Modeling of gas porosity and microstructure formation during dendritic and eutectic solidification of ternary Al-Si-Mg alloys

doi:10.1016/j.jmst.2020.11.008

Abstract

Abstract:

A two-dimensional (2-D) multi-component and multi-phase cellular automaton (CA) model coupled with the Calphad method and finite difference method (FDM) is proposed to simulate the gas pore formation and microstructures in solidification process of hypoeutectic Al-Si-Mg alloys. In this model, the pore growth, and dendritic and eutectic solidification are simulated using a CA technique. To achieve the equilibrium among multiple phases during ternary Al-based alloy solidification, the phase transition thermodynamics and kinetics are evaluated by adopting the Calphad method. The diffusion equations of hydrogen and two solutes are solved by FDM. The developed CA-FDM coupled model can be used for simulating the evolution of gas microporosity and microstructures, involving dendrites and irregular binary and ternary eutectics, of ternary hypoeutectic Al-Si-Mg alloys. It has the capability of reproducing the interactions between the hydrogen microporosity formation and the growth of dendrites and eutectics, the competitive growth among the growing gas pores of different sizes, together with the time-evolving concentration fields of hydrogen and solutes. The simulated morphology of gas pore and microstructure has a good agreement with the experimental observation. The influences of the initial hydrogen concentration and cooling rate on the microporosity formation are investigated. It is found that the main portion of porosity formation occurs in the eutectic solidification stage through analyzing the profiles of porosity percentage and solid fraction varying with solidification time. The varying features of simulated porosity percentage, the maximum and average pores radii indicate that increasing initial hydrogen concentration promotes the formation of higher final porosity percentage and larger pores, while the size of gas pores will significantly reduce with increasing cooling rate, leading to a lower final porosity percentage.

Key words: Porosity, Solidification microstructures, Ternary Al-Si based alloys, Diffusion, Cellular automaton

Mengdan Hu, Taotao Wang, Hui Fang, Mingfang Zhu. Modeling of gas porosity and microstructure formation during dendritic and eutectic solidification of ternary Al-Si-Mg alloys[J]. J. Mater. Sci. Technol., 2021, 76: 76-85.

Figures/Tables 8

Table 1 Physical parameters used in the simulations for Al-Si-Mg alloys.

Symbol	Definition and units	Value	References
R	Ideal gas constant (J/(mol K))	8.314	[23]
D_l(H)	Diffusion coefficient of H in liquid (m²/s)	3.8 × 10^-6exp (-19247/RT)	[29]
D_s(H)	Diffusion coefficient of H in solid (m²/s)	1.1 × 10^-5exp (-40922/RT)	[29]
D_l(Si)	Diffusion coefficient of Si in liquid (m²/s)	1.1 × 10^-5exp (-47357/RT)	[40]
D_s(Si)	Diffusion coefficient of Si in solid (m²/s)	2.02 × 10^-4exp (-133598/RT)	[40]
D_l(Mg)	Diffusion coefficient of Mg in liquid (m²/s)	9.9 × 10^-5exp (-71584/RT)	[40]
D_s(Mg)	Diffusion coefficient of Mg in solid (m²/s)	6.23 × 10^-6exp (-114991/RT)	[40]
$\bar{\Gamma}$	Average Gibbs-Thomson coefficient (m K)	1.7 × 10^-7	[26,29,40]
k_H	Partition coefficient of H	0.069	[17,29]
λ_LG	Surface energy at G/L interface (J m^-2)	0.889	[29]
ε	Degree of surface energy anisotropy of the α-phase	0.03	estimated
δ_α	Degree of kinetic anisotropy of the α-phase	0.4	estimated
δ_β	Degree of kinetic anisotropy of the β-phase	0.8	estimated
δ_γ	Degree of kinetic anisotropy of the γ-phase	0.8	estimated
$\bar{\mu}_{\alpha}$	Average interface kinetic coefficient of the α-phase (m/(s K))	7 × 10^-4	estimated
$\bar{\mu}_{\beta}$	Average interface kinetic coefficient of the β-phase (m/(s K))	6 × 10^-6	estimated
$\bar{\mu}_{\gamma}$	Average interface kinetic coefficient of the γ-phase (m/(s K))	6 × 10^-6	estimated
C_β(Si)	Si concentration in the β-phase (wt.%)	99.99	[40]
C_γ(Si)	Si concentration in the γ-phase (wt.%)	36.6	[40]
C_γ(Mg)	Mg concentration in the γ-phase (wt.%)	63.4	[40]

