Analysis of a kinked crack in soft ferromagnetic and paramagnetic elastic materials subjected to uniform magnetic field intensity

The kinked crack angles θ just after the crack initiation are achieved for any direction δ of the magnetic field intensity. The directions for 0⩽δ⩽360° are considered. The following three criteria for the crack initiation are considered; (1) The kinked crack initiates in the direction taking maximum value of the Mode I stress intensity factor just after the crack initiation under the additional condition that the Mode I stress intensity factor is positive; (2) The kinked crack initiates in the direction satisfying Mode II stress intensity factor is zero; (3) The kinked crack initiates in the direction taking the maximum value of the strain energy release rate under the additional condition that the Mode I stress intensity factor is positive. It is found that the initiating angles exist in the range of -150°⩽θ⩽150°. It is stated that these criteria give the same results for the kinked crack angles. The distributions of the magnetic field intensity and the stress are investigated for some kinked crack angles and directions of magnetic field intensity. The stress intensity factors for some directions of magnetic field intensity are also investigated versus the crack length for some kinked crack angles.