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Engineering    2017, Vol. 3 Issue (5) : 685-694
Research |
基于激光粉床熔融镍合金(Inconel 718)加热凝固分析的数值模拟和实验分析
Patcharapit Promoppatum1,Shi-Chune Yao1(),P. Chris Pistorius2,Anthony D. Rollett2
1. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
2. Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
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有限元模型和Rosenthal 方程在激光粉床熔融Inconel 718 合金热学现象及微观研究方面具有广泛应用。通过了解 Rosenthal 方程(该方程为有限元分析提供了一种非同寻常的方法)的优点及缺点,研究潜在假设对于估计结果的影响,结合实验对材料物理特性进行对比分析。本文结合有限元模型及 Rosenthal 分析方程预测熔池形状并与文献实验做比较,结果表明这两种方法均能够提供合理准确的估计结果,包括预测出柱状凝固微结构和一次枝晶间距(PDAS)值,与实验结果符合良好。与此同时,基于吸收率选择的灵敏度分析表明,与有限元法相比,Rosenthal 法对吸收率更为敏感,其原因可能是 Rosenthal 法忽略辐射和对流造成的能量流失。
关键词 增材制造有限元建模Rosenthal方程微结构物质的热行为Inconel 718合金    

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.
1 Petrick IJ, Simpson TW. 3D printing disrupts manufacturing: How economies of one create new rules of competition. Res Technol Manag 2013;56(6):12–6
2 Zhao X, Promoppatum P, Yao SC. Numerical modeling of non-linear thermal stress in direct metal laser sintering process of titanium alloy products. In: Proceedings of the First Thermal and Fluids Engineering Summer Conference; 2015 Aug 9–12; New York, NY, USA. New York: American Society of Thermal and Fluids Engineers; 2015. p. 1519–31.
3 Kumar LJ, Nair CGK. Current trends of additive manufacturing in the aerospace industry. In: Wimpenny DI, Pandey PM, Kumar LJ, editors Advances in 3D printing & additive manufacturing technologies. Singapore: Springer; 2017. p. 39–54.
4 Jia Q, Gu D. Selective laser melting additive manufactured Inconel 718 superalloy parts: High-temperature oxidation property and its mechanisms. Opt Laser Technol 2014;62:161–71
5 Wang X, Keya T, Chou K. Build height effect on the Inconel 718 parts fabricated by selective laser melting. Procedia Manuf 2016;5:1006–17
6 Promoppatum P, Onler R, Yao SC. Numerical and experimental investigations of micro and macro characteristics of direct metal laser sintered Ti-6Al-4V products. J Mater Process Technol 2017;240:262–73
7 Sadowski M, Ladani L, Brindley W, Romano J. Optimizing quality of additively manufactured Inconel 718 using powder bed laser melting process. Addit Manuf 2016;11:60–70
8 Rosenthal D. Mathematical theory of heat distribution during welding and cutting. Weld J 1941;20(5):220–34.
9 Tang M, Pistorius PC, Beuth JL. Prediction of lack-of-fusion porosity for powder bed fusion. Addit Manuf 2017;14:39–48
10 Liang YJ, Li A, Cheng X, Pang XT, Wang HM. Prediction of primary dendritic arm spacing during laser rapid directional solidification of single-crystal nickel-base superalloys. J Alloys Compd 2016;688(Pt A):133–42.
