Explicit solutions of magnetoelastic fields in a soft ferromagnetic solid with curvilinear cracks

The problem of curvilinear cracks lying on a soft ferromagnetic solid subjected to a remote uniform magnetic induction is considered. With the complex variable technique, the general solutions of both the magnetic field quantities and the magnetoelastic stresses can be obtained. In order to illustrate the effect of magnetic induction, the solutions for the problem with one arc crack and two arc cracks are presented in a closed form. The stress intensity factors in the vicinity of crack tip and the crack opening condition are also derived. Considering the magnetic stress induced by an oblique magnetic field on the crack surface, one can find that the stress intensity factors of mode-I and mode-II are related to the incident angle of magnetic induction, the crack half angle and the magnetic susceptibility as displayed with figures. It is noticed that the present work is available even for a ferromagnetic material with low susceptibility. For the limiting case of the crack half angle in the one arc crack problem approaching to zero, the stress intensity factors are also provided and analytically compared with the existing ones of the straight crack problem.