| Issue |
Mechanics & Industry
Volume 24, 2023
History of matter: from its raw state to its end of life
|
|
|---|---|---|
| Article Number | 33 | |
| Number of page(s) | 9 | |
| DOI | https://doi.org/10.1051/meca/2023030 | |
| Published online | 12 September 2023 | |
Regular Article
Statistical properties of effective elastic moduli of random cubic polycrystals
Nantes Université, Ecole Centrale Nantes, CNRS, GeM,
UMR 6183,
44000
Nantes,
France
* e-mail: shahram.khazaie@univ-nantes.fr
Received:
23
December
2022
Accepted:
4
August
2023
The homogenized elastic properties of polycrystals depend on the grain morphology and crystallographic orientations. For simplification purposes, the orientations of the grains are usually considered three independent Euler angles. However, experimental investigations reveal spatial correlations in these angles. The Karhunen–Loève expansion is used to generate random fields of Euler angles having exponential kernel functions with varying correlation lengths. The effective elastic moduli for numerically generated statistically equiaxed cubic polycrystals are estimated via the classical Eshelby–Kröner Self-Consistent homogenization model. The influence of the correlation lengths of the orientations’ random fields on the statistical properties of the effective elastic moduli has been investigated. Our results show that spatially correlated Euler angles could increase the variability of the homogenized elastic properties compared to the ones having uncorrelated Euler angles. Nevertheless, using independent random variables for Euler angles remains valid when correlation lengths are close to the average grain size.
Key words: Polycrystals / random fields / effective elastic moduli / Karhonen–Loève expansion
© N. Sheng et al., Published by EDP Sciences, 2023
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