Impact of sudden torsional load of a rigid disk parallel to an internal penny-shaped crack in a finite elastic medium

This article investigated the impact of sudden torsional loading induced by a rigid disk attached to the top of an isotropic elastic material of finite thickness, weakened by a penny-shaped crack, and supported by an undeformable base. The problem was solved by employing Hankel and Laplace transforms. The mixed boundary problem was transformed into a system of dual integral equations, further reduced to Fredholm integral equations of the second kind. Numerical solutions were obtained using the Gaussian quadrature rule initially, followed by Zakian's algorithm for Laplace transform inversion to derive the time-dependent solution. The results reveal the dynamic stress intensity factors' evolution over time for various materials and parameters, providing insights into arresting crack growth and ensuring structural integrity under sudden applied loads.