Reduced-order structure-property linkages for polycrystalline microstructures based on 2-point statistics

Abstract Computationally efficient structure-property (S-P) linkages (i.e., reduced order models) are a necessary key ingredient in accelerating the rate of development and deployment of structural materials. This need represents a major challenge for polycrystalline materials, which exhibit rich heterogeneous microstructure at multiple structure/length scales, and exhibit a wide range of properties. In this study, a novel framework is described for extracting S-P linkages in polycrystalline microstructures that are obtained using 2-point spatial correlations (also called 2-point statistics) to quantify the material's microstructure, and principal component analysis (PCA) to represent this information in a reduced dimensional space. Additionally, it is demonstrated that the use of generalized spherical harmonics (GSH) as a Fourier basis for functions defined on the orientation space leads to a compact and computationally efficient representation of the desired S-P linkages. In this study, these novel protocols are developed and demonstrated for elastic stiffness and yield strength predictions for α − Ti microstructures using a dataset produced through microscale finite element simulations.