Computational Mechanics

, Volume 53, Issue 1, pp 173–188 | Cite as

3D multiscale crack propagation using the XFEM applied to a gas turbine blade

  • Matthias Holl
  • Timo Rogge
  • Stefan Loehnert
  • Peter Wriggers
  • Raimund Rolfes
Original Paper


This work presents a new multiscale technique to investigate advancing cracks in three dimensional space. This fully adaptive multiscale technique is designed to take into account cracks of different length scales efficiently, by enabling fine scale domains locally in regions of interest, i.e. where stress concentrations and high stress gradients occur. Due to crack propagation, these regions change during the simulation process. Cracks are modeled using the extended finite element method, such that an accurate and powerful numerical tool is achieved. Restricting ourselves to linear elastic fracture mechanics, the \(J\)-integral yields an accurate solution of the stress intensity factors, and with the criterion of maximum hoop stress, a precise direction of growth. If necessary, the on the finest scale computed crack surface is finally transferred to the corresponding scale. In a final step, the model is applied to a quadrature point of a gas turbine blade, to compute crack growth on the microscale of a real structure.


XFEM Crack propagation Multiscale  3D Gas turbine blade Fatigue strength  Linear damage accumulation 



The German Research Association is gratefully acknowledged for the support of the Collaborative Research Center (SFB) 871. Furthermore, the first author would like to thank Dr. Tymofiy Gerasimov for splendid discussions about the XFEM.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Matthias Holl
    • 1
  • Timo Rogge
    • 2
  • Stefan Loehnert
    • 1
  • Peter Wriggers
    • 1
  • Raimund Rolfes
    • 2
  1. 1.Institute of Continuum MechanicsLeibniz Universität HannoverHannoverGermany
  2. 2.Institute of Structural AnalysisLeibniz Universität HannoverHannoverGermany

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