Asymptotic analysis of crack interaction with free boundary
This paper employs the beam and dipole asymptotic techniques for modelling interaction of a crack with parallel free boundaries. Two configurations are considered: a crack in a half-plane, and a crack in the centre of an infinite strip. Simple approximation formulae for the stress intensity factors (SIFs) and the areas of crack openings are obtained for all considered cases by interpolation between two asymptotic solutions: for crack close to and far from the boundary. For the crack situated close to the boundary, the part of the material between the crack and the boundary is represented by a beam (plate in plane strain). It is shown that this asymptotic method allows obtaining two leading terms for the SIFs and the crack opening area. When the distance between the crack and the free surface is large, the problem is treated in the far field approximation. Thus, dipole asymptotic method allows to find the leading asymptotic terms responsible for crack-boundary interaction. Examples of cracks loaded by pair of concentrated forces and of crack under uniform loading are considered. It is interesting that the values of the parameters of interpolating formulae obtained by fitting to numerical data are consistent for different geometries and loads.
scientific article; zbMATH DE number 1444155