The paper considers the development and numerical implementation of a two-dimensional discrete dislocation model to describe the inelastic deformation of a hexagonal close-packed (HCP) single crystal, taking into account long-range and short-range dislocation interactions. The analytical results are obtained for image fields using the Fourier series for cases of dislocation approaching the crystal boundaries. The model adequacy tests are carried out, and the evolution of the dislocation structure is illustrated with the gradual inclusion of the mechanisms of dislocation annihilation, dislocation pinning at obstacles, and dislocation nucleation by the Frank-Read sources.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. N. Orlov, Introduction to the Theory of Defects in Crystals [in Russian], VysshayaShkola, Moscow (1983).
O. B. Naimark, Yu. V. Bayandin, V. A. Leontiev, and S. L. Permyakov, Phys. Mesomech., 8, No. 5, 21–26 (2005).
L. P. Kubin, Dislocation Patterns: Experiment, Theory and Simulation, Plenum Press, New York (1996); https://doi.org/10.1007/978-1-4613-0385-5_4.
. F. Sarafanov and V. N. Perevezentsev, Patterns of Deformation Grinding of the Structure of Metals and Alloys [in Russian], Publishing House of Nizhny Novgorod State University, Nizhny Novgorod (2007).
G. A. Malygin, Adv. Phys. Sci., 169, No. 9, 979–1010 (1999); https://doi.org/10.3367/UFNr.0169.199909c.0979.
A. N. Gulluoglu and C. S. Hartley, Modell. Simul. Mater. Sci. Eng., 1, 1–17 (1992); https://doi.org/10.1088/0965-0393/1/1/001.
S. Takeuchi and A.S. Argon, Mater. Sci., 11, 1542–1566 (1976); https://doi.org/10.1007/BF00540888.
A. N. Gulluoglu and C. S. Hartley, Modell. Simul. Mater. Sci. Eng., 1, 383–402 (1993).
F. Meng, E. Ferrie, C. Depres, and M. Fivel, Int. J. Fatigue, 149, 106234 (2021); https://doi.org/10.1016/j.ijfatigue.2021.106234.
H. H. M. Cleveringa, E. Van der Giessen, and A. Needleman, Acta Mater., 45, 3163–3179 (1997); https://doi.org/10.1016/S1359-6454(97)00011-6.
H. G. M. Kreuzer and R. Pippan, Mater. Sci. Eng. A, 400, 460–462 (2005); https://doi.org/10.1016/J.MSEA.2005.01.065.
L. Nicola, A. F. Bower, K.-S. Kim, et al., J. Mech. Phys. Solids, 55, 1120–1144 (2007); https://doi.org/10.1016/j.jmps.2006.12.005.
Z. Zheng, D. S. Balint, and F. P. E. Dunne, Int. J. Plast., 87, 1–17 (2016); https://doi.org/10.1016/j.ijplas.2016.08.009.
M. Wallin, W. A. Curtin, M. Rustinmaa, and A. Needleman, J. Mech. Phys. Solids, 56, 3167–3180 (2008); https://doi.org/10.1016/j.jmps.2008.08.004.
H. M. Zbib, T. D. Rubia, M. Rhee, and J. P. Hirth, J. Nucl. Mater., 276, 154–165 (2000); https://doi.org/10.1016/S0022-3115(99)00175-0.
E. Van der Giessen and A. Needleman, Modell. Simul. Mater. Sci. Eng., 3, 689–735 (1995); https://doi.org/10.1088/0965-0393/3/5/008.
J. Hirth and J. Lothe, Theory of Dislocations, John Wiley & Sons, New York (1982).
W. Cai, A. Arsenlis, C. R. Weinberger, and V. V. Bulatov, J. Mech. Phys. Solids, 54, 561–587 (2006); https://doi.org/10.1016/j.jmps.2005.09.005.
M. Tang, W. Cai, G. Xu, and V. V. Bulatov, Modell. Simul. Mater. Sci. Eng., 14, 1139–1151 (2006); https://doi.org/10.1088/0965-0393/14/7/003.
K. Balusu and H. Huang, Modell. Simul. Mater. Sci. Eng., 25, 035007 (2017); https://doi.org/10.1088/1361-651X/aa5a9d.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Knyazev, N.A., Volegov, P.S. Construction of a Two-Dimensional Discrete Dislocation Model to Describe the Plastic Deformation Process of a Single Crystal. Russ Phys J 66, 1194–1205 (2024). https://doi.org/10.1007/s11182-023-03062-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11182-023-03062-4