Simulation of the Dendrite Morphology and Microsegregation in Solidification of Al-Cu-Mg Aluminum Alloys

doi:10.1007/s40195-014-0183-7

Abstract

Abstract:

Since most typical alloys in industrial applications are multicomponent with three or more components, and various CA models proposed in the past mainly focus on the binary alloys, a two-dimensional modified cellular automaton model allowing for the quantitatively predicting dendrite growth of multicomponent alloys in the low Péclet number regime is presented. The elimination of the mesh-induced anisotropy is achieved by adopting a modified virtual front tracking method. A new efficient method based on the lever rule is applied to calculate the solid fraction increment of the interfacial cells. The thermodynamic data such as liquidus temperature, the partition coefficients, and the slope of liquidus surface, needed for determining the dynamics of dendrite growth, are obtained by coupling with PanEngine. This model is applied to simulate the dendrite morphology and microsegregation of Al-Cu-Mg ternary alloy both for single and multi-dendrites growth. The simulated results demonstrate that the difference of the concentration distribution profiles ahead of the dendrite tip for each alloying element mainly results from the different partition coefficients and solute diffusion coefficients. Comparison with the prediction of analytical model is carried out and it reveals the correctness of the model. Consequently, the difference in interdendritic microsegregation behavior of different components is analyzed.

Key words: Cellular automaton, Multicomponent, Dendrite growth, Microsegregation

Rui Chen, Qing-Yan Xu, Bai-Cheng Liu. Simulation of the Dendrite Morphology and Microsegregation in Solidification of Al-Cu-Mg Aluminum Alloys[J]. Acta Metallurgica Sinica (English Letters), 2015, 28(2): 173-181.

Figures/Tables 9

Fig. 1 a Schematic of the virtual front-tracking scheme, b illustration of its capturing rules for new interfacial cells

Table 1 Properties of Al-Cu-Mg alloy used in the following simulations

Properties and symbol	Al-4 wt%Cu-1 wt%Mg	Ref.
Initial compositions \( w_{i}^{0} \) (wt%)	\( w_{\text{Cu}}^{0} \) = 4.0 \( w_{\text{Mg}}^{0} \) = 1.0
Liquidus temperature \( T_{\text{L}}^{\text{liq}} (w_{i}^{0} ) \) (K)	918.2
Solute diffusion coefficient \( D_{i}^{u} \) (m²·s^-1)	\( D_{\text{Cu}}^{\text{L}} = 1.05 \times 10^{ - 7} e^{( - 2856/T)} \)	^[18]
	\( D_{\text{Mg}}^{\text{L}} = 9.9 \times 10^{ - 5} e^{( - 8610/T)} \)	^[18]
	\( D_{\text{Cu}}^{\text{S}} { = 4} . 8\times 1 0^{ - 5} e^{{ ( { - 16069/}T)}} \)	^[18]
	\( D_{\text{Mg}}^{\text{S}} = 6.23 \times 10^{ - 4} e^{( - 13813/T)} \)	^[18]
Gibbs-Thomson coefficient Γ (K·m)	2.4 × 10^-7
Anisotropy coefficient \( \varepsilon \)	0.04
Latent heat of fusion L (J m^-3 K^-1)	9.5 × 10⁸	^[18]
Density ρ (kg m^-3)	2,600
Specific heat c _p (J kg^-1 K^-1)	1,070
Time step δt (s)	Δx ²/4.5max (\( D_{\text{Cu}}^{\text{L}} ,\;D_{\text{Mg}}^{\text{L}} \))

Fig. 2 Predicted dendrite morphologies and Cu concentration a, Mg concentration b fields for Al-4 wt%Cu-1 wt%Mg alloy

Fig. 3 Concentration profiles along the lines L1 and L2 indicated in Fig. 2a, b after solidification time of 0.15, 0.3, 0.45, 0.6 s. L1 for Cu concentration and L2 for Mg concentration

Fig. 4 The solid fraction evolution of primary phase with the temperature for Al-4 wt%Cu-1 wt%Mg alloy calculated by Lever rule, Scheil model as well as the present model with different heat extraction rates

Fig. 5 Simulated dendrite morphologies and the solute fields of Cu a, c, Mg b, d for Al-4 wt%Cu-1 wt%Mg alloy with a heat extraction rate H = 52 MW/m3: a, b \( D_{\text{Mg}}^{\text{S}} \) = 0, \( D_{\text{Cu}}^{\text{S}} \) = 0, c, d \( D_{\text{Mg}}^{\text{S}} \ne \) 0, \( D_{\text{Cu}}^{\text{S}} \ne \) 0. The red color region in the images represents the eutectic region

Fig. 6 Simulated average concentration of Mg in the solid as a function of solid fraction under different cooling conditions. N in the figure represents no solid diffusion taking into consideration while Y represents with solid diffusion

Fig. 7 Magnification of the region indicated by the dashed line in Fig. 6d: a, b, c, d illustrates the dendrite morphologies and concentration fields of Mg at solidification time of 2.5, 3.2, 5.5, 6.1 s, respectively

Fig. 8 Illustration of the differences of solute enrichment of Cu a, Mg b elements in the interdendritic regions as a function of solidification time. Positions of P1, P2, P3 points are indicated in Fig. 7d

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