J. Mater. Sci. Technol. ›› 2020, Vol. 49: 15-24.DOI: 10.1016/j.jmst.2020.01.047
• Research Article • Previous Articles Next Articles
Wonjoo Leea, Yuhyeong Jeonga, Jae-Wook Leeb, Howon Leeb, Seong-hoon Kangb, Young-Min Kimb, Jonghun Yoonc,*()
Received:
2019-10-24
Revised:
2019-12-11
Accepted:
2020-01-15
Published:
2020-07-15
Online:
2020-07-17
Contact:
Jonghun Yoon
Wonjoo Lee, Yuhyeong Jeong, Jae-Wook Lee, Howon Lee, Seong-hoon Kang, Young-Min Kim, Jonghun Yoon. Numerical simulation for dendrite growth in directional solidification using LBM-CA (cellular automata) coupled method[J]. J. Mater. Sci. Technol., 2020, 49: 15-24.
Property and symbol | Value | Units |
---|---|---|
Density, ρ | 2.475×103 | kg m-3 |
Solute diffusivity in liquid, Dl | 3×10-9 | m2 s-1 |
Gibbs-Thomson coefficient, Γ | 2.4×10-7 | mK |
Partition coefficient, k0 | 0.17 | |
Liquidus slope, mL | -2.6 | K wt%-1 |
Liquidus temperature, Teq | 921.15 | K |
Initial composition, C0 | 4 | wt% |
Anisotropy coefficient, ε | 0.0267 |
Table 1 Material properties of Al-4 wt% Cu alloy [35].
Property and symbol | Value | Units |
---|---|---|
Density, ρ | 2.475×103 | kg m-3 |
Solute diffusivity in liquid, Dl | 3×10-9 | m2 s-1 |
Gibbs-Thomson coefficient, Γ | 2.4×10-7 | mK |
Partition coefficient, k0 | 0.17 | |
Liquidus slope, mL | -2.6 | K wt%-1 |
Liquidus temperature, Teq | 921.15 | K |
Initial composition, C0 | 4 | wt% |
Anisotropy coefficient, ε | 0.0267 |
Fig. 3. Schematic representation of each phases based on cell structure in CA analysis: (a) single solid cell surrounded by interface cells, (b) growth of solid and interface cells.
Fig. 4. Comparison between LGK analytic solution and LBM-CA prediction in terms of dendrite tip velocity and radius: (a) dendrite tip velocity, (b) dendrite tip radius.
Property and symbol | Value | Units |
---|---|---|
Density, ρ | 7.020×103 | kg m-3 |
Solute diffusivity in liquid, Dl | 6.36×10-9 | m2 s-1 |
Gibbs-Thomson coefficient, Γ | 1.9×10-7 | mK |
Partition coefficient, k0 | 0.34 | |
Liquidus slope, mL | -78.0 | K wt%-1 |
Liquidus temperature, Teq | 1809 | K |
Initial composition, C0 | 0.82 | wt% |
Anisotropy coefficient, ε | 0.04 | |
Viscosity, μ | 5.5×10-3 | kg m-1 s-1 |
Table 2 Material properties of Fe-0.82 wt% C alloy [52].
Property and symbol | Value | Units |
---|---|---|
Density, ρ | 7.020×103 | kg m-3 |
Solute diffusivity in liquid, Dl | 6.36×10-9 | m2 s-1 |
Gibbs-Thomson coefficient, Γ | 1.9×10-7 | mK |
Partition coefficient, k0 | 0.34 | |
Liquidus slope, mL | -78.0 | K wt%-1 |
Liquidus temperature, Teq | 1809 | K |
Initial composition, C0 | 0.82 | wt% |
Anisotropy coefficient, ε | 0.04 | |
Viscosity, μ | 5.5×10-3 | kg m-1 s-1 |
Elements | Cr | Al | Ti | Ta | W | Mo | Zr | Hf | Co | Ni |
---|---|---|---|---|---|---|---|---|---|---|
wt.% | 7.94 | 5.22 | 0.67 | 3.07 | 9.07 | 0.60 | 0.02 | 1.23 | 9.21 | Bal. |
Table 3 Chemical composition of the Ni-based superalloy.
Elements | Cr | Al | Ti | Ta | W | Mo | Zr | Hf | Co | Ni |
---|---|---|---|---|---|---|---|---|---|---|
wt.% | 7.94 | 5.22 | 0.67 | 3.07 | 9.07 | 0.60 | 0.02 | 1.23 | 9.21 | Bal. |
Property and symbol | Value | Units |
---|---|---|
Maximum density, nmax | 5.0×107 | m-3 |
Standard deviation, ΔTσ | 0.1 | K |
Mean undercooling, ΔTm | 10 | K |
Table 4 Nucleation parameters for numerical simulations.
Property and symbol | Value | Units |
---|---|---|
Maximum density, nmax | 5.0×107 | m-3 |
Standard deviation, ΔTσ | 0.1 | K |
Mean undercooling, ΔTm | 10 | K |
Property and symbol | Value | Units |
---|---|---|
Density, ρ | 8.780×103 | kg m-3 |
Solute diffusivity in liquid, Dl | 3.6×10-9 | m2 s-1 |
Gibbs-Thomson coefficient, Γ | 3.65×10-7 | mK |
Partition coefficient, k0 | 0.788 | |
Liquidus slope, mL | -3.95 | K wt%-1 |
Liquidus temperature, Teq | 1672 | K |
Initial composition, C0 | 37.0 | wt% |
Anisotropy coefficient, ε | 0.02 | |
Viscosity, μ | 8.5×10-3 | kg m-1 s-1 |
Table 5 Material properties of Ni-based superalloy [53,54].
Property and symbol | Value | Units |
---|---|---|
Density, ρ | 8.780×103 | kg m-3 |
Solute diffusivity in liquid, Dl | 3.6×10-9 | m2 s-1 |
Gibbs-Thomson coefficient, Γ | 3.65×10-7 | mK |
Partition coefficient, k0 | 0.788 | |
Liquidus slope, mL | -3.95 | K wt%-1 |
Liquidus temperature, Teq | 1672 | K |
Initial composition, C0 | 37.0 | wt% |
Anisotropy coefficient, ε | 0.02 | |
Viscosity, μ | 8.5×10-3 | kg m-1 s-1 |
Fig. 13. Various types of dendrite formation with respect to the processing conditions (cell size = 4 μm, domain size = 4 mm): (a-c) $\dot{T}$ = 1.5 K/s, (d-f) $\dot{T}$ =3.0 K/s.
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