Issue 43

F. Berto et alii, Frattura ed Integrità Strutturale, 43 (2018) 1-32; DOI: 10.3221/IGF-ESIS.43.01 13 Finally, a variety of diamond-like notches were considered, all characterized by a notch angle of 135 degrees. R 0 is measured along the notch bisector, while the origin of the arc delimitating the volume is at a distance r 0 from the notch tip, being 0. The results are as shown in Fig. 14. On the left hand side, the plateau does not vary with respect to the crack and U-slit cases, while different is the intersection between the plateau and the LEFM line; on the right hand side of the diagram, the fatigue limit is greater than the double U-notch case, because of the reduction of the stress concentration factor K t . The capacity of unifying notch mechanics and fracture mechanics in a single diagram by means of SED can be advantageously used for facing the structural integrity of complex components obtained by means of additive manufacturing processes. A PPLICATIONS Multiaxial Fatigue he strain energy density approach has been recently applied to complex multiaxial fatigue loadings [107-110]. In this section as example the last results dealing with the multiaxial fatigue strength of severely notched titanium grade 5 alloy (Ti-6Al-4V) is discussed [110]. Experimental tests under combined tension and torsion loading, both in-phase and out-of-phase, have been carried out on axisymmetric V-notched specimens considering different nominal load ratios ( R = -1, 0, 0.5). All specimens were characterized by a notch tip radius less than 0.1 mm, a notch depth of 6 mm and a notch opening angle equal to 90 degrees. The diameter of the net transverse area is equal to 12 mm in all the specimens. The experimental data from multiaxial tests are compared with those from pure tension and pure torsion tests on un-notched and notched specimens, carried out at load ratio ranging from R = -3 to R =0.5. In total over 160 new fatigue data are analyzed, first in terms of nominal stress amplitudes referred to the net area and then in terms of the local strain energy density averaged over a control volume surrounding the V-notch tip. The dependence of the control radius by the loading mode has been analyzed showing a very different notch sensitivity for tension and torsion. For the titanium alloy Ti-6Al-4V the control volume has been found to be strongly dependent on the loading mode [110]. It has been possible to estimate the control volume radii R 1 and R 3 , considering separately the loading conditions of Mode I and Mode III. These radii are functions of the high cycle fatigue strength of smooth specimens, Δ σ 1 A = 950 MPa, Δ τ 3 A = 776 MPa, and of the mean values of the NSIFS, Δ K 1 A and Δ K 3 A , all referred to the same number of cycles, N A = 2  10 6 . In [110] it has been found as a result: R 1 = 0.051 mm and R 3 = 0.837 mm. The obtained values have been used to summarize 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. In particular, a control volume of radius R 1 will be used to evaluate the averaged contribution to local stress and strains due to tensile loading, whereas a radius R 3 will be used to assess the averaged contribution due to torsion loading. The size of R 3 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 [108]. 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 as made also above the weighting factor c w on the basis of mere algebraic considerations. The result of these observations provides as master cases c w = 1.0 for R = 0 and c w = 0.5 for R = -1 [9]. Figs. 15 and 16 show the synthesis by means of local SED of all the experimental data from the fatigue tests at a nominal load ratio R = 0 and R = -1, respectively. The control radii have been found to be 0.051 mm and R 3 = 0.837 mm. The scatterbands have been defined considering the range 10-90% for the probability of survival. It can be observed that the inverse slope k equals 5.44 for R = 0 case and 5.25 for R = -1 case, while the corresponding values of the strain energy density at 2×10 6 cycles are 2.72 MJ/m 3 and 2.60 MJ/m 3 . The SED-based scatter index T W is 1.76 for R = 0 and 2.25 for R = -1 case, which would become equal to 1.33 and 1.50 respectively once reconverted a posteriori into equivalent stress- based scatter indexes T W , by simply making the square root of the SED values. The values of the equivalent scatter index are satisfactory for engineering strength assessment, considering that each synthesis is performed on fatigue data from un- notched and V-notched specimens under pure tension, pure torsion or combined tension-torsion loading, both in phase and out-of-phase. Figs. 17 and 18 show instead the synthesis by means of average SED of all the experimental data from the fatigue tests of un-notched and V-notched specimens, respectively. Also in this case two control radii equal to R 1 = 0.051 mm and R 3 = 0.837 mm respectively have been used. It can be observed that the inverse slope k of the scatterbands equals 6.54 for un-notched specimens and 5.86 for V-notched ones, while the values of the strain energy density at 2×10 6 cycles are equal to 3.34 MJ/m 3 and 3.09 MJ/m 3 , respectively. In this case T W equals 2.50 for un-notched specimens and T