numero25

P. Lazzarin et alii, Frattura ed Integrità Strutturale, 25 (2013) 61-68 ; DOI: 10.3221/IGF-ESIS.25.10 64     3, 3, 3, 3, cos sin s a s s a a w D r D r         (8) where 3, 3, 2 / s a       , so that only the skew-symmetric part of w contributes to the singular behaviour of stress fields. Accordingly the antiplane mode III shear stresses close to the tip can be determined as: (a) (b) Figure 1 : Thick plate weakened by a rectangular hole under tension (a) ; coordinate system used for stress components (b) . 3, 3, 1 1 3 3 3, 3, (z) (z) sin cos 2 2 a a zr a z a K r K r                (9) where: 3, 1 3 0 ( ) lim 2 ( , 0) a r z K z r r          (10) is the mode III NSIF, to be thought of as the natural extension to the out-of-plane mode of Gross and Mendelson’s definitions given for the in-plane modes. In order to validate these theoretical results, a detailed finite element analysis on the geometry shown in figure 1a has been carried out. 20 node brick elements have been used with a very fine mesh pattern, in order to get the desired degree of accuracy. The material has been modelled according to a linear elastic behaviour, with E=206000 MPa and  =0.3. 0.1 1 10 100 1000 10000 0.0001 0.001 0.01 0.1 1 Stress components [MPa] Distance from the notch tip, r [mm]    r   z   100 MPa  100 MPa Slope:  0.456 Slope:  0.333 Slope:  0.091 Figure 2 : Plots of the stress components  z    and  r  along the notch bisector line of a rectangular hole in a thick plate under tension. Distance from the mid plane z=2.5 mm. Applied tension  =100 MPa.