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The interaction between a wedge disclination quadrupole and the crack in deformed nanocrystalline ceramics and metals isinvestigated by the complex variable method. We have theoretically described the effects of the disclination quadrupole produced bythe special rotational deformation on the emission of lattice dislocations from the crack tip. The complex form expressions of thestress field and the force field are divided. The critical stress intensity factors for the first dislocation emission are calculated. Theinfluence of the disclination strength, the quadrupole arms, the location of the disclinations and the angle between the crack plane andone of the quadrupole arms, the crack length, as well as the parameter values of different nanocrystalline materials on the criticalstress intensity factors is discussed in detail. And the results show that, the disclination quadrupole has great influence on thedislocation emission from the crack tip.