Issue 43

F. Berto et alii, Frattura ed Integrità Strutturale, 43 (2018) 1-32; DOI: 10.3221/IGF-ESIS.43.01 9       1 0 2 lim ( ) II II yx x K x (6)       1 0 2 lim ( ) o o yz x K x (7) where K II is according to the definition suggested by Gross and Mendelson [98], and K O represents a natural extension of stress intensity factors for cracks. The scale effect changes for 2α= 135° are due to the non-singular behavior of the in-plane shear stress, see Fig. 9. Once again, the base geometry is scaled in geometrical proportion, by multiplying all geometrical parameters by a factor 4 or by a factor 8. The mode O stress field increases with an increase of t whereas, on the contrary, the mode II stress field decreases with t. Recently Pook and co-authors have analyzed the corner singularities showing the possibilities of taking into account of these effects by means of the strain energy density in cracked plates [99-100] confirming the same results obtained by using J-integral by He et al. [101]. Figs. 10 shows that through the thickness SED distributions, for t/a = 0.50, 1, 2 and 3, is able to take into account the through-the-thickness corner point singularities as a function of the ratio between the thickness of the plate and the crack length. The results show that the change of loading mode from nominal mode III to nominal mode II has had no effect on the distributions of τ yz and τ xy on and near the crack surface, but has significantly changed the through thickness distributions of K II , K III (which are difficult to define close to the free surface of the plate) and the SED. Capacity of treating material defects and geometrical discontinuity in a unified way The SED approach is able to treat in a unified way internal defects and geometrical discontinuities and this is a very strong advantage dealing with additive manufactured materials. As well discussed in [102] approach SED can be applied to components weakened by cracks/defects and blunt V-shaped notches. As a result, Kitagawa [103] and Atzori’s diagrams [104-105] reported in the literature to summarize fatigue limit of cracked and notched components can be immediately derived, creating a natural transition between the Linear Elastic Fracture Mechanics and the Linear Notch Mechanics. Consider a long crack in a plate subject to a remotely applied tensile stress. The mean value of the elastic strain energy referred to the area shown in Fig. 1.b is:   2 1 1 0 ( ) 2 I I K W E R (8) 1 10 100 0.001 0.010 0.100 1.000 2  =135°  0 =100 MPa t=20 mm t=160 mm t=160 mm t=80 mm scale effect mode O increasing t scale effect mode II incresing t t=20 mm t=80 mm 0.2 0.302 1.0 1.0 Figure 9: Mode O and mode II stress fields for three models scaled in geometrial proportion.