Investigating variability of fatigue indicator parameters of two-phase nickel-based superalloy microstructures

Variability of fatigue properties of Nickel-based superalloys induced by microstructure feature uncertainties is investigated. The microstructure at one material point is described by its grain size and orientation features, as well as the volume fraction of the γ′ phase. Principal component analysis (PCA) is introduced to reduce the dimensionality of the microstructure feature space. PCA and kernel PCA (KPCA) techniques are presented and compared. Reduced representations of input features are mapped to uniform or standard Gaussian distributions through polynomial chaos expansion (PCE) so that the sampling of new microstructure realizations becomes feasible. A crystal plasticity constitutive model is adopted to evaluate fatigue properties of two-phase superalloy microstructures under cyclic loading. The fatigue properties are measured by strain-based fatigue indicator parameters (FIP). Adaptive sparse grid collocation (ASGC) and Monte Carlo (MC) methods are used to establish the relation between microstructure feature uncertainties and the variability of macroscopic properties. Convergence with increasing dimensionality of the reduced surrogate stochastic space is studied. Distributions of FIPs and the convex hulls describing the envelope of these parameters in the presence of microstructure uncertainties are shown.