Effects of magnetic fields on cracks in a soft ferromagnetic material

The 2D problem of a soft ferromagnetic solid with a finite crack under a uniform magnetic field has been studied based on the linear theory of Pao and Yeh. Especially, in this work, the Maxwell stresses induced by the applied magnetic field are taken into account in the boundary conditions not only along the crack surfaces, but also at infinity. Based on these boundary conditions, the related boundary-value problem is solved by using Muskhelishvili's complex variable method to obtain the complex potentials. Thus, it is found that the obtained complex potentials are constant, which indicates that both magnetic fields and stress are uniform in the solid. This implies that if only a pure magnetic field is applied, it has no effects on a crack in a soft ferromagnetic solid. To confirm this result, the same boundary-value problem is solved by the integral transform technique, which shows the same finding as that by using the complex variable method. This outcome is consistent with available experimental data but different to previously published theoretical results.