Mode mixity and size effect in V-notched structures

Aim of the present paper is twofold. On one hand, we apply the Finite Fracture Mechanics criterion to address the problem of a V-notched structure subjected to a mixed-mode loading, i.e. we provide a way to determine the direction and the load at which a crack propagates from the notch tip. On the other hand, we make use of the formalism recently introduced by Hills & Dini [Hills D.A., Dini D. Characteristics of the process zone at sharp notch roots. International Journal of Solids and Structures 48:2177–2183] and express the critical conditions in terms of the notch driving force plus a suitable definition of the notch mode mixity. Weight functions of the stress intensity factors for V-notch-emanated cracks available in the literature allow us to implement the fracture criterion proposed in an almost completely analytical manner. Dimensionless values of the critical generalized stress intensity factors are tabled accurately in order to be of help in engineering practice. We then derive some theoretical implications from the obtained results, highlighting the size effect for a V-notched structure under mixed-mode loading and the differences between the structural behaviors of cracked and notched geometries. Some example problems, highlighting the capabilities of the model, conclude the paper.