Internal Vibrations of Edge Dislocation Dipoles

Abstract

The resonance frequency of vibrations of dislocation dipoles in fatigued f.c.c. metals is found rather high, in the range of 100 GHz. Because of high attenuation of ultrasound in the GHz range, the contributions of these self-vibrations to degradation of the dipole structures could be expected only in thin layers.

Resonant interaction of edge dislocations with running acoustic waves

“…For N = 1 (see figure 5(a)) the wall has one degree of freedom and it behaves qualitatively similar to the case of single dislocation, shown in figure 3(a). The case of N = 2 with two degrees of freedom supports two eigenmodes: the zero-frequency translational mode and the staggered mode with the frequency ω max given by (10). Both these peaks can be seen in figure 5(b).…”

“…The solid lines correspond to the sound wave propagating along the x-axis (θ = 0), while the dashed lines correspond to θ = π/4. The other parameters of equations of motion (7) are as follows: A n = 0.05, B n = 0.005 and C = 0.477, and ω 2 = 1.37×10 10 Hz. The vertical dashed lines show the locations of the eigenfrequencies of the corresponding dislocation clusters, as given by (4).…”

“…where ρb 2 n is the mass of unit length of the dislocation [10,18], with ρ being the density of the medium and γ is the viscosity coefficient. The first term on the right-hand side of (1) gives the x-component of the force acting on the unit length of the dislocation from the other dislocations in the system.…”

“…Ultrasound waves exert time-dependent force on dislocations [1][2][3][4][5] resulting in a number of interesting phenomena such as self-organization of dislocation ensembles [6][7][8], cross-slip [9] and dislocation reactions such as dipole breaking [10]. Ultrasound can be used to improve the properties of the metal surface, e.g., by means of a treatment with a metallic indentor vibrating at a high frequency [4].…”

“…It is customary to study the interaction of dislocations with infinitely long sound waves and neglect the inertia term in the equations of motion of dislocations [5][6][7][8][9][10][11][12]. In this study we take into account the finite length of sound waves and also the mass of dislocations.…”