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Prediction of Thermal Residual Stress and Microstructure in Direct Laser Metal Deposition via a Coupled Finite Element and Multiphase Field Framework

  • Qinan Li
  • Balachander Gnanasekaran
  • Yao FuEmail author
  • G. R. LiuEmail author
ICME-Based Design and Optimization of Materials for Additive Manufacturing


Direct laser metal deposition (DLMD) is a modern powder-fed additive manufacturing process, which builds up complex objects layer by layer, providing a potential capacity to produce key structural components specifically for the aerospace industry. The printing process is of a multidisciplinary nature, and has gained increasing attention in the areas of engineering mechanics, material science, control engineering and many other related fields. The quality control of the printed part depends on a large number of process parameters. The aim of this work, therefore, is to develop a coupled finite element and multiphase field framework, that provides an effective way to understand the quantitative relationship between the process parameters, temperature history, thermally-induced residual stresses and microstructures in the DLMD process. More specifically, the established multiscale framework is able to sequentially couple the heat transfer, metal melting/solidification, and stress analysis to simulate the macroscopic temperature distribution, thermal residual stresses and dendrite growth and solute segregation in a thin wall structure made of a binary nickel-copper alloy. The latest simulation technologies are used to model the process of progressive material deposition as well as the movement of the laser beam. It has been found that the high intensity laser introduced in DLMD can produce a complex thermal history and a significant level of thermal residual stresses and distortion. Microstructure predictions demonstrate the location-dependent morphology evolution, e.g., the dendrite spacing and the degree of solute segregation, attributed to the spatially variant temperature history.


Supplementary material

11837_2019_3922_MOESM1_ESM.pdf (1.3 mb)
Supplementary material 1 (PDF 1308 kb)


