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AbstractThis 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. [ABSTRACT FROM AUTHOR]

AbstractThe 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. [ABSTRACT FROM AUTHOR]