Issue 37

F. Berto et alii, Frattura ed Integrità Strutturale, 37 (2017) 69-79; DOI: 10.3221/IGF-ESIS.37.10 70 [3,4] and by some important variants [5-7]. In this context, approaches based on energy calculations find significant applications [8]. A multiaxial fatigue approach based on a frequency-domain formulation of a stress invariant, the so-called “Projection by Projection” (PbP) criterion has been reported in the recent literature [9]. The critical plane-based Carpinteri-Spagnoli approach has recently been extended to a frequency-domain formulation [10]. An energy-based parameter has been adopted to assess the fatigue strength under uniaxial fatigue loadings first by Jasper [11] in 1923. Then, Ellyin suggested a criterion based on the combination of plastic and elastic strain energy [12-13], to deal with multiaxial fatigue loadings. A wide review of energy- based criteria for multiaxial fatigue strength assessment has been reported in [14]. Moreover, the problems relevant to multiaxial fatigue have been investigated both theoretically and experimentally by several researchers [15-22]. This contribution is aimed to analyse the fatigue strength of severely notched titanium grade 5 alloy under multiaxial loadings. The considered titanium alloy (Ti-6Al-4V) is widely employed in advanced military, civil aerospace and naval applications. The in-service conditions of titanium structural components are usually characterized by a complex stress state coupled with an aggressive environment. The titanium grade 5 alloy has high static and fatigue properties, a very good strength-to-mass ratio and an excellent wear resistance. The uniaxial fatigue strength of un-notched and notched titanium components has been extensively analysed in the literature. However, a complete set of experimental data relevant to sharp V-notched specimens made of Ti-6Al-4V and subjected to torsion and combined tension and torsion loadings, both proportional and non-proportional, is not available in the literature. To fill this lack, a complete set of experimental data from sharp V-notched components made of titanium grade 5 alloy (Ti-6Al-4V) under multiaxial fatigue loading is provided here. Experimental fatigue tests under combined tension and torsion loadings have been carried out on circumferentially V- notched specimens, with two nominal load ratios, namely R = -1 and R = 0. The fatigue results obtained by applying multiaxial loadings are compared with those related to pure tension and pure torsion experimental fatigue tests, carried out on both smooth and notched specimens at load ratios R ranging between -3 and 0.5. All in all, more than 250 fatigue data (19 Wöhler curves) are examined in terms of nominal stress amplitudes referred to the net area. Then, the experimental fatigue strength data have been reanalysed in terms of the strain energy density (SED) averaged over a control volume embracing the notch tip [23-31]. The effect of the loading mode on the control volume size has been analysed, highlighting the need to use a different control radius under tension and torsion loading, due to a wide difference in the notch sensitivity of the considered material under tension and torsion loadings. The expressions for calculating the control radii, thought of as material properties, have been derived by imposing the constancy of the averaged SED relevant to un-notched and notched specimens, which depend on the critical notch stress intensity factors (NSIFs) and the control radius, in correspondence of 2·10 6 cycles. The unifying capacity of the averaged SED criterion is highlighted, indeed the synthesis on the basis of the local SED enables to obtain a quite narrow scatter-band, which is characterised by an equivalent stress-based scatter index T  equal to 1.58, taking into account all fatigue strength data relevant to notched and un-notched components subjected to pure tension, pure torsion and multiaxial loadings, independently of the nominal load ratio and the phase angle. Some of the results reported in the present manuscript have been previously presented and extensively discussed in [31]. M ATERIAL AND GEOMETRY OF THE SPECIMENS he material taken into consideration in the present contribution is a titanium grade 5 alloy, also known as Ti-6Al- 4V. The geometries of smooth and sharply notched specimens are reported in Fig. 1, along with some details of the V-notch tip. The hourglass smooth specimens, shown in Fig. 1a, are characterized by a 12-mm-diameter of the net transverse area and by a wide connecting radius between the net and gross sections,  = 100 mm, so that any stress concentration is avoided. The cylindrically V-notched samples, shown in Fig. 1b, are characterized, instead, by a notch depth d equal to 6 mm and a notch angle of 90 degrees, while the notch tip radius,  , is about equal to 0.1 mm. In particular, the notch root radius has been experimentally measured through an optical microscope and the dedicated software LAS (Leica Application Suite) and a mean value of 0.09 mm with a very reduced scatter has been obtained. The precision ensured by the adopted method is about ± 5% of the measured quantity. The typical V-notch profile characterised by two rectilinear flanks tangent to the notch tip radius is reported in Fig. 1b, for an example of the tested samples. To remove any scratches or processing marks on the surface, all specimens were polished before the fatigue test. T