Bonded contact of a rigid disk inclusion with a penny-shaped crack in a transversely isotropic solid

摘要

An analytical treatment is presented for bonded contact of a rigid disk inclusion embedded in a penny-shaped crack in a transversely isotropic full-space. Theoretical analysis is carried out using a complete potential function method, and with the aid of Hankel transforms. Boundary conditions propel the problem toward a set of triple integral equations, which are solved analytically and then reduced to a pair of Fredholm integral equations of the second kind. Furthermore, the results are evaluated and presented graphically using numerical schemes, and comparison is made with well-known classical solutions in transversely isotropic and isotropic media. This can be obtained as special cases for the problem to reveal the efficacy of the proposed method. Eventually, it can be seen that not only the presence of the crack around the disk inclusion decreases the axial stiffness, but also the extension of its length also reduces the fracture parameter, stress intensity factor, for different degrees of material anisotropy.