Special Issue — Mechanical and Physical Problems on Additive Manufacturing Materials and Processes; Edited by Hong Wu, Feng Liu, Jiaming Bai and Kun Zhou; Research ArticlesNo Access

An analytical model of the melt pool and single track in coaxial laser direct metal deposition (LDMD) additive manufacturing

Jian Liu

Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, 15261 PA, USA

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Erica Stevens

Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, 15261 PA, USA

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Qingchen Yang

Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, 15261 PA, USA

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Markus Chmielus

Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, 15261 PA, USA

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, and

Albert C. To

Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, 15261 PA, USA

E-mail Address: albertto@pitt.edu

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https://doi.org/10.1142/S2424913017500138Cited by:31 (Source: Crossref)

Abstract

An analytical model was developed for the melt pool and single scan track geometry as a function of process parameters. For computational efficiency, the developed model has simple mathematical forms with essential physics taken into account, without the need for complicated numerical simulation. In this research, a non-diverging Gaussian laser beam and coaxial diverging Gaussian powder stream combination is used to represent the coaxial laser direct metal deposition (LDMD) process. Analytical laser-powder interaction model is used to obtain the distribution of attenuated laser intensity and temperature of heated powders at the substrate. On the substrate, the melt pool is calculated by integrating Rosenthal's point heat source model. An iterative procedure is used to ensure the mass–energy balances and to calculate the melt pool and catchment efficiency. By assuming that the assimilated powder will reshape due to surface tension before solidification, a simple clad geometry model is established. The proposed model is used to simulate the geometry of single track depositions of Ti6Al4V, which shows a good agreement between model prediction and experimental results. This work demonstrates that the developed model has the potential to be used to narrow the parameter space for process optimization.

Keywords:

