, Volume 51, Issue 2, pp 279–289 | Cite as

Numerical calculation of temperature and surface topology during a laser ablation process for ceramic coatings

  • Peter WeidmannEmail author
  • Ulrich Weber
  • Siegfried Schmauder
  • Giancarlo Pedrini
  • Wolfgang Osten
Computational Micromechanics of Materials


In this paper a numerical procedure is presented to calculate a laser ablation process for ceramic thick film coatings. The code is required to cover temperature dependent material data, projected beam intensities and inhomogeneous coating–substrate combinations to calculate the hole shape geometry, the temperature distribution under the surface and the ablation rate per pulse. Therefore, the ablation speed was calculated by an Arrhenius equation while the temperature distribution was simulated by means of the heat conduction equation, which is solvable by a finite differences scheme. Hence, an adaptive mesh is used and the expansion of the code to three spatial dimensions enables the simulation of more complex ablation geometries. The simulation time was held low by introducing actualization frequencies, where critical and time consuming steps were only run if necessary. A validation of the numerical simulation was done by comparing the calculated temperature depth distribution and hole geometry with micrographs of experimental ablations.


Laser ablation Ceramic thick film coatings Non-steady heat conduction Residual stress determination 



This work was supported by the German Research Foundation (Deutsche Forschungs Gemeinschaft, DFG) under Grant Nos. Schm 746/120 and OS 111/37.


  1. 1.
    Wenzelburger M, Lopez D, Gadow R (2006) Methods and application of residual stress analysis on thermally sprayed coatings and layer composites. Surf Coat Technol 201(5):1995–2001CrossRefGoogle Scholar
  2. 2.
    Weidmann P, Weber U, Schmauder S, Martinez Garcia V (2014) Investigation of influence factors on residual stress determination within coated surfaces in consideration of the differential and integral method. Adv Mater Res 996:307–312CrossRefGoogle Scholar
  3. 3.
    Lorazo P, Lewis LJ, Meunier M (2006) Thermodynamic pathways to melting, ablation, and solidification in absorbing solids under pulsed laser irradiation. Phys Rev 73(134108):1–22Google Scholar
  4. 4.
    Ruf A (2004) Laser in der Materialbearbeitung. Herbert Utz Verlag MünchenGoogle Scholar
  5. 5.
    Modest MF (2006) Effects of multiple reflections on hole formation during short-pulsed laser drilling. J Heat Transf 128:653–661CrossRefGoogle Scholar
  6. 6.
    Eichler J, Eichler HJ (2010) Laser Bauformen, Strahlführung. Anwendungen. Springer, New YorkGoogle Scholar
  7. 7.
    Callies G (1999) Modellierung von qualitats- und effektivitätsbestimmenden Mechanismen beim Laserabtragen. PhD thesis, Univeristät StuttgartGoogle Scholar
  8. 8.
    Araya G, Gutierrez G (2006) Analytical solution for a transient, three-dimensional temperature distribution due to a moving laser beam. Int J Heat Mass Transf 49(21–22):4124–4131CrossRefzbMATHGoogle Scholar
  9. 9.
    Ho CY, Lu JK (2003) A closed form solution for laser drilling of silicon nitride and alumina ceramics. J Mater Process Technol 140(1–3):260–263CrossRefGoogle Scholar
  10. 10.
    Roy S, Modest MF, Bang SY (1993) Cw laser machining of hard ceramics. Int J Heat Mass Transf 36(14):3515–3540CrossRefGoogle Scholar
  11. 11.
    Modest MF (1996) Three-dimensional, transient model for laser machining of ablating/decomposing materials. Int J Heat Mass Transf 39(2):221–234CrossRefGoogle Scholar
  12. 12.
    Tannehill JC, Anderson DA, Pletcher RH (1997) Computational fluid mechanics and heat transfer. Taylor & Francis, WashingtoGoogle Scholar
  13. 13.
    Anisimov SI, Lukyanchuk BS (2002) Selected problems of laser ablation theory. Phys Usp 45(3):293–324ADSCrossRefGoogle Scholar
  14. 14.
    Carslaw HS, Jaeger JC (1959) Conduction of heat in solids. Oxford University Press, OxfordGoogle Scholar
  15. 15.
    Dubey AK, Yadava V (2008) Laser beam machining—a review. Int J Mach Tools Manuf 48(6):609–628CrossRefGoogle Scholar
  16. 16.
    Kabelac S, Kind M, Martin H, Mewes D, Schaber K, Stephan P (2006) VDI-Wärmeatlas. Springer, New YorkGoogle Scholar
  17. 17.
    Schwarz T (1996) Beitrag zur Eigenspannungsermittlung an isotropen, anisotropen sowie inhomogen, schichtweise aufgebauten Werkstoffen mittels Bohrlochmethode und Ringkernverfahren. PhD thesis, Univeristät StuttgartGoogle Scholar
  18. 18.
    Ajovalasit A, Petrucci G, Zuccarello B (1996) Determination of nonuniform residual stresses using the ring-core method. Trans ASME 118:224–228Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Peter Weidmann
    • 1
    Email author
  • Ulrich Weber
    • 1
  • Siegfried Schmauder
    • 1
  • Giancarlo Pedrini
    • 2
  • Wolfgang Osten
    • 2
  1. 1.Institute for Materials Testing, Materials Science and Strength of MaterialsUniversity of StuttgartStuttgartGermany
  2. 2.Institute of Applied OpticsUniversity of StuttgartStuttgartGermany

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