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Analytical modeling of transient temperature in powder feed metal additive manufacturing during heating and cooling stages

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Abstract

This work presents a physics-based predictive model for transient temperature during heating state and cooling state in powder feed metal additive manufacturing (PFMAM). The deposition dimension, heat transfer boundary conditions, laser absorption, and latent heat are considered in the presented model. The temperature solution is constructed from the superposition of moving point heat source solution and heat sink solution based on a stationary coordinate with respect to the part boundary. The heat source solution is activated during heating state and deactivated during cooling state. The temperature profiles and molten pool evolution were predicted with respect to the processing time in single-track deposition of PFMAM of Inconel 718. Close-agreements were observed upon validation to the experimental results in the literature. The presented model has high computational efficiency without resorting to the mesh and iterative calculation. The high prediction accuracy and high computational efficiency allow the temperature prediction for large-scale parts, and process-parameter planning through inverse analysis.

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  • 18 September 2019

    The author found some minor corrections in his online published article.

References

  1. D.S. Thomas, S.W. Gilbert, Costs and cost effectiveness of additive manufacturing. NIST Spec. Publ. 1176, 12 (2014). https://doi.org/10.6028/NIST.SP.1176

    Article  Google Scholar 

  2. I. Gibson, D.W. Rosen, B. Stucker, Additive Manufacturing Technologies, vol. 17 (Springer, New York, 2014)

    Google Scholar 

  3. H. Gong, K. Rafi, H. Gu, T. Starr, B. Stucker, Analysis of defect generation in Ti–6Al–4 V parts made using powder bed fusion additive manufacturing processes. Addit. Manuf. 1, 87–98 (2014). https://doi.org/10.1016/j.addma.2014.08.002

    Article  Google Scholar 

  4. J.P. Kruth, G. Levy, F. Klocke, T.H.C. Childs, Consolidation phenomena in laser and powder-bed based layered manufacturing. CIRP Ann. 56(2), 730–759 (2007). https://doi.org/10.1016/j.cirp.2007.10.004

    Article  Google Scholar 

  5. Z. Wang, E. Denlinger, P. Michaleris, A.D. Stoica, D. Ma, A.M. Beese, Residual stress mapping in Inconel 625 fabricated through additive manufacturing: method for neutron diffraction measurements to validate thermomechanical model predictions. Mater. Des. 113, 169–177 (2017). https://doi.org/10.1016/j.matdes.2016.10.003

    Article  Google Scholar 

  6. A.J. Sterling, B. Torries, N. Shamsaei, S.M. Thompson, D.W. Seely, Fatigue behavior and failure mechanisms of direct laser deposited Ti–6Al–4V. Mater. Sci. Eng. A 655, 100–112 (2016). https://doi.org/10.1016/j.msea.2015.12.026

    Article  Google Scholar 

  7. J.C. Heigel, P. Michaleris, T.A. Palmer, In situ monitoring and characterization of distortion during laser cladding of Inconel® 625. J. Mater. Process. Technol. 220, 135–145 (2015). https://doi.org/10.1016/j.jmatprotec.2014.12.029

    Article  Google Scholar 

  8. J. Ning, S. Liang, Prediction of temperature distribution in orthogonal machining based on the mechanics of the cutting process using a constitutive model. J. Manuf. Mater. Process. 2(2), 37 (2018). https://doi.org/10.3390/jmmp2020037

    Article  Google Scholar 

  9. J. Ning, S.Y. Liang, Predictive modeling of machining temperatures with force-temperature correlation using cutting mechanics and constitutive relation. Materials 12(2), 284 (2019). https://doi.org/10.3390/ma12020284

    Article  ADS  Google Scholar 

  10. J.C. Heigel, M.F. Gouge, P. Michaleris, T.A. Palmer, Selection of powder or wire feedstock material for the laser cladding of Inconel® 625. J. Mater. Process. Technol. 231, 357–365 (2016). https://doi.org/10.1016/j.jmatprotec.2016.01.004

    Article  Google Scholar 

  11. A.J. Pinkerton, M. Karadge, W.U.H. Syed, L. Li, Thermal and microstructural aspects of the laser direct metal deposition of waspaloy. J. Laser Appl. 18(3), 216–226 (2006). https://doi.org/10.2351/1.2227018

    Article  Google Scholar 

  12. D.A. Kriczky, J. Irwin, E.W. Reutzel, P. Michaleris, A.R. Nassar, J. Craig, 3D spatial reconstruction of thermal characteristics in directed energy deposition through optical thermal imaging. J. Mater. Process. Technol. 221, 172–186 (2015). https://doi.org/10.1016/j.jmatprotec.2015.02.021

