Prediction of Primary Dendrite Arm Spacing in Pulsed Laser Surface Melted Single Crystal Superalloy

doi:10.1007/s40195-020-01156-3

Abstract

Abstract:

Primary dendritic arm spacing (PDAS) is an important microstructure feature of the nickel-base single crystal superalloys. In this paper, a numerical model predicting the PDAS evolution with additive manufacturing parameters using pulsed laser is established, which combines the theoretical PDAS models with the temperature field calculation model during pulsed laser process. Based on this model, processing maps that related process parameters to the evolution of PDAS are generated. To obtain more accurate prediction model, the parameters of different solidification conditions, $\overline{{G^{ - 0.5} V^{ - 0.25} }}$ and $\overline{{G}^{-0.5}{V}^{-0.25}}$, are selected to calculate PDAS. The simulation results show that the PDAS increases as the arise of P and t. The processing-PDAS map can accurately predict the evolution of PDAS with pulsed laser process parameters, which is well in accordance with the experimental results. Additionally, the PDAS values calculated by the $\overline{{G}^{-0.5}{V}^{-0.25}}$ are more in line with the experimental results than those calculated by the ${\bar{G}}^{-0.5}{\bar{V}}^{-0.25}$.

Key words: Additive manufacturing, Nickel-base superalloy, Single crystal, Pulsed laser, Primary dendritic arm spacing

Shiwei Ci, Jingjing Liang, Jinguo Li, Haiwei Wang, Yizhou Zhou, Xiaofeng Sun, Hongwei Zhang, Yutian Ding, Xin Zhou. Prediction of Primary Dendrite Arm Spacing in Pulsed Laser Surface Melted Single Crystal Superalloy[J]. Acta Metallurgica Sinica (English Letters), 2021, 34(4): 485-494.

Figures/Tables 13

Fig. 1 a Schematic diagram of pulse laser remelting process, b laser working state, c 3D intensity distributions of top hat beam

Table 1 Processing parameters (laser power, P, pulse width, t and beam diameter, ${D}_{\mathrm{b}}$) and the corresponding calculated and measured diameters of molten pool,${D}_{\mathrm{c}}$ and ${D}_{\mathrm{m}}$, and primary dendritic arm spacing, ${\lambda }_{1}$

No	t, s	P, W	Pt, J	${D}_{\mathrm{b}}$, μm	${D}_{\mathrm{c}}$, μm	${D}_{\mathrm{m}}$, μm	${\lambda }_{1}$, μm
A	0.1	1800	180	2200	1416	1399	3.2±0.45
B	0.1	2200	220	2200	1857	1902	3.7±0.45
C	0.1	2600	260	2200	2054	2305	4.3±0.50
D	0.16	1800	288	2200	1712	2145	4.3±0.55
E	0.16	2200	352	2200	2020	2353	4.6±0.65
F	0.16	2600	416	2200	2159	2558	5.8±0.75
G	0.22	1800	396	2200	1853	2405	4.8±0.60
H	0.22	2200	484	2200	2102	2564	5.2±0.65
I	0.22	2600	572	2200	2205	2743	6.0±0.75
J	0.28	1800	504	2200	1936	2376	5.6±0.65
K	0.28	2200	616	2200	2149	2678	6.0±0.70
L	0.28	2600	728	2200	2242	2827	6.9±0.75

Table 2 Main chemical composition of DD32 alloy (mass fraction, %)

C	Cr	Co	W	Mo	Al	Nb	Ta	Re	Ni
0.12-0.18	4.30-5.60	8.00-10.00	7.70-9.50	0.80-1.40	5.60-6.30	1.40-1.80	3.50-4.50	3.50-4.50	Bal

Table 3 Thermophysical properties of the DD32 SC alloy used for calculation of PDAS

Properties	Values
Melting point of pure Ni, ${T}_{\mathrm{m}}$	1726 (K)
Solidification interval, $\Delta {T}_{0}$	39.3 (K)
Absorption coefficient, $\eta$	0.12
Emissivity, $\varepsilon$	0.7
Ambient temperature, ${\mathrm{T}}_{0}$	293.15 (K)
Partition coefficient, ${k}_{0}$	0.62
Gibbs-Thomson coefficient, $\Gamma$	1.8 × 10^-7 (m k)
Liquid diffusivity, D	3 × 10^-9 (m²/s)
Solid density, ${\rho }_{\mathrm{S}}$	8550 (kg/m³)
Liquid density, ${\rho }_{\mathrm{L}}$	8550 (kg/m³)
Solidus temperature, ${T}_{\mathrm{s}}$	1621.7 (K)
Liquidus temperature, ${T}_{\mathrm{l}}$	1661 (K)
Solid specific heat, ${Cp}_{\mathrm{S}}$	550 (J kg^-1 k^-1)
Liquid specific heat, ${Cp}_{\mathrm{l}}$	550 (J kg^-1 k^-1)
Solid thermal conductivity, ${k}_{\mathrm{S}}$	22 (W m^-1 K^-1)
Liquid thermal conductivity $, {k}_{\mathrm{l}}$	22 (W m^-1 K^-1)

Fig. 2 Solidification microstructure of the cross section of the molten pool. The green dotted line is the dividing line between different growth directions. The area between the red dotted lines in the orange magnification area is planar interface

Fig. 3 Evolution of the ${G}_{\left[001\right]}$ and ${V}_{\left[001\right]}$ with the increase of Z at the S/L interface of the center position of the molten pool under the condition of 2600 W, 0.1 s

Fig. 4 Combined effects of P, t and two characteristic solidification conditions on the PDAS (in μm): a evaluated by using the $\overline{{G}^{-0.5}{V}^{-0.25}}$, b evaluated by using the ${\bar{G}}^{-0.5}{\bar{V}}^{-0.25}$

Fig. 5 a Dendritic morphologies in the transverse section of the molten pool made under different processing conditions, b the histogram of PDAS

Fig. 6 Comparison of the contour map on the PDAS (in μm) between the experimental results and those calculated

Fig. 7 Correlation between the experimental PDAS and those calculated

Fig. 8 Variation trends of the PDAS with t at different powers

Fig. 9 Evolution of the G/V as a function of Z under the condition of 2600 W, 0.1 s

Fig. 10 Contour maps showing the influences of laser power, P, and pulse width, t, on the (a) $\overline{G}$ (K/m) and (b) $\overline{V}$ (m/s) values

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