Publication 14-CNA-026

Numerical Analysis of the Vertex Models for Simulating Grain Boundary Networks

C. E. Torres
Department of Mathematical Sciences
George Mason University
Fairfax VA

Maria Emelianenko
Department of Mathematical Sciences
George Mason University
Fairfax, VA 22030
memelian@gmu.edu

Dmitry Golovaty
Department of Mathematics
University of Akron
Akron OH
dmitry@uakron.edu

David Kinderlehrer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
davidk@andrew.cmu.edu

Shlomo Ta'asan
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
shlomo@andrew.cmu.edu

Abstract: Polycrystalline materials undergoing coarsening can be represented as evolving networks of grain boundaries, whose statistical characteristics determine macroscopic materials properties. The process of formation of various statistical distributions is extremely complex and is strongly influenced by topological changes in the network. This work is an attempt to elucidate the role of these changes by conducting a thorough numerical investigation of one of the simplest types of grain growth simulation models, called vertex models. While having obvious limitations in terms of its ability to represent realistic systems, the vertex model enables full control over topological transitions and retains essential geometric features of the network.
We formulate a self-consistent vertex model and investigate the role of microscopic parameters on the mesoscale network behavior. This study sheds light onto several important questions, such as how statistics are affected by the choice of temporal and spatial resolution and rules governing topological changes. Statistical analysis of the data produced by the simulation is performed for both isotropic and anisotropic grain boundary energy.

Get the paper in its entirety as  14-CNA-026.pdf

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