Analysis of the conditions of crack nucleation during lattice dislocations transition through grain boundary

The formation of deformation facets at high-angle grain boundaries during their interaction with lattice dislocation pile-ups is accompanied by the appearance of wedge disclination dipoles disposed on the plane of the facets. Their elastic energy increases as the dislocations of pile-up penetrate the grain boundary and the deformation facet lengthens. A possibility was considered for the relaxation of elastic energy of the disclination dipole and the pile-up stored in the vicinity of the facet. A concept of the least possible length of the crack in a crystalline solid was introduced, and an energetic criterion of its nucleation was suggested. An analysis of conditions for the crack nucleation in configuration space of considered system parameters – the total Burgers vector of pile-up, the strength of disclination dipoles, and the value of external load – has been carried out.