Abstract
The paper analyzes the redistribution of atomic displacements in an initially defect-free copper crystallite after shear deformation with emphasis on the evolution of dynamic structures formed by self-consistent collective atomic rotations. The analysis is based on an original technique which allows one to identify vortex motion in a vector variable space with a discrete step. The results of research show that the direction of consistent atomic motion in vortex structures varies with time and from vortex to vortex. Such spatial alternation of rotations in the material provides its continuity along the boundaries of vortex structures, and their time-variant direction ensures stress and strain transfer from the bulk of the loaded crystal to its peripheral free boundaries. When the strain goes above its critical value, such redistribution can lead to the formation of structural defects. Thus, the vortex structures formed by elastic atomic displacements can be considered as dynamic defects because they provide a way for internal relaxation in the loaded material.
Similar content being viewed by others
References
Berger, M.A., Introduction to Magnetic Helicity, Plasma Phys. Control. Fusion. B. IOP Publ., 1999, vol. 41, no. 12, pp. 167–175.
Hasegawa, H., Fujimoto, M., Phan, T.-D., Rume, H., Balogh, A., Dunlop, M.W., Hashimoto, C., and Tandokoro, R., Transport of Solar Wind into Earth’s Magnetosphere through Rolled-up Kelvin-Helmholtz Vortices, Nature, 2004, vol. 430, no. 7001, pp. 755–758.
Sayanagi, K.M., Dyudina, U.A., Ewald, S.P., Fischer, G., Ingersoll, A.P., Kurth, W.S., Muro, G.D., Porco, C.C., and West, R.A., Dynamics of Saturn’s Great Storm of 2010–2011 from Cassini ISS and RPWS, Icarus., 2013, vol. 223, no. 1, pp. 460–478.
Filippov, A.E., Simple Model of Dust Medium Evolution, Phys. Lett. A, 1994, vol. 189, no. 5, pp. 361–366.
Kizner, Z. and Khvoles, R., Two Variations on the Theme of Lamb-Chaplygin: Supersmooth Dipole and Rotating Multipoles, Regul. Chaotic Dyn., 2004, vol. 9, no. 4, pp. 509–518.
Proment, D., Onorato, M., and Barenghi, C.F., Vortex Knots in a Bose-Einstein Condensate, Phys. Rev. E, 2012, vol. 85, no. 3, p. 36306.
Filippov, A.E., Radievsky, A.V., and Zeltser, A.S., Kinetics of Vortex Formation in Superconductors with d-Pairing, Phys. Rev. B, 1996, vol. 54, no. 5, pp. 3504–3507.
Geim, A.K., Grigorieva, I.V., Dubonos, S.V., Lok, J.G.S., Maan, J.C., Filippov, A.E., and Peeters, F.M., Phase Transitions in Individual Sub-Micrometre Superconductors, Nature, 1997, vol. 390, no. 6657, pp. 259–262.
Leonov, A.O. and Mostovoy, M., Multiply Periodic States and Isolated Skyrmions in an Anisotropic Frustrated Magnet, Nat. Commun., 2015, no. 6, p. 8275.
Kiselev, N.S., Bogdanov, A.N., Schäfer, R., and Rößler, U.K., Chiral Skyrmions in Thin Magnetic Films: New Objects for Magnetic Storage Technologies? J. Phys. D. Appl. Phys., 2011, vol. 44, no. 39, p. 392001.
Filippov, A.E., Kinetics of Vortex Structure Formation in Magnetic Materials, J. Exp. Theor. Phys., 1997, vol. 84, no. 5, pp. 971–977.
Frank, F.C., LXXXIII, Crystal Dislocations.—Elementary Concepts and Definitions, Philos. Mag., 1951, vol. 42, no. 331, pp. 809–819.
Panin, V.E. and Grinyaev, Yu.V., Physical Mesomechanics: a New Paradigm at the Interface of Solid State Physics and Solid Mechanics, Phys. Mesomech., 2003, vol. 6, no. 4, pp. 7–32.
Surface Layers and Internal Interfaces in Heterogeneous Materials, Panin, V.E., Ed., Novosibirsk: Izd-vo SO RAN, 2006, pp. 32–69.
Egorushkin, V.E. and Panin, V.E., Scale Invariance of Plastic Deformation of the Planar and Crystal Subsystems of Solids under Superplastic Conditions, Phys. Mesomech., 2017, vol. 20, no. 1, pp. 1–9. doi https://doi.org/10.1134/S1029959917010015
Panin, V.E., Egorushkin, V.E., Panin, A.V., and Chernyavskii, A.G., Plastic Distortion as a Fundamental Mechanism in Nonlinear Mesomechanics of Plastic Deformation and Fracture, Phys. Mesomech., 2016, vol. 19, no. 3, pp. 255–268.
