Brittle failure of components weakened by cracks and notches is a topic of active and continuous research. It is a key topic for all researchers who face the problem of fracture of materials under different loading conditions and deals with a large number of applications in different engineering fields. This topic is significant in all the cases where intrinsic defects of materials or geometrical discontinuities give rise to localized stress concentration which, in brittle materials, may generate a crack leading to catastrophic failure or to a shortening of the assessed structural life. Whereas cracks are viewed as unpleasant entities in most engineering materials, U- and V-notches of different acuities are sometimes deliberately introduced in design and manufacturing of structural components. The main aim of the present contribution is to present a short review of some local approaches applicable near stress raisers both sharp and blunt allowing the reader to have an update state of the art for the considered criteria.
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