Issue 47

P. Foti et alii, Frattura ed Integrità Strutturale, 47 (2019) 104-125; DOI: 10.3221/IGF-ESIS.47.09 107 While the skew-symmetric stress distributions, due to mode II loading, are:                         2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 0 1 sin 1 sin 1 1 3 sin 1 1 sin 1 1 1 2 1 cos 1 cos 1 N r r r K                                                                                         (4) 1 K and 2 K being the Notch stress intensity factors (NSIFs) related to mode I and mode II stress distributions. The NSIFs can be assessed by [24]: 1 1 1 0 2 lim ( , 0) N r K r r           (5) 2 1 2 0 2 lim ( , 0) N r r K r r           (6) Where 1  and 2  are Williams’ eigenvalues [23] and 1  and 2  are auxiliary parameters function of opening angle. Tab. 2 gives the parameters for mode I and mode II stress distributions. Exploiting the superposition effect principle, the stress distributions close to the notch tip in a mixed mode loading (I+II) can be expressed as follows:   1 2 (1) (1) (2) (2) 1 (1) (1) 1 (2) (2) 1 2 (1) (2) 0 0 , 0 0 0 0 0 0 r r N ij r rr r rr zz zz r r K r K                                       (7) Where    , rr   and r    for mode I and mode II can be derived from Eqns. (3), (4) as a function of the notch opening angle 2  and of the position whit the polar coordinate  . Eqn. (7) describes the degree of the singularity of the stress fields due to re-entrant corners by mode I and mode II. In the case considered above, as the stresses, also the strain energy density tends towards infinity. On the other hand, the average SED in a local finite volume around the notch tip has a finite value that is considered to control failure. By substituting the expressions for stresses distributions reported in Eqn. (7) into Eqn. (2) it is possible to obtain :         1 2 12 , , , , W r W r W r W r        (8) Being: Figure 2 : Coordinate system and symbols used for the stress field components.