Magnetoelastic Interaction of a Soft Ferromagnetic Elastic Solid With a Penny-Shaped Crack in a Constant Axial Magnetic Field

Abstract

The fundamental equations for soft ferromagnetic elastic materials of multidomain structure are derived in cylindrical coordinates. The basic theory used is one of Pao and Yeh [3] and the soft ferromagnetic elastic solids are considered to be composed of materials with isotropic, cubic or uniaxial symmetry. Using the fundamental equations, the axisymmetric problem for an infinite body with a penny-shaped crack in a constant axial magnetic field is investigated. A solution for the infinite solid is obtained by the method of two simultaneous dual integral equations. The magnetoelastic stresses and the Maxwell stresses are expressed in closed forms. By referring to a set of polar coordinates r1 and θ1 measured from the crack periphery, the dependence of the local stresses on r1 and θ1 is also determined in closed elementary form. As in the classical case, the stresses possess the familiar inverse square-root singularity at the crack boundary. The stress-intensity factor, however, is found to depend on the magnetic field. When the magnetic field reaches a critical value, the surface of a crack is unstable. The effect of magnetic fields on the stresses and the stress-intensity factor, and a comparison of the plane strain and axisymmetric solutions are shown graphically.