Issue 47

Z. Hu et alii, Frattura ed Integrità Strutturale, 47 (2019) 383-393; DOI: 10.3221/IGF-ESIS.47.28 388 2 A,p notch 0 plain 0 ( ) 2 W W R E      (3) where A,p  is the fatigue strength of the plain sample at N A cycles and E is the elastic modulus. By varying the control radius R 0 around the notch tip in an FE model under the nominal stress σ A,n , the corresponding values of strain energy density notch W  averaged over the control volume can be determined. Then the numerical value notch 0 ( ) W R  as a function of the control radius R 0 is generated by a fitting equation. Finally, the control radius R 0 of the critical volume can be calculated since it is equal to the strain density energy of the plain sample, plain 0 W  . Due to the absence of experiment data related to stress intensity factor, the control radius can be easily evaluated by the procedure above. Figure 3 : Definition of the control volume for specimens weakened by rounded V-notch. The averaged SED can also easily and quickly be calculated from FE analyses by summing the energy contributions W element,i for all the finite elements within the control volume V , i.e.: element, V i w W W c V    (4) Eq. (4) defines the so-called direct approach to evaluate the SED parameter. In order to consider the influence of the nominal load ratio R , the weighting parameter c w has to be adopted by using the following expressions [25, 26]: 2 2 2 2 1 for - 0 (1 ) ( ) 1 for 0 1 for 0 1 (1 ) w R R R c R R R R R                (5) Additionally, it is important to know that refined mesh in the control volume around the notch tip is not necessary to determine the value of the SED, because this parameter can be determined via the nodal displacements, without involving their derivatives. This means that the adopted FE meshes can be very coarse inside the control volume having radius R 0 when accurately evaluating the value of the local SED [27]. The assumption of the SED as a damage parameter allows to summarize a large number of fatigue data obtained for notched specimens in a reasonable scatter band [10, 23, 28]. Generally, it is important to understand the fatigue behaviour of notched components and to assess the fatigue strength without performing a large number of experiments. Therefore, in order to predict the fatigue life of components having different geometrical features, the SED, W  , versus the fatigue life, N f , relationship is calculated by considering the notched samples as sharp as possible. The averaged SED, W  , can