Exploring the Stochastic Performance of Metallic Microstructures With Multi-Scale Models

Titanium-7%wt-Aluminum (Ti-7Al) has been of interest to the aerospace industry owing to its good structural and thermal properties. However, extensive research is still needed to study the structural behavior and determine the material properties of Ti-7Al. The homogenized macro-scale material properties are directly related to the crystallographic structure at the micro-scale. Furthermore, microstructural uncertainties arising from experiments and computational methods propagate on the material properties used for designing aircraft components. Therefore, multi-scale modeling is employed to characterize the microstructural features of Ti-7Al and computationally predict the macro-scale material properties such as Young's modulus and yield strength using machine learning techniques. Investigation of microstructural features across large domains through experiments requires rigorous and tedious sample preparation procedures that often lead to material waste. Therefore, computational microstructure reconstruction methods that predict the large-scale evolution of microstructural topology given the small-scale experimental information are developed to minimize experimental cost and time. However, it is important to verify the synthetic microstructures with respect to the experimental data by characterizing microstructural features such as grain size and grain shape. While the relationship between homogenized material properties and grain sizes of microstructures is well-studied through the Hall-Petch effect, the influences of grain shapes, especially in complex additively manufactured microstructure topologies, are yet to be explored. Therefore, this work addresses the gap in the mathematical quantification of microstructural topology by developing measures for the computational characterization of microstructures. Moreover, the synthesized microstructures are modeled through crystal plasticity simulations to determine the material properties. However, such crystal plasticity simulations require significant computing times. In addition, the inherent uncertainty of experimental data is propagated on the material properties through the synthetic microstructure representations. Therefore, the aforementioned problems are addressed in this work by explicitly quantifying the microstructural topology and predicting the material properties and their variations through the development of surrogate models. Next, this work extends the proposed multi-scale models of microstructure-property relationships to magnetic materials to investigate the ferromagnetic-paramagnetic phase transition. Here, the same Ising model-based multi-scale approach used for microstructure reconstruction is implemented for investigating the ferromagnetic-paramagnetic phase transition of magnetic materials. The previous research on the magnetic phase transition problem neglects the effects of the long-range interactions between magnetic spins and external magnetic fields. Therefore, this study aims to build a multi-scale modeling environment that can quantify the large-scale interactions between magnetic spins and external fields.