Out-of-plane singular stress fields in V-notched plates and welded lap joints induced by in-plane shear load conditions

Abstract

When a crack or sharp notch is subjected to antisymmetric plane loading the Poisson's effect leads to the generation of a coupled out-of-plane singular mode. The latter was known to exist for problems with cracks for a long period of time; meanwhile this mode was largely ignored in theoretical studies of V-shaped notches subjected to in-plane loading as well as in practical fracture problems associated with such geometries. Only recently a characteristic equation describing the strength of the singularity of this mode was derived within the first order plate theory. Preliminary numerical investigations confirmed that a highly localized out-of-plane singular state linked to the transverse shear stress components does exist in the close vicinity of the notch tip with the singular behaviour as theoretically predicted. However, until now it is unclear how significant this mode is and whether it has to be taken into consideration in the stress analysis of engineering structures. This paper is aimed to discuss important features of this recently identified singular mode, out-of-plane singular mode, conduct a comprehensive three-dimensional numerical study of a typical problem of a welded lap joint to investigate the contribution of this mode into the overall stress state in the close vicinity of the notch tip and discuss the implementation of these new results to the failure and integrity assessment of plate structures with sharp notches.