Characterization of random stress fields obtained from polycrystalline aggregate calculations using multi-scale stochastic finite elements

Abstract

The spatial variability of stress fields resulting from polycrystalline aggregate calculations involving random grain geometry and crystal orientations is investigated. A periodogram-based method is proposed to identify the properties of homogeneous Gaussian random fields (power spectral density and related covariance structure). Based on a set of finite element polycrystalline aggregate calculations the properties of the maximal principal stress field are identified. Two cases are considered, using either a fixed or random grain geometry. The stability of the method w.r.t the number of samples and the load level (up to 3.5% macroscopic deformation) is investigated.

Keywords

polycrystalline aggregates / crystal plasticity / random fields / spatial variability / correlation structure

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Acknowledgements

The second author is funded by a CIFRE grant at Phimeca Engineering S.A. subsidized by the French Agence Nationale de la Recherche et de la Technologie (convention number 027/2010). The research project is supported by EDF R&D under contract #8610-AAP5910056413. These supports are gratefully acknowledged.

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg