Skip to main content
Log in

Concurrent fatigue crack growth simulation using extended finite element method

  • Research Article
  • Published:
Frontiers of Architecture and Civil Engineering in China Aims and scope Submit manuscript

Abstract

In this paper, a concurrent simulation framework for fatigue crack growth analysis is proposed using a novel small time scale model for fatigue mechanism analysis and the extended finite element method (X-FEM) for fatigue crack growth simulation. The proposed small time scale fatigue model does not require the cycle counting as those using the classical fatigue analysis methods and can be performed concurrently with structural/mechanical analysis. The X-FEM greatly facilitates crack growth simulation without remeshing requirements ahead of the crack tip as in the classical finite element method. The basic concept and theory of X-FEM was briefly introduced and numerical predictions of stress intensity factors are verified with reference solutions under both uniaxial and multiaxial loadings. The small time scale fatigue model is integrated into the numerical simulation algorithm for concurrent fatigue crack growth analysis. Model predictions are compared with available experimental observations for model validation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Sih G C. Multiscale Fatigue Crack Initiation and Propagation of Engineering Materials: Structural Integrity and Microstructural Worthiness. New York: Springer, 2008

    Book  MATH  Google Scholar 

  2. Lu Z, Liu Y. An incremental crack growth model for multi-scale fatigue analysis. In: Proceedings of 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference Palm Springs, CA, USA. 2009

  3. Pommier S, Risbet M. Time derivative equations for mode I fatigue crack growth in metals. International Journal of Fatigue, 2005, 27(10–12): 1297–1306

    Article  Google Scholar 

  4. Emery J M, Hochhalter J D, Wawrzynek P A, Heber G, Ingraffea A R. DDSim: A hierarchical, probabilistic, multiscale damage and durability simulation system-Part I: Methodology and Level I. Engineering Fracture Mechanics, 2009, 76(10): 1500–1530

    Article  Google Scholar 

  5. Schütz W. A history of fatigue. Engineering Fracture Mechanics, 1996, 54(2): 263–300

    Article  Google Scholar 

  6. Paris P, Erdogan F. A critical analysis of crack propagation laws. Journal of Basic Engineering, Transactions of ASME, 1963, 85: 528–534

    Google Scholar 

  7. ASTM. Standard practices for cycle counting in fatigue analysis. E 1048-85 ASTM International, 1985

  8. Lu Z, Liu Y. Small time scale fatigue crack growth analysis. International Journal of Fatigue, 2010

  9. Béchet E, Minnebo H, Moës N, Burgardt B. Improved implementation and robustness study of the X-FEM for stress analysis around cracks. International Journal for Numerical Methods in Engineering, 2005, 64(8): 1033–1056

    Article  MATH  Google Scholar 

  10. Dolbow J, Moës N, Belytschko T. Modeling fracture in Mindlin-Reissner plates with the extended finite element method. International Journal of Solids and Structures, 2000, 37(48–50): 7161–7183

    Article  MATH  Google Scholar 

  11. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620

    Article  MATH  MathSciNet  Google Scholar 

  12. Sukumar N, Chopp D L, Moës N, Belytschko T. Modeling holes and inclusions by level sets in the extended finite-element method. Computer Methods in Applied Mechanics and Engineering, 2001, 190(46–47): 6183–6200

    Article  MATH  MathSciNet  Google Scholar 

  13. Moës N, Belytschko T. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics, 2002, 69(7): 813–833

    Article  Google Scholar 

  14. Stolarska M, Chopp D L, Moës N, Belytschko T. Modelling crack growth by level sets in the extended finite element method. International Journal for Numerical Methods in Engineering, 2001, 51(8): 943–960

    Article  MATH  Google Scholar 

  15. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131–150

    Article  MATH  Google Scholar 

  16. Dolbow J, Moës N, Belytschko T. An extended finite element method for modeling crack growth with frictional contact. Computer Methods in Applied Mechanics and Engineering, 2001, 190(51–52): 6825–6846

    Article  MATH  MathSciNet  Google Scholar 

  17. Daux C, Moës N, Dolbow J, Sukumar N, Belytschko T. Arbitrary branched and intersecting cracks with the extended finite element method. International Journal for Numerical Methods in Engineering, 2000, 48(12): 1741–1760

    Article  MATH  Google Scholar 

  18. Dolbow J. An extended finite element method with discontinuous enrichment for applied mechanics. Dissertation for the Doctoral Degree. Chicago: Northwestern University, 1999, 1–176

    Google Scholar 

  19. Budyn É, Zi G, Moës N, Belytschko T. A method for multiple crack growth in brittle materials without remeshing. International Journal for Numerical Methods in Engineering, 2004, 61(10): 1741–1770

    Article  MATH  Google Scholar 

  20. Khoei A R, Nikbakhta M. Contact friction modeling with the extended finite element method (X-FEM). Journal of Materials Processing Technology, 2006, 177(1–3): 58–62

    Article  Google Scholar 

  21. Sukumar N, Srolovitz D J, Baker T J, Prévost J-h. Brittle fracture in polycrystalline microstructures with the extended finite element method. International Journal for Numerical Methods in Engineering, 2003, 56(14): 2015–2037

    Article  MATH  Google Scholar 

  22. Patzák B, Jirásek M. Process zone resolution by extended finite elements. Engineering Fracture Mechanics, 2003, 70(7–8): 957–977

    Article  Google Scholar 

  23. Sukumar N, Chopp D L, Moran B. Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Engineering Fracture Mechanics, 2003, 70(1): 29–48

    Article  Google Scholar 

  24. Mariani S, Perego U. Extended finite element method for quasi-brittle fracture. International Journal for Numerical Methods in Engineering, 2003, 58(1): 103–126

    Article  MATH  MathSciNet  Google Scholar 

  25. Liu Y, Mahadevan S. Multiaxial high-cycle fatigue criterion and life prediction for metals. International Journal of Fatigue, 2005, 27(7): 790–800

    Article  Google Scholar 

  26. Lu Z, Xiang Y, Liu Y. Crack growth-based fatigue-life prediction using an equivalent initial flaw model. Part II: Multiaxial loading. International Journal of Fatigue, 2010, 32(2): 376–381

    Article  Google Scholar 

  27. Melenk J M, Babuska I. The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1–4): 289–314

    Article  MATH  MathSciNet  Google Scholar 

  28. Soheil M, ed. Extended Finite Element Method. Malden: Blackwell Publishing Ltd. 2008

    MATH  Google Scholar 

  29. Bordas S, Legay A. X-FEM Mini-Course. Ecole Polytehnique Federale de Lausanne, 2005

  30. Isida M. Stress-intensity factors for the tension of an eccentrically cracked strip. Journal of Applied Mechanics, 1966, 33(3): 674–675

    Google Scholar 

  31. Porter T R. Method of analysis and prediction for variable amplitude fatigue crack growth. Engineering Fracture Mechanics, 1972, 4(4): 717–736

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yongming Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lu, Z., Liu, Y. Concurrent fatigue crack growth simulation using extended finite element method. Front. Archit. Civ. Eng. China 4, 339–347 (2010). https://doi.org/10.1007/s11709-010-0078-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11709-010-0078-2

Keywords

Navigation