Local stress field for torsion of a penny-shaped crack in a functionally graded material

A penny-shaped crack embedded in an infinite nonhomogeneous material under torsion has been considered by Ozturk and Erdogan (1993). In order to make problem tractable, they used an exponential form of the shear modulus and t ransformed the mix boundary value problem into a singular integral equation . The singular character of the stresses were then obtained. But they gave fro angular distribution function of the stresses. In this paper, we presen t a model of shear modulus as mu(z) = mu(0)(1+alpha z)(2), alpha > 0. The n onhomogeneity parameter alpha may be adjusted to approximate the actual mat erial property distribution of FGMs. By using Hankel integral transform tec hnique, the problem is reduced to solving a Fredholm integral equation of t he second kind, which is transformed from a pair of dual integral equations . The local stress field around the crack tip is obtained. Pt is found that both of the singular character of the stresses around the crack tip and th e angular distribution function in FGMs are the same as that in homogeneous material.