Advertisement

Computational Mechanics

, Volume 62, Issue 3, pp 273–284 | Cite as

Heat transfer model and finite element formulation for simulation of selective laser melting

  • Souvik Roy
  • Mario Juha
  • Mark S. Shephard
  • Antoinette M. Maniatty
Original Paper

Abstract

A novel approach and finite element formulation for modeling the melting, consolidation, and re-solidification process that occurs in selective laser melting additive manufacturing is presented. Two state variables are introduced to track the phase (melt/solid) and the degree of consolidation (powder/fully dense). The effect of the consolidation on the absorption of the laser energy into the material as it transforms from a porous powder to a dense melt is considered. A Lagrangian finite element formulation, which solves the governing equations on the unconsolidated reference configuration is derived, which naturally considers the effect of the changing geometry as the powder melts without needing to update the simulation domain. The finite element model is implemented into a general-purpose parallel finite element solver. Results are presented comparing to experimental results in the literature for a single laser track with good agreement. Predictions for a spiral laser pattern are also shown.

Keywords

Selective laser melting Finite element simulation Consolidation Melt pool size Additive manufacturing 

Notes

Acknowledgements

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under Award Number DE-SC-0011327. The authors acknowledge Dr. O. Klaas and Dr. M. Beall of Simmetrix, Inc. and Dr. M. Bloomfield, Mr. B. Granzow, and Mr. D. Ibanez of the Scientific Computation Research Center at Rensselaer Polytechnic Institute, who provided valuable contributions to the software development used in this work and feedback on the model development. The authors also thank Dr. G. Hansen from Sandia National Laboratories for providing the Albany finite element simulation tools and providing guidance for implementing new physical models. The simulations presented were carried out using facilities at the Center for Computational Innovations at Rensselaer Polytechnic Institute.

