Open Journal of Metal, 2020, 10, 35-44 https://www.scirp.org/journal/ojmetal ISSN Online: 2164-277X ISSN Print: 2164-2761 DOI: 10.4236/ojmetal.2020.103003 Sep. 9, 2020 35 Open Journal of Metal A Frank-Read Source Model Boris Viktorovich Borts 1 , Stella Fedorovna Skoromnaya 1 , Viktor Ivanovich Tkachenko 1,2 1 NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine 2 V.N. Karazin Kharkiv National University, Kharkov, Ukraine Abstract The temporal dynamics of the edge dislocation (ED) was studied in this work using the inhomogeneous dissipative sine-Gordon (SG) equation. The con- sideration was carried out for the force action levels both less and more criti- cal. By SG equation numerical calculations it is shown that at the external force value below a critical one the ED takes a shape close to a semicircle. This shape was used as an initial condition for describing the ED temporal dynamics in the FR source operating mode. A particular solution of the SG equation is proposed that describes the temporal dynamics of half the ED in the FR mode, which rests on a stopper at the origin. It is shown that the pro- posed particular solution corresponds to the left Archimedes spiral displaced at π/2 counterclockwise relative to the azimuth angle equal to zero. It is noted that the temporal dynamics of the second half of the ED segment rested on the second stopper is described by the proposed particular solution, when it is mirrored relative to the problem symmetry axis and the center of the spiral is displaced to a point with a zero azimuthal angle and a radius equal to the dis- tance between the stoppers. The axis of symmetry is a straight line that is perpendicular and halves the distance between the stoppers. A graphical de- scription of the ED temporal dynamics was plotted in the Cartesian coordi- nate system based on the proposed particular solution and its mirror and dis- placed image. It is shown that the particular solution of the SG equation in the RF source operation mode involves two Archimedes spirals symmetrical relative to the problem symmetry axis with equal radii increasing linearly with time, which rotate: one (the spiral center coincides with the stopper at the origin) counterclockwise, the second (the spiral center coincides with the second stopper) clockwise. Keywords Edge Dislocation, Sine-Gordon (SG) Equation, Frank-Read Source, Archimedes Spiral, Temporal Dynamics How to cite this paper: Borts, B.V., Sko- romnaya, S.F. and Tkachenko, V.I. (2020) A Frank-Read Source Model. Open Journal of Metal, 10, 35-44. https://doi.org/10.4236/ojmetal.2020.10300 3 Received: June 26, 2020 Accepted: September 6, 2020 Published: September 9, 2020 Copyright © 2020 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access