References

Ahsan, M. N. and Pinkerton [2011] “ An analytical–numerical model of laser direct metal deposition track and microstructure formation,” Model. Simul. Mater. Sci. Eng. 19(5), 055003. Crossref, Google Scholar
Carslaw, H. S. and Jaeger, J. C. [1986] Conduction of Heat in Solids, Vol. 528 (Clarendon Press, UK). Google Scholar
Colaço, R. et al., [1996] A simple correlation between the geometry of laser cladding tracks and the process parameters, in Laser Processing: Surface Treatment and Film Deposition, ed. J. Mazumder (Springer, Netherlands), pp. 421–429. Crossref, Google Scholar
Cline, H. E. and Anthony, T. R. [1977] “ Heat treating and melting material with a scanning laser or electron beam,” J. Appl. Phys. 48(9), 3895–3900. Crossref, Google Scholar
Eagar, T. W. and Tsai, N. S. [1983] “ Temperature fields produced by traveling distributed heat sources,” Weld. J. 62(12), 346–355. Google Scholar
El Cheikh, H. et al., [2012] “ Analysis and prediction of single laser tracks geometrical characteristics in coaxial laser cladding process,” Opt. Lasers Eng. 50(3), 413–422. Crossref, Google Scholar
Fathi, A. et al., [2006] “ Prediction of melt pool depth and dilution in laser powder deposition,” J. Phys. D : Appl. Phys. 39(12), 2613. Crossref, Google Scholar
Frewin, M. R. and Scott, D. A. [1999] “ Finite element model of pulsed laser welding,” Weld. J. 78, 15s–22s. Google Scholar
Grong, Ø. [1997] Metallurgical Modelling of Welding (Institute of Materials, London). Google Scholar
Huang, Y.-L. et al., [2006] “ Three-dimensional analytical model on laser-powder interaction during laser cladding,” J. Laser Appl. 18(1), 42–46. Crossref, Google Scholar
Huang, Y., Khamesee, M. B. and Toyserkani, E. [2016] “ A comprehensive analytical model for laser powder-fed additive manufacturing,” Add. Manuf. 12, Part A, 90–99. Google Scholar
Hulst, H. C. and Hulst, H. C. van de [1957] Light Scattering by Small Particles, Vol. 500 (Courier Corporation, New York). Jouvard, J. M. et al., [1997] “Continuous wave Nd:YAG laser cladding modeling: A physical study of track creation during low power processing,” J. Laser Appl. 9(1), 43–50. Google Scholar
Kamath, C. [2016] “ Data mining and statistical inference in selective laser melting,” Int. J. Adv. Manuf. Technol. 86, 1659–1677. Crossref, Google Scholar
Kempen, K. et al., [2014] “ Processing AlSi10Mg by selective laser melting: Parameter optimisation and material characterisation,” Mater. Sci. Technol. 31(8), 917–923. Crossref, Google Scholar
King, W. et al., [2014] “ Overview of modelling and simulation of metal powder bed fusion process at Lawrence Livermore National Laboratory,” Mater. Sci. Technol. 31(8), 957–968. Crossref, Google Scholar
Kruth, J.-P. et al., [2010] “ Part and material properties in selective laser melting of metals,” in Proc. 16th Int. Symp. Electromachining, Leuven, Belgium. Google Scholar
Kummailil, J. et al., [2005] “ Effect of select LENS $^{TM}$ $^{TM}$ processing parameters on the deposition of Ti-6Al-4V,” J. Manuf. Process 7(1), 42–50. Crossref, Google Scholar
Lee, Y. and Farson, D. F. [2016] “ Simulation of transport phenomena and melt pool shape for multiple layer additive manufacturing,” J. Laser Appl. 28(1), 012006. Crossref, Google Scholar
Li, Y. and Gu, D. [2014] “ Parametric analysis of thermal behavior during selective laser melting additive manufacturing of aluminum alloy powder,” Mater. Des. 63, 856–867. Crossref, Google Scholar
Lin, J. [1999] “ A simple model of powder catchment in coaxial laser cladding,” Opt. Laser Technol. 31(3), 233–238. Crossref, Google Scholar
Lin, J. [2000] “ Laser attenuation of the focused powder streams in coaxial laser cladding,” J. Laser Appl. 12(1), 28–33. Crossref, Google Scholar
Liu, J. and Li, L. [2005] “ Effects of powder concentration distribution on fabrication of thin-wall parts in coaxial laser cladding,” Opt. Laser Technol. 37(4), 287–292. Crossref, Google Scholar
Liu, J. et al., [2005] “ Attenuation of laser power of a focused Gaussian beam during interaction between a laser and powder in coaxial laser cladding,” J. Phys. D: Appl. Phys. 38(10), 1546. Crossref, Google Scholar
Nguyen, N. T. et al., [1999] “ Analytical solutions for transient temperature of semi-infinite body subjected to 3-D moving heat sources,” Weld. J. (New York) 78, 265s–274s. Google Scholar
Olakanmi, E. O. Cochrane, R. F. and Dalgarno, K. W. [2015] “ A review on selective laser sintering/melting (SLS/SLM) of aluminium alloy powders: Processing, microstructure, and propertie,” Progr. Mater. Sci. 74, 401–477. Crossref, Google Scholar
Peyre, P. et al., [2008] “ Analytical and numerical modelling of the direct metal deposition laser process,” J. Phys. D: Appl. Phys. 41(2), 025403. Crossref, Google Scholar
Picasso, M. et al., [1994] “ A simple but realistic model for laser cladding,” Metall. Mater. Trans. B 25(2), 281–291. Crossref, Google Scholar
Pinkerton, A. J. et al., [2007] “ A verified model of laser direct metal deposition using an analytical enthalpy balance method,” in Proc. 26th Int. Congress on Applications of Lasers and Electro-Optics (ICALEO). Laser Institute of America. Google Scholar
Qi, H., Mazumder, J. and Ki, H. [2006] “ Numerical simulation of heat transfer and fluid flow in coaxial laser cladding process for direct metal deposition,” J. Appl. Phys. 100(2), 024903. Crossref, Google Scholar
Rosenthal, D. [1946] The Theory of Moving Sources of Heat and its Application to Metal Treatments (ASME, US). Crossref, Google Scholar
Soylemez, E., Beuth, J. L. and Taminger, K. [2010] “ Controlling melt pool dimensions over a wide range of material deposition rates in electron beam additive manufacturing,” in 21st Annual International Solid Freeform Fabrication Symposium — An Additive Manufacturing Conference, Austin, TX, Aug. pp. 9-11. Google Scholar
Toyserkani, E., Khajepour, A. and Corbin, S. [2003] “ Three-dimensional finite element modeling of laser cladding by powder injection: Effects of powder feedrate and travel speed on the process,” Journal of Laser Applications 15, 153–160. Crossref, Google Scholar
Wen, S. Y. et al., [2009] “ Modeling of coaxial powder flow for the laser direct deposition process,” Int. J. Heat Mass Transf. 52(25–26), 5867–5877. Crossref, Google Scholar
Yang, N. [2009] “ Concentration model based on movement model of powder flow in coaxial laser cladding,” Opt. Laser Technol. 41(1), 94–98. Crossref, Google Scholar
Zeng, K. et al., [2014] “ Comparison of 3DSIM thermal modelling of selective laser melting using new dynamic meshing method to ANSYS,” Mater. Sci. Technol. 31(8), 945–956. Crossref, Google Scholar