Esistenza del modo O in piastre tridimensionali con fori circolari ed ellittici soggette a modo II

Abstract

On the mode O existence in three-dimensional plates weakened by circular and elliptical holes under mode II loading It is known for long time that in a cracked plate subjected to anti-symmetric plane loading, the Poisson’s effect leads to the generation of a coupled out-of-plane singular mode (Mode O). Recent theoretical and numerical analyses have shown that this effect is present also in plates weakened by pointed V-notches and might play a role in failure initiation phenomena in plates under mode II loading particularly in the presence of large opening angle. Since the degree of singularity characterising the mode O is greater than that of mode II, the mutual incidence of the two modes depends on the component size. Dealing with circular and elliptic holes, the presence or not of the out-of-plane mode has never been discussed in the literature. The main aim of this work is to demonstrate the existence of a three-dimensional effect tied to mode O. On the basis of a large bulk of numerical results the following conclusions can be drawn: - An out-of-plane mode is present in plates weakened by U-notches and subjected to Mode II loading, as previously demonstrated for plates weakened by cracks and pointed V-notches; its intensity is not negligible also for finite values of the notch radius. - Out-of-plane mode results in a shear stress distribution symmetric with respect to the mid-plane. The intensity of this stress component strongly depends on the Poisson’s ratio. It increases as increases. - The strain energy density averaged on a given control volume which should, in principle, be material dependent is a parameter suitable for the natural of capture all three dimensional effects occurring through the plate thickness. It is surely a powerful tool in practical cases where the role played by three-dimensionality is not negligible, or is not known in detail.