Multiscale Modeling for Texture and Grain Topology of Polycrystalline Microstructures Under Uncertainty

The present work addresses multiscale modeling for grain topology of polycrystalline microstructures under the effects of the microstructural uncertainties. The special focus is on the titanium-7wt%-aluminum alloy (Ti-7Al), which is a candidate material for many aerospace systems owing to its outstanding mechanical performance in elevated temperatures. The electron backscatter diffraction samples of Ti-7Al in small-scales are used to reconstruct the alloy microstructures in larger domains. The reconstruction provides a statistically equivalent synthetic representation to the small-scale test samples while introducing epistemic uncertainty on microstructural features. Here, the grain topology of the polycrystalline microstructures is quantified using shape moment invariants. These invariant parameters can capture the shapes of physical objects with a numerical representation, and they are invariant to shape transformations. To quantify the effects of the uncertainties on the homogenized properties of the microstructures, a surrogate model is developed as a function of shape moment invariants with Gaussian process regression by utilizing the experiments and crystal plasticity simulations for training data.