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

摘要

Highlights?Kinked crack angle and strain energy release rate after crack initiation are achieved.?Magneto elastic stress subjected to uniform magnetic field intensity is analyzed.?Cavities with arbitrary shape can be solved by changing a rational mapping function.?Three ways to solve the present problem are stated.?It is stated from Faraday’s law that the present problem is a pure shear stress one.AbstractA kinked crack initiating from an initial crack in an infinite plate of a soft ferromagnetic and paramagnetic elastic materials is analyzed. Uniform magnetic field intensity applies at the remote area in the plate. Paramagnetic and soft ferromagnetic elastic materials can be belonged to the linear magneto-elastic material. Three ways analyzing this magneto-elastic stress problem are stated, which use ferromagnetic field intensity, paramagnetic field intensity and stress field derived from Faraday’s law of magnetic force line (uniform pure shear stress state), respectively. These three ways give the same result which is a uniform pure shear stress state.The kinked crack anglesθjust after the crack initiation are achieved for any directionδof the magnetic field intensity. The directions for0?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 s