Uncertainty Quantification Framework for Predicting Material Response with Large Number of Parameters: Application to Creep Prediction in Ferritic-Martensitic Steels Using Combined Crystal Plasticity and Grain Boundary Models

Abstract

This paper presents an uncertainty quantification (UQ) framework for the physics-based model prediction of material response with a large number of parameters. The application problem presented in this work is that of predicting creep in Grade 91 steel at 600°C. The material response is defined with a physically based microstructural model with constitutive equations emulating several observed phenomena in Grade 91 and embodied into an explicit geometry mesoscale finite element model for prior austenite grains and grain boundaries. Creep within the grains and in grain boundaries are represented by crystal plasticity for dislocation motion and a physics-based model for cavity growth and nucleation, respectively. The creep behavior of this material is influenced by several parameters, some of which have a wide range of variation based on experimental data. UQ combined with microstructural modeling can discover the core microstructural causes of experimental variability, leading to improved materials with lower variability in critical long-term material properties. In this study, we investigate the model's uncertainty to identify material properties that may be modified during production to increase creep life and analyze different components of the crystal plasticity model for improvements. For this purpose, a quantity of interest is defined as time to minimum creep rate, which correlates well to the creep failure of the material. A deep neural network model was trained and validated to be used as a surrogate for the finite element model. Then, a variance-based sensitivity analysis is performed on the surrogate model to find the Sobol indices of the input parameters in respect to the output quantity of interest. The Sobol indices are used to reduce the dimensionality of the model. Generalized polynomial chaos expansion is used on the reduced basis models to propagate the uncertainty from the input parameters to the quantity of interest using the deep neural network surrogate model. These results are benchmarked against uncertainty propagation using Monte Carlo simulations. In conclusion, the UQ performed through the reduced basis model captures almost all the uncertainty in the model with significantly fewer simulations, making it possible to perform the UQ directly via simulations with the finite element model rather than surrogate machine-learned models.