Issue 41

F. Berto et alii, Frattura ed Integrità Strutturale, 41 (2017) 79-89; DOI: 10.3221/IGF-ESIS.41.12 82 The statistical re-analyses of the fatigue strength data were carried out by assuming a log-normal distribution. All experimental data relevant to specimens with a fatigue life in the range 10 4 ÷ 2·10 6 cycles have been considered, while the run-outs have been excluded. In particular, Tab. 1 reports the nominal stress amplitudes for a probability of survival Ps = 50% and a number of cycles N A = 2·10 6 , the inverse slope k of the Wöhler curves and the scatter-index T, which gives a measure of the width of the scatter band, between the curves with 10% and 90% probabilities of survival (with a confidence level equal to 95%). Under multiaxial loading, the fatigue life results to be reduce if compared to the uniaxial loading case, with reference to the same normal stress amplitude, however the reduction is quite limited for the biaxiality ratios considered herein (  = 0.6 and 2.0). Stronger is the multiaxial fatigue strength reduction tied to the effect of the load ratio R. On the other hand, the phase angle effect is weak for R = -1, being the mean values of the normal stress amplitudes about the same at 2·10 6 cycles. While, it is higher for R = 0, being the out-of-phase loading slightly beneficial with respect to in-phase loading at high-cycle fatigue regime, whereas the fatigue strength is almost the same at low-cycle regime. The sensitivity of the considered titanium alloy to the phase angle effect results to be quite limited, being lower than +15 percent for the R = 0 case and negligible for the R = -1 case. The fracture surfaces relevant to the specimens subjected to multiaxial loadings were examined. The phase angle seems to affect the fracture surface morphology. Indeed, some signs of micro abrasions could be seen on all fracture surfaces and the extent to which the rubbing occurred depends on phase angle. In general, a limited but distinguishable quantity of debris and powder has been emanated from the notch tip, when a visible fatigue crack started to propagate. S YNTHESIS BASED ON THE AVERAGED STRAIN ENERGY DENSITY ith regard to un-notched specimens, all fatigue results have been summarised here in terms of the averaged SED, which can be expressed, under linear elastic conditions, by means of Beltrami’s expression. Accordingly, in the case of pure tension loading, the local strain energy density is given by:     2 2 nom W E (1) while in the case of pure torsion loading it is given by:         2 1 nom W E (2) In previous expressions,  nom and  nom are the nominal stress ranges tied to tension and torsion loadings, respectively. For the considered titanium alloy, the Young’s modulus E results to be 110 GPa, while the Poisson’s ratio ν is 0.3. Then, also the fatigue strength results relevant to notched samples have been reanalysed here in terms of the averaged SED, however, in this case the strain energy calculation is based on the local stress and strain state in a control volume embracing the V-notch tip. Since the notch root radius is reduced (  less than 0.1 mm), the Mode I and Mode III NSIFs, K 1 and K 3 , can be adopted to summarised the experimental data relevant to notched samples in terms of the local strain energy density. These parameters, which describe the local stress fields, have been evaluated from linear elastic FE analyses taking into consideration a sharp V-notch with tip radius  equal to 0 (see Fig. 2). Let us consider a cylindrical coordinate system (r, θ, z) with origin at the notch tip, where r is the radial coordinate,  is the angle between a generic point and the notch bisector line, while z is the longitudinal axis of the specimen. In particular, with reference to this coordinate system (see Fig. 2), the Mode 1 and Mode 3 NSIFs can be defined by means of the following expressions:          1 1 1 0 2 lim ( , 0) r K r r (3)          1 3 3 0 2 lim ( , 0) z r K r r (4) W