Advertisement

Analysis of Mode II and Mixed Mode I-II in Fracture and Fatigue: A Numerical and Experimental Study

  • J. Baganha Marques
  • S. M. O. TavaresEmail author
  • P. M. S. T. de Castro
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 98)

Abstract

The aim of this work is to analyse fatigue crack propagation under pure mode II and mixed mode I-II loading conditions. Bidimensional numerical simulations were carried out using models created with the software Abaqus Standard, making use of the conventional finite element method to calculate the stress intensity factors and of the extended finite element method to predict the crack propagation path. The experimental tests were performed on single edge notch specimens, under asymmetrical four-point bending. By varying the position of supports and loads relatively to the crack several situations of mixed mode loading I-II and pure mode II were achieved. The equivalent stress intensity factor for mixed mode I-II and pure mode II was calculated using the finite element method and the software Abaqus Standard. The \(da/dN=f(\Delta K_{eq})\), where a is the crack length, N is the number o cycles, and \(\Delta K_{eq}\) is the range of the equivalent stress intensity factor, was obtained and compared with the mode I Paris law equation for the given material, NASGRO material database and other authors’ results. The initial fatigue crack growth (FCG) propagation angles were found to be well described by the minimum strain energy density criterion. Regarding the FCG rates, mixed mode results differ from mode I. Several factors like pre-existing flaws in the material, accumulation of experimental and/or post-processing errors and roughness-induced crack closure may have played a part in the differences obtained between the experimental material curve based on \(K_{eq}\) and the NASGRO and Paris law equations based upon \(K_{I}\). It is however noted that other authors also found some difference in the da / dN versus \(\Delta K_{eq}\) or versus \(\Delta K_{I}\) relationships. Finally, as regards cracks paths, xFEM predictions and experiments showed a variable degree of agreement: very good in some cases, and only approximate in others.

Keywords

Fracture mechanics Fatigue Mixed mode loading I-II Mode II loading Extended finite element method 

References

  1. 1.
    Anderson, T.: Fracture Mechanics, 3rd edn. Taylor & Francis Group, LLC (2005)Google Scholar
  2. 2.
    Broek, D.: Elementary Engineering Fracture Mechanics, Fourth revised edn. Martinus Nijhoff Publishers (1986)Google Scholar
  3. 3.
    de Moura Branco, C.: Mecnica dos Materiais, 5th edn. Fundao Calouste Gulbenkian (2011)Google Scholar
  4. 4.
    Richard, H.: Specimens for investigating biaxial fracture and fatigue processes. In: Biaxial and Multiaxial Fatigue, pp. 217–229. Mechanical Engineering Publications (1989)Google Scholar
  5. 5.
    Borrego, L., Antunes, F., Costa, J., Ferreira, J.: Mixed-mode fatigue crack growth behaviour in aluminium alloy. Int. J. Fatigue 28(5–6), 618–626 (2006)CrossRefGoogle Scholar
  6. 6.
    Qian, J., Fatemi, A.: Fatigue crack growth under mixed-mode I and II loading. Fatigue Fract. Eng. Mat. Struct. 19(10), 1277–1284 (1996)CrossRefGoogle Scholar
  7. 7.
    He, M., Hutchinson, J.: Asymmetric four-point crack specimen. J. Appl. Mech. 67(1), 207–209 (2000)CrossRefGoogle Scholar
  8. 8.
    Gicquel, L.: Cracked beam subjected to asymmetric four-point bending. Technical report, Faculdade de Engenharia da Universidade do Porto (July 2017)Google Scholar
  9. 9.
    Erdogan, F., Sih, G.C.: On the crack extension in plates under plane loading and transverse shear. J. Basic Eng. 85(4), 519–525 (1963)CrossRefGoogle Scholar
  10. 10.
    Sih, G.C.: Mechanics of Fracture Initiation and Propagation. Springer Science+Business Media (1991)Google Scholar
  11. 11.
    Dassault Systèmes: Abaqus documentation. Dassault Systèmes Simulia Corporation (2017)Google Scholar
  12. 12.
    NASGRO.: Fracture Mechanics and Fatigue Crack Growth Analysis Software, Version 4.02. Southwest Research Institute (SwRI), September (2002)Google Scholar
  13. 13.
    Ferreira, M.A.C.: Mixed mode crack propagation: numerical and experimental study. Master thesis, Faculade de Engenharia da Universidade do Porto (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • J. Baganha Marques
    • 1
  • S. M. O. Tavares
    • 1
    Email author
  • P. M. S. T. de Castro
    • 1
  1. 1.Faculdade de Engenharia da Universidade do PortoPortoPortugal

Personalised recommendations