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J. Mater. Sci. Technol.  2020, Vol. 49 Issue (0): 91-105    DOI: 10.1016/j.jmst.2020.02.028
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Predicting gas and shrinkage porosity in solidification microstructure: A coupled three-dimensional cellular automaton model
Cheng Gua, Colin D. Ridgewaya, Emre Cinkilica, Yan Lua, Alan A. Luoa,*()
a Department of Materials Science and Engineering, The Ohio State University, Columbus, OH 43210, USA
b Department of Integrated Systems Engineering, The Ohio State University, Columbus, OH 43210, USA
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Abstract  

Porosity formation during solidification of aluminum-based alloys, due to hydrogen gas and alloy shrinkage, has been a major issue adversely affecting the performance of solidification products such as castings, welds or additively manufactured components. A three-dimensional cellular automaton (CA) model has been developed, for the first time, to couple the predictions of hydrogen-induced gas porosity and shrinkage porosity during solidification microstructure evolution of a binary Al-Si alloy. The CA simulation results are validated under various cooling rates by porosity measurements in an experimental wedge die casting using X-ray micro computed tomography (XMCT) technique. This validated porosity moel provides a critical link in integrated computation materials engineering (ICME) design and manufacturing of solidification products.

Key words:  Solidification      Cellular automaton      Microstructure simulation      Microporosity evolution     
Received:  23 November 2019     
Corresponding Authors:  Alan A. Luo     E-mail:  luo. 445@osu.edu

Cite this article: 

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. Mater. Sci. Technol., 2020, 49(0): 91-105.

URL: 

https://www.jmst.org/EN/10.1016/j.jmst.2020.02.028     OR     https://www.jmst.org/EN/Y2020/V49/I0/91

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 [43]
Liquidus slope of Si $\frac{\partial T}{\partial C_{\text{Si}}^{L}}$ K/(mass)% -6.6 [43]
Diffusion coefficient of Si in gradient Si in liquid $D_{\text{Si}}^{L}$ m2/s 2.38E-9 [26]
Diffusion coefficient of Si in gradient Si in solid $D_{\text{Si}}^{S}$ m2/s 1.30E-12 [26]
Partition coefficient of Si kSi \ 0.117 [32]
Diffusion coefficient of H in liquid $D_{H}^{L}$ m2/s 3.8E-9×exp(-2315/T) [13]
Diffusion coefficient of H in solid $D_{H}^{S}$ m2/s 1.1E-5×exp(-4922/T) [13]
Average Gibbs-Thomson coefficient Γ m·K 1.7E-7 [32]
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.
Fig. 2.  (a) Schematic of wedge die casting; (b) casting sample; and (c) a cross-section of the sample.
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.
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. 5.  Percentage of porosity as a function of time with different shrinkage pressures.
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. 9.  Percentage of porosity as a function of temperature with different cooling rates of 50 K/s, 20 K/s, and 5 K/s.
Fig. 10.  Simulated porosity with different shrinkage pressures: (a) 0 atm; (b) 1.0 atm; and (c) 1.5 atm.
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. 12.  Initial hydrogen concentration and shrinkage pressure as a function of macrocosmic solid fraction.
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.
Fig. 14.  Comparison of porosity percentage between experiment results and simulation results of hydrogen gas pore and coupled gas and shrinkage pore.
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