At the microscopic level, many materials are made of smaller and randomly oriented grains. These grains are separated by grain boundaries which tend to decrease the electrical and thermal conductivity of the material. The motion of grain boundaries is an important phenomenon controlling the grain growth in materials processing and synthesis. Mathematical modeling and simulation is a powerful tool for studying the motion of grain boundaries. The research reported in this thesis is focused on the numerical simulation and analysis of a coupled surface and grain boundary motion which models the evolution of grain boundary and the diffusion of the free surface during the process of grain growth. The “quarter loop” geometry provides a convenient model for the study of this coupled motion. Two types of normal curve velocities are involved in this model: motion by mean curvature and motion by surface diffusion. They are coupled together at a triple junction. A front tracking method is used to simulate the migration. To describe the problem, different formulations are presented and discussed. A new formulation that comprises partial differential equations and algebraic equations is proposed. It preserves arc length parametrization up to scaling and exhibits good numerical performance. This formulation is shown to be well-posed in a reduced, linear setting. Numerical simulations are implemented and compared for all formulations. The new formulation is also applied to some other related problems. We investigate numerically the linear stability of the travelling wave solutions for the quarter loop problem and a simple grain boundary motion problem for both curves in two dimensions and surfaces in three dimensions. The numerical results give evidence that they are convectively stable. A class of high order three-phase boundary motion problems are also studied. We consider a region where three phase boundaries meet at a triple junction and evolve with specified normal velocities. A system of partial differential algebraic equations (PDAE) is proposed to describe this class of problems by extending the discussion for the coupled surface and grain boundary motion. The linear well-posedness of the system is analyzed and numerical simulations are performed.

At the microscopic level, many materials are made of smaller and randomly oriented grains. These grains are separated by grain boundaries which tend to decrease the electrical and thermal conductivity of the material. The motion of grain boundaries is an important phenomenon controlling the grain growth in materials processing and synthesis. Mathematical modeling and simulation is a powerful tool for studying the motion of grain boundaries. The research reported in this thesis is focused on the numerical simulation and analysis of a coupled surface and grain boundary motion which models the evolution of grain boundary and the diffusion of the free surface during the process of grain growth. The “quarter loop” geometry provides a convenient model for the study of this coupled motion. Two types of normal curve velocities are involved in this model: motion by mean curvature and motion by surface diffusion. They are coupled together at a triple junction. A front tracking method is used to simulate the migration. To describe the problem, different formulations are presented and discussed. A new formulation that comprises partial differential equations and algebraic equations is proposed. It preserves arc length parametrization up to scaling and exhibits good numerical performance. This formulation is shown to be well-posed in a reduced, linear setting. Numerical simulations are implemented and compared for all formulations. The new formulation is also applied to some other related problems. We investigate numerically the linear stability of the travelling wave solutions for the quarter loop problem and a simple grain boundary motion problem for both curves in two dimensions and surfaces in three dimensions. The numerical results give evidence that they are convectively stable. A class of high order three-phase boundary motion problems are also studied. We consider a region where three phase boundaries meet at a triple junction and evolve with specified normal velocities. A system of partial differential algebraic equations (PDAE) is proposed to describe this class of problems by extending the discussion for the coupled surface and grain boundary motion. The linear well-posedness of the system is analyzed and numerical simulations are performed.

At the microscopic level, many materials are made of smaller and randomly oriented grains. These grains are separated by grain boundaries which tend to decrease the electrical and thermal conductivity of the material. The motion of grain boundaries is an important phenomenon controlling the grain growth in materials processing and synthesis. Mathematical modeling and simulation is a powerful tool for studying the motion of grain boundaries. The research reported in this thesis is focused on the numerical simulation and analysis of a coupled surface and grain boundary motion which models the evolution of grain boundary and the diffusion of the free surface during the process of grain growth. The “quarter loop” geometry provides a convenient model for the study of this coupled motion. Two types of normal curve velocities are involved in this model: motion by mean curvature and motion by surface diffusion. They are coupled together at a triple junction. A front tracking method is used to simulate the migration. To describe the problem, different formulations are presented and discussed. A new formulation that comprises partial differential equations and algebraic equations is proposed. It preserves arc length parametrization up to scaling and exhibits good numerical performance. This formulation is shown to be well-posed in a reduced, linear setting. Numerical simulations are implemented and compared for all formulations. The new formulation is also applied to some other related problems. We investigate numerically the linear stability of the travelling wave solutions for the quarter loop problem and a simple grain boundary motion problem for both curves in two dimensions and surfaces in three dimensions. The numerical results give evidence that they are convectively stable. A class of high order three-phase boundary motion problems are also studied. We consider a region where three phase boundaries meet at a triple junction and evolve with specified normal velocities. A system of partial differential algebraic equations (PDAE) is proposed to describe this class of problems by extending the discussion for the coupled surface and grain boundary motion. The linear well-posedness of the system is analyzed and numerical simulations are performed. / Science, Faculty of / Mathematics, Department of / Graduate

