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Research Papers

Fourier Spectral Phase Field Simulations of Elastically Anisotropic Heterogeneous Polycrystals

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

Information Technology Laboratory,
U.S. Army Engineer Research and
Development Center,
Vicksburg, MS 39180;
Department of Mechanical and
Aerospace Engineering,
Utah State University,
Logan, UT 84322
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 30, 2017; final manuscript received April 4, 2018; published online May 7, 2018. Assoc. Editor: Vikas Tomar.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 140(4), 041003 (May 07, 2018) (8 pages) Paper No: MATS-17-1185; doi: 10.1115/1.4039896 History: Received June 30, 2017; Revised April 04, 2018

In this study, we developed a multi-order, phase field model to compute the stress distributions in anisotropically elastic, inhomogeneous polycrystals and study stress-driven grain boundary migration. In particular, we included elastic contributions to the total free energy density and solved the multicomponent, nonconserved Allen–Cahn equations via the semi-implicit Fourier spectral method. Our analysis included specific cases related to bicrystalline planar and curved systems as well as polycrystalline systems with grain orientation and applied strain conditions. The evolution of the grain boundary confirmed the strong dependencies between grain orientation and applied strain conditions and the localized stresses were found to be maximum within grain boundary triple junctions.

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Figures

Grahic Jump Location
Fig. 1

Time evolution showing shrinkage of a circular grain: (a) t=0, R0=20.0Δx; (b) t=150, R0=10.0Δx; and (c) evolution of the area fraction of grain 1 and grain 2

Grahic Jump Location
Fig. 2

Time evolution of polycrystalline boundary layer evolution, ηϕ, (ϕ0=25) under normal, curvature driven grain growth; topology evolution at (a) t = 0, (b) t = 150, and (c) evolution of the average grain size showing good agreement with the power law prediction

Grahic Jump Location
Fig. 3

Planar bi-crystal boundary layer evolution of two grains with differing orientations at (a) time t = 0, (b) time t = 700, and (c) axial stress (σ22) along Y=N/2 and at various time steps (t=0…700)

Grahic Jump Location
Fig. 4

Curved bicrystal boundary layer evolution of two grains with differing orientations and applied strains; axial (σ22) and shear (σ12) stress components shown for Y=N/2: (a) ε11a=ε22a=0.02, t=0; (b) ε11a=ε22a=0.02,t=400; (c) axial stress (σ22), ε11a=ε22a=0.02; (d) ε22a=0.02, t=0; (e) ε22a=0.02, t=300; (f) axial stress (σ22), ε22a=0.02; (g) ε12a=0.02, t=0; (h) ε12a=0.02, t=700; and (i) shear stress (σ12), ε22a=0.02

Grahic Jump Location
Fig. 5

Polycrystalline boundary layer evolution, ηϕ, (ϕ0=25) subject to applied axial (ε11a,ε22a), and shear (ε12a) strains: (a) ε22a=0.02, t=0; (b) ε22a=0.02, t=500, (c) ε22a=0.02, t=1000; (d) ε22a=0.02, t=1000; (e) ε12a=0.02, t=1000; and (f) ε11a=ε22a=0.02,t=1000

Grahic Jump Location
Fig. 6

Localized stress components subject to applied axial (ε11a,ε22a) and shear (ε12a) strains; t = 1000 in all cases: (a) axial stress (σ22), (ε22a=0.02); (b) axial stress (σ11), (ε22a=0.02); (c) shear stress (σ12), (ε22a=0.02); (d) stress components (ε22a=0.02); and (e) axial stress (σ22) (ε22a=0.02;ε12a=0.02;ε11a,ε22a=0.02)

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