Mechanics of Composite Materials

, Volume 55, Issue 3, pp 315–324 | Cite as

Finite-Layer Method: Determining the Critical Size of an Interlaminar Crack in the Curved Zone of a composite T-Stringer

  • A. M. TimoninEmail author

Using the finite-layer method, values of the modal components GI and GII and the total value of energy release rate GT for tips of an interlaminar cylindrical crack in the curved zone of a reinforcing composite stringer are calculated. Reliability of the results is confirmed by convergence on sequentially increasing the number of layers and by comparison of the values GT obtained in two different ways. Parametric studies are carried out, and the ranges of allowable crack dimensions are constructed for two loading cases: the crack is opened (1) and closed (2).


panel stringer delamination finite-layer method boundary-value problem stiff system of equations numerical solution energy release rate critical crack size 


  1. 1.
    A. M. Timonin, “Finite-layer method: Calculation of interface stresses in a composite panel reinforced by T-stringers,” Mech. Compos. Mater., 54, No. 3, 359-368 (2018).CrossRefGoogle Scholar
  2. 2.
    E. F. Rybicki and M. F. Kanninen, “A finite element calculation of stress intensity factors by a modified crack closure integral,” Eng. Fracture Mech., 9, 931-938 (1977).CrossRefGoogle Scholar
  3. 3.
    R. Krueger, “The virtual crack closure technique for modeling interlaminar failure and delamination in advanced composite materials,” in Numerical Modelling of Failure in Advanced Composite Materials, Eds: P. Camanho, S. Hallet, Woodhead Publishing (2015).Google Scholar
  4. 4.
    A. M. Timonin, “Finite-layer method: a unified approach to a numerical analysis of interlaminar stresses, large deflections, and delamination stability of composites. Part 1. Linear behavior,” Mech. Compos. Mater., 49, No. 3, 231-244 (2013).CrossRefGoogle Scholar
  5. 5.
    A. M. Timonin, “Finite-layer method: exact numerical and analytical calculations of the energy release rate for unidirectional composite specimens in double-cantilever beam and end-notched flexure tests,” Mech. Compos. Mater., 52, No. 4, 469-488 (2016).CrossRefGoogle Scholar
  6. 6.
    A. M. Timonin, “Finite-layer method: evaluation of stresses and the modal components of energy release rate on the midplane of edge-cracked composite specimens,” Mech. Compos. Mater., 52, No. 5, 583-600 (2016).CrossRefGoogle Scholar
  7. 7.
    S. K. Godunov, “Numerical solution of boundary-value problems for a system of linear ordinary differential equations,” Uspekhi Matem. Nauk, 16, No. 3, 171-174 (1961).Google Scholar
  8. 8.
    Ya. M. Grigorenko, Isotropic and Anisotropic Layered Shells of Revolution with a Variable Stiffness [in Russian], Kiev: Naukova Dumka (1973).Google Scholar
  9. 9.
    A. M. Timonin, “Application of the finite-layer method for the analysis of stress-strain state of multiply connected shell structures,” Proc. of the Fourth All-Russian Science and Tech. Conf. “Dynamics and Strength of the Constructions of Aeroelastic Systems. Numerical methods,” IMASH RAN, Moscow (2017).Google Scholar
  10. 10.
    A. M. Timonin, “A new refined theory of orthotropic shells and its employment in the finite-layer method,” Proc. of 2nd Int. Conf. “Deformation and Failure of Composite Materials and Structures,” IMASH RAN, Moscow (2016).Google Scholar
  11. 11.
    D. F. Adams, L. A. Carlsson, and R. B. Pipes, Experimental Characterization of Advanced Composite Materials, CRC Press, New York (2003).Google Scholar
  12. 12.
    G. Wimmer, C. Schuecker, and H. E. Pettermann. “Numerical simulation in laminated composite components. A combination of a strength criterion and fracture mechanics,” Composites: Part B, 40, 158-165 (2009).CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.ProgresstekhMoscowRussia

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