Mesoscale Computational Modeling and Analysis of Materials Microstructure

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Most metallic and ceramic materials used in a variety of applications, including aircraft, automobiles, and devices such as computers are polycrystalline, i.e. are made up of many microscopic crystals (grains) held together by boundaries. Grain boundaries have a property called ?grain boundary energy?, which is responsible for how strong the grains are connected to each other. Depending on the energy, polycrystalline structures may have very different properties. Very little is known about this energy and its dependence on the crystallographic nature of the boundary. The main objective of this work is to create efficient mathematical models and numerical algorithms for predicting and controlling materials microstructure by quantifying the kinetics of the coarsening processes and understanding the influence of grain boundary energy on microstructural evolution. The novelty of the proposed approach lies in placing focus on understanding statistical effects of the topological reconfigurations during the grain boundary network evolution. This project will allow to develop a new stochastic framework for mesoscopic analysis of materials based in part on recently discovered evolution equations and an in-depth study of grain disappearance rates. This research will link coarsening processes common to nearly all materials with underlying stochastic processes that characterize specific microstructures by means of accurate and validated computational modeling based on random walk theory, modulated Poisson processes and distributed Boltzmann equations. Significant effort will be dedicated to optimizing performance of numerical algorithms, such as numerical schemes for solving fractional integro-differential equations with nonlocal kernels and methods for parameter estimation in stochastic processes. The models and algorithms developed and analyzed in this project will offer an accurate and low cost alternative to large-scale simulations and other numerical techniques traditionally used in studying interfacial properties of complex materials. This work will lead to control over grain growth kinetics, a primary issue for materials science applications, and to a deeper understanding of the materials parameters and their interaction across different scales. This will have a direct impact on many practically important areas by advancing the synthesis of novel ?smart? materials - highly sophisticated materials, possessing very specific set of properties to target particular applications necessary to meet increasing demands of the society in the era of tremendous economic and environmental challenges. For instance, functional materials that can reliably withstand extreme thermal and pressure environments are indispensable for solving energy-related problems such as improving power plant efficiency, while lighter weight high strength components are required for designing new generation vehicles with reduced fuel consumption. The models developed by the investigator and collaborators will be used to build a suite of algorithms capable of simulating and analyzing microstructures that can be predisposed to certain type of behavior under external stimuli. These methods will allow for faster and more reliable analysis, control and optimization of materials properties and will equip engineers with powerful predictive tools that can be readily transferred to industry for modeling the processing of commodity materials.