A BEM analysis of a penny-shaped interface crack using the open and the frictionless contact models: Range of validity of various asymptotic solutions

The global elastic solution for the problem of a pressurized penny-shaped crack at the interface of two dissimilar half spaces has been numerically obtained employing the boundary element method (BEM). Using the Williams’ open model (for the whole range of feasible bi-material combinations), the comparison of the global BEM solution with an existing analytical asymptotic solution has shown: (i) that the extent of the zone in which the first term is dominant is always larger than the extent of the zone in which the interpenetrations take place and (ii) that, in the former zone, a recently proposed relation between the components of the complex stress intensity factor (SIF) and the components of the energy release rate (ERR) always yields accurate results. Consequently, the appearance of negative values of the normal contribution to the ERR in certain cases has been confirmed by the BEM solution, thus questioning the significance of the asymptotic results obtained from the open model in those cases. If the Comninou's frictionless contact model is employed, the ability of the BEM formulation employed to obtain accurate elastic solutions is shown by comparisons with an existing semi-analytical solution (for a particular bi-material combination).