Mesoscale Computational Modeling and Analysis of Materials Microstructure

在各种应用中使用的大多数金属和陶瓷材料，包括飞机、汽车和诸如计算机之类的设备都是多晶的，即由许多微观晶体（颗粒）通过边界结合在一起组成。晶界有一个属性叫？晶界能？这决定了颗粒之间的连接强度。根据能量的不同，多晶结构可能具有非常不同的性质。我们对这种能量以及它对边界的晶体性质的依赖所知甚少。本工作的主要目标是通过量化粗化过程的动力学和了解晶界能对微观组织演变的影响，建立有效的数学模型和数值算法来预测和控制材料的微观组织。该方法的新颖之处在于将重点放在理解晶界网络演化过程中拓扑重构的统计效应上。该项目将开发一种新的随机框架，用于材料的介观分析，部分基于最近发现的进化方程和对颗粒消失率的深入研究。本研究将通过基于随机游走理论、调制泊松过程和分布玻尔兹曼方程的精确和有效的计算模型，将几乎所有材料共同的粗化过程与表征特定微观结构的潜在随机过程联系起来。重要的工作将致力于优化数值算法的性能，例如求解非局部核分数阶积分微分方程的数值方案和随机过程中参数估计的方法。在这个项目中开发和分析的模型和算法将为大规模模拟和其他传统上用于研究复杂材料界面特性的数值技术提供准确和低成本的替代方案。这项工作将导致对晶粒生长动力学的控制，这是材料科学应用的一个主要问题，并有助于更深入地了解材料参数及其在不同尺度上的相互作用。这将对许多实际重要领域产生直接影响，因为它推动了新颖智能的合成。材料-高度复杂的材料，具有非常具体的一套属性，以满足社会在巨大的经济和环境挑战的时代日益增长的需求，以满足特定的应用。例如，能够可靠地承受极端高温和高压环境的功能材料对于解决能源相关问题（如提高发电厂效率）是必不可少的，而设计具有更低油耗的新一代汽车则需要更轻重量的高强度部件。研究者和合作者开发的模型将用于建立一套能够模拟和分析微观结构的算法，这些微观结构可以在外部刺激下倾向于某些类型的行为。这些方法将允许更快、更可靠地分析、控制和优化材料性能，并将为工程师提供强大的预测工具，这些工具可以很容易地转移到工业中对商品材料的加工进行建模。

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.