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On problems of fracture of materials in compression along two internal parallel cracks

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Abstract

The fracture of materials under the action of compressive forces, directed along cracks which are parallel in plane cannot be described within the framework of the linear fracture mechanics. The criteria of fracture of the Griffith-Irvin or COC type, used in classical linear fracture mechanics, are not applicable in this problem, since these forces have no influence on stress intensity coefficients and on values of cracks opening.

The problems of such a class may be described only by using new approaches. One of possible approaches is presented by the first author, which involves using linearized relations, derived from exact non-linear equations of deformable solid body mechanics. It should be remarked here that this approach has been widely used in problems of deformable bodies stability.

As a criterion of the initiation of fracture the criterion of local instability near defects of the crack type is used. In these cases the process of loss of stability initiates the fracture process.

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References

  1. G. P. Chevepanov,Mechanics of Brittle Fracture: Nauka, Moscow (1974) (in Russian)

    Google Scholar 

  2. M. K. Kassir and G. C. Sih,Mechanics of Fracture, Three-Dimensional Crack Problems, Vol. 2, Noordhoff, Leiden (1975).

    Google Scholar 

  3. A. N. Guz,Mechanics of Brittle Fracture of Materials with Initial Stresses, Naukova Dumka, Kiev (1983). (in Russian)

    Google Scholar 

  4. A. N. Guz,Foundations of Three-Dimensional Theory of Deformable Bodies Stability, Vyshcha Shkola, Kiev (1986). (in Russian).

    Google Scholar 

  5. A. N. Guz, Foundation of mechanics of brittle fracture of materials with initial stresses,Adv. Fract. Rec. Proc. 6th Int. Conf. (ICF6), New Delhi, 4–10 Dec., 1984, Vol. 2 (1984), 1223–1230.

    Google Scholar 

  6. A. N. Guz, V. M. Nazarenko and I. P. Starodubtsev, Plane problem of fracture of materials with two parallel cracks in compression along the cracks,Problems of Mechanics of Deformable Solid Body, University of Kalinin, Kalinin (1986), 138–151. (in Russian)

    Google Scholar 

  7. I. P. Starodubtsev, Fracture of the body in compression along two parallel cracks in plane deformation condition,Prikl. Mechanika,24, 6 (1988), 79–84. (in Russian)

    MATH  Google Scholar 

  8. A. N. Guz and V. M. Nazarenko, Symmetric failure of the half-space with penny-sheped cracks in compression,Theor. Appl. Fract. Mech.,3, 3 (1985), 233–245. (in Russian)

    Article  MathSciNet  Google Scholar 

  9. V. V. Bolotin, Defects of the delamination type in structures of composite materials,Mechanics of Composite Materials,2 (1984), 239–255. (in Russian)

    Google Scholar 

  10. A. N. Guz,Mechanics of Composite Materials and Structures Elements, Vol. 1, Naukova Dumka, Kiev (1982). (in Russian)

    Google Scholar 

  11. A. M. Mikhailov, Some problems of cracks theory in beam approximation,J. Appl. Mech. and Techni. Fizi.,5 (1967), 128–133. (in Russian)

    Google Scholar 

  12. A. N. Polilov and Yu. N. Rabotnov, Development of delaminations in compression of composites,Izv., AN SSSR, Mechanika Tverdogo Tela,4 (1983), 166–171. (in Russian)

    Google Scholar 

  13. L. I. Slepyan,Mechanics of Cracks, Leningrad (1981). (in Russian)

  14. W. L. Yin, Axisymmetric buckling and growth of a circular delamination in compressed laminate,Int. J. Solids Struct.,21, 5 (1985), 503–514.

    Article  MATH  Google Scholar 

  15. S. G. Mikhlin and Kh. L. Smolitsky,Approximate Methodas of Solutions of Differential and Integral Equations, Nauka, Moscow (1965). (in Russian)

    Google Scholar 

  16. B. P. Maslov, Investigation of stochastic composites with nonlinear and anisotropic properties of components, Dissertation for Doctor Degree, Kiev (1983). (in Russian)

  17. D. Kolarov, A. Baltov and N. Boncheva,Mechanics of Plastic Media, Mir, Moscow (1979). (in Russian)

    Google Scholar 

  18. A. N. Fuz, V. I. Knukh and V. M. Nazarenko, Compressive failure of materials with two parallel cracks: small and large deformation,Theor. Appl. Fracture Mech.,11 (1989), 213–223.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics of the National Academy of Sciences of Ukraine, Ulitsa Nesterova 3, 252057, Kiev, Ukraine

    A. N. Guz, V. M. Nazarenko & I. P. Starodubtsev

Authors
  1. A. N. Guz
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  2. V. M. Nazarenko
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  3. I. P. Starodubtsev
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Guz, A.N., Nazarenko, V.M. & Starodubtsev, I.P. On problems of fracture of materials in compression along two internal parallel cracks. Appl Math Mech 18, 517–528 (1997). https://doi.org/10.1007/BF02454110

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  • DOI: https://doi.org/10.1007/BF02454110

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