Microcrack interaction with circular inclusion and interfacial zone

A geometrically simplified plane elasticity problem of a finite small crack emanating from a thin interfacial zone surrounding the circular inclusion situated in the finite bounded domain is investigated. The crack is arbitrarily oriented and modelled using the distribution dislocation technique. This model represents the inner solution of the studied problem. The corresponding fundamental solution is based on the application of Muskhelishvili complex potentials in the form of the Laurent series. The coefficients of the series are evaluated from the compatibility conditions along the interfaces of the inclusion, the interfacial zone and the enclosing matrix. The fundamental solution is also used in the solution of the boundary integral method approximating the stress and strain relations of the so-called outer solution. The asymptotic analysis at the point of the crack initiation combines the inner and the outer solution and results in the evaluation of the stress intensity factors of the crack tip, which lies in the matrix. The topological derivative is subsequently used to approximate the energy release rate field associated with the perturbing crack in the matrix. The extreme values of the energy release rate allow one to assess the crack path direction of the initiated microcrack.