Bayesian inference and uncertainty quantification for modeling of body-centered-cubic single crystals

TL;DR

This paper applies Bayesian inference and sensitivity analysis to calibrate and validate crystal plasticity models for bcc molybdenum, quantifying uncertainties and physical mechanisms across various loading conditions.

Contribution

It introduces a probabilistic framework for calibrating and validating bcc crystal plasticity models, enhancing understanding of deformation mechanisms under different strain rates.

Findings

Sensitivity indices reveal physical basis of model predictions at various strain rates.

Calibrated models accurately predict responses beyond calibration regimes.

Uncertainty quantification identifies key parameters influencing deformation behavior.

Abstract

Uncertainties in the high-dimensional space of material parameters pose challenges for the predictive modeling of bcc single crystals, especially under extreme loading conditions. In this work, we identify the key physical assumptions and associated uncertainties in constitutive models that describe the deformation behavior of bcc single crystal molybdenum subjected to quasi-static to shock loading conditions. We employ two representative physics-based bcc single crystal plasticity models taken from our previous work (Nguyen et al. 2021a; Lee et al. 2023b), each prioritizing different key deformation mechanisms. The Bayesian model calibration (BMC) is used for probabilistic estimates of material parameters in both bcc crystal plasticity models. In conjunction with the BMC procedure, the global sensitivity analysis is conducted to quantify the impact of uncertainties in the material parameters on the key simulation results of quasi-static to shock responses. The sensitivity indices at various loading conditions clearly illustrate the physical basis underlying the predictive capabilities of the two distinct bcc crystal plasticity models at low to high strain rates. Both of the calibrated bcc models are then further validated beyond the calibration regime, by which we further identify critical physical mechanisms that govern the transient elastic-plastic responses of single crystal molybdenum under shock loading. The statistical inference framework demonstrated here facilitates the further development of continuum crystal plasticity models that account for a broad range of deformation mechanisms.