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Motion of Grain Boundaries in Polycrystalline Materials

Many common materials, such as most metals and ceramics, are polycrystalline: They are made up of tiny crystallites called grains that are distinguished from their neighbors by their differing crystallographic orientation. When these materials are heated (i.e. annealed) -- for instance during a manufacturing process -- grain growth occurs: The network of grains decreases its energy through a coarsening procedure, which involves the growth of some of the grains at the expense of others. Statistical measures of the grain network, such as the grain size distribution, have important implications for the macroscopic properties of the material, such as its conductivity and brittleness. As such, simulating how the grain network evolves is of great technological interest. We developed new, efficient, and accurate numerical methods for simulating grain growth and related dynamics. This work has been supported by NSF grant DMS-0748333.

Software:

The following software implements some of the grain boundary motion algorithms in:

Esedoglu, S.; Otto, F. Threshold dynamics for networks with arbitrary surface tensions. Communications on Pure and Applied Mathematics. 68:5 (2015), pp. 808-864.

Clicking on the apporpriate link will take you to a dedicated webpage with the downloadable source code, instructions for setting it up on your system, and examples of how to use it. There are multiple versions. For small scale experiments (e.g. convergence tests) with a few phases, download the few phase versions, as these are much shorter, easier to use, and due to lack of overhead, faster if the number of phases is small. The large scale versions are suitable for simulations with up to hundreds of thousands of grains in 2D or 3D.

Publications and Preprints:

Esedoglu, S.; Otto, F. Threshold dynamics for networks with arbitrary surface tensions. Max Planck Institute for Mathematics in the Sciences (Leipzig) Preprint 2/2013. Communications on Pure and Applied Mathematics. 68:5 (2015), pp. 808-864.
Elsey, M.; Esedoglu, S.; Smereka, P. Simulations of anisotropic grain growth: effiicent algorithms and misorientation distributions. Acta Materialia. 61:6 (2013), pp. 2033-2043.
Esedoglu, S. Large-scale simulations of grain boundary motion in polycrystals. SIAM News. 43:8 Oct. 2010.
Elsey, M.; Esedoglu, S.; Smereka, P. Large scale simulations and parameter study for a simple model of recrystallization. Philosophical Magazine. 91:11 (2011), pp. 1607-1642.
Elsey, M.; Esedoglu, S.; Smereka, P. Large scale simulation of normal grain growth in two and three dimensions. Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences. 467:2126 (2011), pp. 381-401.
Elsey, M.; Esedoglu, S.; Smereka, P. Diffusion generated motion for grain growth in two and three dimensions. Journal of Computational Physics. 228:21 (2009), pp. 8015-8033.
Esedoglu, S.; Ruuth, S.; Tsai, R. Diffusion generated motion using signed distance functions. Journal of Computational Physics. 229:4 (2010), pp. 1017-1042.

3D Simulation Results:

The large scale simulation shown below was carried out on a 512x512x512 grid (joint work with Matt Elsey and Peter Smereka), using the distance function based diffusion generated motion algorithm.

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Below are a few individual grains from the simulation shown above, at the final time.

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There is a "no flash" version of this webpage here.