Methodology for recovering and analyzing two-point pair correlation functions in polycrystalline materials
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I. INTRODUCTION
TRADITIONAL engineering has relied on homogeneous approximations of material properties throughout the past century. However, as engineering design continues to push the limits of material performance, such approximations do not adequately predict real material behavior. Increasingly in the past several decades there have been efforts to characterize and predict anisotropic material properties in heterogeneous materials using statistical models of material microstructure. Two aspects of microstructure are known to affect anisotropy in polycrystalline materials, namely the distribution of crystallite orientations among the grains, and anisotropy in shape and morphology among the grains. Considerable success has been achieved by models that incorporate volume fractions of grains of specified lattice phase and orientation. In particular, the volume fraction density of orientation g in a single-phase polycrystal is defined by f(g), commonly called the orientation distribution function (ODF).[1] First-order bounding relationships for anisotropic properties, incorporating the ODF, have been widely studied.[2–6] Comparatively little investigation of the morphologic features of microstructure and their influence on effective properties has appeared in the literature, although in terms of effective linear properties the effects are well known.[7] Effective properties theory illustrates that a natural way to incorporate morphologic features of microstructure is through the correlation functions, beginning with the two-point or pair correlation functions (PCFs) that are the subject of this paper. To successfully incorporate the morphologic features into the estimate of an effective property, an experimental methodology needs to be developed to address the question of how to measure and retrieve the two-point pair correlation function and how to determine the coherence length X. GAO, formerly Research Assistant with Brigham Young University and is now with the University of Kentucky, Lexington, KY. C. P. PRZYBYLA, formerly Research Assistant with Brigham Young University and is now with the Georgia Institute of Technology, Atlanta, GA. B.L. ADAMS, Dusenberry Professor, is with Brigham Young University, Provo, UT. Manuscript submitted August 29, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A
beyond which the microstructure is assumed to be spatially random. With the advent of orientation imaging microscopy (OIM), it has become relatively easy to measure both lattice phase and orientation through the automated indexing of Kikuchi patterns. In typical samples, as many as 50 sampling points per second can be examined and indexed. What is not so well understood is that the PCFs of lattice phase and orientation are also accessible via the same data sets. The purpose of this paper is to facilitate a better understanding of what is required to recover the pair correlations in polycrystalline materials, and how they are connected with important features of microstructure such as the grain size distribution and the cohere
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