The problem of axisymmetric torsion of a rigid disk parallel to an internally penny crack and interface in a bilayer medium

The aim of this work was to investigate an axisymmetric problem involving a penny-shaped crack embedded in a bi-material with finite thickness under torsion. This torsion is caused by a circular rigid disk attached to the upper layer and fixed by an undeformable support at the lower layer. The location of the crack can be found in the upper layer (case 1) or the lower layer (case 2), both cases are considered. The problem was solved by applying the Hankel transform to reduce it to a system of dual integral equations, which further simplified into Fredholm integral equations of the second-kind, These equations were then solved numerically using the Gaussian quadrature rule. Dimensionless plots were presented to demonstrate the influence of layers thickness, the distance between the support and the crack, and the shear modulus ratio between layers on the stress intensity factor of the crack. The obtained results illustrated the agreement between the analytical solution and the numerical results.