Abstract
The temporal dynamics of the edge dislocation (ED) was studied in this work using the inhomogeneous dissipative sine-Gordon (SG) equation. The consideration was carried out for the force action levels both less and more critical. 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 proposed 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 distance between the stoppers. The axis of symmetry is a straight line that is perpendicular and halves the distance between the stoppers. A graphical description of the ED temporal dynamics was plotted in the Cartesian coordinate system based on the proposed particular solution and its mirror and displaced 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.
Highlights
The mechanism of continuous generation of dislocations in the slip plane was first proposed by Frank and Reed [1]
A particular solution of the SG equation is proposed that describes the temporal dynamics of half the edge dislocation (ED) in the Frank—Reed source (FR) mode, which rests on a stopper at the origin
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 counterclockwise, the second clockwise
Summary
Boris Viktorovich Borts, Stella Fedorovna Skoromnaya, Viktor Ivanovich Tkachenko.
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