Mechanics of Composite Materials

, Volume 50, Issue 5, pp 593–602 | Cite as

Fracture of a composite reinforced by unidirectional fibers

  • F. F. Hasanov

An elastic medium weakened by a periodic system of circular holes filled with homogeneous elastic fibers whose surface is coated with a homogeneous film is considered. A fracture model for a medium with a periodic structure is proposed, which is based on an analysis of the fracture zone near the crack tip. It is assumed that the fracture zone is a layer of finite length containing a material with partially broken bonds between separate structural elements (end zone). The fracture zone is considered as part of the crack. The bonds between crack faces in the end zone are modeled by applying the cohesive forces caused by the presence of bonds to the crack surface. An analysis of the limit equilibrium of shear cracks in the end zone of the model is performed on the basis of a nonlocal fracture criterion together with a force condition for the motion of crack tip and a deformation condition for determining the motion of faces of end-zone cracks. In the analysis, relationships between the cohesive forces and the shear of crack faces are established, the stress state near the crack is assessed with account of external loading, cohesive forces, and fiber arrangement, and the critical external loads as functions of geometric parameters of the composite are determined.


cohesive forces shear cracks with interfacial bonds medium with a periodic structure transverse shear 


  1. 1.
    G. I. Barenblatt, “Mathematical theory of equilibrium cracks formed in brittle fracture,” Zh. Prikl. Mekh. Tekhn. Fiz., No. 4, 3-56 (1961).Google Scholar
  2. 2.
    M. Ya. Leonov and V. V. Panasyuk, “Development of fine cracks in a solid body,” Prikl. Mekh., 5, No. 4, 391-401 (1959).Google Scholar
  3. 3.
    D. S. Dugdale, “Yelding of steel sheets containing slits,” J. Mech. Phys. Solids, 8, No. 2, 100-108 (1960).CrossRefGoogle Scholar
  4. 4.
    The special issue: Cohesive models, Eng. Fract. Mech., 70, No. 14, 1741-1987 (2003).Google Scholar
  5. 5.
    L. R. F. Rose, “Crack reinforcement by distributed springs,” J. Mech. Phys. Solids, 35, No. 4, 383-405 (1987).CrossRefGoogle Scholar
  6. 6.
    B. Budianscky and Y. L. Cui, “On the tensile strength of a fiber-reinforced ceramic composite containing a crack-like flaw,” J. Mech. and Phys. Solids, 42, No. 1, 1-19 (1994).CrossRefGoogle Scholar
  7. 7.
    B. N. Cox and D. B. Marshall, “Concepts for bridged cracks fracture and fatigue,” Acta metal mater., 42, No. 2, 341-363 (1994).CrossRefGoogle Scholar
  8. 8.
    R. V. Goldstein and M. N. Perelmuter, “A crack at the interface between materials with interfacial bonds,” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 94-112 (2001).Google Scholar
  9. 9.
    M. А. Grekov and N. F. Morozov, “Equilibrium cracks in composites reinforced with unidirectional fibers,” Prikl. Matem. Mekh., 70, Iss. 6, 1054-1066 (2006).Google Scholar
  10. 10.
    N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966).Google Scholar
  11. 11.
    V. Panasyuk, M. Savruk, and A. Datsyshin, Stress Distribution near Cracks in Plates and Shells (in Russian), Naukova Dumka, Kiev (1976).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Azerbaijan Technical UniversityBakuAzerbaijan

Personalised recommendations