Multi-scale modeling of liquid-metal cooling directional solidification and solidification behavior of nickel-based superalloy casting

doi:10.1016/j.jmst.2020.06.051

Abstract

Abstract:

Liquid-metal cooling (LMC) process can offer refinement of microstructure and reduce defects due to the increased cooling rate from enhanced heat extraction, and thus an understanding of solidification behavior in nickel-based superalloy casting during LMC process is essential for improving mechanical performance of single crystal (SC) castings. In this effort, an integrated heat transfer model coupling meso grain structure and micro dendrite is developed to predict the temperature distribution and microstructure evolution in LMC process. An interpolation algorithm is used to deal with the macro-micro grids coupling issues. The algorithm of cells capture is also modified, and a deterministic cellular automaton (DCA) model is proposed to describe neighborhood cell tracking. In addition, solute distribution is also considered to describe the dendrite growth. Temperature measuring, EBSD, OM and SEM experiments are implemented to verify the proposed model, and the experiment results agree well with the simulation results. Several simulations are performed with a range of withdrawal rates, and the results indicate that 12 mm·min ^-1 is suitable for LMC process in this work, which can result in a fairly narrow and flat mushy zone and correspondingly exhibited fairly straight grains. The mushy zone length is about 4.8 mm in the steady state and the average deviation angle of grains is about 13.9° at the height 90 mm from the casting base under 12 mm·min ^-1 withdrawal process. The competitive phenomenon of dendrites at different withdrawal rates is also observed, which has a great relevant to the temperature fluctuation.

Key words: Multi-scale model, Numerical simulation, Liquid-metal cooling, Microstructure

Xuewei Yan, Qingyan Xu, Guoqiang Tian, Quanwei Liu, Junxing Hou, Baicheng Liu. Multi-scale modeling of liquid-metal cooling directional solidification and solidification behavior of nickel-based superalloy casting[J]. J. Mater. Sci. Technol., 2021, 67: 36-49.

Figures/Tables 18

Fig. 1. Complex heat transfer boundaries of LMC furnace.

Fig. 2. Schematic of macro-micro coupling calculation: (a) temperature interpolation between macro grid and micro grid; (b) modified CA capture algorithm in 2-D gridding.

Fig. 3. (a) Mold shell configuration; (b) geometry of one plate casting.

Fig. 4. Thermophysical properties of DZ24 superalloy calculated by JMatPro software.

Table 1 Thermophysical parameters of DZ24 superalloy.

Parameters	Values
Liquidus temperature (°C)	1323
Solidus temperature (°C)	1268
Latent heat (kJ·kg^-1)	90
Liquidus slope	-3.73
Solute partition coefficient	0.562
Anisotropy coefficient ε	0.03 [37]
Gibbs-Thomson coefficient Γ (K·m)	3.65 × 10^-7 [37]
Liquid diffusion coefficient D_L (m²·s^-1)	1.73 × 10^-9 [37]
Solid diffusion coefficient D_s (m²·s^-1)	1.16 × 10^-12 [37]

Table 2 Parameters for the location-dependent boundary condition [13]

Location	Emissivity of mold shell	Interface heat transfer coefficient (W·m^-2·K^-1)	Ambient temperature (°C)
Above ceramic beads	0.4	0	1500
Within ceramic beads	0	500	1100-325
Within coolant	0	4000	250

Fig. 5. Experiment and simulation results of cooling curves at different positions of the plate casting: (a) position 3; (b) position 4.

Fig. 6. Temperature field (a1-a5) and mushy zone (b1-b5) evolution of plate casting during DS process at a withdrawal rate 8 mm·min-1: (a1, b1) t = 15 s, fs = 2%; (a2, b2) t = 41 s, fs = 8%; (a3, b3) t = 115 s, fs = 20%; (a4, b4) t = 323 s, fs = 40%; (a5, b5) t =560 s, fs = 60%.

Fig. 7. Simulation and experiment results of grain structures in the plate casting: (a) simulation result; (b) experiment result.

Fig. 8. Simulation results of grain morphologies for different transverse sections and EBSD orientation image maps of different samples: (a) simulation result for Section 1; (b) simulation result for Section 2; (c) IPF map for Sample I; (d) IPF map for Sample II.

Fig. 9. Experiment and simulation results of dendritic morphologies in different domains: (a1~d1) for Sample I; (a2~d2) for Sample II; (a1, c1 and a2, c2) for cross sections; (b1, d1 and b2, d2) for longitudinal sections; (a1, b1 and a2, b2) experiment results; (c1, d1 and c2, d2) simulation results.

Fig. 10. Coupling simulation between meso grain and micro dendrites in 3D space: (a) meso grain structures; (b) micro dendrites; (c and d) dendrites in cross section; (e) experiment result.

Fig. 11. Mushy zone evolution at different withdrawal rates, and the solid fractions are 5%, 10%, 20%, 30% 40% and 50%, respectively: (a1-a6) 6 mm·min-1; (b1-b6) 8 mm·min-1; (c1-c6) 10 mm·min-1; (d1-d6) 12 mm·min-1; (e1-e6) 16 mm·min-1; (f1-f6) 20 mm·min-1.

Fig. 12. The change of mushy zone length at different withdrawal rates.

Fig. 13. Simulation results of grain structures at different withdrawal rates: (a) 6 mm·min-1; (b) 8 mm·min-1; (c) 10 mm·min-1; (d) 12 mm·min-1; (e) 16 mm·min-1; (f) 20 mm·min-1.

Fig. 14. Distributions of grain numbers and average deviation angle between the [001] orientation of grains and z axis at different withdrawal rates: (a) 6 mm·min-1; (b) 8 mm·min-1; (c) 10 mm·min-1; (d) 12 mm·min-1; (e) 16 mm·min-1; (f) 20 mm·min-1.

Fig. 15. Schematic of the competitive growth of dendrites with different orientations relative to the isothermal line: (a) vertical and tilting growth under the horizontal isothermal line; (b) vertical and tilting growth under the curving isothermal line; (c) converging relationship with tilting and tilting growth under the curving isothermal line; (d) diverging relationship with tilting and tilting growth under the curving isothermal line.

Fig. 16. Simulation results of dendrite growth at different withdrawal rates: (a) 6 mm·min-1; (b) 8 mm·min-1; (c) 10 mm·min-1; (d) 12 mm·min-1; (e) 16 mm·min-1; (f) 20 mm·min-1.

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