Singular stresses in a soft ferromagnetic elastic solid with a flat annular crack

Following a linear theory for the soft ferromagnetic elastic materials, we investigate the axisymmetric problem for an infinite body with a flat annular crack in a constant axial magnetic field. It is assumed that the soft ferromagnetic elastic solid is a homogeneous and isotropic one. Using an integral transform technique, the problem is reduced to that of solving a singular integral equation of the first kind. The solution of the singular integral equation is obtained in the form of the product of the series of Chebyshev polynomials of the first kind and their weight function. Thus the essential feature of the singular stress field near the crack is preserved and the crack tip stress-intensity factor is easily evaluated. The singular stresses near the crack tip are obtained in closed elementary forms and the influence of the magnetic fields upon the stress-intensity factors is shown graphically.