Multi-model Monte Carlo estimation for crystal plasticity structure–property simulations of additively manufactured metals

Abstract

Significant uncertainty in the mechanical behavior of additively manufactured metals can arise from complex, stochastic microstructures. Using experiments alone to quantify this uncertainty incurs significant time and monetary costs. Quantitative relationships across processing, microstructure, and micromechanical behavior are also difficult to establish with limited experiments. Crystal plasticity simulations can help to reduce reliance on experiments for predicting the influence of microstructural uncertainty on micromechanical quantities of interest (QoIs). However, full-field crystal plasticity models are computationally expensive to evaluate, making them unattractive for uncertainty propagation with standard Monte Carlo (MC) methods. Lower-fidelity models may be faster to evaluate but are generally biased and less accurate. Multi-model MC methods combine two or more models of varying fidelities to more efficiently propagate uncertainty and provide unbiased QoI estimates. In this work, a multi-model MC framework is applied to predict crystal plasticity QoIs using an ensemble of full-field and homogenization-based models with microstructures based on additively manufactured Ni-base superalloys. The QoIs are the aggregate yield strength and the mean and maximum values of grain-average stress and strain quantities in each microstructure instantiation. By optimally allocating samples to each model, up to $\sim 20\times$ variance reduction is achieved for the QoIs relative to standard MC with the same computational cost constraint. Equivalently, the variance reduction can be viewed as a computational cost reduction given the same target variance. Multi-model MC is thereby shown to be a promising approach for efficiently propagating uncertainty with crystal plasticity models.