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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

Abstract

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.

Keywords

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

Notes

Acknowledgments

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.

References

  1. 1.
    Anderson T (2005) Fracture mechanics: fundamentals and applications. CRC, 3rd edn. CRC Press Inc, Taylor and Francis Group, Boca RatonGoogle Scholar
  2. 2.
    Barsoum R (1976) On the use of isoparametric finite elements in linear fracture mechanics. Int J Numer Methods Eng 10(1):25–37CrossRefzbMATHGoogle Scholar
  3. 3.
    Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5):601–620CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Belytschko T, Loehnert S, Song J (2008) Multiscale aggregating discontinuities: a method for circumventing loss of material stability. Int J Numer Methods Eng 73(6):869–894CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Benzley S (1974) Representation of singularities with isoparametric finite elements. Int J Numer Methods Eng 8(3):537–545CrossRefzbMATHGoogle Scholar
  6. 6.
    Bräunling W (2009) Flugzeugtriebwerke: Grundlagen, Aero-Thermodynamik, ideale und reale Kreiselprozesse, Thermische Turbomaschinen, Emissionen und Systeme, 3rd edn. Springer, BerlinCrossRefGoogle Scholar
  7. 7.
    Budyn É, Zi G, Moës N, Belytschko T (2004) A method for multiple crack growth in brittle materials without remeshing. Int J Numer Methods Eng 61(10):1741–1770CrossRefzbMATHGoogle Scholar
  8. 8.
    Domen Š, Matija F, Marko N (2011) Creep damage calculation for thermo mechanical fatigue. J Mech Eng 57(5):371–378CrossRefGoogle Scholar
  9. 9.
    Duarte C, Babuška I, Oden T (2000) Generalized finite element methods for three-dimensional structural mechanics problems. Comput Struct 77(2):215–232CrossRefGoogle Scholar
  10. 10.
    Erdogan F, Sih G (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85(4):519–527CrossRefGoogle Scholar
  11. 11.
    Fries T (2008) A corrected XFEM approximation without problems in blending elements. Int J Numer Methods Eng 75(5):503–532CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Fries T, Baydoun M (2012) Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description. Int J Numer Methods Eng 88(12):1527–1558CrossRefMathSciNetGoogle Scholar
  13. 13.
    Fries T, Belytschko T (2010) The extended/generalized finite element method: an overview of the method and its applications. Int J Numer Methods Eng 84(3):253–304zbMATHMathSciNetGoogle Scholar
  14. 14.
    Geers M, Kouznetsova V, Brekelmans W (2010) Multi-scale computational homogenization: trends and challenges. J Comput Appl Math 234(7):2175–2182CrossRefzbMATHGoogle Scholar
  15. 15.
    Gravouil A, Moës N, Belytschko T (2002) Non-planar 3D crack growth by the extended finite element and level sets—Part II: level set update. Int J Numer Methods Eng 53(11):2569–2586CrossRefGoogle Scholar
  16. 16.
    Gross D, Seelig T (2011) Fracture mechanics: with an introduction to micromechanics. Springer, BerlinCrossRefGoogle Scholar
  17. 17.
    Grote K, Feldhusen J (2011) Dubbel: Taschenbuch für den Maschinenbau, 23rd edn. Springer, BerlinGoogle Scholar
  18. 18.
    Haibach E (2006) Betriebsfestigkeit: Verfahren und Daten zur Bauteilberechnung, 3rd edn. Springer, BerlinGoogle Scholar
  19. 19.
    Henshell R, Shaw K (1975) Crack tip finite elements are unnecessary. Int J Numer Methods Eng 9(3):495–507CrossRefzbMATHGoogle Scholar
  20. 20.
    Hesse W (2012) Aluminium-Schlüssel, 10th edn. Beuth, BerlinGoogle Scholar
  21. 21.
    Holl M, Loehnert S, Wriggers P (2013) An adaptive multiscale method for crack propagation and crack coalescence. Int J Numer Methods Eng 93(1):23–51Google Scholar
  22. 22.
    Hou J, Wicks B, Antoniou R (2002) An investigation of fatigue failures of turbine blades in a gas turbine engine by mechanical analysis. Eng Fail Anal 9(2):201–211CrossRefGoogle Scholar
  23. 23.
    Kaufman J (2006) Properties of aluminium alloys: tensile, creep, and fatigue data at high and low temperatures, 3 edn. ASM International, Materials Park (Ohio), Washington, DCGoogle Scholar
  24. 24.
    Kaufman J (2008) Parametric analyses of high-temperature data for aluminium alloys, 1st edn. ASM International, Materials Park (Ohio), Washington, DCGoogle Scholar
  25. 25.
