Table of Contents
Textures and Microstructures
Volume 14 (1991)–18

N-Point Measures of Polycrystalline Microstructure: Measurement, Representation and Applications

Department of Mechanical Engineering, Yale University, New Haven, CT, USA

Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Advanced models for engineering properties of polycrystalline materials require description of the spatial distribution of lattice phase and orientation. For this purpose the n-point statistical measures present a natural extension of the orientation distribution function, which is equivalent to the one-point measure of lattice orientation in single-phase microstructures. This paper describes the origin of the n-point measures in the context of statistical theory, and some aspects of their experimental determination. Fourier representation of the n-point measures in terms of tensorial basis functions is described. It is proposed that tensorial representations have some natural advantages over the ordinary representation using generalized spherical functions. An example of the application of occurrence of the n-point statistics of lattice orientation in a theory of creep in polycrystals is presented, and some limited comparisons with the uniform strain-rate and self-consistent theories are described.