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Engineering    2017, Vol. 3 Issue (5) : 685-694
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The finite-element (FE) model and the Rosenthal equation are used to study the thermal and microstructural phenomena in the laser powder-bed fusion of Inconel 718. A primary aim is to comprehend the advantages and disadvantages of the Rosenthal equation (which provides an analytical alternative to FE analysis), and to investigate the influence of underlying assumptions on estimated results. Various physical characteristics are compared among the FE model, Rosenthal equation, and experiments. The predicted melt pool shapes compared with reported experimental results from the literature show that both the FE model and the analytical (Rosenthal) equation provide a reasonably accurate estimation. At high heat input, under conditions leading to keyholing, the reported melt width is narrower than predicted by the analytical equation. Moreover, a sensitivity analysis based on choices of the absorptivity is performed, which shows that the Rosenthal approach is more sensitive to absorptivity, compared with the FE approach. The primary reason could be the effect of radiative and convective losses, which are assumed to be negligible in the Rosenthal equation. In addition, both methods predict a columnar solidification microstructure, which agrees well with experimental reports, and the primary dendrite arm spacing (PDAS) predicted with the two approaches is comparable with measurements.

Keywords Additive manufacturing      Finite-element modeling      Rosenthal equation      Microstructure      Thermal behavior      Inconel 718     
在线预览日期:    发布日期: 2017-11-08
Patcharapit Promoppatum
Shi-Chune Yao
P. Chris Pistorius
Anthony D. Rollett
Patcharapit Promoppatum,Shi-Chune Yao,P. Chris Pistorius, et al. A Comprehensive Comparison of the Analytical and Numerical Prediction of the Thermal History and Solidification Microstructure of Inconel 718 Products Made by Laser Powder-Bed Fusion[J]. Engineering, 2017, 3(5): 685-694.
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Fig.1  Thermophysical properties for Inconel 718 as functions of temperature [11]. (a) Density; (b) specific heat; (c) thermal conductivity; (d) emissivity.
Absorptivity Sources
0.87 Romano et al. [11]
0.3–0.55 Sainte-Catherine et al. [18]
0.51 Montgomery et al. [19]
0.38 Lee and Zhang [20]
Tab.1  Reported absorptivity of Inconel 718 for a laser wavelength of 1.06?µm.
Fig.2  (a) Thermal boundary conditions: ① laser heat input on the top surface; ② heat losses due to convection and radiation; ③ insulated walls; ④ constant temperature at the bottom. (b) Bulk 3D geometry considered in the FE calculation.
Property Value
Thermal conductivity, k 11.4 W·(m·K)−1 [11]
Density, ρ 8220 kg·m−3 [11]
Specific heat, CP 435 J·(kg·K)−1 [11]
Absorptivity, λ 0.3–0.87 (from Table 1)
Tab.2  Room-temperature thermal properties of Inconel 718 used in the Rosenthal equation.
Fig.3  (a) Cross-sectional view (yz) of the temperature contour (°C) and melt pool boundary (indicated by the black line) from the FE model; (b) longitudinal view (xz) of the temperature contour (°C) and melt pool boundary (indicated by the black line) from the FE model. Simulated with a laser power of 200?W, scanning velocity of 960?mm·s−1, and absorptivity of 0.5.
Fig.4  Plan view of a Rosenthal plot of the melt pool boundary, calculated for Inconel 718 with an absorbed power of 142?W and with V?=?960?mm·s−1. The point heat source is at the intersection between the horizontal and vertical axes. W is the melt pool width and D is the melt pool depth.
Fig.5  Melt pool width comparison between the experimental results from Ref. [7] and predictions from the Rosenthal equation and the FE model. The shaded area shows the range of predictions when varying the absorptivity from 0.3 to 0.87, while the dashed lines show the fitted absorptivity of the two approaches.
Fig.6  Illustration of the melt pools in two layers; regions with and without remelting are identified.
Fig.7  (a) Temperature as a function of time from various locations within the melt pool; (b) temperature gradient as a function of time from various locations within the melt pool; (c) temperature gradient as a function of temperature from various locations within the melt pool during the cooling process. Simulated by the FE model with a laser power of 200?W, scanning velocity of 960?mm·s−1, and absorptivity of 0.5.
Fig.8  A comparison of (a) temperature gradient, (b) cooling rate, and (c) solidification rate from the Rosenthal equation and the FE model. The shaded area indicates sensitivity to absorptivity in the range 0.3–0.87. Dashed lines indicate results from the fitted absorptivities of 0.4 and 0.5 for the Rosenthal equation and the FE model, respectively.
Fig.9  A comparison of the solidification maps from (a) the Rosenthal equation and (b) the FE model. Results are from an absorptivity of 0.4 (Rosenthal equation) and 0.5 (FE model).
Property Value
Solidification interval, ΔT0 82?K [16]
Liquid diffusivity, D 3?×?10−9?m2·s−1 [10]
Partition coefficient, k0 0.7 [10]
Gibbs-Thomson coefficient, Γ 1.8?×?10−7?m·K [10]
Tab.3  Material properties of the Inconel 718 used for predicting the PDAS.
Fig.10  A comparison of PDAS predictions from the Rosenthal equation and the FE model, and the experimental result from Ref. [20]. The shaded area indicates the result’s sensitivity for various absorptivities from 0.3 to 0.87. Dashed lines indicate the results from the fitted absorptivities of 0.4 and 0.5 for the Rosenthal equation and the FE model, respectively.
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