On the problem of an axisymmetric thin film bonded to a transversely isotropic substrate

In this paper, the mechanics of a thin film perfectly adhered to a transversely isotropic substrate is studied. Neglecting the peeling stress on the interface, the equilibrium equation of stress components for the film is extracted. For the axi-symmetric condition, the Hankle transform is employed to determine the displacement components within the substrate. In view of the surface strains compatibility, the governing integral equation is established in terms of the unknown interfacial shear stress. Finally using a suitable Chebyshev expansion for the shear stress, a numerical solution is provided for the integral equation. The numerical results are given for both the thermal and the mechanical loadings applied the film. Also, the analytical results are supported by finite element simulations. The results indicate that the ratio of the film stiffness to the substrate stiffness plays the key role in the variation of the stress components. For a given substrate, an increase of the film stiffness can dramatically increase the edge singularity of the shear stress. For a relatively stiff substrate, the distribution of the film stresses remains almost uniform from the center up to 80% of the film length and builds up around the edge.