A Model Describing Solidification Microstructure Evolution in an Inoculated Aluminum Alloys

doi:10.1007/s40195-020-01154-5

Abstract

Abstract:

A population dynamics-cellular automaton (PD-CA) model is developed to describe the microstructure formation in an inoculated Al alloys. The model involves the dynamics behaviors of the inoculated particles and the nucleation, initial spherical growth of nuclei as well as the subsequent dendritic growth. The model was validated by using the experimental results for the Al-Cu alloys inoculated by Al-Ti-C refiner first, and then used to simulate the detailed solidification process in an inoculated Al-Cu alloy. The results indicate that the TiC is not stable in Al melt. The heterogeneous nucleation process consists of two stages: a very short initial stage dominated by the cooling rate and the later stage dominated by the number of the active TiC. It stops at the very moment the recalescence occurs. The average grains size d of the aluminum alloys inoculated by the Al-Ti-C refiner can be calculated by $d(\mu{\text{m}}) = \frac{{a \cdot \exp (t/60 \cdot \ln (C_{ 0} /w))}}{{(\nu_{\text{cool}} \cdot t)^{1/3} w^{1/3} }} + \frac{b \cdot \ln t}{{Q \cdot v_{\text{cool}}^{1/2} }}$ where Q is the growth restriction factor, C₀ (%) is the initial solutes composition, w (%) is the additive amount of Al-Ti-C refiner. t (min) is the holding temperature time since the Al-Ti-C refiner is added into the melt. a and b are the constants.

Key words: Grain refinement, Nucleation, Dendritic growth, Simulation, Solidification

Yan Song, Hongxiang Jiang, Lili Zhang, Shixin Li, Jiuzhou Zhao, Jie He. A Model Describing Solidification Microstructure Evolution in an Inoculated Aluminum Alloys[J]. Acta Metallurgica Sinica (English Letters), 2021, 34(6): 861-871.

Figures/Tables 12

Fig. 1 Measured and fitted radius RTiC distributions of the TiC in the Al-5Ti-0.5C

Fig. 2 Schematic of the cylindrical iron mold and the position of the thermal couples

Fig. 3 Measured and calculated cooling curves of the Al-1.0Cu melt during solidification

Fig. 4 Measured and predicted grain sizes of the inoculated Al-1.0Cu alloy vs a the additive amount of Al-5Ti-0.5C for a given HTT of 10 min at 993 K and b the HTT at 993 K for a given refiner addition lever of 0.4%. The error bars represent standard deviations

Table 1 Thermo-physical parameters used in the calculations

Parameter	Value
Diffusion coefficient of solute Cu in Al melt, D^Cu (m²/s)	4.65 × 10^-9 [12]
Diffusion coefficient of solute Ti in Al melt, D^Ti (m²/s)	2.52 × 10^-9 [9]
Interfacial energy between the TiC and liquid Al, σ_mTiC (J/m²)	0.72 [33]
Interfacial energy between the α-Al and liquid Al, σ_mα-Al (J/m²)	0.158 [9]
Strength of the anisotropy of the interfacial energy, ε	0.04 [26]
Partion coefficient for Al-Cu alloys, k_0,Cu	0.14 [35]
Liquidus slope for Al-Cu alloys, m_l,Cu	- 2.6 [35]
Partion coefficient for Al-Ti alloys, k_0,Ti	25.63 [9]
Liquidus slope for Al-Ti alloys, m_l,Ti	7 [9]
Gibbs-Thomson coefficient for Al-Cu alloys, $\bar{\varGamma }$(mk)	2.4 × 10^-7 [35]
Heat capacity of Al melt, C_P (J/K·m³)	2.58 × 10⁶ [2]

Fig. 5 Solidification microstructure evolution of the Al-1.0Cu inoculated by 0.1% Al-5Ti-0.5C. The number density (NTiC) and average radius (<?RTiC?>) of TiC as a function of time; Nall is the total number density of α-Al nuclei, Ndendrities is the number density of the α-Al nuclei with dendritic morphology, Nspherical is the number density of the spherical α-Al nuclei

Fig. 6 Radius RTiC distribution of the TiC particles in the Al-1.0Cu melt inoculated by 0.1% Al-5Ti-0.5C at different holding temperature time at 993 K

Fig. 7 Undercooling ?T of the melt and nucleation rate Iα-Al of α-Al during cooling the Al-1.0Cu melt inoculated by 0.1% Al-5Ti-0.5C. The HTT at 993 K is 10 min

Fig. 8 Simulated solidification microstructure evolution of the Al-1.0Cu inoculated by 0.1% Al-5Ti-0.5C. a fs?=?0.1%, b fs?=?0.8%, c fs?=?22.0%, d fs?=?90.0%. The size of computational domain is 600 μm?×?600 μm?×?600 μm

Fig. 9 Solidification microstructures of the Al-1.0Cu with 10 min HTT at 993 K. The additive amount of Al-5Ti-0.5C is a, d 0.05%, b, e 0.2% and c, f 1.2%. a-c are the simulation results, d-f are the experimental results

Fig. 10 Solidification microstructures of the Al-1.0Cu inoculated by 0.4% Al-5Ti-0.5C. The HTT at 993 K is a, d 20 min, b, e 40 min, and c, f 60 min. a-c are the simulation results, d-f are the experimental results

Fig. 11 Grain size vs the HTT for the Al-4.5Cu inoculated by Al-24Ti-6C solidified at the cooling rate of 100 K/s. The experimental results are from Ref. [38]

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