The linear magnetoelastic problem of a uniform current flow disturbed by a penny-shaped crack in a constant axial magnetic field

This paper deals with the magnetoelastic problem of an infinite conductor with a penny-shaped crack under a uniform axial electric current flow and a constant axial magnetic field. The current flow is disturbed by the presence of the crack and the torsional stresses are caused by the interaction between the magnetic field and the disturbed current. Integral transform techniques are used to reduce two problems concerning the electric-current density field and the magnetoelastic field to those of solving two pairs of dual integral equations. These integral equations are solved exactly, and the current densities, the displacement of the crack surface and the singular stresses near the crack tip are expressed in closed forms.