References

  1. 1.
    Bourell DL, Leu MC, Rosen DW (eds) (2009) Roadmap for additive manufacturing: identifying the future of freeform processing. University of Texas, AustinGoogle Scholar
  2. 2.
    Markl M, Körner C (2016) Multiscale modeling of powder bed-based additive manufacturing. Annu Rev Mater Res 46:93–123CrossRefGoogle Scholar
  3. 3.
    Körner C, Bauereiß A, Attar E (2013) Fundamental consolidation mechanisms during selective beam melting of powders. Modell Simul Mater Sci Eng 21:085011CrossRefGoogle Scholar
  4. 4.
    Khairallah SA, Anderson A (2014) Mesoscopic simulation model of selective laser melting of stainless steel powder. J Mater Process Technol 214:2627–2636CrossRefGoogle Scholar
  5. 5.
    Khairallah SA, Anderson A, Rubenchik A, King WE (2016) Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater 108:36–45CrossRefGoogle Scholar
  6. 6.
    Protasov CE, Khmyrov RS, Grigoriev SN, Gusarov AV (2017) Selective laser melting of fused silica: interdependent heat transfer and powder consolidation. Int J Heat Mass Transf 104:665–674CrossRefGoogle Scholar
  7. 7.
    Gusarov AV, Yadroitsev I, Bertrand P, Smurov I (2009) Model of radiation and heat transfer in laser–powder interaction zone at selective laser melting. J Heat Transf 131(7):072101-1–072101-10CrossRefGoogle Scholar
  8. 8.
    Verhaeghe F, Craeghs T, Heulens J, Pandelaers L (2009) A pragmatic model for selective laser melting with evaporation. Acta Mater 57:6006–6012CrossRefGoogle Scholar
  9. 9.
    Hodge NE, Ferencz RM, Solberg JM (2014) Implementation of a thermomechanical model for the simulation of selective laser melting. Comput Mech 54:33–51MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Yan W, Ge W, Smith J, Lin S, Kafka OL, Lin F, Liu WK (2016) Multi-scale modeling of electron beam melting of functionally graded materials. Acta Mater 115:403–412CrossRefGoogle Scholar
  11. 11.
    Dai K, Shaw L (2006) Parametric studies of multi-material laser densification. Mater Sci Eng 430:221–229CrossRefGoogle Scholar
  12. 12.
    Ma L, Bin H (2007) Temperature and stress analysis and simulation in fractal scanning-based laser sintering. Int J Adv Manuf Technol 34:898–903CrossRefGoogle Scholar
  13. 13.
    Hussein A, Hao L, Yan C, Everson R (2013) Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Mater Des 52:638–647CrossRefGoogle Scholar
  14. 14.
    Paul R, Anand S, Gerner F (2014) Effect of thermal deformation on part errors in metal powder based additive manufacturing processes. J Manuf Sci Eng Trans ASME 136:031009CrossRefGoogle Scholar
  15. 15.
    Denlinger ER, Irwin J, Michaleris P (2014) Thermomechanical modeling of additive manufacturing large parts. J Manuf Sci Eng Trans ASME 136:061007CrossRefGoogle Scholar
  16. 16.
    Yu J, Lin X, Ma L, Wang J, Fu X, Chen J, Weidong H (2011) Influence of laser deposition patterns on part distortion, interior quality, and mechanical qualities by laser solid forming. Mater Sci Eng A 528:1094–1104Google Scholar
  17. 17.
    King WE, Barth HB, Castillo VM, Gallegos GF, Gibbs JW, Hahn DE, Kamath C, Rubenchik AM (2014) Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing. J Mater Process Technol 214:2915–2925CrossRefGoogle Scholar
  18. 18.
    Xiao B, Zhang Y (2007) Analysis of melting of alloy powder bed with constant heat flux. Int J Heat Mass Transf 50:2161–2169CrossRefMATHGoogle Scholar
  19. 19.
    Salinger AG, Bartlett RA, Bradley AM, Chen Q, Demeshko IP, Gao X, Hansen GA, Mota A, Muller RP, Nielsen E, Ostien JT, Pawlowski RP, Perego M, Phipps ET, Sun W, Tezaur IK (2016) Albany: using component-based design to develop a flexible, generic multiphysics analysis code. Int J Multiscale Comput Eng 14(4):415–438CrossRefGoogle Scholar
  20. 20.
    Wang S-L, Sekerka RF, Wheeler AA, Murray BT, Coriell SR, Braun RJ, McFadden GB (1993) Thermodynamically-consistent phase-field models for solidification. Physica D 69:189–200MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Davis JR (ed) (1994) Stainless steels. ASM specialty handbook. ASM, Materials ParkGoogle Scholar
  22. 22.
    Song B, Dong S, Liao H, Coddet C (2012) Process parameter selection for selective laser melting of Ti\(_6\)Al\(_4\)V based on temperature distribution simulation and experimental sintering. Int J Adv Manuf Technol 61:967974CrossRefGoogle Scholar
  23. 23.
    Antony K, Arivazhagan N, Senthilkumaran K (2014) Numerical and experimental investigations on laser melting of stainless steel 316l metal powders. J Manuf Process 16:345–355CrossRefGoogle Scholar
  24. 24.
    Mazumder J, Steen WM (1980) Heat transfer model for cw laser material processing. J Appl Phys 51(2):941–947CrossRefGoogle Scholar
  25. 25.
    Cremers DA, Lewis GK, Korzekwa DR (1991) Measurement of energy deposition during pulsed laser welding. Weld J 40(7):159-s–167-sGoogle Scholar
  26. 26.
    Rai R, Elmer JW, Palmer TA, DebRoy T (2007) Heat transfer and fluid flow during keyhole mode laser welding of tantalum, Ti\(_6\)Al\(_4\)V, 304L stainless steel and vanadium. J Phys D Appl Phys 40:5753–5766CrossRefGoogle Scholar
  27. 27.
    Hansen G Albany project website. https://github.com/gahansen/albany/wiki
  28. 28.
    Heroux MA, Bartlett RA, Howle VE, Hoekstra RJ, Hu JJ, Kolda TG, Lehoucq RB, Long KR, Pawlowski RP, Phipps ET, Salinger AG, Thornquist HK, Tuminaro RS, Willenbring JM, Williams A, Stanley KS (2005) An overview of the trilinos project. ACM Trans Math Softw 31(3):397–423MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Prokopenko A, Siefert CM, Hu JJ, Hoemmen M, Klinvex A (2016) Ifpack2 users guide 1.0. Technical report SAND2016-5338, Sandia National Labs, 2016Google Scholar
  30. 30.
    Beall M, Simmetrix, Inc. website. http://www.simmetrix.com/
  31. 31.
    Yadroitsev I, Gusarov A, Yadroitsava I, Smurov I (2010) Single track formation in selective laser melting of metal powders. J Mater Process Technol 210:1624–1631CrossRefGoogle Scholar
  32. 32.
    Bristow DA, Tharayil M, Alleyne AG (2006) A survey of iterative learning control. IEEE Control Syst 26(3):96–114CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Souvik Roy
    • 1
  • Mario Juha
    • 1
    • 2
  • Mark S. Shephard
    • 1
  • Antoinette M. Maniatty
    • 1
  1. 1.Department of Mechanical, Aerospace, and Nuclear EngineeringRensselaer Polytechnic InstituteTroyUSA
  2. 2.Programa de Ingeniería MecánicaUniversidad de La SabanaChíaColombia

Personalised recommendations