Issue 33

F. Berto et alii, Frattura ed Integrità Strutturale, 33 (2015) 229-237; DOI: 10.3221/IGF-ESIS.33.29 234 It is possible to estimate the control volume radii described in Fig. 2, R 1c and R 3c , considering separately the loading conditions of Mode I and Mode III. These radii are functions of the high cycle fatigue strength of smooth specimens,  1A = 950 MPa,  3A = 776 MPa, and of the mean values of the NSIFS,  K 1A and  K 3A , all referred to the same number of cycles, N A = 2·10 6 : 1 1 1 1 1c 1 1 2 A A K R e              (9a) 3 1 1 3 3 3c 3 1 A A e K R                (9b) Eq. 9a and 9b provide as a result: R 1c = 0.051 mm and R 3c = 0.837 mm. The obtained values will be used to summarise all fatigue strength data by means of the averaged SED. The expressions for estimating the control radii, thought of as material properties, have been obtained imposing at N A cycles the constancy of the SED from smooth and V-notched specimens, which depends on the notch stress intensity factors and the radius of the control volume. Considering instead cracked specimens, the critical NSIFs should be replaced by the threshold values of the stress intensity factors. Figure 2 : Control volumes for V-shaped notches under tension and torsion loading. In particular, a control volume of radius R 1c will be used to evaluate the averaged contribution to local stress and strains due to tensile loading, whereas a radius R 3c will be used to assess the averaged contribution due to torsion loading. The size of R 3c radius is highly influenced by the presence of larger plasticity under torsion loading with respect to tensile loading and by friction and rubbing between the crack surfaces, as discussed extensively for different materials [31]. With the aim to unify in a single diagram the fatigue data related to different values of the nominal load ratio R, it is necessary to introduce a weighting factor c w on the basis of mere algebraic considerations. The result of these observations [24], provides as master cases c w = 1.0 for R = 0 and c w = 0.5 for R = -1. The expression of c w as a function of the nominal load ratio R is:     2 2 2 2 1 0 1 1 0 1 0 1 1 R for R R for R R for R R                     (10) By applying the weighting factor c w , the expressions for calculating the strain energy density under linear elasticity, for un- notched specimens (Eqs. (1, 2)) and for V-notched ones (Eq. (8)), become: