numero25

P. Lazzarin et alii, Frattura ed Integrità Strutturale, 25 (2013) 61-68; DOI: 10.3221/IGF-ESIS.25.10 66 as the maximum value of K III at the mid plane, have been plotted through the plate thickness for different values of the Poisson’s ratio (see Fig. 6). As it can be observed from the figure also the limit case  =0 has been considered. The figure refers to a distance x=0.1 mm from the crack tip fully included in the zone governed by the leading order terms. The analysis shows that by applying a remote Mode III loading automatically a coupled Mode II is generated in the plate. As well visible from the figure the coupled Mode is only slightly influenced by the Poisson’s ratio and that, more important, it arises also when  =0. By considering different plate thicknesses it is possible to investigate the scale effect when an externally applied Mode III induces a coupled Mode II. Figure 7 reports the induced in plane shear stress component  xy for different plate thicknesses (h=2.5, 10 and 40 mm). It is evident that decreasing the plate thickness the intensity of the induced stress increases according to the square root of the ratio between the considered plate thicknesses. Figure 5 : Three-dimensional plate weakened by crack under torsion loading. Two forces have been applied in z-direction while all displacements have been constrained on the dashed surface opposite to the notch. Figure 6 : Variations of the stress intensity factors (mode III and coupled mode) along the plate thickness. C ONCLUSIONS n this paper a stress field theory for plates of finite thickness is revisited and applied to some cases of practical interest. According to this theory the three-dimensional governing equations of elasticity can be simplified into a bi- harmonic equation and a harmonic one. The former provides the solution of the corresponding plane notch I