Bayesian analysis of parametric uncertainties and model form probabilities for two different crystal plasticity models of lamellar grains in α plus β Titanium alloys

The properties of individual phases and complex interactions of phases that affect mechanical behavior of metastable lamellar and Widmanstaetten morphologies of alpha+beta Titanium alloys has long eluded quantitative assessment. As a result, the uncertainty of models for these complex multiphase morphologies is high, despite their importance in practical high-value applications. In this work, we present a comprehensive three-step framework for the estimation of intrinsic single crystal properties and the assessment of model plausibility for crystal plasticity models of lamellar alpha+beta colonies of Titanium alloys using a dataset of experimentally obtained nanoindentation measurements on multiple grains in a polycrystalline sample. This approach does not rely upon submicron scale measurements within individual phases of defects, but rather exploits mesoscale measurements of collective response, making use of modern data science to assess uncertainties of both model form and model parameters. The first step of the three-step framework requires the establishment of a low-cost Gaussian Process Regression (GPR) surrogate (reduced order) model that predicts the indentation yield strength estimated by computationally expensive crystal plasticity finite element simulations. To reduce the number of finite element simulations necessary to establish the surrogate model, this work adopts an information-driven approach that selects additional simulations based on their potential to improve model accuracy. The second step involves the application of Markov Chain Monte Carlo (MCMC) sampling techniques in order to estimate the feasible intrinsic parameter configurations that are capable of capturing the trends in the experimental data. The sampling process provides rigorous uncertainty estimates for the intrinsic properties, in addition to providing an approximation for the model evidence. The model evidence is used to compute the relative probabilities of the chosen physics-based crystal plasticity model forms in the third step of the framework to enable model fusion. This framework is delineated and demonstrated in this paper through a case study involving two currently used crystal plasticity models for the colony morphology of Ti-6Al-4V.