Fig. 1. Simulated evolution of gas porosity, columnar dendrites, and eutectics during directional solidification of an Al-7 wt.% Si-0.4 wt.% Mg alloy, shown in the concentration fields of (a, b) hydrogen, (c, d) Mg and (e) Si: (a, b) primary dendrite growth and coarsening; (c, d) eutectic growth; (e) final microstructure; (f) experimental micrograph [8]. The numbers in the figures indicate the local (a, b) hydrogen and (c, d) Mg concentrations in melt.

Fig. 2. Simulated evolution of gas porosity, equiaxed dendrites, and eutectics of an Al-7 wt.% Si-1 wt.% Mg alloy, shown in the concentration fields of (a-c) hydrogen, (d, e) Mg and (f) Si: (a) T = 600.9 °C, Fs = 21 %, Fg = 0.0 %; (b) T = 583.1 °C, Fs = 40 %, Fg = 0.7 %; (c) T = 569.6 °C, Fs = 48.8 %, Fg = 1.4 %; (d) T = 564.8 °C, Fs = 69 %, Fg = 1.6 %; (e, f) T = 554.9 °C, Fs = 97.7 %, Fg = 2.4 %; The numbers in the figures indicate the local (a-c) hydrogen and (d, e) Mg concentrations in melt. T, Fs, and Fg are the temperature, total solid fraction and porosity percentage in the simulation domain, respectively.

Fig. 3. Simulated profiles of solid fraction and porosity percentage versus temperature in the case of Fig. 2. Areas I and II represent the primary dendrite and irregular eutectic solidification stages, respectively.

Fig. 4. Simulated evolution of gas porosity, equiaxed dendrites, and eutectics of an Al-7 wt.% Si-0.4 wt.% Mg alloy with different initial hydrogen concentrations (H0) of (a1, a2, a3) H0 = 0.3 mol/m3, (b1, b2, b3) H0 = 0.45 mol/m3, (c1, c2, c3) H0 = 0.6 mol/m3 at (a1, b1, c1) T =606 °C (shown in Mg concentration field), (a2, b2, c2) T =574 °C (shown in hydrogen concentration field), and (a3, b3, c3) T =557 °C (the final microstructures shown in Si concentration field): (a1) Fg = 0.0 %; (b1) Fg = 0.0 %; (c1) Fg = 0.1 %; (a2) Fg = 0.1 %; (b2) Fg = 0.9 %; (c2) Fg = 2.0 %; (a3) Fg = 1.3 %; (b3) Fg = 2.2 %; (c3) Fg = 3.3 %. The numbers in the figures indicate the local concentrations of (a1, b1, c1) Mg and (a2, b2, c2) hydrogen in the liquid and solid phases, respectively. T and Fg are the temperature and total porosity percentage in the domain, respectively.

Fig. 5. Comparison of the simulated percentage of porosity versus temperature under different initial hydrogen concentrations in the cases of Fig. 4. Areas I and II represent the primary dendrite and irregular eutectic solidification stages, respectively.

Fig. 6. Simulated final percentage of porosity versus initial hydrogen concentration in the solidified Al-7 wt.% Si-0.4 wt.% Mg alloy under the cooling rates of 3 °C/s and 12 °C/s.

Fig. 7. Simulated (a) maximum pore radius and (b) average pore radius versus initial hydrogen concentration in the solidified Al-7 wt.% Si-0.4 wt.% Mg alloy under the cooling rates of 3 °C/s and 12 °C/s.

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