The present work aims to investigate a penny-shaped crack problem in the
interior of a homogeneous elastic material under axisymmetric torsion by a
circular rigid inclusion embedded in the elastic medium. With the use of the
Hankel integral transformation method, the mixed boundary value problem is
reduced to a system of dual integral equations. The latter is converted into
a regular system of Fredholm integral equations of the second kind which is
then solved by quadrature rule. Numerical results for the displacement,
stress and stress intensity factor are presented graphically in some
particular cases of the problem.