Journal of Mechanical Science and Technology

, Volume 32, Issue 12, pp 5889–5895 | Cite as

On fracture analysis of cracked curved beams

  • Maryam ZareEmail author


This paper focuses on evaluating stress intensity factors (SIFs), for a curved beam of circular cross section with an external ring crack, applying an approach on the basis of estimating the strain energy release rate. The out of plane vibration of the beam is investigated. This approach requires an additional factor namely correction factor, on the basis of the energy release zone slope to approximate the SIFs. The initial curvature of the beam, however, adds some complication in using this factor. The second part of this study is investigating a numerical approach namely differential quadrature element method (DQEM) to gain the natural frequencies of the cracked beam. This method is applied to show the application of the SIFs to calculate the compliance of the cracked section for modeling the crack. The other method which is used to obtain the natural frequencies is the finite element method (FEM). The results of these two methods are found to be in good agreement, which shows the precision of the stress intensity factors of the cracked beam.


Cracked curved beam Compliance Differential quadrature element method Natural frequencies Out-of-plane vibration Stress intensity factor 


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  1. [1]
    C. Karaagac, H. Ozturk and H. Sabuncu, Crack effects on the in–plane static and dynamic stabilities of a curved beam with an edge crack, Journal of Sound and Vibration, 330 (2011) 1718–1736.CrossRefGoogle Scholar
  2. [2]
    B. K. Lee, S. J. Oh, J. M. Mo, H. Öztürk and T. E. Lee, Outof–plane free vibrations of curved beams with variable curvature, Journal of Sound and Vibration, 318 (2008) 227–246.CrossRefGoogle Scholar
  3. [3]
    R. Dimitri, Y. Li, N. Fantuzzi and F. Tornabene, Innovation modeling of the crack path and stress intensity factor for arbitrary shaft configurations, Advanced Materials & Technologies (2017) 20–35.Google Scholar
  4. [4]
    H. A. Özyiğit, M. Yetmez and U. Uzun, Out–of–plane vibration of curved uniform and tapered beams with additional mass, Mathematical Problems in Engineering (2017) 1–8.Google Scholar
  5. [5]
    Y. J. Xie, X. H. Wang and Y. C. Lin, Stress intensity factors for cracked rectangular cross–section thin–walled tubes, Engineering Fracture Mechanics, 71 (2004) 1501–1513.CrossRefGoogle Scholar
  6. [6]
    W. H. Muller, G. Herrmann and H. Gao, A note on curved cracked beams, International Journal of Solids and Structures, 30 (1993) 1527–1532.CrossRefzbMATHGoogle Scholar
  7. [7]
    C. S. Huang, Y. P. Tseng and S. H. Chang, Out–of–plane dynamic responses of non–circular curved beams by numerical Laplace transform, Journal of Sound and Vibration, 215 (1998) 407–424.CrossRefGoogle Scholar
  8. [8]
    Y. U. Aiming and L. I. Xiangrong, Explicit analytical solutions for the shearing and radial stresses in curved beams, Communications in Nonlinear Science and Numerical Simulation, 4 (1999) 151–156.CrossRefzbMATHGoogle Scholar
  9. [9]
    T. Oden, Mechanics of elastic structures, McGraw–Hill Book Company, New York (1967).Google Scholar
  10. [10]
    H. Gao and G. Herrmann, On estimates of stress intensity factors for cracked beams and pipes, Engineering Fracture Mechanics, 41 (1992) 695–706.CrossRefGoogle Scholar
  11. [11]
    S. Timoshenko and J. N. Goodier, Theory of elasticity, McGraw–Hill Book Company, New York (1951).zbMATHGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentShahid Chamran UniversityAhvazIran

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