Computational Tools for Polycrystalline Materials

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This project will develop new algorithms for computer simulation of how the internal structure (called microstructure) of many technologically essential materials, such as most metals and ceramics, change during common manufacturing processes such as heat treatment. The microstructure of such materials is known to have implications for the physical properties, such as conductivity or yield strength, of the material. Although models describing how the microstructure evolves, for example during heat treatment, have been available, their efficient numerical simulation at scales large enough to be of practical interest to materials scientists have remained a challenge. The project will address this challenge. Understanding the evolution of microstructure holds the promise of materials with more desirable characteristics. The project will also develop machine learning and computer vision algorithms for automatically extracting microstructure information from experimental measurements (microscopy images) of such materials, so that predictions of the models to be simulated can be more readily checked against experiments. One Ph.D. student's training and thesis work will be an integral part of the research.Continuum models of interfacial motion in polycrystalline materials often take the form of a system of nonlinear partial differential equations describing the geometric flow of a network of surfaces. For certain important interfacial phenomena, such as grain boundary motion, the evolution is given by second order differential equations describing motion by mean curvature of the network. For that setting, a surprisingly simple, elegant, and efficient class of algorithms known as threshold dynamics have been developed that makes large scale simulation particularly feasible. Other phenomena, such as the motion of the free surface of a thin polycrystalline film, or that of pores in a sintered metal, are described by higher order geometric evolutions, such as motion by surface diffusion, and are more challenging to simulate. This project will develop efficient algorithms for such high order multi-phase geometric evolutions. In particular, it will explore whether threshold dynamics or a combination of it with phase field methods can be devised to simulate the motion of networks of surfaces in which some of the interfaces evolve via motion by mean curvature, and others via motion by surface diffusion, coupled along free boundaries known as junctions along which appropriate boundary conditions are satisfied. Some of these models describing the multi-phase geometric motion of networks of interfaces also arise almost verbatim in the context of computer vision and machine learning. By leveraging this mathematical connection, the project will also develop new algorithms for automatically extracting grain boundaries in microscopy images of real polycrystalline materials.