Cracks on or near an interface

Problems for finite cracks on or near a bi-material interface were investigated. The crack under uniform pressure or a pair of concentrated loads on its faces was modelled by a dislocation density function along the crack length. For sub-interface crack problems, we investigated the case when the crack is near the interface of two half-planes and when the crack is near a coating-substrate system. In both cases the singular integral equations are of the first kind and were solved numerically by expanding the unknown dislocation density function. When the crack is near the interface of two half-planes, the stress intensity factors and the energy release rate were obtained as a function of the crack-to-interface distance, and they approach the asymptotic solutions derived by Hutchinson et al. (1987) as the crack approaches the interface. In the case of a soft coating, $\alpha$ $\u3c$ 0 with $\beta$ = 0.0, for all values of the thickness of the coating and the crack-to-interface distance the normalized stress intensity factor $K\sb{I}/K\sb{I0}$ and the normalized energy release rate $G/G\sb0$ are greater than 1, and the normalized stress intensity factor $K\sb{II}/K\sb{I0}$ whether $K\sb{II}/K\sb{I0}$ is positive or negative depends on the values of $\alpha$, the crack-to-interface distance and the thickness of the coating. When the crack is on the interface of two half-planes, the singular integral equations are of the second kind and were solved exactly for the dislocation density function. We obtain an explicit expression for the stress intensity factors. The correction to the homogeneous stress intensity factor is of order $\epsilon$ apart from a multiplicative factor 2$\sp{i\epsilon}$, and the explicit expression to any order can be obtained once the coefficients of the expansion of the loading are known. The stress intensity factors for a finite crack in an infinite homogeneous medium depend only on the first two coefficients of the loading in terms of Chebyshev polynomials. (Abstract shortened with permission of author.