Abstract
Two of the microstructural parameters most influential in the properties of polycrystalline materials are grain size and crystallographic texture. Although both properties have been extensively studied and there are a wide range of analysis tools available, they are generally considered independently, without taking into account the possible correlations between them. However, there are reasons to assume that grain size and orientation are correlated microstructural state variables, as they are the result of single microstructural formation mechanisms occurring during material processing. In this work, the grain size distribution and orientation distribution functions are combined in a single multivariate grain size orientation distribution function (GSODF). In addition to the derivation of the function, several examples of practical applications to low carbon steels are presented, in which it is shown how the GSODF can be used in the analysis of 2D and 3D electron backscatter diffraction data, as well as in the generation of representative volume elements for full-field models and as input in simulations using mean-field methods.
Highlights
When polycrystalline materials are studied, it is usually observed that local microstructural properties such as crystallographic orientation, grain size and aspect ratio are regularly distributed along the volume of the material with non-uniform frequencies
If the orientation distribution function (ODF) corresponding to the grains of size d is given by the function fdðgÞ and the grain size distribution of the material is given by a function pðdÞ, the grain size orientation distribution function (GSODF) is given by the product of p and fd: Fðd; gÞ 1⁄4 pðdÞfdðgÞ: ð5Þ
Since the GSODF combines the data of all the bins’ ODFs, the ODFs predicted for the equivalent sizes are closer to the global ODF calculated from the 2D electron backscatter diffraction (EBSD) shown in Fig. 2 than to the ODFs of the bins
Summary
When polycrystalline materials are studied, it is usually observed that local microstructural properties such as crystallographic orientation, grain size and aspect ratio are regularly distributed along the volume of the material with non-uniform frequencies. Parametric statistical distributions allow these frequencies, and in some way, the complexities of the microstructure, to be represented in an efficient manner. It is common in the materials science community to work with distributions of crystallographic orientations and grain sizes (Bunge, 1987; Randle & Engler, 2014; Ohser & Mucklich, 2000), since these two properties are some of the most influential in material behaviour at the macroscopic level. Cryst. (2021). 54, 148–162 research papers that takes into account this correlation is the main topic of this article
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