A mathematical model is devised for the formation of a crystallographic shear zone for a closed piecewisecontinuous dislocation loop which is represented in its initial configuration by a regular polygon with sides that are as small as desired and which preserves its polygonal shape as it expands. The model takes into account the orientational dependence of the line tension of the dislocation loop, and of the resistance from a dislocation pileup and generation of point defects on the orientation of the Burgers vector relative to the dislocation line.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. E. Popov, S. N. Kolupaeva, N. A. Vikhor’, and S. I. Puspesheva, Russ. Phys. J., 43, No. 1, 71–76 (2000).
S. I. Puspesheva, S. N. Kolupaeva, and L. E. Popov, Fizich. Mezomekh., 3, No. 3, 61–68 (2000).
J. P. Hirth and J. Lothe, Theory of Dislocations, McGraw-Hill, New York (1968).
S. N. Kolupaeva and A. E. Petelin, Vestn. Permsk. Nats. Issled. Politekhn. Univ., Mekh., No. 4, 20–32 (2012).
L. E. Popov, V. S. Kobytev, and T. A. Kovalevskaya, Plastic Deformation of Alloys [in Russian], Metallurgiya, Moscow (1984).
G. Thomas and J. Washburn, eds., Electron Microscopy and the Strength of Crystals, Interscience, New York (1963).
R. Berner and G. Kronmüller, Plastic Deformation of Single Crystals, A. Seeger, ed. [Russian translation], Springer, Berlin (1965).
K. H. Pfeiffer, P. Schiller, аnd A. Seeger, Phys. Status Solidi, 8, No. 2, 517–532 (1965).
T. Suzuki, S. Takeuchi, and H. Yoshinaga, Dislocation Dynamics and Plasticity, Springer-Verlag, New York (1991).
A. E. Petelin and S. N. Kolupaeva, Izv. Tomsk. Politekhn. Univ., 316, No. 5, 141–146 (2010).
S. N. Kolupaeva and A. E. Petelin, Vestn. Tomsk. Gosud. Arkhit. Stroit. Univ., No. 3, 159–163 (2011).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 15–20, February, 2014.
Rights and permissions
About this article
Cite this article
Kolupaeva, S.N., Petelin, A.E. Mathematical Model of Formation of a Crystallographic Shear Zone in the Representation of a Piecewise-Continuous Closed Dislocation Loop. Russ Phys J 57, 152–158 (2014). https://doi.org/10.1007/s11182-014-0220-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11182-014-0220-z