On the presence of the out-of-plane singular mode induced by plane loading with KII = KI = 0

Abstract

Previous studies by a number of researchers demonstrated that in the case of a plane crack subjected to shear loading conditions characterized by a remote stress intensity factor, KII, a three-dimensional singular mode (called mode O or outof-plane mode) develops at the crack tip. This singular mode occurs due to the primary shear loading and Poisson's effect. Similar to mode III, the O-mode is associated with the transverse shear stress components. Recent theoretical and numerical studies have also demonstrated a strong presence of this singular mode in plates weakened by pointed V-notches. Therefore, it was suggested that O-mode can play an important role in fracture initiation, particularly at large opening angles (above 102.6°) when the applied mode II is non-singular. One exciting development in 3D fracture mechanics is to investigate this singular mode when the remote anti-symmetric loading doesn't produce the in-plane singularities, or when KII (KI) = 0 for plane problems with cracks. In this case, the classical energy fracture criterion, which is based on the plane theory of elasticity, indicates zero energy release rate at the crack tip; which, generally speaking, excludes the possibility of brittle fracture by crack extension. In this letter we will demonstrate that when KII = 0, the three-dimensional effects, in particular the presence of the singular mode O coupled with the plane shear loading, can lead to non-zero energy release rate and provoke the fracture initiation at the crack tip. © 2010 Springer Science+Business Media B.V.