The propagation front of a crack generates large strain gradients and it is therefore a strong source of gradient-induced polarization (flexoelectricity). Herein, we demonstrate that, in piezoelectric materials, a consequence of flexoelectricity is that crack propagation is helped or hindered depending on whether it is parallel or antiparallel to the piezoelectric polar axis. The discovery of crack propagation asymmetry proves that fracture physics cannot be assumed to be symmetric in polar materials, and indicates that flexoelectricity should be incorporated in any realistic model.