Issue34

F. Berto, Frattura ed Integrità Strutturale, 34 (2015) 11-26; DOI: 10.3221/IGF-ESIS.34.02 18 1 1/(2 2 ) 2 1 1C 0 1 c 4 (π ) I K R EW              (6) When 2  =0, 1C K equals the fracture toughness K IC . (a) (b) (c) Figure 3 : Critical volume (area) for sharp V-notch (a) , crack (b) and blunt V-notch (c) under mode I loading. Distance 0 ( 2 )/(2 2 ) r R         . (a) (b) Figure 4 : Critical volume for U-notch under mode I (a) and mixed mode loading (b) . Distance 0 / 2 r R  according to Refs. [15] and [67]. In the case of blunt notches, the area assumes a crescent shape, with R 0 being its maximum width as measured along the notch bisector line (Fig. 2c) [11]. Under mixed-mode loading, the control area is no longer centred with respect to the notch bisector, but rigidly rotated with respect to it and centred on the point where the maximum principal stress reaches its maximum value [58, 59]. This rotation is shown in Figure 4 where the control area is drawn for a U-shaped notch both under mode I loading (Fig. 4a) and mixed-mode loading (Fig. 4b). The parameter a 1 of Eq. (1) can be linked to the mode I notch stress intensity factor by means of the simple expression 1 1 2π K a  (7) where K 1 assumes the following form according to the definition given in Ref.[ 68]:   1 1 1 0 2π lim ( , 0) r K r r         (8)