Bridged and Cohesive Crack Models for Fracture in Composite Materials

  • Roberta Massabò


The presentation revisits work done by the author and her collaborators over the last decade on two fundamental approaches for studying fracture in composite material systems, the bridged- and cohesive-crack models. Characteristic length scales and dimensionless groups that control fracture characteristics in finite size members and slender bodies, including the stability of crack growth, scaling transitions in the mechanical response and modes of failure, are recalled and discussed. Applications to composite materials for civil, naval and aeronautical structures are presented to highlight the significance of the bridged-crack model in the design of and with advanced composites. Recent results on the problem of multiple dynamic delamination fracture in multilayered systems are used to show how controlled fracture via material/structure design can be exploited to improve mechanical performance.


Process Zone Linear Elastic Fracture Mechanics Crack Model Characteristic Length Scale Double Cantilever Beam 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barenblatt, G.I.: The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks. J. Applied Mathematics and Mechanics 23, 622–636 (1959)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Dugdale, D.S.: Yielding of steel sheets containing slits. J. Mechanics Physics Solids 8, 100–104 (1960)CrossRefGoogle Scholar
  3. 3.
    Bao, G., Suo, Z.: Remarks of crack-bridging concepts. Applied Mechanics Review 24, 355–366 (1992)CrossRefGoogle Scholar
  4. 4.
    Cox, B.N., Marshall, D.B.: Concepts for bridged cracks in fracture and fatigue. Acta. Metall. Mater. 42, 341–363 (1994)CrossRefGoogle Scholar
  5. 5.
    Massabò, R.: The bridged-crack model. In: Carpinteri, A., Gladwell, G. (eds.). Nonlinear Crack Models for Nonmetallic Materials. Solid Mechanics and its Applications Series, pp. 141–208. Kluwer Academic Publisher, Dordrecht (1999) ISBN 0-7023-5750-7Google Scholar
  6. 6.
    Massabò, R.: Single and multiple delamination in the presence of nonlinear crack phase mechanisms. In: Delamination Behavior of Composites (Ed. Sridharan), pp. 514–558. Woodhead Publishing Ltd., Cambridge (2008) ISBN: 978-1-84569-244-5CrossRefGoogle Scholar
  7. 7.
    Rugg, K.L., Cox, B.N., Massabò, R.: Mixed mode delamination of polymer composite laminates reinforced through the thickness by z-fibers. Composites, Part A 33(2), 177–190 (2002)Google Scholar
  8. 8.
    Massabò, R., Mumm, D., Cox, B.N.: Characterizing mode II de-lamination cracks in stitched composites. Int. Journal of Fracture 92(1), 1–38 (1998)CrossRefGoogle Scholar
  9. 9.
    Carpinteri, A., Massabò, R.: Bridged versus cohesive crack in the flexural behavior of brittle matrix composites. Int. Journal of Fracture 81, 125–145 (1996)CrossRefGoogle Scholar
  10. 10.
    Carpinteri, A.: Stability of fracturing process in r.c. beams. J. Structural Engineering 110, 544–558 (1984)CrossRefGoogle Scholar
  11. 11.
    Bosco, C., Carpinteri, A.: Discontinuous constitutive response of brittle matrix fibrous composites. J. Mechanics Physics Solids 43, 261–274 (1995)zbMATHCrossRefGoogle Scholar
  12. 12.
    Carpinteri, A., Massabò, R.: Continuous versus discontinuous bridged crack model for fiber-reinforced materials in flexure. Int. Journal of Solids and Structures 34(18), 2321–2338 (1997)zbMATHCrossRefGoogle Scholar
  13. 13.
    Carpinteri, A., Massabò, R.: Reversal in the failure scaling transition of brittle matrix fibrous composites. Journal of Engineering Mechanics (ASCE) 123(2), 107–114 (1997)CrossRefGoogle Scholar
  14. 14.
    Massabò, R., Brandinelli, L., Cox, B.N.: Mode I Weight Functions for an Orthotropic Double Cantilever Beam. International Journal of Engineering Science 41, 1497–1518 (2003)CrossRefGoogle Scholar
  15. 15.
    Brandinelli, L., Massabò, R.: Mode II Weight Functions for isotropic and orthotropic Double Cantilever Beams. Int. Journal of Fracture 139, 1–25 (2006)zbMATHCrossRefGoogle Scholar
  16. 16.
    Bilby, B.A., Cottrell, A.H., Swinden, K.H.: The spread of plastic yield from a notch. Proceedings Royal Society London A 272, 304–314 (1963)CrossRefGoogle Scholar
  17. 17.
