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Research Papers

Simulations of Anisotropic Texture Evolution on Paramagnetic and Diamagnetic Materials Subject to a Magnetic Field Using Q-State Monte Carlo

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

Information Technology Laboratory,
U.S. Army Engineer Research
and Development Center,
3909 Halls Ferry Road,
Vicksburg, MS 39180-6199
e-mail: Jeffrey.B.Allen@erdc.dren.mil

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 16, 2015; final manuscript received June 1, 2016; published online July 19, 2016. Assoc. Editor: Said Ahzi.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. Eng. Mater. Technol 138(4), 041012 (Jul 19, 2016) (9 pages) Paper No: MATS-15-1137; doi: 10.1115/1.4033908 History: Received June 16, 2015; Revised June 01, 2016

The present work incorporates a modified Q-state Monte Carlo (Potts) model to evaluate two-dimensional annealing of representative paramagnetic and diamagnetic polycrystalline materials in the presence of a magnetic field. Anisotropies in grain boundary energy, caused by differences in grain orientation (texturing), and the presence of an external magnetic field are examined in detail. In the former case, the Read–Shockley equations are used, in which grain boundary energies are computed using a low-angle misorientation approximation. In the latter case, magnetic anisotropy is simulated based on the relative orientation between the principal grain axis and the external magnetic field vector. Among other findings, the results of texture development subject to a magnetic field showed an increasing orientation distribution function (ODF) asymmetry over time, with higher intensities favoring the grains with principal axes most closely aligned with the magnetic field direction. The magnetic field also tended to increase the average grain size, which was accompanied by a corresponding decrease in the total grain boundary energy.

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Figures

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Fig. 1

Magnetic anisotropy between grains ρ1 and ρ2 promotes grain boundary mobility in the direction of the largest free energy; in this case toward grain ρ1

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Fig. 2

Magnetic field and c-axis vectors relative to the RD, TD, and ND

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Fig. 3

Results of grain size evolution showing the convergence of average grain area for a resolution of N = 500 (a) and the slope of a straight fit through a plot of log R versus log (t) (b). As shown in (b), to a good approximation, the slope (0.49) is in agreement with the power-law prediction (isotropic; t = 1000 MCS).

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Fig. 4

Grain growth contours at t = 0 and t = 200 MCS for WMF ((a) and (b)) and WOMF ((d) and (e)) representative hexagonal polycrystalline materials. Also shown is the WMF/WOMF evolution of average grain size (c) and total grain boundary energy(f).

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Fig. 5

WOMF/WMF misorientation angle distributions corresponding to case 1 at t = 200 MCS for representative (a) hexagonal and (b) cubic polycrystalline materials

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Fig. 6

WOMF/WMF Φ distributions corresponding to case 1 at t = 200 MCS for representative (a) hexagonal and (b) cubic polycrystalline materials

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Fig. 7

WOMF/WMF misorientation distributions corresponding to case 2 at t = 200 MCS for representative (a) hexagonal and (b) cubic polycrystalline materials

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Fig. 8

WOMF/WMF Φ distributions corresponding to case 2 at t = 200 MCS for representative hexagonal (a) and cubic (b) polycrystalline materials

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Fig. 9

(0002) pole density plots corresponding to case 3 at t = 100 MCS for representative WOMF/hexagonal ((a) and (b)) and WMF/hexagonal ((c) and (d)) polycrystalline materials

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Fig. 10

(001) pole density plots corresponding to case 3 at t = 100 MCS for representative WOMF/cubic ((a) and (b)) and WMF/cubic ((c) and (d)) polycrystalline materials

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Fig. 11

WMF (0002) pole density plots corresponding to case 3 at t = 100 MCS for representative hexagonal (a) and cubic (b) polycrystalline materials. Results show the effects of anisotropy on the (0002) pole density.

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