Energy radiation and limiting speeds of fast moving edge dislocations in tungsten

The energy loss of a uniformly moving dislocation radiating lattice waves is quantitatively studied by atomistic simulations. The velocity dependence of the energy radiation provides a unique way to understand limiting behavior exhibited by fast moving dislocations. In combination with theoretical analyses, the simulations provide a consistent atomic-level picture of near-sonic, transonic, and supersonic dislocation motions in crystalline materials.

Figure 1

(Color online) Schematic drawing of a perfect edge dislocation $(\mathbf{b}=\frac{1}{2}\left[\overline{1}1\overline{1}\right])$, located in the center of the simulation box. The dislocation may glide either to the twinning (TW) or to the antitwinning (ATW) direction, depending on the direction of applied shear.

Figure 2

(Color online) Dislocation velocity as a function of applied strain for uniform dislocation motion, obtained by MD simulations. Full symbols represent velocities achieved by applying a constant shear strain to a standstill dislocation (with zero initial temperature); open ones correspond to velocities reached by gradually changing the strain to a higher or lower value after uniform motion in a certain velocity regime has been established.

Figure 3

(Color online) The velocity of uniform dislocation motion at finite temperature $\left(T\right)$ for ${\epsilon }_{\mathit{appl}}=4\%$ (filled squares), ${\epsilon }_{\mathit{appl}}=6\%$ (open circles), and ${\epsilon }_{\mathit{appl}}=8\%$ (filled circles). Sound wave speeds were calculated according to the $T$ dependence of the corresponding Born moduli of the bulk lattice, obtained via MD simulations at thermal equilibrium.

Figure 4

(Color online) Atomic profiles of fast moving dislocations. (A) Subsonic motion: $\upsilon =2.09\mathrm{km}{\mathrm{s}}^{-1}$ at ${\epsilon }_{\mathit{appl}}=3\%$. (B) Transonic motion: $\upsilon =4.51\mathrm{km}{\mathrm{s}}^{-1}$ at ${\epsilon }_{\mathit{appl}}=6\%$. (C) Supersonic motion: $\upsilon =6.76\mathrm{km}{\mathrm{s}}^{-1}$ at ${\epsilon }_{\mathit{appl}}=9\%$. (i) Far-field snapshots of dislocation radiation (A1, B1, and C1), colored according to the transient “temperature” (kinetic energy) of individual atoms. (ii) Close view on core structures (A2, B2, and C2), colored according to the potential energy of individual atoms. (iii) Flow fields at dislocation core (A3, B3, and C3), measured by atomic displacements in the $x\text{−}y$ plane $\left(\Delta \mathbf{u}\right)$ within a time interval $\delta t$ according to $\Delta \mathbf{u}\left(\delta t\right)=\Delta u_x\left(\delta t\right)\mathbf{i}+\Delta u_y\left(\delta t\right)\mathbf{j}$, where $\delta t=w{\upsilon }^{-1}$ with $w\approx 1.5\mathrm{nm}$ (or $5\sim 6b$, which is of the order of the core width). Flow currents are dipolelike in orthogonal orientations as inset indicated (A3). For a better view of those localized shear wave fronts, $\Delta u$ has been multiplied by a factor of 5 in these plots.

Figure 5

(Color online) [(A) and (B)] Atomic profiles of a subsonic dislocation moving into the twinning direction ($\upsilon \sim 2400\mathrm{m}{\mathrm{s}}^{-1}$ at ${\epsilon }_{\mathit{appl}}=-4\%$). Such a dislocation turned into an emissary dislocation, i.e., [(C) and (D)] it dissociates and triggers twinning.

Figure 6

(Color online) (A) System kinetic energy calculated as a function of time. Each curve corresponds to an independent simulation run where a different ${\epsilon }_{\mathit{appl}}$ has been applied to the standstill dislocation (from bottom, ${\epsilon }_{\mathit{appl}}=0.5\%$, 1%, 2%, 3%, 4%, 4.5%, 5%, 6%, 7%, 8%, 9%, 10%, and 10.5%, respectively). Within the time window the dislocation exhibits a uniform motion, $G_K$ has been measured according to Eq. (4) and its ${\epsilon }_{\mathit{appl}}$ dependence is plotted in (B) in comparison with $G_e∕2$ [see Eqs. (1, 5)]. $G_K$ versus dislocation velocity is shown in (C), where the theoretical solution based on Eq. (6) is obtained using $c_2=c_t\left({\epsilon }_0\right)$ and $c_1=c_l\left({\epsilon }_0\right)$ with ${\epsilon }_0=3\%$.