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Research Papers

Multiscale Simulations of Anisotropic Grain Growth Using Wavelet Based Multiresolution Analysis

[+] Author and Article Information
J. B. Allen

Information Technology Laboratory,
U.S. Army Engineer Research and Development Center,
3909 Halls Ferry Road,
Vicksburg, MS 39180
e-mail: Jeffrey.B.Allen@usace.army.mil

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 9, 2016; final manuscript received July 29, 2016; published online August 22, 2016. Assoc. Editor: Harold S. Park.This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Appl. Mech 83(10), 101011 (Aug 22, 2016) (7 pages) Paper No: JAM-16-1284; doi: 10.1115/1.4034388 History: Received June 09, 2016; Revised July 29, 2016

The present work serves to document the development and findings associated with a wavelet-based multiscale simulation analysis for anisotropic grain growth of a two-dimensional polycrystalline material. In particular, lattice-based Monte Carlo and atomically-based Molecular Dynamics simulations are used to compute the grain boundary energies over their respective spatial domains. Serial coupling is performed utilizing an orthonormal set of Haar wavelet transforms embedded within a corresponding multiresolution analysis. For the Monte Carlo approach, anisotropies in grain boundary energies, caused by differences in grain orientation (texturing), are examined using two distinct methods, while the molecular dynamics simulations, offering inherent anisotropy, are conducted assuming the interatomic Lennard Jones potential. Among other findings, under the present context, the results confirm the viability of the wavelet-based multiresolution analysis (MRA) method for use as a potential coupling agent, and provide substantiation for its use with other applications. The results further offer quantitative comparisons between isotropic and anisotropic modeling results, and demonstrate their range of applicability.

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Figures

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Fig. 1

The two-dimensional multiresolution decomposition process; consisting of approximation and detail wavelet coefficients ranging over a prescribed number of decomposition levels: (a) wavelet matrix decomposition and (b): determination of wavelet coefficients

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Fig. 2

Results of grain size evolution showing the slope of a straight-line fit through a plot of log R versus log (t). As shown, to a good approximation, the slope (0.49) is in agreement with the power law prediction.

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Fig. 3

Grain growth contours at energy ratios of E/E0 = 30% and E/E0 = 20% corresponding to both the Q-state Monte Carlo (MC) and molecular dynamics (MD) simulation methods: (a) MC; isotropic: E/E0 = 30%, (b) MC; isotropic; E/E0 = 20%, (c) MC: anisotropic; E/E0 = 30%, (d) MC: anisotropic; E/E0 = 20%, (e) MD; E/E0 = 30%, and (f) MD; E/E0 = 20%

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Fig. 4

Evolution of the normalized energy with time (in MD steps) corresponding to both the MC isotropic/anisotropic and MD simulation methods

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Fig. 5

Wavelet-based MRA results corresponding to both the MC and MD simulations; The MC simulations were conducted over a resolution of 128 × 128 (seven scales) and the MD results were averaged over a regular grid of resolution 256 × 256 (eight scales): (a) representative wavelet matrix plot; (MC; E/E0 = 30%; MRA), (b) anisotropic MC results for energy ratios; E/E0 = 30% and E/E0 = 20%, (c) coupled MC/MD results at E/E0 = 30%, and (d) coupled MC/MD results at E/E0 = 20%

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