Alternative Length Scales for Polycrystalline Materials
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ALTERNATIVE LENGTH SCALES FOR POLYCRYSTALLINE MATERIALS C.S. NICHOLS,0) R.F. COOK,( 2) D.R. CLARKE,(3 ) and D.A. SMITH(2 ) (1) Department of Materials Science and Engineering, Cornell University, Ithaca, NY (2) IBM Research Division, T.J. Watson Research Center, Yorktown Heights, NY (3) Materials Department, University of California-Santa Barbara, CA
Abstract It is well established from studies of bicrystals that the properties of a grain boundary depend on the atomic structure of the boundary. However, constitutive relations for the properties of polycrystalline materials do not currently take into account this boundary-toboundary variability. Instead, such relations depend on a single length scale, typically the average grain diameter. We extend the traditional viewpoint by proposing that boundaries may be divided into two distinct categories, depending on their misorientation angle. The relevant length scale in constitutive relations for polycrystals is then the average cluster size, where clusters consist of grains connected by boundaries in the same misorientation category. A brief discussion of this additional length scale and how it may be reflected in various constitutive relations for physical and mechanical properties of polycrystals is given.
Introduction It is widely recognized that the properties of a polycrystalline material differ markedly from those of the same material in single-crystal form. Attempts to describe quantitatively the behavior of polycrystals have generally followed two lines. One approach is to formulate scaling laws in which properties depend on a length scale linearly related to the grain size and often assumed to be the grain size, d. Familiar examples include the Hall-Petch relation for plastic yield stress, a cx d- 1 /2 and the Herring-Nabarro relation for the strain rate in lattice-diffusion-controlled creep, i oc d- 2 . Implicit in these relations, however, is the assumption that all grain boundaries behave in the same way, which is in contradiction to numerous bicrystal experiments.[1-14] The second approach is to focus on "prototypal" interfaces with the expectation that their properties are somehow generalizable to arbitrary interfaces. What has been lacking in this approach is the synthesis of the knowledge about various intefaces into a coherent description of a polycrystal. Furthermore, it is being recognized that the properties of these prototypal intefaces do not necessarily generalize to arbitrary interfaces.[15] It is the intention of the present work to integrate these two lines of research by exploring the relevant length scale for polycrystalline materials when boundary-to-boundary variability is explicitly considered. The simplest extension of the traditional viewpoint is to classify boundaries into two distinct categories. Watanabe [14,16-18] has pointed out that low-angle and special boundaries generally have low energy, low mobility, low diffusivity, etc., while high-angle boundaries have the opposite properties. It is not entirely clear what the experimenta
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