Analysis of Plane-Strain Crack Problems (Mode-I & Mode-II) in the Presence of Surface Elasticity

We consider plane deformations of a linearly elastic solid in the case where either a mode-I or mode-II crack is present but, perhaps more significantly, when surface effects are included in the mechanics of the crack faces. The surface effects lead to a more accurate description of deformation and are incorporated using a version of the continuum based surface/interface model of Gurtin and Murdoch. We obtain a semi-analytic solution valid throughout the entire domain of interest (including at the crack tips) via two series of coupled Cauchy singular integro-differential equations which are solved numerically using an adapted collocation technique. It is shown that, among various other interesting phenomena, when the solid incorporates a traction-free crack face and is subjected to uniform far-field stresses (tension and in-plane shear), the surface effects result in the elastic response and corresponding stress fields being size-dependent. In particular, we note that, in contrast to classical linear elastic fracture mechanics, our model allows for finite stresses at the (sharp) crack tip.