Equation of motion for dislocations with inertial effects

An approximate equation of motion is proposed for screw and edge dislocations, which accounts for retardation and for relativistic effects in the subsonic range. Good quantitative agreement is found, in accelerated or in decelerated regimes, with numerical results of a more fundamental nature.

Figure 1

(Color online) Upper: relationship between dimensionless applied stress $\sigma ∕\mu$ and asymptotic velocity $v∕c_S$ provided by the PNG code (Ref. 9) for an accelerated edge dislocation in the stationary regime (dots), compared to that predicted by Rosakis’ model I (Ref. 11) (lines) for different viscosity parameters $\alpha$, for a screw dislocation in the subsonic regime. Lower: normalized velocity-dependent core width $\zeta \left(v\right)∕\zeta \left(0\right)$ measured under same conditions. $c_R$ is the Rayleigh velocity.

Figure 2

(Color online) Velocities vs time for accelerated screw dislocations: white dots, PNG code; solid, Ref. 4; dots (in left curve only), Eq. (1); dash-dots, linear approximation to Eq. (16); and dashes, fully relativistic equation [Eq. (16)].

Figure 3

(Color online) Velocities vs time for accelerated edge dislocations: white dots, PNG code; solid, Ref. 4; dash-dots, linear approximation to Eq. (16); and dashes, fully relativistic equation [Eq. (16)]. Curves obtained from Eq. (16) are duplicated using $t_0$ computed either with $c_S$ (upper) or with $c_L$ (lower) (see text).

Figure 4

(Color online) Velocities vs time for a decelerated screw dislocation. Comparison between the PNG method (white dots) (Ref. 7) and Eq. (16) with (dashes) or without (dot-dash) fully relativistic expressions.