11 Romano J, Ladani L, Sadowski M. Laser additive melting and solidification of Inconel 718: Finite element simulation and experiment. JOM 2016;68(3):967–77
12 Romano J, Ladani L, Sadowski M. Thermal modeling of laser based additive manufacturing processes within common materials. Procedia Manuf 2015;1:238–50
13 Yan W, Ge W, Smith J, Lin S, Kafka OL, Lin F, et al.Multi-scale modeling of electron beam melting of functionally graded materials. Acta Mater 2016;115:403–12
14 Yan W, Ge W, Qian Y, Lin S, Zhou B, Liu WK, et al.Multi-physics modeling of single/multiple-track defect mechanisms in electron beam selective melting. Acta Mater 2017;134:324–33
15 Bonacina C, Comini G, Fasano A, Primicerio M. Numerical solution of phase-change problems. Int J Heat Mass Transfer 1973;16(10):1825–32
16 Hosaeus H, Seifter A, Kaschnitz E, Pottlacher G. Thermophysical properties of solid and liquid Inconel 718 alloy. High Temp High Press 2001;33(4):405–10
17 Hu D, Kovacevic R. Modelling and measuring the thermal behaviour of the molten pool in closed-loop controlled laser-based additive manufacturing. Proc Inst Mech Eng Part B 2003;217(4):441–52
18 Sainte-Catherine C, Jeandin M, Kechemair D, Ricaud JP, Sabatier L. Study of dynamic absorptivity at 10.6 μm (CO2) and 1.06 μm (Nd-YAG) wavelengths as a function of temperature. J Phys IV France 1991;1(C7):C7-151–7.
19 Montgomery C, Beuth J, Sheridan L, Klingbeil N. Process mapping of Inconel 625 in laser powder bed additive manufacturing. In: Proceedings: 26th Annual International Solid Freeform Fabrication Symposium—An additive manufacturing conference; 2015 Aug 10–12; Austin, T X, USA; 2015. p. 1195–204.
20 Lee YS, Zhang W. Modeling of heat transfer, fluid flow and solidification microstructure of nickel-base superalloy fabricated by laser powder bed fusion. Addit Manuf 2016;12(Pt B):178–88.
21 Gong H, Gu H, Zeng K, Dilip JJS, Pal D, Stucker B, et al.Melt pool characterization for selective laser melting of Ti-6Al-4V pre-alloyed powder. In: Proceedings of the 25th Annual International Solid Freeform Fabrication Symposium ; 2014 Aug 4–6; Austin, TX, USA; 2014. p. 256–67.
22 Bontha S, Klingbeil NW, Kobryn PA, Fraser HL. Effects of process variables and size-scale on solidification microstructure in beam-based fabrication of bulky 3D structures. Mater Sci Eng A 2009;513– 514:311–8.
23 Goldak J, Chakravarti A, Bibby M. A new finite element model for welding heat sources. Metall Mater Trans B 1984;15(2):299–305
24 Wei HL, Mukherjee T, DebRoy T. Grain growth modeling for additive manufacturing of nickel based superalloys. In: Holm EA, Farjami S, Manohar P, Rohrer GS, Rollett AD, Srolovitz D, et al., editors Proceedings of the 6th International Conference on Recrystallization and Grain Growth (ReX&GG 2016); 2016 Jul 17–21; Pittsburgh, PA , USA. Cham: Springer; 2016. p. 265–9.
25 ]Wang X, Gong X, Chou K. Review on powder-bed laser additive manufacturing of Inconel 718 parts. In: Proceedings of the ASME 10th International Manufacturing Science and Engineering Conference 2015: Volume 1; 2015 Jun 8–12; Charlotte, NC , USA. New York: American Society of Mechanical Engineers; 2015. p. V001T02A063.
26 Nastac L, Valencia JJ, Tims ML, Dax FR. Advances in the solidification of IN718 and RS5 alloys. In: Loria EA, editor Superalloys 718, 625, 706, and various derivatives: Proceedings of the International Symposium on Superalloys 718, 625, 706 and Various Derivatives; 2001 Jun 17–20; Pittsburgh , PA, USA. Pittsburgh: The Minerals, Metals & Materials Society; 2001. p. 103–12.
27 Lu SZ, Hunt JD. A numerical analysis of dendritic and cellular array growth: The spacing adjustment mechanisms. J Cryst Growth 1992;123(1–2):17–34.
28 Kurz W, Fisher DJ. Dendrite growth at the limit of stability: Tip radius and spacing. Acta Metall 1981;29(1):11–20
29 Wang G, Liang J, Zhou Y, Jin T, Sun X, Hu Z. Prediction of dendrite orientation and stray grain distribution in laser surface-melted single crystal superalloy. J Mater Sci Technol (Shenyang, China) 2017;33(5):499–506
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