  1. 1.
    C.L. Weber, V. Peña, and M.K. Micali, IDA Paper 5091, (2013).Google Scholar
  2. 2.
    J. Ning and S. Liang, J. Manuf. Mater. Process. 2, 37 (2018).Google Scholar
  3. 3.
    J. Ning and S. Liang, Materials 12, 284 (2019).CrossRefGoogle Scholar
  4. 4.
    A.J. Pinkerton and L. Li, Proc. Inst. Mech. Eng. Part C 218, 531 (2004).CrossRefGoogle Scholar
  5. 5.
    A. Vasinonta, J.L. Beuth, and M. Griffith, J. Eng. Ind. 129, 101 (2006).Google Scholar
  6. 6.
    J.C. Heigel, P. Michaleris, and E.W. Reutzel, Addit. Manuf. 5, 9 (2015).CrossRefGoogle Scholar
  7. 7.
    R. Gardon and J.C. Akfirat, Int. J. Heat Mass Transfer 8, 1261 (1965).CrossRefGoogle Scholar
  8. 8.
    K.P. Perry, Proc. - Inst. Mech. Eng. 168, 775 (1954).CrossRefGoogle Scholar
  9. 9.
    A.F.A. Hoadley and M. Rappaz, Metall. Trans. B 23, 631 (1992).CrossRefGoogle Scholar
  10. 10.
    R. Gardon, and J. Cobonpu, Heat transfer between a flat plate and jets of air impinging on it, in International Development in Heat Transfer, Proceedings of Heat Transfer Conference (1962), p. 454.Google Scholar
  11. 11.
    S. Ghosh and J. Choi, J. Laser Appl. 17, 144 (2005).CrossRefGoogle Scholar
  12. 12.
    Y. Fu, J. Michopoulos, and B. Gnanasekaran, Comput. Mater. Sci. 155, 457 (2018).CrossRefGoogle Scholar
  13. 13.
    Y. Fu, J.G. Michopoulos, and J.-H. Song, J. Comput. Sci. 20, 187 (2017).MathSciNetCrossRefGoogle Scholar
  14. 14.
    J.H. Song, Y. Fu, T.Y. Kim, Y.C. Yoon, J.G. Michopoulos, and T. Rabczuk, Int. J. Mech. Mater. Des. 14, 491 (2018).CrossRefGoogle Scholar
  15. 15.
    A. Almasi, A. Beel, T.Y. Kim, J.G. Michopoulos, and J.H. Song, J. Eng. Mech. Div. Am. Soc. Civ. Eng. 145, 0401908282 (2019).CrossRefGoogle Scholar
  16. 16.
    G.R. Liu, and S.S. Quek, The Finite Element Method: A Practical Cours, 2nd edn. (Elsevier (BH), 2014), p. 464.Google Scholar
  17. 17.
    J. Eiken, B. Böttger, and I. Steinbach, Phys. Rev. E 73, 066122 (2006).CrossRefGoogle Scholar
  18. 18.
    M.K. Thompson, G. Moroni, T. Vaneker, G. Fadel, R.I. Campbell, I. Gibson, A. Bernard, J. Schulz, P. Graf, B. Ahuja, and F. Martina, CIRP Ann. 65, 737 (2016).CrossRefGoogle Scholar
  19. 19.
    M.K. Thompson, A. Stolfi, and M. Mischkot, CIRP J. Manuf. Sci. Technol. 12, 25 (2016).CrossRefGoogle Scholar
  20. 20.
    G. Marion, G. Cailletaud, C. Colin, and M. Mazière, A finite element model for the simulation of direct metal deposition, in ICALEO (2014).Google Scholar
  21. 21.
    Abaqus, Dassault Systèmes Simulia Corp., (2019).Google Scholar
  22. 22.
    G.R. Liu and N.T. Trung, Smoothed Finite Element Methods (Boca Raton: CRC, 2010).Google Scholar
  23. 23.
    S. Kim, W. Kim, T. Suzuki, and M. Ode, J. Cryst. Growth 261, 135 (2004).CrossRefGoogle Scholar
  24. 24.
    S.G. Kim, W.T. Kim, and T. Suzuki, Phys. Rev. E 60, 7186 (1999).CrossRefGoogle Scholar
  25. 25.
    J.J. Valencia, and P.N. Quested, Thermophysical properties, in Casting, (New York: ASM International, 2008), p. 468–481.Google Scholar
  26. 26.
    R.E. Pawel and E.E. Stansbury, J. Phys. Chem. Solids 26, 607 (1965).CrossRefGoogle Scholar
  27. 27.
    C.Y. Ho, M.W. Ackerman, K.Y. Wu, S.G. Oh, and T.N. Havill, J. Phys. Chem. Ref. Data7(3), 959 (1978).CrossRefGoogle Scholar
  28. 28.
    G.R. Liu, Comp. Struct. 40, 313 (1997).CrossRefGoogle Scholar
  29. 29.
    D. Jeong and J. Kim, Phys. A 442, 510 (2016).MathSciNetCrossRefGoogle Scholar
  30. 30.
    J. Li, J. Wang, and G. Yang, J. Cryst. Growth 309, 65 (2007).CrossRefGoogle Scholar
  31. 31.
    M. Asta, J.J. Hoyt, and A. Karma, Phys. Rev. B 66, 100101 (2002).CrossRefGoogle Scholar
  32. 32.
    J.A. Warren and W.J. Boettinger, Acta Metall. Mater. 43, 689 (1995).CrossRefGoogle Scholar
  33. 33.
    J.A. Warren, T. Pusztai, L. Környei, and L. Gránásy, Phys. Rev. B 79, 014204 (2009).CrossRefGoogle Scholar
  34. 34.
    T. Takaki, M. Ohno, Y. Shibuta, S. Sakane, T. Shimokawabe, and T. Aoki, J. Cryst. Growth, 442, 14 (2016).CrossRefGoogle Scholar
  35. 35.
    J.C. Heigel, Chapter 8—thermo-mechanical modeling of thin wall builds using powder fed directed energy deposition, in Thermo-Mechanical Modeling of Additive Manufacturing, eds. by M. Gouge and P. Michaleris (London, Butterworth-Heinemann, 2018), p. 137–151.Google Scholar
  36. 36.
    M. Tonks, D. Gaston, P. Millett, D. Andrs, and P. Talbot, Comput. Mater. Sci. 51, 20 (2012).CrossRefGoogle Scholar
  37. 37.
    D. Schwen, L. Aagesen, J. Peterson, and M. Tonks, Comput. Mater. Sci. 132 (2017).Google Scholar

Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  1. 1.Department of Aerospace Engineering and Engineering MechanicsUniversity of CincinnatiCincinnatiUSA

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