Abstract—
A pseudodifferential operator is constructed that describes the stress field in an anisotropic medium caused by a dislocation with a variable Burgers vector.
Under the assumption \({\mathbf{b}} \in {{H}_{{1/2}}}(\Pi ,{{R}^{3}})\), analytical expressions for the energy of circular dislocations with a variable Burgers vector in an elastic medium with general anisotropy are obtained for the first time. It was found that in an isotropic medium the energy of formation of an edge dislocation and a slip dislocation is determined only by the uniform norm of the Burgers vector.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Mechanics of Generalized Continua: Proceedings of the IUTAM-Symposium, Ed. by E. Kroner (Springer, Berlin, 1968).
Collected Works of J. D. Eshelby: The Mechanics of Defects and Inhomogeneities, Ed. by X. Markenscoff and A. Gupta (Springer, 2006).
F. R. N. Nabarro, “The mathematical theory of stationary dislocations,” Adv. Phys. 1 (3), 269–394 (1952).
Y. T. Chou and J. D. Eshelby, “The energy and line tension of a dislocation in a hexagonal crystal,” J. Mech. Phys. Solids 10 (1), 27–34 (1962).
S. V. Kuznetsov, “On the operator of the theory of cracks,” C. R. Acad. Sci. Paris, 323 (7), 427–432 (1996).
M. O. Peach and J. S. Koehler, “The forces exerted in dislocations and the stress field produced by them,” Phys. Rev. Ser. 2 80, 436–439 (1950).
S. V. Kuznetsov, “Fundamental and singular solutions of Lame equations for media with arbitrary elastic anisotropy,” Quart. Appl. Math. 63, 455–467 (2005).
A. V. Ilyashenko and S. V. Kuznetsov, “3D Green’s function for equations of harmonic vibrations,” Arch. Appl. Mech. 87, 159–165 (2017). https://doi.org/10.1007/s00419-016-1184-y
E. M. Stein and R. Shakarchi, Princeton Lectures in Analysis III. Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Univ. Press, Princeton, Oxford, 2005).
J. R. Willis, “A penny-shaped crack on an interface,” Quart. J. Mech. Appl. Math. 25 (3), 367–385 (1972).
Funding
This work was carried out with financial support from the Russian Science Foundation grant no. 19-19-00616.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by M. Katuev
About this article
Cite this article
Kuznetsov, S.V. Circular Dislocations in an Anisotropic Medium: Specific Energy and Stress Fields. Mech. Solids 56, 34–39 (2021). https://doi.org/10.3103/S002565442101009X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S002565442101009X