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As it is well known the Poisson's effect in a cracked plate subjected to anti-symmetric plane loading leads to the generation of a coupled out-of-plane singular mode. Recent theoretical and numerical analyses have shown that this effect is present also in plates weakened by sharp V-notches and might play a role in failure initiation phenomena of notched plates subjected to Mode II loading, especially in the presence of a large notch opening angle. Dealing with blunt notches with a large notch radius, and not just with sharp notches, the presence or not of an out-of-plane mode does not appear to have been systematically investigated in the past. The main aim of this work is to confirm the existence of the stress field associated with the out-of-plane mode (Mode O) and to describe its main features in the presence of a notch radius significantly different from zero. The analyses include U-notches, as well as circular and elliptic holes. The strain energy density in a 3D control volume is utilized to identify the most critical zone (with respect to failure initiation) through the plate thickness at the notch tip

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

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Application of the plane theory of elasticity to planar crack or angular corner geometries leads to the concept of stress singularity and stress intensity factor, which are the cornerstone of contemporary fracture mechanics. However, the stress state near an actual crack tip or corner vertex is always three-dimensional, and the meaning of the results obtained within the plane theory of elasticity and their relation to the actual 3D problems is still not fully understood. In particular, it is not clear whether the same stress field as found from the well-known 2D solutions of the theory of elasticity do describe the corresponding stress components in a plate made of a sufficiently brittle material and subjected to in-plane loading, and what effect the plate thickness has. In the present study we adopt, so called, first order plate theory to attempt to answer these questions. New features of the elastic solutions obtained within this theory are discussed and compared with 2D analytical results and experimental studies as well as with 3D numerical simulations.

The stress singularities in angular corners of plates of arbitrary thickness with various boundary conditions subjected to in-plane loading are studied within the first-order plate theory. By adapting an eigenfunction expansion approach a set of characteristic equations for determining the structure and orders of singularities of the stress resultants in the vicinity of the vertex is developed. The characteristic equations derived in this paper incorporate that obtained within the classical plane theory of elasticity (M.L. WilliamsÕ solution) and also describe the possible singular behaviour of the out-of-plane shear stress resultants induced by various boundary conditions.

After the embargo period • via non-commercial hosting platforms such as their institutional repository • via commercial sites with which Elsevier has an agreement Second harmonic generation at fatigue cracks by low-frequency Lamb waves: experimental and numerical studies

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