Journal
ACTA MATERIALIA
Volume 53, Issue 13, Pages 3563-3577Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.actamat.2005.03.052
Keywords
mesostructure; microstructure-texture; statistical mechanics; mechanical properties-elastic behavior
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Extension of the first-order theory of microstructure design to considerations of morphological texture is addressed in this paper. The main challenges include the r-interdependence of the 2-point correlation functions of lattice orientation, construction of the corresponding microstructure hull, and its corresponding properties closure(s). It is shown that the correlation functions can be expressed in terms of an intermediate construct, called the texture function; the correlation functions have quadratic dependence in the texture functions. A complete (finite) texture hull is readily constructed for the texture functions in Fourier space, and is found to be a convex polytope. Eigen-texture functions occupy its corner (extreme) points. Microstructure design proceeds directly from homogenization relations evaluated at the corner points. This gives rise to (combined) properties closures, from which second-order microstructure design can proceed. This is demonstrated in a brief case study. (c) 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
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