    Article  Google Scholar 

  13. S.K. Everton, M. Hirsch, P. Stravroulakis, R.K. Leach, A.T. Clare, Review of in situ process monitoring and in situ metrology for metal additive manufacturing. Mater. Des. 95, 431–445 (2016). https://doi.org/10.1016/j.matdes.2016.01.099

    Article  Google Scholar 

  14. G. Tapia, A. Elwany, A review on process monitoring and control in metal-based additive manufacturing. J. Manuf. Sci. Eng. 136(6), 060801 (2014). https://doi.org/10.1115/1.4028540

    Article  Google Scholar 

  15. S. Clijsters, T. Craeghs, S. Buls, K. Kempen, J.P. Kruth, In situ quality control of the selective laser melting process using a high-speed, real-time melt pool monitoring system. Int. J. Adv. Manuf. Technol. 75(5–8), 1089–1101 (2014). https://doi.org/10.1007/s00170-014-6214-8

    Article  Google Scholar 

  16. L.E. Criales, Y.M. Arısoy, B. Lane, S. Moylan, A. Donmez, T. Özel, Laser powder bed fusion of nickel alloy 625: experimental investigations of effects of process parameters on melt pool size and shape with spatter analysis. Int. J. Mach. Tool Manuf. 121, 22–36 (2017). https://doi.org/10.1016/j.ijmachtools.2017.03.004

    Article  Google Scholar 

  17. I.A. Roberts, C.J. Wang, R. Esterlein, M. Stanford, D.J. Mynors, A three-dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing. Int. J. Mach. Tool Manuf. 49(12–13), 916–923 (2009). https://doi.org/10.1016/j.ijmachtools.2009.07.004

    Article  Google Scholar 

  18. R.B. Patil, V. Yadava, Finite element analysis of temperature distribution in single metallic powder layer during metal laser sintering. Int. J. Mach. Tool Manuf. 47(7–8), 1069–1080 (2007)

    Article  Google Scholar 

  19. C.H. Fu, Y.B. Guo, Three-dimensional temperature gradient mechanism in selective laser melting of Ti-6Al-4V. J. Manuf. Sci. Eng. 136(6), 061004 (2014). https://doi.org/10.1115/1.4028539

    Article  Google Scholar 

  20. K. Dai, L. Shaw, Finite element analysis of the effect of volume shrinkage during laser densification. Acta Mater. 53(18), 4743–4754 (2005). https://doi.org/10.1016/j.actamat.2005.06.014

    Article  Google Scholar 

  21. M. Labudovic, D. Hu, R. Kovacevic, A three dimensional model for direct laser metal powder deposition and rapid prototyping. J. Mater. Sci. 38(1), 35–49 (2003). https://doi.org/10.1023/A:1021153513925

    Article  ADS  Google Scholar 

  22. L.E. Criales, Y.M. Arısoy, T. Özel, Sensitivity analysis of material and process parameters in finite element modeling of selective laser melting of Inconel 625. Int. J. Adv. Manuf. Technol. 86(9–12), 2653–2666 (2016). https://doi.org/10.1007/s00170-015-8329-y

    Article  Google Scholar 

  23. K. Zhang, S. Wang, W. Liu, R. Long, Effects of substrate preheating on the thin-wall part built by laser metal deposition shaping. Appl. Surf. Sci. 317, 839–855 (2014). https://doi.org/10.1016/j.apsusc.2014.08.113

    Article  ADS  Google Scholar 

  24. M. Xia, D. Gu, G. Yu, D. Dai, H. Chen, Q. Shi, Porosity evolution and its thermodynamic mechanism of randomly packed powder-bed during selective laser melting of Inconel 718 alloy. Int. J. Mach. Tool Manuf. 116, 96–106 (2017). https://doi.org/10.1016/j.ijmachtools.2017.01.005

    Article  Google Scholar 

  25. P. Wei, Z. Wei, Z. Chen, Y. He, J. Du, Thermal behavior in single track during selective laser melting of AlSi10Mg powder. Appl. Phys. A 123(9), 604 (2017). https://doi.org/10.1007/s00339-017-1194-9

    Article  ADS  Google Scholar 

  26. Y. Xiang, S. Zhang, Z. Wei, J. Li, P. Wei, Z. Chen, L. Jiang, Forming and defect analysis for single track scanning in selective laser melting of Ti6Al4V. Appl. Phys. A 124(10), 685 (2018). https://doi.org/10.1007/s00339-018-2056-9

    Article  ADS  Google Scholar 

  27. G. Vastola, G. Zhang, Q.X. Pei, Y.W. Zhang, Controlling of residual stress in additive manufacturing of Ti6Al4V by finite element modeling. Addit. Manuf. 12, 231–239 (2016). https://doi.org/10.1016/j.addma.2016.05.010

