International Journal of Fracture

, Volume 155, Issue 2, pp 127–142 | Cite as

Behavior of a flat internal delamination within a fiber reinforced cross-ply composite

  • Leslie Banks-Sills
  • Yuval Freed
  • Arkady Alperovitch
Original Paper


A penny-shaped delamination is modeled as a flat octahedral shaped crack between layers of a cross-ply laminate. The fibers of the laminate intersect the edges of the delamination at angles of 0°/90°, +45°/−45°, 90°/0° and −45°/+45° as one proceeds along the delamination edge. Two lay-ups are considered, a cross-ply consisting of two layers, and a symmetric composite, consisting of three layers. The delamination is always between two of the layers. Both tension and shear are applied to the outer boundary of the body. Stress intensity factors about the delamination edge are calculated by means of a conservative M-integral. These are employed to calculate the interface energy release rate and corresponding phase angles. Use is made of existing experimental results to predict the location of propagation along the edge of the delamination. It was found that the most dangerous regions along the delamination front occurred for the 0°/90° or 90°/0° interfaces.


Internal delamination Interface fracture toughness Fiber-reinforced composite material Cross-ply Three-dimensional conservative integrals Finite elements 


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  1. Aboudi J, Pindera MJ, Arnold SM (2003) Higher-order theory for periodic multiphase materials with inelastic phases. Int J Plast 19: 805–847MATHCrossRefGoogle Scholar
  2. Aliyu AA, Daniel IM (1985) Effects of strain rate on delamination fracture toughness of graphite/epoxy. In: Johnson WS (eds) Delamination and debonding of materials. ASTM-STP 876. American Society for Testing and Materials, Philadelphia, pp 336–348CrossRefGoogle Scholar
  3. ASTM D 5528 ASTM Standard (2001) Standard test method for mode I interlaminar fracture of unidirectional fiber-reinforced polymer matrix composites D 5528-94a. Annual Book of ASTM Standards 15.03 American Society for Testing and Materials, Philadelphia USAGoogle Scholar
  4. Banks-Sills L, Boniface V (2000) Fracture mechanics for an interface crack between a special pair of transversely isotropic materials. In: Chuang T-J, Rudnicki JW (eds) Multiscale deformation and fracture in materials and structures—The James R. Rice 60th anniversary volume. Kluwer Academic Publishers, The Netherlands, pp 183–204Google Scholar
  5. Banks-Sills L, Boniface V, Eliasi R (2005) Development of a methodology for determination of interface fracture toughness of laminate composites—the 0°/90° pair. Int J Solids Struct 42: 663–680MATHCrossRefGoogle Scholar
  6. Banks-Sills L, Freed Y, Eliasi R, Fourman V (2006) Fracture toughness of the + 45°/−45° interface of a laminate composite. Int J Fract 141: 195–210CrossRefGoogle Scholar
  7. Bathe KJ (2007) ADINA -Automatic Dynamic Incremental Nonlinear Analysis, Version 8.4.Google Scholar
  8. Freed Y, Banks-Sills L (2005) A through interface crack between a ± 45° transversely isotropic pair of materials. Int J Fract 133: 1–41CrossRefGoogle Scholar
  9. Gillespie JW Jr, Carlsson LA, Smiley AJ (1987) Rate-dependent mode I interlaminar crack growth mechanisms in graphite/epoxy and graphite/peek. Compos Sci Technol 28: 1–15CrossRefGoogle Scholar
  10. Hwu C (1993) Fracture parameters for the orthotropic bimaterial interface cracks. Eng Fract Mech 45: 89–97CrossRefGoogle Scholar
  11. Lekhnitskii SG (1963) Theory of elasticity of an anisotropic body. Holden-Day, San Francisco. Translated by Fern P (1950) in RussianGoogle Scholar
  12. Nagai M, Ikeda T, Miyazaki N (2007) Stress intensity factor analysis of a three-dimensional interface crack between dissimilar anisotropic materials. Eng Fract Mech 74: 2481–2497CrossRefGoogle Scholar
  13. Noda NA, Xu C (2008) Controlling parameter of the stress intensity factors for a planar interfacial crack in three-dimensional bimaterials. Int J Solids Struct 45: 1017–1031CrossRefGoogle Scholar
  14. Prombut P, Michel L, Lachaud F, Barrau JJ (2006) Delamination of multidirectional composite laminates at 0°/θ° ply interfaces. Eng Fract Mech 73: 2427–2442CrossRefGoogle Scholar
  15. Stroh AN (1958) Dislocations and cracks in anisotropic elasticity. Phil Mag 3: 625–646MATHCrossRefADSMathSciNetGoogle Scholar
  16. Suo Z (1990) Singularities interfaces and cracks in dissimilar anisotropic media. Proc R Soc London A 427: 331–358MATHCrossRefADSMathSciNetGoogle Scholar
  17. Ting TCT (1986) Explicit solutions and invariance of the singularities at an interface crack in anisotropic composites. Int J Solids Struct 9: 965–983CrossRefMathSciNetGoogle Scholar
  18. Ting TCT (1995) Generalized Dundurs constants for anisotropic bimaterials. Int J Solids Struct 32: 483–500MATHCrossRefGoogle Scholar
  19. Ting TCT (1996) Anisotropic elasticity—theory and applications. Oxford University Press, OxfordMATHGoogle Scholar
  20. Ting TCT, Hwu C (1988) Sextic formalism in anisotropic elasticity for almost non-semisimple matrix N. Int J Solids Struct 24: 65–76MATHCrossRefGoogle Scholar
  21. Whitney JM, Browning CE, Hoogsteden W (1982) A double cantilever beam test for characterizing mode I delamination of composite materials. J Reinf Plast Compos 1: 297–313CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Leslie Banks-Sills
    • 1
  • Yuval Freed
    • 1
  • Arkady Alperovitch
    • 1
  1. 1.The Dreszer Fracture Mechanics Laboratory, School of Mechanical Engineering, The Fleischman Faculty of EngineeringTel Aviv UniversityRamat Aviv, Tel AvivIsrael

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