Crack in an elastic thin-film with surface effect

A two-dimensional fracture problem on a crack embedded in an elastic thin-film with surface effect is studied. An elastic analysis of an infinite isotropic homogeneous elastic thin-film with a crack penetrating its thickness is made when subjected in-plane applied loading. Since the elastic thin-film in question is sufficiently thin, the surface stress and surface elasticity are taken into account. First, the principle of virtual work is applied to derive basic equations. Furthermore, coupled governing equations on elastic displacements are obtained, which are then transformed to a single bi-harmonic equation. Mode-I and mode-II cracks are solved and two singular integral equations with Cauchy kernel of the first kind are derived by the Fourier transform technique. Exact elastic field in the whole elastic plane is determined for each case. Fundamental fracture parameters such as the stress intensity factor (SIF) are obtained. Results show that both surface stress and surface elasticity can decrease the SIF, and the SIF is related to material properties. When neglecting surface effects, the SIF is independent of the material properties.