- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Simulation and analysis of coupled surface and grain...
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
Simulation and analysis of coupled surface and grain boundary motion Pan, Zhenguo
Abstract
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.
Item Metadata
Title |
Simulation and analysis of coupled surface and grain boundary motion
|
Creator | |
Publisher |
University of British Columbia
|
Date Issued |
2008
|
Description |
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.
|
Extent |
2043312 bytes
|
Genre | |
Type | |
File Format |
application/pdf
|
Language |
eng
|
Date Available |
2008-10-30
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0066768
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Graduation Date |
2009-05
|
Campus | |
Scholarly Level |
Graduate
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International