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Acta Metall Sin  2015, Vol. 51 Issue (6): 733-744    DOI: 10.11900/0412.1961.2014.00560
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NUCLEATION MODEL AND DENDRITE GROWTH SIMULATION IN SOLIDIFICATON PROCESS OF Al-7Si-Mg ALLOY
Rui CHEN1,Qingyan XU1(),Qinfang WU2,Huiting GUO2,Baicheng LIU1
1 Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing 100084
2 Mingzhi Technology Co. Limited, Suzhou 215006
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Abstract  

Due to the extensive applications in automotive and aerospace industries of Al-7Si-Mg casting alloys, its understanding of the dendrite microstructural formation is of great importance to control the desirable microstructure and thereby to modify the performance of castings. In this work, through analyzing the measured cooling curves in different cooling conditions of Al-7Si-0.36Mg ternary alloy during sand casting, a theoretical nucleation model correlated maximum nucleation undercooling with the nucleation density is proposed. Besides, a 2D and 3D cellular automaton (CA) model allowing for the quantitatively predicting dendrite growth of ternary alloys is presented. This model introduces a new tracking neighboring rule algorithm to eliminate the effect of mesh dependency on dendrite growth. The thermodynamic and kinetic data needed in the simulations is obtained by coupling with Pandat software package in combination with thermodynamic/kinetic/equilibrium phase diagram calculation databases. This model has also taken account the multi-component diffusion, constitutional undercooling, curvature undercooling, dendrite preferential growth angles as well as the effect of interactions between the alloying elements etc. This model is applied to quantitatively simulate the dendrite growth with various crystallographic orientations of Al-7Si-0.36Mg ternary alloy in 2D and 3D during polycrystalline solidification, and the predicted secondary dendrite arm spacing (SDAS) shows a reasonable agreement with the experimental results. The experimental observed complicated and diverse dendrite microstructure occurring in solidification process can be well reproduced by this 3D-CA model which has considered the effects of various preferred growth orientations, the interactions of adjacent dendrites as well as the influence of S/L interface anisotropies. The simulated results effectively demonstrated the abilities of this model in prediction of dendrite microstructure in ternary alloys.

Key words:  ternary aluminum alloy      nucleation model      cellular automaton      dendrite growth      secondary dendrite arm spacing     
Fund: Supported by National Basic Research Program of China (No.2011CB706801), National Natural Science Foundation of China (Nos.51374137 and 51171089) and National Science and Technology Major Projects (Nos. 2012ZX04012-011 and 2011ZX04014-052)

Cite this article: 

Rui CHEN, Qingyan XU, Qinfang WU, Huiting GUO, Baicheng LIU. NUCLEATION MODEL AND DENDRITE GROWTH SIMULATION IN SOLIDIFICATON PROCESS OF Al-7Si-Mg ALLOY. Acta Metall Sin, 2015, 51(6): 733-744.

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2014.00560     OR     https://www.ams.org.cn/EN/Y2015/V51/I6/733

Fig.1  Schematic of active circular nucleant surface of TiB2 (a) and the growth of a-Al phase from such a nucleant site with a diameter of dN (b) (L and S represent liquid and solid phases, respectively. h is the height of the nucleus on the nucleant site)
Fig.2  
Fig.3  Schematic of the various growth orientations of different grains (a), and the location relationship between the local coordinate system (x0, y0, z0) and the world coordinate system (x, y, z) (b) (a, b, g are the three Euler angles used to determine the relationship between (x0, y0, z0) and (x, y, z))
Fig.4  Schematic of dimensions of the step shape casting used to study the effects of cooling rate (unit: mm)
Fig.5  Cooling curves of different steps (No.1~No.7) with various thicknesses of Al-7Si-0.36Mg alloy sample casting ( Inset show the enlarged view of the nucleation interval on the cooling curves)
Fig.6  OM images under polarized light showing the dendrite microstructure and grain size corresponding to the positions of No.1 (a), No.2 (b), No.3 (c), No.4 (d), No.5 (e), No.6 (f) and No.7 (g) (No.1~No.6: diameter 8 mm, No.7: diameter 6 mm)
No. Tmin / ℃ ΔTm / ℃ Te / ℃ Δt / s Rc / (℃?s-1) NS / cm-2 NV / cm-3 l2 / mm
1 611.3 3.3 565.6 257.0 0.18 54.2 226.6 70.1
2 611.0 3.6 563.1 208.0 0.23 64.1 291.5 66.8
3 610.2 4.4 562.0 134.0 0.36 80.2 407.9 60.7
4 608.8 5.8 560.8 83.0 0.58 101.6 581.6 53.2
5 606.0 8.6 559.8 50.0 0.92 135.6 896.8 43.0
6 604.1 10.6 558.7 30.0 1.51 172.1 1282.3 36.7
7 595.0 19.6 557.0 7.5 5.00 418.2 4854.3 24.9
Table 1  Experimental measured of solidification parameters and microstructure data for Al-7Si-0.36Mg alloy
Fig.7  Linear relationship between grain density lnNV and maximum nucleation undercooling ΔTm-1 in the Al-7Si-0.36Mg alloy
Fig.8  Evolution of simulated dendrite morphologies and the distributions of Si solute solidified at the position of No.6 for solidification time t=5.5 s (a), 9.7 s (b) and 20.1 s (c)
Definition and symbol Value Unit
Initial compositions, w S i 0 , w M g 0 w S i 0 =7.0, w M g 0 =0.36 %
Liquidus temperature, T L l i q ( w S i L , w M g L ) Calculated K
Liquidus slope, m S i L , m M g L Calculated K%-1
Partition coefficient, k S i , k M g Calculated
Gibbs-Thomson coefficient, G 2.4×10-7 K m
Anisotropy coefficient, e 0.03
Diffusion coefficient, D i j ? Calculated m2s-1
Timestep, dt Δ x 2 / 6 m a x ( D i j ? ) s
Table 2  Parameters of Al-7Si-0.36Mg alloy used in the simulations
Fig.9  Simulated final dendrite microstructures of the positions No.2 (a), No.4 (b), No.6 (c) and No.7 (d) (Different colors represent different dendrites)
Fig.10  Comparison between the predicted secondary dendrite arm spacing and the experimental ones solidified in different cooling conditions
Fig.11  Simulated evolution of multi-equiaxed dendrites for Al-7Si-0.36Mg alloy solidified at the position of No.7 (fs—solid fraction)
Fig.12  Simulated final dendrite morphologies on arbitrarily two dimensional sections (a) and the obtained experimental metallographic microstructure solidified at the position of No.7 (b)
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