Issue 41

G. Meneghetti et alii, Frattura ed Integrità Strutturale, 41 (2017) 8-15; DOI: 10.3221/IGF-ESIS.41.02 12 Eqs. (3) and (4) derived in [4,14]. Berto et al. obtained the following values for the control radius R 0 of Ti-6Al-4V [24] dealing with tension (mode I) and torsion (mode III) loadings, respectively, with a load ratio R = -1: mm 051 .0 K e2 R 1 1 1 A A,I 1 I,0             (3) mm 837 .0 K 1 e R 3 1 1 A A, III 3 III ,0              (4) It should be noted that the control radius R 0 for fatigue strength assessment of Ti-6Al-4V notched components assumes extremely different values under mode I and mode III, so that the energy contributions related to the two different loadings should be averaged in control volumes of different size [4]. The idea of a control volume size dependent on the loading mode has been proposed for the first time in [4] dealing with the multiaxial fatigue strength assessment of notched specimens made of 39NiCrMo3 steel, then it has been successfully applied also for the fatigue strength assessment of notched components made of AISI 416 [25] and cast iron EN-GJS400 [26] subjected to combined tension and torsional loading. Figure 4 : Control volume for specimens weakened by (a) sharp [14] and (b) blunt V-notches [15]. Once the size of the control volume is properly defined, the averaged SED can be evaluated directly from the FE results, W  , by summation of the strain-energies W FEM,i calculated for each i-th finite element belonging to the control volume V (or area A in two-dimensional problems, as shown in Fig. 4): V W cW V i, FEM W   (5) where the coefficient c w accounts for the effect of the nominal load ratio R [27], when the range value of the nominal stress is applied to the FE model. It is equal to 1 for R = 0 and to 0.5 for R =  1. Eq. (5) represents the so-called direct approach to calculate the averaged SED. According to a recent contribution of Lazzarin et al. [28], very coarse FE meshes can be adopted within the control volume (see Fig. 5). R 0  r 0  Notch bisector line R 0 + r 0 A   Notch bisector line R 0 A (a) (b)