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The applicability and limitation of some fracture criteria in the fracture mechanics of magnets are studied.It is shown that the magnetic field intensity factor can be used as a fracture criterion when the crack in a magnet is only affected by a magnetic field. For some magnetostrictive materials in which the components of magnetostriction strain do not satisfy the compatibility equation of deformation, the stress intensity factor can no longer be effectively applicable as a fracture criterion when the crack in a magnet is affected by a magnetic field and mechanical loads simultaneously.