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Research Papers

Simulations of Anisotropic Grain Growth Subject to Thermal Gradients Using Q-State Monte Carlo

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

e-mail: Jeffrey.B.Allen@erdc.dren.mil

C. R. Welch

Information Technology Laboratory,
U.S. Army Engineer Research
and Development Center,
3909 Halls Ferry Road,
Vicksburg, MS 39180

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received November 21, 2012; final manuscript received July 31, 2013; published online August 30, 2013. Assoc. Editor: Irene Beyerlein.

J. Eng. Mater. Technol 135(4), 041005 (Aug 30, 2013) (9 pages) Paper No: MATS-12-1261; doi: 10.1115/1.4025171 History: Received November 21, 2012; Revised July 31, 2013

The Q-state Monte Carlo, Potts model is used to investigate 2D, anisotropic, grain growth of single-phase materials subject to temperature gradients. Anisotropy is simulated via the use of nonuniform grain boundary surface energies, and thermal gradients are simulated through the use of variable grain boundary mobilities. Hexagonal grain elements are employed, and elliptical Wulff plots are used to assign surface energies to grain lattices. The mobility is set to vary in accordance with solutions to a generalized heat equation and is solved for two separate values of the mobility coefficient. Among other findings, the results reveal that like isotropic grain growth, under the influence of a thermal gradient, anisotropic grain growth also demonstrates locally normal growth kinetics.

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Figures

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Fig. 1

Plot of mobility versus x-position (using Eq. (7)) for mobility constants: α = 0.1 and α = 4.0 × 10−5

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Fig. 2

Hexagonal grain elements and definition of orientation angle (ϕ)

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Fig. 3

Elliptical (n = 2) Wulff plot with surface energy determination

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Fig. 4

Schematic illustrating the computation of the grain aspect ratio (A/B)

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Fig. 5

Lattice independent results, showing the convergence of average grain area for a resolution of N = 500 (isothermal, isotropic, Q = 60, t = 1000 MCS)

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Fig. 6

The slope of a straight fit through a plot of log R versus log (t) by least squares fitting provides an estimate for the inverse grain growth exponent (1/r). As shown, to a good approximation, the slope (0.49) is in agreement with the power-law prediction (isothermal, isotropic, Q = 60, t = 1000 MCS, N = 500).

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Fig. 7

The evolution of the CV at different simulation temperatures (isothermal, isotropic, N = 500, Q = 60, t = 1000 MCS)

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Fig. 8

Contours of anisotropic grain growth evolution (isothermal; anisotropic; Q = 60; t = 0 MCS, 100 MCS, 1000 MCS, 4000 MCS; N = 500). (a) t = 0 MCS; (b) t = 100 MCS; (c) t = 1000 MCS; (d) t = 4000 MCS.

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Fig. 9

Isotropic and anisotropic grain growth subject to a mobility gradient (α = 0.1, α = 4.0 × 10−5; anisotropic; Q = 60; t = 4000 MCS; N = 500). (a) Isotropic (α = 0.1); (b) isotropic (α = 4.0 × 10−5); (c) isotropic (α = 0.1); (d) isotropic (α = 4.0 × 10−5).

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Fig. 10

Average grain area (A) as a function of x-position showing the effect of a mobility gradient (α = 0.1; isotropic; t = 1000 MCS, t = 4000 MCS; Q = 60; N = 500; NDIV = 100)

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Fig. 11

Average grain area (A) as a function of x-position for isotropic/isothermal conditions (M = 1.0; t = 100 MCS, 500 MCS, 1000 MCS; Q = 60; N = 500; NDIV = 100)

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Fig. 12

Average grain area along the x-axis with changing mobility for both isotropic and anisotropic cases (t = 4000 MCS; Q = 60; N = 500; NDIV = 100); (a) isotropic and (b) anisotropic (see online figure for color)

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Fig. 13

Plot of the average AR as a function of position for both isotropic and anisotropic cases (α=0.1; t = 4000 MCS; Q = 60; N = 500; NDIV = 100)

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Fig. 14

Plot of orientation angle distribution for the anisotropic (n = 2) case pertaining to three different temperature profiles: isothermal, α = 0.1, and α = 4.0 × 10−5 (t = 4000 MCS; Q = 60; N = 500)

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