Asymptotic solutions for large fractures growing parallel to a free plane

Abstract

Straight 2D and disc-like cracks situated close to a parallel free plane are considered and asymptotic solutions for the stress intensity factors (SIFs) and crack opening are developed. Two asymptotic terms with respect to the small ratio of distance from the surface to the crack length/radius are derived. The derivation is based on considering the material between the crack and the free surface as an elastically supported beam or circular plate. The crack is considered to be opened either by uniform tensile stress or a pair of concentrated forces or moments representing the action of central defects (these represent for instance the crack growth from initial inclined crack or pore under compression acting parallel to the free surface). A crack with non-interacting surfaces (the conventional crack) and a crack with linear links between the surfaces are considered. Interaction with the free surface is shown to considerably increase the crack opening and SIFs, while the presence of the elastic links can reduce these crack parameters. In particular, the opening and SIFs of a crack with linear links under a pair of concentrated forces/moments exponentially vanish with the crack dimensions tending to infinity. The obtained asymptotic solutions provide a simple and accurate tool for investigating mechanisms of surface delamination and spallation (including thermal spallation and strain rockbursts).