Failure initiation at V-notch tips in quasi-brittle materials

A failure initiation criterion at V-notch tips for quasi-brittle is presented, in which a small damaged or plastic zone is evident that cannot not be neglected in terms of dissipated energy and stress state. This criterion is based on the finite fracture mechanics (FFM) coupled criterion, which requires a simultaneously fulfillment of an energy and a stress criteria. Under the assumption that the damaged zone and the virtual crack extension are small, matched asymptotic expansions are used. The damaged zone grows first, proportionally to the square of the applied load and then, above a threshold, a virtual crack of a given length simultaneously satisfies the energy and stress criteria, and failure occurs.