Crystal mechanics-based thermo-elastic constitutive modeling of orthorhombic uranium using generalized spherical harmonics and first-order bounding theories

In earlier works, a mathematical procedure for invertible microstructure-property linkages was devel-oped using computationally efficient spectral methods for polycrystalline cubic and hexagonal metals. This paper formulates such invertible microstructure-property linkages for orthorhombic polycrystalline metals relying on the generalized spherical harmonics (GSH) spectral basis. The procedure is used to compute property closures of orthorhombic polycrystals. The closures represent the complete set of the-oretically possible combinations of effective properties for a selected material. The procedure relies on the first-order bounding theories and considers orientation distribution functions (ODFs) as the main microstructural descriptor influencing homogenized properties. Numerous examples of these closures in-volving second-rank thermal expansion and fourth-rank elastic stiffness tensorial properties over a broad range of temperatures are presented for alpha-uranium (alpha-U). In doing so, certain key properties of these closures are exploited to facilitate their computation with drastically reduced computational effort. Along with the recently developed GSH-based interpolation procedure for ODFs from coarsely spaced exper-imental measurement grids to finely spaced finite element mesh resolution grids presented in Barrett et al., the developed computationally efficient ODF-effective property linkages are used to establish a crystal mechanics-based simulation framework coupled with the finite element method (FEM). The ODF dependent thermal expansion and elastic stiffness tensors are efficiently calculated at every integration point and used by the FEM to predict the overall distortion of a hemispherical part made of alpha-U during heating. It is shown that the developed framework can be used to simulate microstructurally heteroge-neous components under thermo-mechanical loadings in a computationally efficient manner. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper presents a mathematical procedure for invertible microstructure-property linkages for orthorhombic polycrystalline metals using the generalized spherical harmonics (GSH) spectral basis. The procedure allows for the computation of property closures and enables the simulation of microstructurally heterogeneous components under thermo-mechanical loadings in a computationally efficient manner. The developed framework has been demonstrated using alpha-uranium as a case study.