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Mathematical model of a brittle crack that takes into account the distribution of cohesive forces between the crack faces and the distance between them

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

A mathematical model of a circular disk-shaped brittle crack whose faces are acted upon by cohesive forces, whose magnitude depends on the distance between the faces. An algorithm of numerical solution of the singular nonlinear improper integral equation defining the crack profile was developed which can be used for other integral equations of this type. It is shown that taking into account the coupling forces between the crack faces leads to their gradual closing with distance from the center of the crack.

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References

  1. E. M. Kartashov, B. Tsoi, and V. V. Shevelev, Structural and Statistical Kinetics of Fracture of Polymers (Khimiya, Moscow, 2002) [in Russian].

    Google Scholar 

  2. V. R. Regel’, A. I. Slutsker, and E. E. Tomashevskii, Kinetic Nature of the Strength of Solids (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  3. V. V. Shevelev and E. M. Kartashov, “Some Statistical Aspects of Brittle Fracture and Durability of Polymers. Materials with Cracks,” Vysokomolekulyar. Soed. 39B(2), 371–381 (1997).

    Google Scholar 

  4. M. Ya. Leonov and V. V. Panasyuk, “Development of Tiny Cracks in Solids,” Prikl. Mekh. 5(4), 391–401 (1959).

    MathSciNet  Google Scholar 

  5. D. S. Dugdale, “Yielding of Steel Sheets Containing Slits,” J. Mech. Phys. Solids 8, 100–104 (1960).

    Article  ADS  Google Scholar 

  6. Yu. P. Raizer, “Physical Foundations of the Theory of Brittle Fracture Cracks,” Usp. Fiz. Nauk 100(2), 329–347 (1970).

    Article  Google Scholar 

  7. L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 7: Theory of Elasticity (Nauka, Moscow, 1987; Pergamon Press, 1975).

    Google Scholar 

  8. V. V. Shevelev and R. A. Osipov, “Model of the Crack Profile with the Cohesive Forces between the Crack Faces,” in Abstracts Int. Conf. Mathematics. Computer. Education, Pushchino, January 24–29, 2011 (Regularnaya i Khaoticheskaya Dinamika, Izhevsk, 2011).

    Google Scholar 

  9. I. S. Berezin and N. P. Zhidkov, Computational Methods (Fizmatgiz, Moscow, 1960) [in Russian].

    Google Scholar 

  10. Advanced Numerical Integration in Mathematica (Wolfram Res. Inc., Champaign, 2008).

  11. Wolfram Mathematica Tutorial Collection (Wolfram Res. Inc., Champaign, 2008).

  12. M. Trott, The Mathematica Guidebook for Numerics (Wolfram Res. Inc., Springer, 2006).

    MATH  Google Scholar 

  13. V. V. Shevelev, “Criterion of Brittle Fracture and Durability of Materials under Thermomechanical Action,” Inzh.-Fiz. Zh. 81(2), 394–400 (2008).

    Google Scholar 

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Authors and Affiliations

  1. Lomonosov Moscow State University of Fine Chemical Technologies, Moscow, 119571, Russia

    V. V. Shevelev & R. A. Osipov

Authors
  1. V. V. Shevelev
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  2. R. A. Osipov
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Correspondence to V. V. Shevelev.

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Original Russian Text © V.V. Shevelev, R.A. Osipov.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 54, No. 3, pp. 170–180, May–June, 2013.

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Shevelev, V.V., Osipov, R.A. Mathematical model of a brittle crack that takes into account the distribution of cohesive forces between the crack faces and the distance between them. J Appl Mech Tech Phy 54, 491–499 (2013). https://doi.org/10.1134/S0021894413030206

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  • DOI: https://doi.org/10.1134/S0021894413030206

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