Probabilistic calibration of crystal plasticity material models with synthetic global and local data

TL;DR

This paper introduces a two-stage Bayesian calibration method combining global and local data to efficiently estimate crystal plasticity model parameters, reducing uncertainty and improving local behavior predictions.

Contribution

It presents a novel two-stage calibration procedure that balances surrogate modeling with full-field simulations and incorporates uncertainty quantification using parallelized sequential Monte Carlo.

Findings

The method efficiently calibrates parameters using synthetic data.

Local data reduces parameter uncertainty significantly.

The approach is robust even with noisy and limited local data.

Abstract

Crystal plasticity models connect macroscopic deformation with the physics of microscale slip in polycrystalline materials. These models can be calibrated using global stress-strain curves, but the resulting parametrization is often not unique: multiple parametrizations can predict the same global behavior but different local, grain-scale behavior. Using local data for calibration can mitigate uniqueness issues, but expensive specialized experiments like high-energy X-ray diffraction (HEDM) are typically required to gather the data. The computational expense of full-field simulations also often prevents uncertainty quantification with sampling-based calibration algorithms like Markov chain Monte Carlo. This study presents a two-stage calibration procedure that combines global and local data and balances the efficiency of a surrogate model with the accuracy of full-field crystal plasticity simulations. The procedure quantifies uncertainty using Bayesian inference with an efficient, parallelized sequential Monte Carlo algorithm. Calibrations are completed using synthetic data with a microstructure representative of Inconel 718 to assess uncertainty and accuracy of the parameters relative to a known ground truth. Global data comes from the uniaxial stress-strain curve, while local data comes from grain-average stresses, reflecting typical outputs of HEDM experiments. Additional calibrations with limited and noisy local data demonstrate robustness of the procedure and identify the most important features of the data. Overall, the results demonstrate the computational efficiency of the two-stage procedure and the value of local data for reducing parameter uncertainty. In addition, joint distributions of the calibrated parameters highlight key considerations in choosing constitutive models and calibration data, including challenges resulting from correlated parameters.