Sudden Twisting of an Infinite Elastic Conductor with a Penny‐Shaped Crack in a Constant Axial Magnetic Field

The problem of a torque applied suddenly to the surface of a penny‐shaped crack in an infinite elastic conductor permeated by a uniform axial magnetic field is considered. The singular solution is equivalent to that of the sudden appearence of a crack in a body under torsion. We discuss two special cases here. First, the quasistatic electromagnetic field is considered. Laplace and Fourier transforms are used to reduce the problem to a pair of dual integral equations. The solution to the dual integral equations is expressed in terms of a Fredholm integral equation of the second kind having the kernel that is a finite integral. The dynamic singular stress distributions near the crack tip are obtained in closed forms and the influence of the magnetic field upon the dynamic stress‐intensity factors is shown graphically. Second, perfect conductivity is also considered.