Application of a Phase Field Model to Multicomponent Al-Cu-Si alloys

Bezerra, Bruna Norat; Ferreira, Diego José Sacramento; Ferreira, Alexandre Furtado; Garcia, Amauri; Ferreira, Ivaldo Leão

doi:10.1590/1980-5373-MR-2020-0198

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Articles • Mat. Res. 23 (4) • 2020 • https://doi.org/10.1590/1980-5373-MR-2020-0198 copy

Application of a Phase Field Model to Multicomponent Al-Cu-Si alloys

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The solidification of metals and alloys and the resulting microstructures, which as a function of thermal and solutal parameters can evolve as planar, cellular and dendritic, are important from a practical point of view, since they strongly influence the properties and quality of the final product. In many practical situations it is impracticable to develop analytical solutions permitting reliable predictions of microstructural growth during unsteady-state solidification conditions. The Phase Field method has become very popular and effective in modeling complex solid/liquid interfaces due to its ability to simulate the interface kinetics and the formation and evolution of different morphologies along the solidification process. In this work, a numerical analysis of the microstructural evolution during the transient solidification of dilute alloys of the Al-Cu-Si system is developed, which uses a phase-field approach for the simulation of ternary alloys. The phase-field, energy and solute concentration equations were numerically solved for the correspondent ternary system, varying the mesh parameters, temperature and alloy composition. The analysis performed were confronted with existing theoretical models and the results obtained are in agreement with the solidification theory.

Keywords:
Phase field method; Aluminum alloys; Multicomponent alloys; Microstructural development

Thermophysical Properties, symbol	Units	Value
Thermophysical Properties, symbol	Units	Al	Cu	Si
Partition coefficient, $k_{i}$			0.14	0.114
Slope of liquidus isotherm, $m_{i}$	$[K . m o l^{- 1}]$		724.63	678.81
Diffusion coefficient in the solid phase, $D_{S, i}$	$[m . s^{- 2}]$		8.43x10^-13	2.91x10^-12
Diffusion coefficient in the liquid phase, $D_{S, i}$	$[m . s^{- 2}]$		4.33x10^--09	2.46 x10^-09
Molar volume of the solvent, $\forall$	$[m^{3} . m o l^{- 1}]$	1.095x10^-5
Solvent melting temperature, $T_{m}$	$[K]$	933.15
Interface energy, $σ$	$[J . m o l^{- 2}]$	0.093

Parameter, symbol	Units	Value
Magnitude of anisotropy, $δ_{e}$		0.03
Phase field gradient energy, $ε_{0}$	${[J . m^{- 1}]}^{1 / 2}$	1.055x10^-3
Height of double-well potential, $W$	$[J . m^{- 3}]$	673.2x10³
Time step, $d t$	$[s]$	1.0x10^-8
Mesh size, $Δ x = Δ y$	$[m]$	1.0x10^-8
Noise amplitude, $a$		0.03

Property, symbol	Units	Values
Property, symbol	Units	Al-0.5Cu-0.5Si	Al-2.0Cu-0.1Si	Al-2.0-Cu-1.0Si	Al-4.0Cu-0.1Si
Density in the solid phase, $ρ_{S}$	$[k g . m^{- 3}]$	2646.76	2676.40	2673.07	2711.51
Density in the liquid phase, $ρ_{L}$	$[k g . m^{- 3}]$	2404.12	2424.12	2429.15	2460.0
Specific heat in the solid phase, $C_{P}$	$[J . k g^{- 1} K^{- 1}]$	1076.0	1069.0	1066.0	1056.0
Specific heat in the solid phase, $C_{L}$	$[J . k g^{- 1} K^{- 1}]$	1169.0	1156.0	1151.0	1136.0
Thermal conductivity in the solid, $k_{S}$	$[W . m^{- 1} K^{- 1}]$	192.5	193.35	192.6	193.6
Thermal conductivity in the liquid, $k_{L}$	$[W . m^{- 1} K^{- 1}]$	82.7	82.5	82.3	82.2
Latent heat, $Δ H$	$[J . k g^{- 1}]$	395500	366800	368500	349800

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