On a coupled mode at sharp notches subjected to anti-plane loading

Abstract

When a crack or sharp notch is subjected to anti-plane shear loading the boundary conditions negate the transverse shear stress components at the free surfaces and generate a coupled in-plane shear stress field, which can be singular. For sharp V-notches with zero notch opening angle (or cracks) this 3D phenomenon was known for a long period of time. However this mode was largely ignored in stress analysis of notched components. Till now it is still unclear how significant this mode is and whether it has to be taken into consideration in integrity and failure analysis of engineering structures. The present paper is aimed to investigate this singular mode by means of the 3D Finite Element method, which is applied to notched plates with different notch opening angles and plate thicknesses. The stress state associated with the coupled mode is localised and quickly decays with the distance from the notch tip. Therefore, the obtained theoretical results can be applied to a wide range of notched components provided that the boundaries are sufficiently far from the notch tip. Among these results is the effect of the plate thickness on the intensity of the coupled mode; the latter increases with the decrease of the plate thickness. Significance of these new results to failure and integrity assessments of plate and shell components with sharp notches, including through-the-thickness cracks, is discussed in the final section of the paper. © 2012 Elsevier Masson SAS. All rights reserved.