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Fracture Process Zone at the Tip of a Mode I Crack in a Nonlinear Elastic Orthotropic Material

  • A. A. KaminskyEmail author
  • E. E. Kurchakov
Article

A body with a fracture process zone at the crack front is considered. The constitutive equations relating the components of the stress vectors at points on the opposite boundaries of the fracture process zone and the components of the vector of relative displacements of these points are derived. A local fracture criterion is formulated. A boundary-value problem for a plate made of a nonlinear elastic orthotropic material with a mode I crack is stated in terms of the components of the displacement vector. By solving the problem numerically, it is revealed how the fracture process zone develops under loading. Features of the deformation field at the end of the fracture process zone are established. The critical load on the plate that causes the crack to grow is determined.

Keywords

nonlinear elastic orthotropic material mode I crack fracture process zone constitutive equations local fracture criterion 

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References

  1. 1.
    O. S. Bogdanova, A. A. Kaminsky, and E. E. Kurchakov, “Fracture process zone at the front of a crack in a solid,” Dop. NAN Ukrainy, No. 5, 25–33 (2017).Google Scholar
  2. 2.
    E. E. Kurchakov, “Stress–strain relations for nonlinear anisotropic medium,” Int. Appl. Mech., 15, No. 9, 803–807(1979).ADSMathSciNetzbMATHGoogle Scholar
  3. 3.
    E. E. Kurchakov, “Thermodynamic validation of the constitutive equations for a nonlinear anisotropic body,” Dop. NAN Ukrainy, No. 5, 46–53 (2015).Google Scholar
  4. 4.
    H. Hencky, “Development and modern state of plasticity theory,” Prikl. Mat. Mekh., 4, No. 3, 31–36 (1940).zbMATHGoogle Scholar
  5. 5.
    L. Banks-Sills, N. Travitzky, D. Ashkenazi, and R. Eliasi, “A methodology for measuring interface fracture properties of composite materials,” Int. J. Fract., 99, No. 3, 143–160 (1999).CrossRefGoogle Scholar
  6. 6.
    A. A. Kaminsky and O. S. Bogdanova, “Long-term crack-resistance of orthotropic viscoelastic plate under biaxial loading,” Int. Appl. Mech., 31, No. 9, 747–753 (1995).ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    A. A. Kaminsky and E. E. Kurchakov, “Influence of tension along a mode I crack in an elastic body on the formation of a nonlinear zone,” Int. Appl. Mech., 51, No. 2, 130–148 (2015).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    A. A. Kaminsky and M. F. Selivanov, “On modeling of subcritical crack growth in viscoelastic body under point forces,” Int. Appl. Mech., 53, No. 5, 538–544 (2017).ADSCrossRefGoogle Scholar
  9. 9.
    E. E. Kurchakov, “Experimental study of the plastic zone at the front of a mode I crack,” Int. Appl. Mech., 54, No. 2, 213–219 (2018).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    A. Love, Treatise on the Mathematical Theory of Elasticity, The University Press, Cambridge (1927).zbMATHGoogle Scholar
  11. 11.
    A. Needleman, “A continuum model for void nucleation by inclusion debonding,” J. Appl. Mech., 54, No. 3, 525–531 (1987).ADSCrossRefzbMATHGoogle Scholar
  12. 12.
    K. Park and G. H. Paulino, “Cohesive zone models: A critical review of traction-separation relationship across fracture surfaces,” Appl. Mech. Rev., 64, No. 11, 1–20 (2011).Google Scholar
  13. 13.
    G. N. Savin, and A. A. Kaminsky, “The growth of cracks during the failure of hard polymers,” Sov. Appl. Mech., 3, No. 9, 22–25 (1967).ADSCrossRefGoogle Scholar
  14. 14.
    V. Tvergaard and J. W. Hutchinson, “The influence of plasticity on mixed mode interface toughness,” J. Mech. Phys. Solids, 41, No. 6, 1119–1135 (1993).ADSCrossRefzbMATHGoogle Scholar
  15. 15.
    A. A. Wells, “Critical tip opening displacement as fracture criterion,” in: Proc. Crack. Propagation Symp., 1, Granfield (1961), pp. 210–221.Google Scholar
  16. 16.
    F. H. Wittmann, K. Rokugo, E. Bruehwiler, H. Mihashi, and P. Simonin, “Fracture energy and strain softening of concrete as determined by means of compact tension specimens,” Mater. Struct., 21, No. 1, 21–32 (1988).CrossRefGoogle Scholar

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

Authors and Affiliations

  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyivUkraine

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