    Article  Google Scholar 

  28. S. Afazov, W.A. Denmark, B.L. Toralles, A. Holloway, A. Yaghi, Distortion prediction and compensation in selective laser melting. Addit. Manuf. 17, 15–22 (2017). https://doi.org/10.1016/j.addma.2017.07.005

    Article  Google Scholar 

  29. B. Schoinochoritis, D. Chantzis, K. Salonitis, Simulation of metallic powder bed additive manufacturing processes with the finite element method: a critical review. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 231(1), 96–117 (2017). https://doi.org/10.1177/0954405414567522

    Article  Google Scholar 

  30. A.J. Pinkerton, Advances in the modeling of laser direct metal deposition. J. Laser Appl. 27(S1), S15001 (2015). https://doi.org/10.2351/1.4815992

    Article  Google Scholar 

  31. J.L. Bartlett, X. Li, An overview of residual stresses in metal powder bed fusion. Addit. Manuf. 27, 131–149 (2019). https://doi.org/10.1016/j.addma.2019.02.020. (In Press)

    Article  Google Scholar 

  32. J. Ning, S.Y. Liang, A comparative study of analytical thermal models to predict the orthogonal cutting temperature of AISI 1045 steel. Int. J. Adv. Manuf. Technol. 102, 1–11 (2019). https://doi.org/10.1007/s00170-019-03415-9

    Article  Google Scholar 

  33. J. Ning, V. Nguyen, S.Y. Liang, Analytical modeling of machining forces of ultra-fine-grained titanium. Int. J. Adv. Manuf. Technol. 101, 1–10 (2018). https://doi.org/10.1007/s00170-018-2889-6

    Article  Google Scholar 

  34. M. Van Elsen, M. Baelmans, P. Mercelis, J.P. Kruth, Solutions for modelling moving heat sources in a semi-infinite medium and applications to laser material processing. Int. J. Heat Mass Transf. 50(23–24), 4872–4882 (2007). https://doi.org/10.1016/j.ijheatmasstransfer.2007.02.044

    Article  MATH  Google Scholar 

  35. H. Carslaw, J. Jaeger, Conduction of Heat in Solids (Oxford Science Publication, Oxford, 1990)

    MATH  Google Scholar 

  36. J. Ning, D.E. Sievers, H. Garmestani, S.Y. Liang, Analytical modeling of in-process temperature in powder bed additive manufacturing considering laser power absorption, latent heat, scanning strategy, and powder packing. Materials 12(5), 808 (2019). https://doi.org/10.3390/ma12050808

    Article  ADS  Google Scholar 

  37. Y. Huang, M.B. Khamesee, E. Toyserkani, A new physics-based model for laser directed energy deposition (powder-fed additive manufacturing): from single-track to multi-track and multi-layer. Opt. Laser Technol. 109, 584–599 (2019). https://doi.org/10.1016/j.optlastec.2018.08.015

    Article  ADS  Google Scholar 

  38. A. Fathi, E. Toyserkani, A. Khajepour, M. Durali, Prediction of melt pool depth and dilution in laser powder deposition. J. Phys. D Appl. Phys. 39(12), 2613 (2006). https://doi.org/10.1088/0022-3727/39/12/022

    Article  ADS  Google Scholar 

  39. H.E. Cline, T. Anthony, Heat treating and melting material with a scanning laser or electron beam. J. Appl. Phys. 48(9), 3895–3900 (1977). https://doi.org/10.1063/1.324261

    Article  ADS  Google Scholar 

  40. A.J. Pinkerton, L. Li, Modelling the geometry of a moving laser melt pool and deposition track via energy and mass balances. J. Phys. D Appl. Phys. 37(14), 1885 (2004). https://doi.org/10.1088/0022-3727/37/14/003

    Article  ADS  Google Scholar 

  41. A.J. Pinkerton, L. Li, The significance of deposition point standoff variations in multiple-layer coaxial laser cladding (coaxial cladding standoff effects). Int. J. Mach. Tool Manuf. 44(6), 573–584 (2004). https://doi.org/10.1016/j.ijmachtools.2004.01.001

    Article  Google Scholar 

  42. D. Rosenthal, The theory of moving sources of heat and its application of metal treatments. Trans. ASME 68, 849–866 (1946)

    Google Scholar 

  43. H. Tan, J. Chen, F. Zhang, X. Lin, W. Huang, Process analysis for laser solid forming of thin-wall structure. Int. J. Mach. Tool Manuf. 50(1), 1–8 (2010). https://doi.org/10.1016/j.ijmachtools.2009.10.003

