The Reissner-Sagoci problem for an interfacial crack in an elastic bilayer medium under torsion of an embedded rigid circular disc

This paper studies an axisymmetric problem of a penny-shaped crack at the interface of a bi-material under a static torsion by an embedded circular rigid disc. By using the Hankel integral transformation method, the angular displacements and the shear stresses are formulated. The faces of the crack are supposed stress free, and the displacement is continuous outside in the crack plane while the rigid circular disc inclusion rotates about the axis passing through their centers and the stress is continuous outside in the rigid disc plane. Considering these mixed conditions associated with the embedded rigid disc and the interfacial crack, the mixed boundary values are taken into account, that are transformed, to a system of dual integral equations. By appropriate transform, the dual integral equations are converted into a regular system of Fredholm integral equations of the second kind with two unknown functions which is then solved by quadrature rule. Numerical results for displacements and stresses in the interaction zone, the stress intensity factor at the edges of the crack and the rigid disc and the applied torque are obtained and discussed according to certain relevant parameters. The torsional effects of the disc on the elastic bilayer are evaluated by the analysis of the Mode III stress intensity factor in the crack vicinity depending on the degree of nonhomogeneity at the interfacial plane, crack size and the depth of embedment of the rigid disc. The efficiency of the method and of the mathematical formulation are checked by comparison with the results available for a relevant analysis in homogeneous solids. © 2020 Elsevier Ltd