Effect of special rotational deformation on the dislocation emission from a branched crack tip in deformed nanocrystalline materials

The problem of the special rotational deformation interacting with an internal crack is studied by developing a theoretical model of deformed nanocrystalline materials. Using the complex variable method of Muskhelishvili and the conformal mapping technique, the expressions of complex potentials and stress fields are obtained analytically. The stress intensity factors (SIFs) near the crack tips and the critical SIFs for the first lattice dislocation emission from the branched crack tip are calculated. The effects of important parameters such as grain size, the length of internal crack, and the angle between the main crack and its branched crack on the critical SIFs for dislocation emission are evaluated in detail. As a result, the special rotational deformation has great influence on the growth of internal crack and the emission of lattice dislocations from the branched crack tip. The disclination quadrupole produced by the special rotational deformation will shield the branched crack tip under a certain condition. Moreover, when the main crack approaches its branched crack, it will stop the emission of lattice dislocations from the branched crack tip.