Dislocation structure of shear bands in single crystals

  • S. P. Kiselev


A mathematical model is proposed for the development of a shear band in crystals. The model is based on the mechanism of double cross-slips of screw-dislocation segments. Equations are derived to study instability of the uniform distribution of dislocations. A solution is found in the form of a traveling wave, which describes the shear-band structure.

Key words

stresses strain dislocations shear band 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Friedel, Dislocations, Pergamon Press, Oxford-New York (1967).MATHGoogle Scholar
  2. 2.
    A. Ziegenbein, J. Plessing, and H. Neuhauser, “Mesoscale studies on Luders band deformation in concentrated Cu-based alloy single crystals,” Phys. Mesomech. 1, No. 2 (1998).Google Scholar
  3. 3.
    B. I. Smirnov, Dislocation Structure and Hardening of Crystals [in Russian], Nauka, Leningrad (1981).Google Scholar
  4. 4.
    G. A. Malygin, “Self-organization of dislocations and plasticity of crystals,” Usp. Fiz. Nauk, 169, No. 9, 979–1010 (1999).CrossRefGoogle Scholar
  5. 5.
    P. Hahner, “Theory of solitary plastic waves. 1. Lüders bands in polycrystals,” Appl. Phys., A, 58, 41–48 (1994).CrossRefADSGoogle Scholar
  6. 6.
    P. Hahner, “Theory of solitary plastic waves. 2. Lüders bands in single glide-oriented crystals,” Appl. Phys., A, 58, 49–58 (1994).CrossRefADSGoogle Scholar
  7. 7.
    S. P. Kiselev, “Internal stresses in a solid with dislocations,” J. Appl. Mech. Tech. Phys., 45, No. 4, 567–571 (2004).MATHMathSciNetCrossRefADSGoogle Scholar
  8. 8.
    S. K. Godunov and E. I. Romensky, Elements of Continuum Mechanics and Conservation Laws, Kluwer Acad. Publ., Dordrecht (2003).MATHGoogle Scholar
  9. 9.
    N. V. Karlov and N. A. Kirichenko, Oscillations, Waves, and Structures [in Russian], Fizmatlit, Moscow (2001).Google Scholar
  10. 10.
    S. K. Godunov and V. S. Ryaben’kij, “Difference schemes. An introduction to the underlying theory,” in: Studies in Mathematics and Its Applications, Vol. 19, North-Holland, Amsterdam (1987).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • S. P. Kiselev
    • 1
  1. 1.Khristianovich Institute of Theoretical and Applied Mechanics, Siberian DivisionRussian Academy of SciencesNovosibirsk

Personalised recommendations