivalent grain radius, R. That model leads to severalinteresting results concerning normal and abnormal grain growth as well as grain size distribution.Nevertheless, representation of grains by spheres entails a fundamental limitation: namely, all topo-logical information of the polyhedral grain is forsaken. The rich variety of grain shapes occurringin three-dimensional polycrystalline networks, however, makes their energetic and kinetic analysesextremely difficult. To simplify analyses of isotropic polycrystals, average N-hedra and generalizedN-hedra ANHs or GNHs .N D 3; 4; 5;1/ were created as a set of regular polyhedra, consisting ofN identical faces that act as topological proxies for analyzing irregular grains containing N mixedfaces. The adoption of ANH/GNH as representations of polyhedral grains led to further progress inour understanding of grain growth, particularly those aspects related to topological behavior. This pa-per summarizes some recent advances of representing polyhedral grains by ANHs/GNHs rather thanby spheres.

Abstract: Theories of abnormal grain growth (AGG) in three dimensions usually approximate an abnormal grain by a sphere. The abnormal grain is then represented by its spherical equivalent grain radius. This study, by contrast, treats AGG in terms of concepts that include both the boundary curvature and the number of faces of the abnormal grain. We treat AGG for the case of pinned matrices, including the phenomena of initiation and growth kinetics. The influence of interfacial energy and mobility of the abnormal grain boundary are also discussed.

Abstract: The multiplicity and variety of grain shapes in three-dimensional polycrystalline metals makes their energetic and kinetic analyses difficult. To help simplify the analysis of isotropic polycrystals, average N-hedra (ANHs) (N=3,4,5,…∞) were created as a set of regular polyhedra, consisting of N identical faces, which act as topological “proxies” for analyzing the corresponding class of irregular grains containing mixed faces of the same number. This paper outlines a further generalization of the ANH concept that extends three-dimensional analysis to include the growth or shrinkage of a small population of grains embedded in a textured matrix.

Abstract: One common point amongst extant theories of abnormal grain growth (AGG) is that they treat this phenomenon in terms of the relative grain size, or grain radius, of the abnormal grains. Topological and metrical quantities of abnormal grains, such as the number of their faces, or their grain boundary curvature, are taken into account only indirectly through the grain size itself. This paper, by contrast, treats AGG in terms of concepts, that include both the boundary curvature and the number of faces of the abnormal grain. Two cases are examined: 1) AGG, in which the matrix grains are fully pinned, so normal grain growth cannot occur; 2) AGG in which the matrix grains are free to evolve, so that normal grain growth ensues simultaneously in the matrix.

Abstract: Space-filling in kinetically active 3-d network structures, such as polycrystalline solids at high temperatures, is treated using topological methods. The theory developed represents individual network elements—the polyhedral cells or grains—as a set of objects called average N-hedra, where N, the topological class, equals the number of contacting neighbors in the network. Average N-hedra satisfy network topological averages for the dihedral angles and quadrajunction vertex angles, and, most importantly, act as “proxies” for real irregular polyhedral grains with equivalent topology. The analysis provided in this paper describes the energetics and kinetics of grains represented as average N-hedra as a function of their topological class. The new approach provides a quantitative basis for constructing more accurate models of three-dimensional grain growth. As shown, the availability of rigorous mathematical relations for the curvatures, areas, volumes, free energies, and rates of volume change provides precise predictions to test simulations of the behavior 3-d networks, and to guide quantitative experiments on microstructure evolution in three-dimensional polycrystals.