Motion and Rotation of Small Glissile Dislocation Loops in Stress Fields

We derive here for the first time the equations that describe the combined motion and rotation of small prismatic dislocation loops in stress fields. When the applied torque is balanced by the self-torque of the loop, we show how the solution can be obtained for the loop orientation, and how this orientation affects the glide force on the loop.

Figure 1

The inset shows the three vectors required to characterize the orientation of a prismatic, interstitial-type loop. The Burger vector $\mathbf{b}$ which is given determines the glide direction. The traction vector field $\mathbf{t}(\mathbf{r})$ is defined by the source of stress, here an edge dislocation, and the normal vector $\mathbf{n}$. As the loop glides along its glide cylinder, parallel to the dotted line, the orientations of $\mathbf{t}$ and $\mathbf{n}$ change.

Figure 2

The rotation angle $\alpha$ as a function of the loop position along its glide path. The results shown here and in Fig. 3 are for a loop with a radius of $R_0=5r_0$, and for a distance $h=3R_0$ from the glide plane of the edge dislocation.

Figure 3

The normalized glide force (see text for details) exerted by an edge dislocation on a prismatic interstitial-type loop moving parallel to the glide plane of the dislocation. The thin curve shows this force when the loop orientation remains fixed, and the thick curve when the loop rotates such that the applied torque is balanced by the loop’s self-torque.