Self-energy, line tension and bow-out of grain boundary dislocation sources

Abstract

Experimental observation and numerical modelling of plastic deformation of sub-micrometre grains show that the importance of grain boundary dislocation sources (GBDS) increases as the grain size dg decreases below 1 μm. Grain boundary (GB) ledges and grain boundary dislocations (GBD) define limiting cases of the general concept of disconnections. Although the former have often been identified as potential GBDS, the latter are generally used in models for GBD-nucleation. In absence of pre-existing GBDs, (i.e. boundary ledges or disconnection-free boundaries), conservation of the Burgers vector imposes the creation of a residual GBD-segment when a mobile segment is emitted. This GBD exercises a back-stress on the emitted dislocation, which was analysed using two approaches. The first one calculates the self-energy (SE) of a dislocation loop consisting of a straight segment and a circular arc with arbitrary angle 2α and radius r, providing new results in the elastic theory of dislocations. The second model uses a line-tension (LT) approach, calculating the curvature of the dislocation as a function of the local stress field, defining a prescribed curvature problem. The models provide different details about the activation of GBDS but are remarkably compatible. They predict that the GB-segment formed upon initial bow-out will become shorter until the loop is cut off at the root, leaving a closed dislocation loop within the grain. This defines a GB-equivalent for the classical Frank-Read (FR) source, with a low activation energy for the smallest source lengths.