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.

Learning to Predict Crystal Plasticity at the Nanoscale: Deep Residual Networks and Size Effects in Uniaxial Compression Discrete Dislocation Simulations

“…In this section, the performance of the proposed model is compared with a benchmark method, which is the correlation function based method. The correlation function based method is widely used in materials science research [48][49][50] . For the correlation function based method, two-point correlation function of the strain profile is first computed, then Principal Component Analysis is applied to obtain the reduced-order representations, and finally Random forest 51 is implemented to train the predictive model.…”

Materials knowledge system for nonlinear composites

“…Another new framework based on emerging data science strategies -Materials Knowledge Systems (MKS) [51,54] -has also shown potential for addressing the trade-offs described earlier. Specifically, MKS demonstrated a combination of high accuracy and modest computation cost in addressing both localization and homogenization problems [55][56][57][58]. The central idea underlying the MKS approach is the calibration of the Green's function-based convolution kernels in the series expansions employed in the statistical continuum theories to the numerical datasets produced by micromechanical finite element simulations on ensembles of digitally created microstructure exemplars [56][57][58].…”

“…In prior work, the MKS homogenization approach has been demonstrated for predictions of the effective elastic stiffness and initial yield strength of composites [56][57][58]. However, many applications in integrated material-product design demand computationally efficient predictions of the stress-strain response (e.g., tensile stress-strain curve) beyond the elastic stiffness and the yield strength.…”

“…Indeed, functions overfitted to the calibration dataset will perform badly on new microstructures. In prior work[56][57][58], leave-one-out cross validation (LOOCV) proved to be an effective technique to evaluate overfits, especially in the context of micromechanics when the calibration data is often limited because of the computational expenses associated with generating the calibration data (with FE simulations). LOOCV tests the sensitivity of the calibrated functions to exclusion of a single data point from calibration: high sensitivity indicates overfit of the functions, while well fitted functions are insensitive to leaving out only one sample.…”

Data-Driven Microstructure Property Relations

“…For instance, a PCA of the n-point correlation functions of the microstructure is performed and the principal scores are used to in a polynomial regression model in order to predict material properties. The MKS is actively researched for different material structures [19][20][21]. For instance, [19,20] successfully predict the elastic strain and yield stress for the underlying microstructure using the MKS approach, however they confine their focus on either the topological features of the microstructure or a confined range of allowed volume fractions (0-20%), often held constant in individual studies.…”