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Finite element simulation of coating-induced heat transfer: application to thermal spraying processes

  • Computational Micromechanics of Materials
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Abstract

Thermal spraying is a widely applied coating technique. The optimisation of the thermal spraying process with respect to temperature or temperature induced residual stress states requires a numerical framework for the simulation of the coating itself as well as of the quenching procedure after the application of additional material. This work presents a finite element framework for the simulation of mass deposition due to coating by means of thermal spraying combined with the simulation of nonlinear heat transfer of a rigid heat conductor. The approach of handling the dynamic problem size is highlighted with focus on the thermodynamical consistency of the derived model. With the framework implemented, numerical examples are employed and material parameters are fitted to experimental data of steel as well as of tungsten-carbide–cobalt-coating.

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References

  1. Baumann CE, Oden JT (1999) A discontinuous hp finite element method for convection—diffusion problems. Comput Methods Appl Mech Eng 175(3–4):311–341. doi:10.1016/S0045-7825(98)00359-4

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Berthelsen R, Wiederkehr T, Denzer R, Menzel A, Müller H (2014) Efficient simulation of nonlinear heat transfer during thermal spraying of complex workpieces. World J Mech 04(09):289–301. doi:10.4236/wjm.2014.49029

    Article  Google Scholar 

  3. Bonet J, Wood RD (2008) Nonlinear continuum mechanics for finite element analysis. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  4. Clyne TW, Gill SC (1996) Residual stresses in thermal spray coatings and their effect on interfacial adhesion: a review of recent work. J Therm Spray Technol 5(4):401–418. doi:10.1007/BF02645271

    Article  ADS  Google Scholar 

  5. Coleman BD, Noll W (1963) The thermodynamics of elastic materials with heat conduction and viscosity. Arch Ration Mech Anal 13(1):167–178. doi:10.1007/BF01262690

    Article  MathSciNet  MATH  Google Scholar 

  6. Delfosse D, Cherradi N, Ilschner B (1997) Numerical and experimental determination of residual stresses in graded materials. Compos B: Eng 28(1–2):127–141. doi:10.1016/S1359-8368(96)00037-6

    Article  Google Scholar 

  7. Engel G, Garikipati K, Hughes T, Larson M, Mazzei L, Taylor R (2002) Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity. Comput Methods Appl Mech Eng 191(34):3669–3750. doi:10.1016/S0045-7825(02)00286-4

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Fagerstrom M, Larsson R (2008) A thermo-mechanical cohesive zone formulation for ductile fracture. J Mech Phys Solids 56(10):3037–3058. doi:10.1016/j.jmps.2008.06.002

    Article  ADS  MathSciNet  Google Scholar 

  9. Fleischhauer R, Behnke R, Kaliske M (2013) A thermomechanical interface element formulation for finite deformations. Comput Mech 52(5):1039–1058. doi:10.1007/s00466-013-0862-7

    Article  MathSciNet  MATH  Google Scholar 

  10. Gérard B (2006) Application of thermal spraying in the automobile industry. Surf Coatings Technol 201(5):2028–2031. doi:10.1016/j.surfcoat.2006.04.050

    Article  Google Scholar 

  11. Gross M, Betsch P (2011) Galerkin-based energy momentum consistent time-stepping algorithms for classical nonlinear thermo-elastodynamics. Math Comput Simul 82(4):718–770. doi:10.1016/j.matcom.2011.10.009

    Article  MathSciNet  MATH  Google Scholar 

  12. Hanson T, Hackett C, Settles G (2002) Independent control of HVOF particle velocity and temperature. J Therm Spray Technol 11(1):75–85. doi:10.1361/105996302770349005

    Article  ADS  Google Scholar 

  13. Hu C, Lepsky O, Shu CW (2000) The effect of the least square procedure for discontinuous Galerkin methods for Hamilton–Jacobi equations. In: Griebel M, Keyes DE, Nieminen RM, Roose D, Schlick T, Cockburn B, Karniadakis GE, Shu CW (eds) Discontinuous Galerkin methods, vol 11. Springer, Berlin, pp 343–348

    Chapter  Google Scholar 

  14. Hussainova I, Kubarsepp J, Pirso J (2001) Mechanical properties and features of erosion of cermets. Wear 250(1–12):818–825. doi:10.1016/S0043-1648(01)00737-2

