Multi-scale simulation of columnar-to-equiaxed transition during laser selective melting of rare earth magnesium alloy

doi:10.1016/j.jmst.2021.12.029

Abstract

Abstract:

A model of coupling macro finite volume method (FVM) and cellular automata (CA) is proposed in this paper to explore the columnar-to-equiaxed transition (CET) during selective laser melting (SLM) of rare earth magnesium alloy. Taking into account the impact of recoil pressure and Marangoni convection on the molten pool temperature field, the grain structure is simulated. As suggested by the simulation results, with the undissolved Zr serving as heterogeneous nucleation sites, the liquid undercooled layer under the combined action of forced cooling, the temperature gradient and the liquid solute concentration gradient leads to CET. While considering the dissolution of Zr in magnesium matrix, the results demonstrate that the dissolution of element Zr is effective in significantly inhibiting the growth of columnar crystals and ensuring the sufficient constitutional supercooling (CS) required for nucleation. In addition, to raise the preheating temperature contributes to enhancing the outcome of nucleation and incresing the grain size. Invoking the interdependence model (IM), with the cooling rate gradually increasing in the SLM process of magnesium alloy, the nucleation-free zone (NFZ) reduces by decreasing the solute diffusion layer in the front of the solid/liquid (SL) interface and the temperature gradient. The reduction in temperature gradient can promote undercooling for nucleation and facilitate the development of equiaxed crystals. The simulation results are qualitatively verified as highly consistent through experimentation.

Key words: Multi-scale simulation, Columnar-to-equiaxed transition, Selective laser melting, Rare earth magnesium alloy, Constitutional supercooling

W.L. Wang, W.Q. Liu, X. Yang, R.R. Xu, Q.Y. Dai. Multi-scale simulation of columnar-to-equiaxed transition during laser selective melting of rare earth magnesium alloy[J]. J. Mater. Sci. Technol., 2022, 119: 11-24.

Figures/Tables 14

Fig. 1. Schematic diagram of multi-scale simulation of macro-micro coupling. (a) Macro model of heat transfer and convection based on FVM. (b) The local region of the macro model is selected for dendrite calculation, and the macro temperature field is converted into the micro temperature field using the bilinear interpolation method. (c) CET is simulated by using the CA method.

Table 1. Proc e ss parameters and thermo-physical properties of Mg-3.4Y-3.6Sm-2.6Zn-0.8Zr as used in this paper [20].

Physical properties	Value
Laser power, P	60 W
Laser scanning speed, V	0.3 m/s
Absorption coefficient of powder, η	0.37
S olidus temperature, T_s	798.41 K
L iquidus temperature, T_l	904.05 K
Surface tension, γ₀	0.55 N/m
Solid viscosity, µ_s	5 kg/(m s)
Liquid viscosity, µ_l	0.002 kg/(m s)
Latent heat of fusion, L_f	3.5 × 10⁶ J/kg
Heat transfer coefficient, h_c	15 W/(m² K)
Radiation emissivity,ε	0.4
The Stefan-Boltzmann constant, σ_s	5.6 7 × 10^-8 W/(m ² K⁴)
Shielding gas	Ar

Table 2. Properties of Mg-3.4Y magnesium alloy as used in this paper.

Physical properties	Value	Ref.
Initial alloy concentration, C₀	3.4%	-
Solute partition coefficient of Y, k_Y	0.42	[31]
Solute partition coefficient of Zr, k_Zr	6.55	[17]
Liquidus slope of Y, m_LY	-3.5 K/wt.%	[31]
Liquidus slope of Zr, m_LZr	6.9 K/wt.%	[17]
Solute diffusion coefficient in Liquid, D_L	2.77 × 10^-9 m²/s	JMatPro
Solute diffusion coefficient in Solid, Ds	2.8 × 10^-13 m²/s	JMatPro
Gibbs-Thomson coefficient, Г	1.7 × 10^-9 m K	[33]
Degree of kinetic anisotropy, δ	0.1	[14]

Fig. 2. The distribution of flow and temperature given the laser power P=60 W and the scanning speed V=0.3 m/s. (a) Keyhole-shaped molten pool in 3D view. (b) and (c) show a comparison of cross-section molten pool morphology between experiment and numerical simulation given the same process parameters. (d) Marangoni convection distribution in the longitudinal molten pool.

Fig. 3. (a) Thermal history curve of temperature detection points along the height direction. (b) Temperature gradient and cooling rate distribution from the bottom to the top of the molten pool.

Fig. 6. Evolution of the undercooling layer's thickness in front of the SL interface and nucleation number with time, the calculated undercooling layer's thickness is at x=13.5µm.

Fig. 7. Variables evolve with distance at the front of the SL interface with 500 CAs, 800 CAs, 1100 CAs, and 1400 CAs. (a) Liquid phase solute component, and (b) Undercooling.

Fig. 8. (a) Relationship between growth velocity and undercooling at different levels of Zr solubility. (b) Evolution of growth parameter with Zr solubility.

Fig. 9. Relationship between Zr solubility and CET: (a) without Zr, (b) 0.1Zr, (c) 0.25Zr, and (d) 0.5Zr.

Fig. 10. Variables evolve with distance at the front of the SL interface with 600 CAs. (a) Liquid phase solute component, and (b) Undercooling.

Fig. 11. Relationship between preheating temperature and CET: (a) 300 K, (b) 350 K, and (c) 400 K.

Fig. 12. SEM images of molten pool and block of SLM-processed Mg-Y-Sm-Zn-Zr alloy. (a) The solidification structure in the cross-section of the molten pool by single-pass scanning. (b) The microstructure of the longitudinal section of the block as printed by rotating 0° layer by layer [34]. (c) The solidification structure of the longitudinal section of the block as printed by rotating 67° layer by layer [34].

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