Advancing Graph-Theoretic Techniques for Microstructure Reconstructions, Evolutions, and Property Evaluations

Abstract

Complex applications in modern aerospace technology urgently call for advanced structural materials that are high-strength, lightweight, and yet tolerant to damage from loading conditions, extreme temperature, particle radiation, or environmental exposure. To swiftly fulfill these emerging material requirements, a multi-scale understanding of the relationships between processing, microstructure, and properties of metallic materials needs to be developed. Toward these goals, this dissertation presents computational models and software for ($i$) building three-dimensional (3D) microstructural maps of materials through Markovian inference from a set of three orthogonal two-dimensional (2D) experimental measurements, ($ii$) insertion of microstructural information into a geometrical grid at the component-scale level with iterative refinement using experimental measurements at locations of maximum uncertainty, ($iii$) implementation of Cauchy-Crofton technique as a post-processing step to minimize surface energies for the purposes of physics-based segmentation and texture evolution of microstructural aggregates, and ($iv$) development of crystal plasticity peridynamics (CPPD) technique for predicting fine-scale stress/strain localizations at micro-scale level. These numerical efforts serve as multi-scale modeling tools for the reconstruction of surrogate models to proactively simulate structural performance and quantify/reduce the uncertainty in computational materials prognosis, involving the complex nature of polycrystalline formation and texture simulation.

Traditionally, the underlying 3D microstructural information of polycrystalline structures has been digitized through experimental acquisition techniques, such as tomography or serial sectioning. These methods, however, only provide images over relatively small volumes of material. Furthermore, due to the stochasticity of material formation, a single snapshot of a microstructure does not adequately capture the property distributions in a component. In addition, currently-available numerical methods for microstructure synthesis, such as geometry-based (e.g., Voronoi tessellation), physics-based (e.g., phase-field, kinetic Monte Carlo), or feature-based (e.g., simulated annealing) techniques, run into various difficulties when modeling microstructural complexities including non-equilibrium grain structures, non-convex morphologies, multi-phase features, twins, and cell structures that naturally arise from material processing. These features, however, play an important role in the properties and performance of modern structural materials.

Therefore, this dissertation attempts to create a suite of data-driven computational models based on graph theoretic techniques to rapidly synthesize complex 3D polycrystalline microstructures with validated features that are extremely critical for microstructure quantification, property analysis, and materials design. The efficacy of this new procedure for the 3D characterization of microstructural components is demonstrated for a wide range of microstructures fabricated by conventional and additive manufacturing processes, along with quantitative comparisons against published experimental/analytical/simulated data in the literature. This approach is consistent with the goals of the integrated computational materials engineering (ICME) and Materials Genome Initiative for Global Competitiveness, which aims to deploy advanced materials more expeditiously.