Interacting micro-cracks near the tip in the process zone of a macro-crack

For a linearly elastic and isotropic solid containing two or more cracks, cavities and other interacting defects of complex geometries, a method called “the method of pseudo-tractions” has been recently proposed by Hori and Nemat-Nasser (1983, 1985a), which can effectively solve two-dimensional problems of this kind, when cracks or cavities with sharp corners are suitably far apart. The method, however, breaks down when a crack or cavity is situated very close to the tip of another crack, which is the case when the process zone at the tip of a crack contains many micro-cracks.In this work, modifications of the method of pseudo-tractions are introduced, which will permit effective calculation of the stress intensity factors when a large crack interacts with small cracks which are situated very close to its tip in its process zone. Explicit asymptotic expressions are obtained for the stress intensity factors of the macro-crack, as well as those of the micro-cracks. It is shown that the presence of the microcracks in the process zone of a macro-crack may induce out-of-plane crack growth even under far-field hydrostatic tension. Several illustrative examples are worked out, including two collinear cracks for which an exact solution exists, arriving at an excellent correlation.