Crystal plasticity finite element model (CPFEM) is a powerful numerical simulation in the integrated computational materials engineering toolboxes that relates microstructures to homogenized materials properties and establishes the structure–property linkages in computational materials science. However, to establish the predictive capability, one needs to calibrate the underlying constitutive model, verify the solution and validate the model prediction against experimental data. Bayesian optimization (BO) has stood out as a gradient-free efficient global optimization algorithm that is capable of calibrating constitutive models for CPFEM. In this paper, we apply a recently developed asynchronous parallel constrained BO algorithm to calibrate phenomenological constitutive models for stainless steel 304 L, Tantalum, and Cantor high-entropy alloy.
Quantifying uncertainty associated with the microstructure variation of a material can be a computationally daunting task, especially when dealing with advanced constitutive models and fine mesh resolutions in the crystal plasticity finite element method (CPFEM). Numerous studies have been conducted regarding the sensitivity of material properties and performance to the mesh resolution and choice of constitutive model. However, a unified approach that accounts for various fidelity parameters, such as mesh resolutions, integration time-steps and constitutive models simultaneously is currently lacking. This paper proposes a novel uncertainty quantification (UQ) approach for computing the properties and performance of homogenized materials using CPFEM, that exploits a hierarchy of approximations with different levels of fidelity. In particular, we illustrate how multi-level sampling methods, such as multi-level Monte Carlo (MLMC) and multi-index Monte Carlo (MIMC), can be applied to assess the impact of variations in the microstructure of polycrystalline materials on the predictions of homogenized materials properties. We show that by adaptively exploiting the fidelity hierarchy, we can significantly reduce the number of microstructures required to reach a certain prescribed accuracy. Finally, we show how our approach can be extended to a multi-fidelity framework, where we allow the underlying constitutive model to be chosen from either a phenomenological plasticity model or a dislocation-density-based model.
The structure-property linkage is one of the two most important relationships in materials science besides the process-structure linkage, especially for metals and polycrystalline alloys. The stochastic nature of microstructures begs for a robust approach to reliably address the linkage. As such, uncertainty quantification (UQ) plays an important role in this regard and cannot be ignored. To probe the structure-property linkage, many multi-scale integrated computational materials engineering (ICME) tools have been proposed and developed over the last decade to accelerate the material design process in the spirit of Material Genome Initiative (MGI), notably crystal plasticity finite element model (CPFEM) and phase-field simulations. Machine learning (ML) methods, including deep learning and physics-informed/-constrained approaches, can also be conveniently applied to approximate the computationally expensive ICME models, allowing one to efficiently navigate in both structure and property spaces effortlessly. Since UQ also plays a crucial role in verification and validation for both ICME and ML models, it is important to include UQ in the picture. In this paper, we summarize a few of our recent research efforts addressing UQ aspects of homogenized properties using CPFEM in a big picture context.
