Dynamic behaviour of planar dislocation pile-ups

The dynamic behaviour of a twin and a slip band is considered when simulated as the planar pile-ups of partial and complete dislocations, respectively, with a continuum distribution density. A similarity between solutions has been found for the equations describing the twin shrinking under the action of surface tension forces, and the slip band growth under the action of a δ-function type force. It turns out that the twin length decreases according to the law $\text{L～ (τ ? t)}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$, where τ is the full time of the twin shrinking. It has been also shown that within a small region directly adjacent to the twin center the dislocation density increases according to the law $\text{1}\text{x}$, where x is the distance to the center. Annihilation of opposite-sign dislocations takes place in the twin center where the twin cannot be considered planar and where a two-dimensional region is formed. An attempt has been made to describe this region and its evolution in the process of the twin shrinking. The theoretical results obtained are in good agreement with the experimental data for the process of elastic twin shrinking and sound emission arising in this case.