Sigma 3 grain boundaries play a large role in the microstructure of fcc materials in general, and particularly so in grain boundary engineered materials. A recent survey of grain boundary properties revealed that many of these grain boundaries possess very large mobilities, and that these mobilities increase at lower temperature, contrary to typical models of thermallyactivated grain boundary motion. Such boundaries would have a tremendous mobility advantage over other boundaries at low temperature, which may explain some observed instances of abnormal grain growth at low temperature. This work explains the boundary structure and motion mechanism that allows for such mobilities, and explores several of the unique factors that must be considered when simulating the motion of these boundaries. The mobilities of a number of boundaries, both thermally-activated and antithermal, were then calculated over a wide temperature range, and several trends were identified that relate boundary crystallography to thermal behavior and mobility. An explanation of the difference in thermal behavior observed in sigma 3 boundaries is proposed based on differences in their dislocation structure.

Nanocrystalline (NC) metals with averaged grain size smaller than 100 nm have shown promising mechanical properties such as higher hardness and toughness than conventional coarse-grained metals. Unlike conventional metals in which the deformation is controlled by dislocation activities, the microstructural evolution in NC metals is mainly dominated by grain rotation and stress-driven grain boundary motion (SDGBM) due to the high density of grain boundaries (GBs). SDGBM is thus among the most studied modes of microstructural evolution in NC materials with particular interests on their fundamental atomistic mechanisms. In the first part of this thesis, molecular dynamics simulations were used to investigate the influences of Triple Junctions (TJs) on SDGBM of symmetric tilt GBs in copper by considering a honeycomb NC model. TJs exhibited asymmetric pinning effects to the GB migration and the constraints by the TJs and neighboring grains led to remarkable non-linear GB motion in directions both parallel and normal to the applied shear. Based on these findings, a generalized model for SDGBM in NC Cu was proposed. In the second part, the interaction of SDGBM with crack, voids and precipitates was investigated. It was found that depending on the GB structure, material type and temperature, there is a competition between different atomistic mechanisms such as crack healing, recrystallization and GB decohesion. It is hoped that the findings of this work could clarify the micro-mechanisms of various experimental phenomena such as grain refinement in metals during severe plastic deformation, which can be used to design optimized route of making stabilized bulk NC metals. / February 2016

<p>Low angle grain boundary (LAGB) mobility is an essential parameter for developing the analytical models that describe the kinetics of recovery and predict the nucleation of recrystallized grains. The thesis is aimed at the molecular dynamics (MD) simulations study of LAGB mobility determination in pure Al and Al-Mg alloys. All the previous experimental studies reported that the presence of several defects, such as solutes and dislocations, retard the boundary motion and provide lower mobility. However, very few studies have been conducted in MD simulation to capture the interactions of those defects with the migrating grain boundary. This thesis is focused on providing complete understanding of LAGB determination along with a comprehensive explanation of solute and dislocation retarding effects on boundary motion.</p> <p>The LAGB mobility in pure Al was computed from two different MD techniques as a function of temperature and misorientation. Within numerical uncertainties, both techniques provide the same magnitude of mobility at 300K for 7.785^o boundary and at 700K for 23.07^o boundary. It was observed that ADF method is not applicable to determine LAGB mobility at high temperature due to failure of order parameter computation. The MD derived activation energy is found to be approximately ten times lower than the experimental observations.</p> <p>A strong solute pinning effect on boundary motion was observed at all misorientations and solute concentrations studied in Al-Mg alloys. An approximate linear relationship is found between the restraining force and the solute concentration in a distributed solute approach. In addition, the extrinsic dislocations are found to completely pin both 7.785^o and 23.07^o boundary motion at low driving forces in pure Al at 300K. The MD results do not reveal significant qualitative differences of the pinned boundary structure for the low and high angle boundaries and will be discussed in terms of the previous experimental observations.</p> / Doctor of Philosophy (PhD)