Data-Driven Bayesian Model for Predicting Fatigue Crack Nucleation in Polycrystalline Ni-based Superalloys

This paper develops a Bayesian, probabilistic crack nucleation model in the Ni-based superalloy Ren\'e 88DT for fatigue loading. A data-driven, machine learning approach is developed to identify the underlying mechanics driving crack nucleation. An experimental set of fatigue-loaded microstructures is characterized near crack nucleation sites using scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) images to correlate grain morphology and crystallography to the spatial location of crack nucleation sites. A concurrent multiscale model that embeds polycrystalline microstructures, created from the EBSD images, in a self-consistent homogenized material is developed for low cycle fatigue simulations needed to create a database of state variables. The polycrystalline domain is modeled by a crystal plasticity finite element model (CPFEM), while a homogenized anisotropic plasticity model is used for the exterior domain. A Bayesian classification method is introduced to optimally select the most informative state variable predictors of crack nucleation and constructs a near-Pareto frontier of models with varying complexity. From this principal set of state variables, a simplified scalar crack nucleation indicator is formulated which encompasses all of the relevant components derived from the main discriminators. This Bayesian approach allows the micromechanical state variables responsible for causing crack nucleation events to come out naturally from existing data. The final result is a model that predicts the probability of nucleating a crack at a microstructural location, given the mechanical state of the material.