Psakhie, S.G., Zolnikov, K.P., Dmitriev, A.I., Smolin, A.Yu., and Shilko, E.V., Dynamic Vortex Defects in Deformed Material, Phys. Mesomech., 2014, vol. 17, no. 1, pp. 15–22.
Zhang, Z., He, G., Zhang, H., and Eckert, J., Rotation Mechanism of Shear Fracture Induced by High Plasticity in Ti-Based Nano-Structured Composites Containing Ductile Dendrites, Scripta Mater., 2005, vol. 52, no. 9, pp. 945–949.
Ovid’ko, I.A. and Sheinerman, A.G., Special Rotational Deformation in Nanocrystalline Metals and Ceramics, Scripta Mater., 2008, vol. 59, no. 1, pp. 119–122.
Morozov, N.F., Ovid’ko, I.A., Sheinerman, A.G., and Aifantis, E.C., Special Rotational Deformation as a Toughening Mechanism in Nanocrystalline Solids, J. Mech. Phys. Solids, 2010, vol. 58, pp. 1088–1099.
Gutkin, M.Y., Ovid’ko, I.A., and Skiba, N.V., Crossover from Grain Boundary Sliding to Rotational Deformation in Nanocrystalline Materials, Acta Mater., 2003, vol. 51, pp. 4059–4071.
Feng, H., Fang, Q.H., Zhang, L.C., and Liu, Y.W., Special Rotational Deformation and Grain Size Effect on Fracture Toughness of Nanocrystalline Materials, Int. J. Plasticity, 2013, vol. 42, pp. 50–64.
Ovid’ko, I.A. and Sheinerman, A.G., Nanoscale Rotational Deformation in Solids at High Stresses, Appl. Phys. Lett., 2011, vol. 98, p. 181909.
Ovid’ko, I.A. and Sheinerman, A.G., Nanoscale Rotational Deformation near Crack Tips in Nanocrystalline Solids, J. Phys. D. Appl. Phys., 2012, vol. 45, p. 335301.
Psakhie, S.G., Shilko, E.V., Popov, M.V., and Popov, V.L., The Key Role of Elastic Vortices in the Initiation of Intersonic Shear Cracks, Phys. Rev. E, 2015, vol. 91, p. 063302.
Psakhie, S.G., Zolnikov, K.P., Dmitriev, A.I., Kryzhevich, D.S., and Nikonov, A.Yu., Local Structural Transformations in the FCC Lattice in Various Contact Interaction. Molecular Dynamics Study, Phys. Mesomech., 2012, vol. 15, no. 3–4, pp. 147–154.
Dmitriev, A.I., Nikonov, A.Yu., Filippov, A.E., and Popov, V.L., Identification and Space-Time Evolution of Vortex-Like Motion of Atoms in a Loaded Solid, Phys. Mesomech., 2018, vol. 21, no. 5, pp. 419–429. doi https://doi.org/10.1134/S1029959918050065
Plimpton, S., Fast Parallel Algorithms for Short-Range Molecular Dynamics, J. Comput. Phys., 1995, vol. 117, no. 1, pp. 1–19.
Mishin, Y., Mehl, M.J., Papaconstantopoulos, D.A., Voter, A.F., and Kress, J.D., Structural Stability and Lattice Defects in Copper: Ab Initio, Tight-Binding, and Embedded-Atom Calculations, Phys. Rev. B, 2001, vol. 63, no. 22, p. 224106.
Stukowski, A., Visualization and Analysis of Atomistic Simulation Data with OVITO—the Open Visualization Tool, Model. Simul. Mater. Sci. Eng., 2010, vol. 18, no. 1, p. 15012.
Funding
The work was supported by Fundamental Research Program of the State Academies of Sciences for 2013–2020 (project No. III.23.2.4 project). The results related to lattice defect formation due to elastic stress redistribution were obtained under Russian Science Foundation grant No. 17-19-01374. The molecular dynamics simulation was performed on a Skif Cyberia supercomputer under Competitiveness Enhancement Program of Tomsk State University.
Author information
Authors and Affiliations
Corresponding author
Additional information
Russian Text © The Author(s), 2019, published in Fizicheskaya Mezomekhanika, 2019, Vol. 22, No. 3, pp. 36–43.
Deceased.
Rights and permissions
About this article
Cite this article
Dmitriev, A.I., Nikonov, A.Y., Filippov, A.E. et al. Molecular Dynamics Study of the Evolution of Rotational Atomic Displacements in a Crystal Subjected to Shear Deformation. Phys Mesomech 22, 375–381 (2019). https://doi.org/10.1134/S1029959919050047
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1029959919050047