The problem of a penny-shaped crack in a non-homogeneous medium under shear

An integral transform method is used to find the axisymmetric stress distribution in an infinite non-homogeneous elastic solid containing a penny-shaped crack under axial torsion. The non-homogeneity of the medium varies according to the relationship G(z)=G1+G2exp(−ρz), where z is the z-coordinate in the cylindrical polar coordinate system (r,θ,z). A Hankel transform development of the governing equations yields a set of dual integral equations which can in turn be reduced to a Fredholm integral equation of the second kind. Numerical values of the stress intensity factors are displayed graphically to demonstrate the effect of non-homogeneity of the material.