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Research Papers

Phase-Field Microstructure Solidification of Al–2 wt% Si Alloys

[+] 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 December 18, 2018; final manuscript received June 25, 2019; published online August 2, 2019. Assoc. Editor: Curt Bronkhorst.

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 142(1), (Aug 02, 2019) (7 pages) Paper No: MATS-18-1330; doi: 10.1115/1.4044280 History: Received December 18, 2018; Accepted July 10, 2019

In this work, we develop one- and two-dimensional phase-field simulations to approximate dendritic growth of a binary Al–2 wt% Si alloy. Simulations are performed for both isothermal as well as directional solidification. Anisotropic interface energies are included with fourfold symmetries, and the dilute alloy assumption is imposed. The isothermal results confirm the decrease in the maximum concentration for larger interface velocities as well as reveal the presence of parabolic, dendrite tips evolving along directions of maximum interface energy. The directional solidification results further confirm the formation of distinctive secondary dendritic arm structures that evolve at regular intervals along the unstable solid/liquid interface.

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Figures

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Fig. 1

Computational domain showing the direction of heat flow and imposed boundary conditions

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Fig. 2

Steady-state interfacial concentration and phase-field profiles as a function of grid number for T = 870 K

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Fig. 3

Interfacial concentration showing the effect of variable interface velocity

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Fig. 4

Isothermal PFM contours of phase-field and concentration: (a) and (b) contrasting isotropic interfacial energies and (c) and (d) anisotropic energies. (a) Phase field (ϕ); isotropic (ε(θ)=ε¯); ∅-Noise (α = 0.0). (b) Concentration field (c); isotropic (ε(θ)=ε¯); ∅-Noise (α = 0.0). (c) Phase field (ϕ); anisotropic (γ = 0.05); noise (α = 0.01). (d) Concentration field (c); anisotropic (γ = 0.05); noise (α = 0.01).

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Fig. 5

Evolutionary contours of the phase field (ϕ) for Al–2 wt% Si comparing the resulting microstructure for two different temperature gradients (VP = 100.0 μm/s): (a) G = 80 × 104 K/m; t = 0.5 s, (b) G = 80 × 104 K/m; t = 1.0 s, (c) G = 80 × 104 K/m; t = 2.0 s, (d) G = 120 × 104 K/m; t = 0.5 s, (e) G = 120 × 104 K/m; t = 1.0 s, and (f) G = 120 × 104 K/m; t = 2.0 s

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Fig. 6

SDAS as a function of solidification time, showing the cube root dependency and agreement with theoretical values [30]

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