Stress concentration at a penny-shaped crack in a nonhomogeneous medium under torsion

The problem of a penny-shaped crack in a nonhomogeneous medium under torsion is investigated. The shear modulus is allowed to vary in an arbitrarily continuous manner along its thickness direction. By approximating the shear modulus with a series of linear functions of the thickness, the problem can be solved by employment of Hankel integral transforms technique and transfer matrix method, which reduces it to the solution of a Cauchy singular integral equation. Numerical stress intensity factors are then obtained.