Issue34

F. Berto, Frattura ed Integrità Strutturale, 34 (2015) 11-26; DOI: 10.3221/IGF-ESIS.34.02 19 In the presence of a notch root radius equal to zero, the distance r 0 is also zero, and all  -related terms in Eq. (1) disappear. It is possible to determine the total strain energy over the area of radius R 0 and then the mean value of the elastic SED referred to the area  . The final relationship is: 1 2 1 1 1 1 1 0 4 ( ) I K W E R              (9) where  1 is Williams’ eigenvalue and 1 K the mode I notch stress intensity factor. The parameter I 1 is different under plane stress and plane strain conditions for different values of the Poisson’s ratio  [60]. Equation (9) was extended to pointed V-notches in mixed, I+II, mode [7] as well as to cases where mode I loads where combined with mode III loads [9]. It is important to underline the influence of the Poisson’s ratio on the I 1 values in the case of sharp notches. For a notch opening angle smaller than 60 degrees, I 1 varies strongly from  =0.1 to  =0.4. This fact confirms the important and not negligible effect of the Poisson’s ratio while discussing sharp or quasi-sharp notches in agreement with the effect of this parameter on the kind of singularities, weak or strong, highlighted in Ref. [1] in the case of a constrained micro-notch at the front of a free edge macro-crack. In the presence of rounded V-notches it is possible to link the parameter a 1 of Eq. (1) to the maximum principal stress present at the notch tip: 1 1 0 1 1 1 tip r a        (10) where 1   is the parameter already listed in the original paper. By using the elastic maximum notch stress, it is possible to determine the total strain energy over the area  and then the mean value of the SED. When the area embraces the semicircular edge of the notch (and not its rectilinear flanks), the mean value of SED can be expressed in the following form [11]: 2 tip 0 1 (2 ) (2 , ) R W F H R E       (11) where F(2  ) depend on previously defined parameters     1 2 2 1 1 1 2π 2 1 q F q                    (12) By simply using the definition of the mode I NSIF for blunt V-notches [69] a simple relationship between  tip and K V R,I  can be obtained as follows: 1 1 1 1 1 σ q 1 K 2π R F(2α) σ R 1 ω q tip V R,I tip                (13) Then it is possible to rewrite Eq. (11) in a more compact form:   1 2 V R,I 0 1 2(1 ) 0 1 (2 , ) K R W H R E R       (14) Equation (14) will be used to summarise all results from blunt notches (U- and V-notches) subjected to mode I loading.