© 2015 Taylor & Francis. We consider rotational mechanism of macrocrack propagation based on breakage of the bonds between mutually rotating grains. The mechanism is multiscale with the macroscopic scale corresponding to the macrocrack, the next, smaller scale corresponding to the grain rotations and the smallest scale corresponding to the microcracks formed in the bonds whose propagation causes the bond breakage. The bond breakage is initiated by their bending or twisting caused by the corresponding moments. The sign of the moments only affects the side of the bond where the microfracturing starts. The independence of the microfracturing of the sign of the moment stresses provides a unified way of describing such apparently different types of fractures as tensile (Mode I) cracks, compaction bands (Mode I anticracks) and shear bands (Mode II and III). Modelling of this mechanism is based on the Cosserat theory. The bending/twisting moments are controlled by the corresponding components of moment stress. In the cases, when the Cosserat characteristic lengths are comparable with the grain sizes, the Cosserat theory is reduced to the couple-stress theory. It is found that the stress exhibits the square root singularity that coincides with the conventional ones, while the moment stress has singularity of the power -3/2. The J-integral, however, reflects only stress singularities, while the moment stress singularities do not contribute to the energy release rate. Subsequently, the energy criterion of macrofracture propagation can be based on the conventional J-integral and is not affected by the strong moment stress singularity.