    Article  Google Scholar 

  15. Hutter K (2004) Continuum methods of physical modeling: continuum mechanics, dimensional analysis, turbulence. Springer, Berlin

    Book  Google Scholar 

  16. Klusemann B, Denzer R, Svendsen B (2012) Microstructure-based modeling of residual stresses in WC-12co-sprayed coatings. J Therm Spray Technol 21(1):96–107. doi:10.1007/s11666-011-9690-5

    Article  ADS  Google Scholar 

  17. Kuroda S, Clyne T (1991) The quenching stress in thermally sprayed coatings. Thin Solid Films 200(1):49–66. doi:10.1016/0040-6090(91)90029-W

    Article  ADS  Google Scholar 

  18. Lewis RW, Nithiarasu P, Seetharamu K (2004) Fundamentals of the finite element method for heat and fluid flow. Wiley, New Jersey

    Book  Google Scholar 

  19. Liu IS (2002) Continuum mechanics. Springer, Berlin

    Book  MATH  Google Scholar 

  20. Müller I (1973) Thermodynamik: die Grundlagen d. Materialtheorie. Bertelsmann-Universitätsverlag, Düsseldorf

    Google Scholar 

  21. Nomura T, Moriguchi H, Tsuda K, Isobe K, Ikegaya A, Moriyama K (1999) Material design method for the functionally graded cemented carbide tool. Int J Refract Metals Hard Mater 17(6):397–404. doi:10.1016/S0263-4368(99)00029-3

    Article  Google Scholar 

  22. Sahraoui T, Fenineche NE, Montavon G, Coddet C (2003) Structure and wear behaviour of HVOF sprayed Cr3c2-NiCr and WC-Co coatings. Mater Design 24(5):309–313. doi:10.1016/S0261-3069(03)00059-1

    Article  Google Scholar 

  23. Steinmann P, Häsner O (2005) On material interfaces in thermomechanical solids. Arch Appl Mech 75(1):31–41. doi:10.1007/s00419-005-0383-8

    Article  MATH  Google Scholar 

  24. Thorpe ML, Richter HJ (1992) A pragmatic analysis and comparison of HVOF processes. J Therm Spray Technol 1(2):161–170. doi:10.1007/BF02659017

    Article  ADS  Google Scholar 

  25. Toparli M, Sen F, Culha O, Celik E (2007) Thermal stress analysis of HVOF sprayed WC-Co/NiAl multilayer coatings on stainless steel substrate using finite element methods. J Mater Process Technol 190(1–3):26–32. doi:10.1016/j.jmatprotec.2007.03.115

    Article  Google Scholar 

  26. Utzinger J, Bos M, Floeck M, Menzel A, Kuhl E, Renz R, Friedrich K, Schlarb AK, Steinmann P (2008) Computational modelling of thermal impact welded PEEK/steel single lap tensile specimens. Comput Mater Sci 41(3):287–296. doi:10.1016/j.commatsci.2007.04.015

    Article  Google Scholar 

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Acknowledgments

This research was funded by the German Research Foundation (DFG) as part of the collaborative research center 708 “3D-Surface Engineering of Tools for Sheet Metal Forming—Manufacturing, Modeling, Machining” within the project B6.

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Authors and Affiliations

  1. Institute of Mechanics, TU Dortmund, Leonhard-Euler-Straße 5, 44227, Dortmund, Germany

    Rolf Berthelsen, Dennis Tomath & Andreas Menzel

  2. Division of Solid Mechanics, Lund University, Ole Römers väg, 22363, Lund, Sweden

    Ralf Denzer & Andreas Menzel

Authors
  1. Rolf Berthelsen
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  2. Dennis Tomath
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  3. Ralf Denzer
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  4. Andreas Menzel
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Correspondence to Rolf Berthelsen.

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Berthelsen, R., Tomath, D., Denzer, R. et al. Finite element simulation of coating-induced heat transfer: application to thermal spraying processes. Meccanica 51, 291–307 (2016). https://doi.org/10.1007/s11012-015-0236-7

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  • DOI: https://doi.org/10.1007/s11012-015-0236-7

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