    Article  Google Scholar 

  44. J. Li, Q. Wang, P.P. Michaleris, An analytical computation of temperature field evolved in directed energy deposition. J. Manuf. Sci. Eng. 140(10), 101004 (2018). https://doi.org/10.1115/1.4040621

    Article  Google Scholar 

  45. M.N. Ahsan, A.J. Pinkerton, An analytical–numerical model of laser direct metal deposition track and microstructure formation. Modell. Simul. Mater. Sci. Eng. 19(5), 055003 (2011). https://doi.org/10.1088/0965-0393/19/5/055003

    Article  ADS  Google Scholar 

  46. P. Peyre, P. Aubry, R. Fabbro, R. Neveu, A. Longuet, Analytical and numerical modelling of the direct metal deposition laser process. J. Phys. D Appl. Phys. 41(2), 025403 (2008). https://doi.org/10.1088/0022-3727/41/2/025403

    Article  Google Scholar 

  47. Y. Yang, M.F. Knol, F. van Keulen, C. Ayas, A semi-analytical thermal modelling approach for selective laser melting. Addit. Manuf. 21, 284–297 (2018). https://doi.org/10.1016/j.addma.2018.03.002

    Article  Google Scholar 

  48. T.R. Walker, C.J. Bennett, T.L. Lee, A.T. Clare, A validated analytical-numerical modelling strategy to predict residual stresses in single-track laser deposited IN718. Int. J. Mech. Sci. 151, 609–621 (2019). https://doi.org/10.1016/j.ijmecsci.2018.12.004

    Article  Google Scholar 

  49. C.D. Boley, S.A. Khairallah, A.M. Rubenchik, Calculation of laser absorption by metal powders in additive manufacturing. Appl. Opt. 54(9), 2477–2482 (2015). https://doi.org/10.1364/AO.54.002477

    Article  ADS  Google Scholar 

  50. A.A. Deshpande, D.W.J. Tanner, W. Sun, T.H. Hyde, G. McCartney, Combined butt joint welding and post weld heat treatment simulation using SYSWELD and ABAQUS. Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl. 225(1), 1–10 (2011). https://doi.org/10.1177/14644207JMDA349

    Article  Google Scholar 

  51. H. Qi, J. Mazumder, L. Green, G. Herrit, Laser beam analysis in direct metal deposition process. J Laser Appl. 17(3), 136–143 (2005). https://doi.org/10.2351/1.1896965

    Article  Google Scholar 

  52. T.T. Roehling, S.S. Wu, S.A. Khairallah, J.D. Roehling, S.S. Soezeri, M.F. Crumb, M.J. Matthews, Modulating laser intensity profile ellipticity for microstructural control during metal additive manufacturing. Acta Mater. 128, 197–206 (2017). https://doi.org/10.1016/j.actamat.2017.02.025

    Article  Google Scholar 

  53. M. Rasch, C. Roider, S. Kohl, J. Strauß, N. Maurer, K.Y. Nagulin, M. Schmidt, Shaped laser beam profiles for heat conduction welding of aluminium-copper alloys. Opt. Lasers Eng. 115, 179–189 (2019). https://doi.org/10.1016/j.optlaseng.2018.11.025

    Article  Google Scholar 

  54. J. Ning, S.Y. Liang, Model-driven determination of Johnson-Cook material constants using temperature and force measurements. Int. J. Adv. Manuf. Technol. 97(1–4), 1053–1060 (2018). https://doi.org/10.1007/s00170-018-2022-x

    Article  Google Scholar 

  55. J. Ning, V. Nguyen, Y. Huang, K.T. Hartwig, S.Y. Liang, Inverse determination of Johnson-Cook model constants of ultra-fine-grained titanium based on chip formation model and iterative gradient search. Int. J. Adv. Manuf. Technol. 99(5–8), 1131–1140 (2018). https://doi.org/10.1007/s00170-018-2508-6

    Article  Google Scholar 

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Acknowledgements

The authors would like to acknowledge the funding support from The Boeing Company.

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Authors and Affiliations

  1. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 801 Ferst Drive, Atlanta, GA, 30332-0405, USA

    Jinqiang Ning & Steven Y. Liang

  2. The Boeing Company, 499 Boeing Boulevard, Huntsville, AL, 35824, USA

    Daniel E. Sievers

  3. School of Materials Science and Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, Atlanta, GA, 30332, USA

    Hamid Garmestani

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Ning, J., Sievers, D.E., Garmestani, H. et al. Analytical modeling of transient temperature in powder feed metal additive manufacturing during heating and cooling stages. Appl. Phys. A 125, 496 (2019). https://doi.org/10.1007/s00339-019-2782-7

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