    Kaufman J (2008) Properties of aluminium alloys: Fatigue data and the effects of temperature, product form, and processing, 1 edn. ASM International, Materials Park (Ohio), Washington, DCGoogle Scholar
  26. 26.
    Laborde P, Pommier J, Renard Y, Salaün M (2005) High-order extended finite element method for cracked domains. Int J Numer Methods Eng 64(3):354–381CrossRefzbMATHGoogle Scholar
  27. 27.
    Loehnert S, Belytschko T (2007) Crack shielding and amplification due to multiple microcracks interacting with a macrocrack. Int J Fract 145(1):1–8CrossRefzbMATHGoogle Scholar
  28. 28.
    Loehnert S, Belytschko T (2007) A multiscale projection method for macro / microcrack simulations. Int J Numer Methods Eng 71(12):1466–1482CrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    Loehnert S, Mueller-Hoeppe D (2008) Multiscale methods for fracturing solids. In: Reddy B (ed) IUTAM symposium on theoretical, computational and modelling aspects of inelastic media, vol 11. Springer, Netherlands, pp 79–87 Google Scholar
  30. 30.
    Loehnert S, Mueller-Hoeppe D, Wriggers P (2011) 3D corrected XFEM approach and extension to finite deformation theory. Int J Numer Methods Eng 86(4–5):431–452CrossRefzbMATHMathSciNetGoogle Scholar
  31. 31.
    Melenk J, Babuška I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139(1–4):289–314CrossRefzbMATHGoogle Scholar
  32. 32.
    Miner M (1945) Cumulative damage in fatigue. J Appl Mech 12:A-159–A-164Google Scholar
  33. 33.
    Moës N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69(7):813–833CrossRefGoogle Scholar
  34. 34.
    Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150CrossRefzbMATHGoogle Scholar
  35. 35.
    Moës N, Gravouil A, Belytschko T (2002) Non-planar 3D crack growth by the extended finite element and level sets—Part I: mechanical model. Int J Numer Methods Eng 53(11):2549–2568CrossRefzbMATHGoogle Scholar
  36. 36.
    Moran B, Shih CF (1987) Crack tip and associated domain integrals from momentum and energy balance. Int J Fract 27(6):615–642Google Scholar
  37. 37.
    Osher S, Sethian J (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79(1):12–49CrossRefzbMATHMathSciNetGoogle Scholar
  38. 38.
    Palmgren A (1924) Die Lebensdauer von Kugellagern (The service life of ball bearings). Zeitschrift des Vereins Deutscher Ingenieure 68(14):339–341 (NASA TT F-13460)Google Scholar
  39. 39.
    Pereira J, Kim DJ, Duarte C (2012) A two-scale approach for the analysis of propagating three-dimensional fractures. Comput Mech 49(1):99–121CrossRefzbMATHMathSciNetGoogle Scholar
  40. 40.
    Radaj D, Vormwald M (2007) Ermüdungsfestigkeit: Grundlagen für Ingenieure, 3rd edn. Springer, Berlin Google Scholar
  41. 41.
    Rice J (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35(2):379–386CrossRefMathSciNetGoogle Scholar
  42. 42.
    Rogge T, Rolfes R (2012) Stochastische Untersuchungen regenerationsbedingter Imperfektionen einer Turbinenschaufel: Modellierung des deterministischen Modells zur effizienten Berechnung des Schwingungs- und Festigkeitsverhaltens. In: 5. Dresdner-Probabilistik-Workshop. Dresden, Germany. http://www.probabilistik.de/artikel/a2012_rogge.pdf
  43. 43.
    Sabour M, Bhat R (2008) Lifetime prediction in creep-fatigue environment. Mater Sci Pol 26(3):563–584Google Scholar
  44. 44.
    Stolarska M, Chopp D, Moës N, Belytschko T (2001) Modelling crack growth by level sets in the extended finite element method. Int J Numer Methods Eng 51(8):943–960Google Scholar
  45. 45.
    Sukumar N, Chopp D, Moran B (2003) Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Eng Fract Mech 70(1):29–48CrossRefGoogle Scholar
  46. 46.
    Sukumar N, Moës N, Moran B, Belytschko T (2000) Extended finite element method for three-dimensional crack modelling. Int J Numer Methods Eng 48(11):1549–1570CrossRefzbMATHGoogle Scholar
  47. 47.
    Voigt M (2010) Probabilistische Simulation des strukturmechanischen Verhaltens von Turbinenschaufeln. TUD press, DresdenGoogle Scholar
  48. 48.
    Weiß T, Schlums H (2008) Probabilistische Finite-Elemente Analysen zum Einfluss von Materialstreuungen auf die Lebensdauer einer einkristallinen Turbinenschaufel. 1. Dresdner-Probabilistik-Workshop. Dresden, Germany. http://www.probabilistik.de/artikel/Artikel0505_Weiss_RollsRoyce.pdf

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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