Gaussian process autoregression models for the evolution of polycrystalline microstructures subjected to arbitrary stretching tensors

Abstract

Crystal plasticity finite element models (CPFEM) have shown tremendous potential for simulating the microstructure evolution paths in polycrystalline aggregates subjected to large plastic strains. However, their high computational cost has hindered their broader deployment in design efforts where large process design spaces need to be explored. In this work, a novel machine learning framework is developed to establish low-computational cost reduced-order models for predicting the details of microstructure evolution in face-centered cubic (FCC) polycrystalline microstructures subjected to arbitrary stretching tensors. Within this framework, the previously established feature engineering of polycrystalline materials within the material knowledge system (MKS) framework is extended such that it is applicable to the highly deformed microstructures obtained during large deformations. Gaussian process autoregression (GPAR) approaches combined with Bayesian design of experiment strategies are employed for building the desired surrogate models to optimize the generation of the computationally expensive training data (produced using CPFEM). It is demonstrated that a relatively small training set of 1400 datapoints is adequate to produce a high-fidelity reduced-order model for predicting the details of the microstructure evolution in a very broad set of FCC polycrystalline aggregates subjected to arbitrary macroscopically imposed stretching tensors.