Effect of cooperative grain boundary sliding and migration on dislocation emission from a branched crack tip in deformed nanocrystalline solids

A theoretical model is established to describe the effect of cooperative grain boundary (GB) sliding and migration on dislocation emission from the tip of branched crack in deformed nanocrystalline solids. The explicit solutions of complex potentials are obtained by means of complex variable method and conformal mapping technique. The critical stress intensity factors (SIFs) for the first lattice dislocation emission from the tip of branched crack are calculated. The effects of the lengths of branched crack and main crack, and the angle between their planes on the critical SIFs for dislocation emission are evaluated in detail. The results indicate that the emission of lattice dislocations from the tip of branched crack is strongly influenced by cooperative GB sliding and migration. When main crack approaches the branched crack, dislocation emission from the tip of branched crack will be suppressed. The main crack tends to propagate while shorter branched crack is prone to be blunted by emitting lattice dislocations from its tip. As a special case, when the planes of main crack and the branched crack are flattened out into one, the present results are in good agreement with previously known results.