Transverse singular effects in V-shaped notches stressed in mode II

The concept of a stress singularity is a cornerstone of modern fracture mechanics. A new mode of stress singularity, the out-of-plane singular mode or K (O) mode, was recently identified for V-shaped notches subjected to in-plane loading. This new mode is coupled with the shear mode and related to Poisson's effect. The previous studies based on the first order plate theory focused on the derivation of a characteristic equation describing the strength of this singularity and provide no information regarding the intensity, extent and relevance of this mode to practical problems. This paper aims to fill this gap. The approach utilises the 3D finite element method and a standard regression technique for characterisation of the notch singular modes. A comprehensive study of the influence of Poisson's ratio, plate thickness and notch opening angle on the value of the notch stress intensity factor associated with this mode is conducted for infinite plates. Additionally, to demonstrate the relevance of this new singular mode to practical problems an investigation of the out-of-plane mode and associated three-dimensional effects are presented for the case of a welded lap joint. Main areas of further research are also identified.