Effect of magnetostriction on fracture of a soft ferromagnetic medium with a crack-like flaw

The magnetic-induction field in the vicinity of an elliptical inclusion embedded in an infinite soft ferromagnetic medium is determined based on complex potential theory. By using a constitutive relation of magnetostriction for isotropic materials, the stress field in the vicinity of an elliptical flaw is obtained. Furthermore, the stress field at the tip of a slender elliptical crack is determined for the case in which only an external magnetic field perpendicular to the major axis of the ellipse is applied at infinity. The results indicate that the stress field in the neighbourhood of the tip is governed by the magnetostriction and permeability of the soft ferromagnetic material. The induction magnetostrictive modulus is a key parameter in determining which of the two mechanisms, i.e., magnetostriction and magnetic-force-induced deformation, is dominant in determining the stress field in the neighbourhood of the tip of a crack-like flaw. With regard to the influence of the magnetic field on the apparent toughness of a soft ferromagnetic body with a crack-like flaw, soft ferromagnetic materials can be roughly divided into two categories: one possesses a large induction magnetostrictive modulus and the other has a small modulus. An approximate criterion for categorizing the materials is presented. For the benefit of engineering design, the expressions of the stress-intensity factor for these two categories of soft ferromagnetic materials are presented. The results show that the stress-intensity factor is affected not only by the flaw geometry, but also by the permeability of the medium inside the flaw.