ON THE PRESENCE OF THE OUT-OF-PLANE SINGULAR MODE INDUCED BY PLANE LOADING WITH K_Ⅱ = K_Ⅰ = 0

摘要

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, K_Ⅱ, 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 (K_Ⅰ) = 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 K_Ⅱ = 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.