Skip to main content
SpringerLink
Log in

Model of crack opening in a molecular crystal

  • Published:
Mechanics of Composite Materials Aims and scope

Conclusion

The mechanical behavior of the discrete structure of a solid can be modeled by a linear system of three particles interacting in accordance with the approximate Born-Oppenheimer law with Lennard-Jones coefficients. Such a model manifests the following properties: elasticity (with small strains); plasticity (residual strains in the presence of two different equilibrium positions); viscosity (change in the frequency of the vibrations with an increase in the forces); hysteresis (with the jump of the middle particle from the left to the right equilibrium position and back); fusion (change in the frequency of the vibrations with an increase in strains).

The phenomenon of the interaction of three particles, referred to a linear chain of particles and an organic crystal model, offers a representation of the mechanism of crack opening in a discrete solid.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. M. V. Klassen-Neklyudova, Mechanical Twinning of Crystals [in Russian], Moscow (1960).

  2. T. A. Kontorova and Ya. I. Frenkel', “Theory of plastic deformation and twinning,” Zh. Éksp. Teor. Fiz., No. 8, 89 (1938).

    Google Scholar 

  3. A. K. Malmeister, “Deformations and strength of a system capable of twinning,” in: Aspects of Dynamics and Dynamic Strength [in Russian], Vol. 2, Riga (1954), pp. 5–20.

    Google Scholar 

  4. A. K. Malmeister, “Deformation of a medium capable of twinning,” in: Aspects of Dynamics and Dynamic Strength [in Russian], Vol. 3, Riga (1955), pp. 97–122.

    Google Scholar 

  5. M. Ya. Leitane, “Duplication of a planar six-atom model,” Mekh. Polim., No. 4, 584–588 (1974).

    Google Scholar 

  6. V. F. Mezhgailis, “Internal stresses due to molecular interaction,” Mekh. Polim., No. 4, 741–743 (1974).

    Google Scholar 

  7. A. P. Dreimanis, “Dislocation mechanism of the initial stage of plastic deformation of polyethylene,” Mekh. Polim., No. 5, 771–777 (1974).

    Google Scholar 

  8. A. P. Dreimanis, “Transformation of a lattice in a model of a polymer crystal with a defect,” Mekh. Polim., No. 6, 992–997 (1974).

    Google Scholar 

  9. A. P. Dreimanis, “Energy characteristics of. mechanical twinning in a model of a polymer crystal with a defect,” Mekh. Polim., No. 2, 228–233 (1975).

    Google Scholar 

  10. M. Ya. Leitane, “Special case of deformation of a nine-atom model,” Mekh. Polim., No. 3, 545–547 (1975).

    Google Scholar 

  11. A. P. Dreimanis, “Plastic deformation of models of a crystalline polymer in hydrostatic tension,” Mekh. Polim., No. 1, 20–25 (1976).

    Google Scholar 

  12. M. Ya. Leitane, “Special case of twinning of a planar nine-atom model,” Mekh. Polim., No. 6, 1087–1089 (1975).

    Google Scholar 

  13. M. Ya. Leitane, “Evaluation of the surface tension of a fiber,” Mekh. Polim., No. 1, 12–14 (1977).

    Google Scholar 

  14. A. P. Dreimanis, “Plastic deformation of models of a crystallographic polymer with a high density of lattice defects,” Mekh. Polim., No. 3, 397–402 (1977).

    Google Scholar 

  15. V. F. Mazhgailis, “Interaction forces in a ten-atom model,” Mekh. Polim., No. 5, 914–940 (1977).

    Google Scholar 

  16. M. Ya. Leitane, “Surface forces in models of hexagonal and cubic crystalline plane structures,” Mekh. Polim., No. 5, 799–801 (1978).

    Google Scholar 

  17. M. Ya. Leitane, “Intermolecular surface forces of adsorptive interaction in a plane, close-packed hexagonal model,” Mekh. Kompozitn. Mater., No. 1, 156–167 (1979).

    Google Scholar 

  18. A. P. Dreimanis, “End defects in crystalline polyethylene. 1. Formulation of the problem and modeling of the three-dimensional structure of end defects,” Mekh. Polim., No. 3, 400–407 (1978).

    Google Scholar 

  19. A. P. Dreimanis, “End defects in crystalline polyethylene. 2. Transverse motion of defects and transverse strain of a defective crystallite,” Mekh. Polim., No. 4, 588–595 (1978).

    Google Scholar 

  20. A. P. Dreimanis, “End defects in crystalline polyethylene. 3. Formation of screw dislocations and longitudinal motion of defects,” Mekh. Polim., No. 5, 793–798 (1978).

    Google Scholar 

  21. A. K. Malmeister, “Certain aspects of the mechanics of a medium capable of twinning,” in: Aspects of Dynamics and Dynamic Strength [in Russian], Vol. 1, Riga (1953), pp. 22–43.

    Google Scholar 

  22. A. P. Dreimanis, “Effect of a lattice defect on the mechanism of local plastic deformation of a polymer crystal,” Mekh. Polim., No. 5, 784–790 (1975).

    Google Scholar 

  23. N. G. Rambidi and V. M. Zamalin, Intermolecular Microelectronics, Moscow (1985).

  24. S. P. Timoshenko, Vibrations in Engineering [Russian translation], Moscow (1959).

Download references

Author information

Authors and Affiliations

  1. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga

    A. K. Malmeister

Authors
  1. A. K. Malmeister
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 446–452, May–June, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Malmeister, A.K. Model of crack opening in a molecular crystal. Mech Compos Mater 22, 318–323 (1986). https://doi.org/10.1007/BF00608357

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00608357

Keywords

Search

Navigation