    Marshall, D.B., Cox, B.N., Evans, A.G.: The mechanics of matrix cracking in brittle-matrix fiber composites. Acta. Metal. Mater. 33, 2013–2021 (1985)CrossRefGoogle Scholar
  18. 18.
    Cottrell, A.H.: Mechanics of Fracture. In: Tewksbury Symposium of Fracture, pp. 1–27. University of Melbourne, Australia (1963)Google Scholar
  19. 19.
    Hillerborg, A., Modeer, M., Petersson, P.E.: Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research 6, 773–782 (1976)CrossRefGoogle Scholar
  20. 20.
    Suo, Z., Bao, G., Fan, B.: Delamination R-Curve phenomena due to damage. J. Mech. Phys. Solids 40, 1–16 (1992)CrossRefGoogle Scholar
  21. 21.
    Massabò, R., Cox, B.N.: Concepts for bridged mode II delamination cracks. Journal of the Mechanics and Physics of Solids 47(6), 1265–1300 (1999)zbMATHCrossRefGoogle Scholar
  22. 22.
    Aveston, J., Cooper, G.A., Kelly, A.: Single and multiple fracture. In: The Properties of Fiber Composites, Conf. Proc., National Physical Laboratory, pp. 15–24. IPC Science and Technology Press Ltd. (1971)Google Scholar
  23. 23.
    Carpinteri, A.: Cusp catastrophe interpretation of fracture instability. J. Mechanics Physics Solids 37, 567–582 (1989)zbMATHCrossRefGoogle Scholar
  24. 24.
    Levi, F., Bosco, C., Debernardi, P.G.: Two aspects of the behavior of slightly reinforced structures. CEB Bulletin d’Information 185, 39–50 (1988)Google Scholar
  25. 25.
    Jenq, Y.S., Shah, S.P.: Crack propagation in fiber-reinforced concrete. J. Structural Engineering 112, 19–34 (1986)CrossRefGoogle Scholar
  26. 26.
    Massabò, R., Cox, B.N.: Unusual characteristics of mixed mode delamination fracture in the presence of large scale bridging. Mechanics of Composite Materials and Structures 8(1), 61–80 (2001)CrossRefGoogle Scholar
  27. 27.
    Sridhar, N., Massabò, R., Cox, B.N., Beyerlein, I.: Delamination dynamics in through-thickness reinforced laminates with application to DCB specimen. International Journal of Fracture 118, 119–144 (2002)CrossRefGoogle Scholar
  28. 28.
    Andrews, M.G., Massabò, R., Cox, B.N.: Elastic interaction of multiple delaminations in plates subject to cylindrical bending. International Journal of Solids and Structures 43(5), 855–886 (2006)zbMATHCrossRefGoogle Scholar
  29. 29.
    Andrews, M.G., Massabò, R.: Delamination in flat sheet geometries in the presence of material imperfections and thickness variations. Composites Part B 39, 139–150 (2008) (special issue on Marine Composites)CrossRefGoogle Scholar
  30. 30.
    Andrews, M.G., Massabò, R., Cavicchi, A., Cox, B.N.: Dynamic interaction effects of multiple delaminations in plates subject to cylindrical bending. Int. Journal of Solids and Structures 46, 1815–1833 (2009)zbMATHCrossRefGoogle Scholar
  31. 31.
    Andrews, M.G.: The Static and Dynamic Interaction of Multiple De-laminations in Plates Subject to Cylindrical Bending, Dissertation. Ph.D. Degree, Northwestern University, Evanston, IL, U.S.A. (2005)Google Scholar
  32. 32.
    Massabò, R., Cavicchi, A.: Influence of crack wake mechanisms on the dynamic fracture of multiply delaminated plates. In: Proceedings of the 16th Int. Conference on Composite Materials, ICCM 16, Kyoto, CDrom. Japan Society of Composite Materials, pp. 1–7 (July 2007)Google Scholar
  33. 33.
    Massabò, R.: Dynamic interaction of multiple damage mechanisms in multilayered systems. In: Proceedings of the XVIII National Congress of the Italian Association of Theoretical and Applied Mechanics, AIMETA 2007, Brescia. CDROM, pp. 1–12 (September 2007)Google Scholar
  34. 34.
    Massabò, R.: Interaction of multiple damage mechanisms in composite and sandwich structures. In: Daniels, et al. (eds.) Major Accomplishments in Composite Materials and Sandwich Structures – An Anthology of ONR Sponsored Research, pp. 133–168. Springer (2009) (in press)Google Scholar
  35. 35.
    Robinson, P., Besant, T., Hitchings, D.: Delamination growth prediction using a finite element approach. In: 2nd ESIS TC4 Conference on Polymers and Composites, Les Diablerets, Switzerland (1999)Google Scholar

Copyright information

© © Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Civil, Environmental and Architectural EngineeringUniversity of GenovaGenovaItaly

Personalised recommendations