A Variational Approach to Modeling and Simulation of Grain Growth

• Published in: SIAM journal on scientific computing 2006-01, Vol.28 (5), p.1694-1715
• Main Authors: Kinderlehrer, David, Livshits, Irene, Ta’asan, Shlomo
• Format: Article
• Language: English
• Subjects: Applied mathematics; Energy; Grain boundaries; Grain growth; Grain size; Materials science; Microprocessors; Simulation
• ISSN: 1064-8275; 1095-7197
• DOI: 10.1137/030601971

Most technologically useful materials arise as polycrystalline microstructures, composed of a myriad of small crystallites, called grains, separated by their interfaces, called grain boundaries. The orientations and arrangements of the grains and their network of boundaries are implicated in many properties across wide scales, for example, functional properties, like conductivity in microprocessors, and lifetime properties, like fracture toughness in structures. Simulation is becoming an important tool for understanding both materials properties and their processing requirements. Here we offer a consistent variational approach to the mesoscale simulation of these systems subject to the Mullins equation of curvature-driven growth in a two-dimensional setting. The main objective is to provide a calibration for future two-dimensional and three-dimensional efforts. We discuss several novel features of our approach, which we anticipate will render it a flexible, scalable, and robust tool to aid in microstructural prediction. Simulation results offer compelling evidence of the predictability and robustness of statistical properties of large systems, such as grain size distribution and texture, that are of immediate interest in materials science.