J. Mater. Sci. Technol. ›› 2020, Vol. 49: 91-105.DOI: 10.1016/j.jmst.2020.02.028
• Research Article • Previous Articles Next Articles
Cheng Gua, Colin D. Ridgewaya, Emre Cinkilica, Yan Lua, Alan A. Luoa,*()
Received:
2019-11-23
Revised:
2020-01-10
Accepted:
2020-01-20
Published:
2020-07-15
Online:
2020-07-17
Contact:
Alan A. Luo
Cheng Gu, Colin D. Ridgeway, Emre Cinkilic, Yan Lu, Alan A. Luo. Predicting gas and shrinkage porosity in solidification microstructure: A coupled three-dimensional cellular automaton model[J]. J. Mater. Sci. Technol., 2020, 49: 91-105.
Fig. 1. Schematic diagram of dendrite growth and pore formation: (a) 2-D microstructure of dendrite and porosity; (b) optical micrograph of an Al-Si alloy; and (c) 3-D pore morphology by X-ray micro computed tomography.
Parameter | Symbol | Units | Value | Ref. |
---|---|---|---|---|
Liquidus temperature of pure aluminum | TP | K | 933.5 | [ |
Liquidus slope of Si | $\frac{\partial T}{\partial C_{\text{Si}}^{L}}$ | K/(mass)% | -6.6 | [ |
Diffusion coefficient of Si in gradient Si in liquid | $D_{\text{Si}}^{L}$ | m2/s | 2.38E-9 | [ |
Diffusion coefficient of Si in gradient Si in solid | $D_{\text{Si}}^{S}$ | m2/s | 1.30E-12 | [ |
Partition coefficient of Si | kSi | \ | 0.117 | [ |
Diffusion coefficient of H in liquid | $D_{H}^{L}$ | m2/s | 3.8E-9×exp(-2315/T) | [ |
Diffusion coefficient of H in solid | $D_{H}^{S}$ | m2/s | 1.1E-5×exp(-4922/T) | [ |
Average Gibbs-Thomson coefficient | Γ | m·K | 1.7E-7 | [ |
Maximum dendrite nucleation density | Nmax | m-3 | 1E12 | \ |
Average nucleation undercooling | ΔTN | K | 5.0 | \ |
Deviation of nucleation undercooling | ΔTσ | K | 0.5 | \ |
Maximum pore nucleation density | $N_{H}^{\text{max}}$ | m-3 | 1E9 | \ |
Maximum pore nucleation saturation | $S_{H}^{\text{max}}$ | mL/100 g Al | 2.0 | \ |
Minimum pore nucleation saturation | $S_{H}^{\text{min}}$ | mL/100 g Al | 1.4 | \ |
Critical saturation criterion | $S_{H}^{N}$ | \ | 1.2 | \ |
Time step | t | s | 1E-4 | \ |
Table 1 Input Parameters Used in the Microstructure Simulation.
Parameter | Symbol | Units | Value | Ref. |
---|---|---|---|---|
Liquidus temperature of pure aluminum | TP | K | 933.5 | [ |
Liquidus slope of Si | $\frac{\partial T}{\partial C_{\text{Si}}^{L}}$ | K/(mass)% | -6.6 | [ |
Diffusion coefficient of Si in gradient Si in liquid | $D_{\text{Si}}^{L}$ | m2/s | 2.38E-9 | [ |
Diffusion coefficient of Si in gradient Si in solid | $D_{\text{Si}}^{S}$ | m2/s | 1.30E-12 | [ |
Partition coefficient of Si | kSi | \ | 0.117 | [ |
Diffusion coefficient of H in liquid | $D_{H}^{L}$ | m2/s | 3.8E-9×exp(-2315/T) | [ |
Diffusion coefficient of H in solid | $D_{H}^{S}$ | m2/s | 1.1E-5×exp(-4922/T) | [ |
Average Gibbs-Thomson coefficient | Γ | m·K | 1.7E-7 | [ |
Maximum dendrite nucleation density | Nmax | m-3 | 1E12 | \ |
Average nucleation undercooling | ΔTN | K | 5.0 | \ |
Deviation of nucleation undercooling | ΔTσ | K | 0.5 | \ |
Maximum pore nucleation density | $N_{H}^{\text{max}}$ | m-3 | 1E9 | \ |
Maximum pore nucleation saturation | $S_{H}^{\text{max}}$ | mL/100 g Al | 2.0 | \ |
Minimum pore nucleation saturation | $S_{H}^{\text{min}}$ | mL/100 g Al | 1.4 | \ |
Critical saturation criterion | $S_{H}^{N}$ | \ | 1.2 | \ |
Time step | t | s | 1E-4 | \ |
Point A | Point B | Point C |
---|---|---|
2.5 | 10.7 | 64.8 |
Table 2 Instantaneous cooling rate (K/s) at different locations A, B and C.
Point A | Point B | Point C |
---|---|---|
2.5 | 10.7 | 64.8 |
Fig. 3. Evolutions of pore morphology and hydrogen concentration field with an initial hydrogen concentration of 0.8 mL/100 g Al and a shrinkage pressure of 0.1 atm at different time: (a) 0.05 s; (b) 0.1 s; (c) 0.15 s; and (d) 0.25 s.
Fig. 4. Evolutions of pore morphology and hydrogen concentration field at 0.1 s with an initial hydrogen concentration of 0.8 mL/100 g Al and different shrinkage pressure of: (a) 0 atm; (b) 0.2 atm; (c) 0.5 atm; and (d) 1.0 atm.
Fig. 6. Simulated results of single dendrite and single pore morphologies: (a) with the cross-section of Si concentration at Y = 100 μm, t = 0.2 s; (b) with the cross-section of Si concentration at Y = 100 μm, t = 0.5 s; (c) Si concentration distribution along the line A-A shown in Fig. 6(a); (d) with the cross-section of hydrogen concentration at Y = 100 μm, t = 0.2 s; (e) with the cross-section of hydrogen concentration at Y = 100 μm, t = 0.5 s; and (f) hydrogen concentration distribution along the line A-A shown in Fig. 6(a).
Fig. 7. Simulated dendrite morphologies (a1, b1, c1, d1; dendrites are shown in color green), pore morphologies (a2, b2, c2, d2; pores are shown in color black), Si concentration field (a3, b3, c3, d3), and hydrogen concentration field (a4, b4, c4, d4) at different time and temperatures: (a) 0.2 s, 870 K (597 °C); (b) 0.3 s, 865 K (592 °C); (c) 0.4 s, 860 K (587 °C); (d) 0.6 s, 850 K (577 °C).
Fig. 8. Simulated results of porosity morphology, dendrite morphology and hydrogen concentration with different cooling rates: (a, d) 50 K/s; (b, e) 20 K/s; and (c, f) 5 K/s.
Fig. 11. Percentage of porosity as a function of time with (a) different shrinkage pressures of 0 atm, 0.5 atm, 1.0 atm, and 1.5 atm; (b) different initial hydrogen concentrations of 0.5 mL/100 g Al, 0.55 mL/100 g Al, and 0.6 mL/100 g Al.
Fig. 13. Porosity morphology of XMCT results: (a), (c), and (e); and CA simulated results: (b), (d), and (f). The cooling rates are: (a)-(b) 64.8 K/s; (c)-(d) 10.7 K/s; (e)-(f) 2.5 K/s.
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