Issue 37

L. Susmel et alii, Frattura ed Integrità Strutturale, 37 (2016) 207-214; DOI: 10.3221/IGF-ESIS.37.27 210 tool was designed and optimised. Figure 2b shows an example of a FS welded aluminium specimen manufactured using this technology. The parent material employed in the present investigation was Al 6082-T6 with ultimate tensile strength,  UTS , equal to 303 MPa. The tubular specimens had outer nominal diameter equal to  38 mm and inner nominal diameter to  31 mm. All the samples were tested in the as-welded condition. The FS welded specimens were tested under axial fatigue loading at the University of Ferrara, Italy, using an MTS 810 Mod. 318.25 servo-hydraulic machine. The samples were tested under a load ratio, R, equal to 0.1 and to -1. The biaxial fatigue tests were carried out at the University of Sheffield, UK, using a SCHENCK servo-hydraulic axial/torsional testing machine equipped with two MTS hydraulic grips. The force/moment controlled tests were run under in-phase and 90° out-of-phase constant amplitude sinusoidal load histories with load ratios equal to -1 and 0. The pictures seen in Figure 3 show some examples of the typical cracking behaviours displayed by the Al 6082-T6 FS welded joints tested under biaxial loading. B R =0, R=-1 N f =1664764 ctf B R = 3 , R=-1,  =0° N f =369237 ctf B R =1, R=-1,  =0° N f =650684 ctf B R = 3 , R=-1,  =90° N f =173954 ctf B R =0, R=0 N f =1071840 ctf B R = 3 , R=0,  =0° N f =501988 ctf B R =1, R=0,  =0° N f =857370 ctf B R = 3 , R=0,  =90° Nf=224230 ctf Figure 3 : Examples of the observed macroscopic cracking behaviour under biaxial fatigue loading (ctf=cycles to failure). The experimental fatigue data were re-analysed using the hypothesis of a log-normal distribution of the number of cycles to failure for each stress level with a confidence level equal to 95% [12]. The results of the statistical reanalysis are listed in Tab. 1 in terms of nominal stresses referred to the annular section of the parent tube, where: B R =  nom,a /  nom,a is the ratio between the amplitudes of the axial and torsional nominal stress, R is the nominal load ratio,  is the out-of-phase angle, k is the negative inverse slope,  A and  A are the amplitudes of the axial and torsional endurance limits extrapolated at N  =2  10 6 cycles to failure, and T  is the scatter ratio of the amplitude of the endurance limit for 90% and 10% probabilities of survival. V ALIDATION BY EXPERIMENTAL RESULTS s far as conventional aluminium welded joints are concerned, the MWCM can be applied not only in terms of nominal [11, 13] and notch stresses [14], but also using the Theory of Critical Distances (in the form of the Point Method) [15]. Owing to the high level of accuracy which was obtained with standard welded connections [6], in the present investigation the above three stress analysis strategies were used, with the MWCM being applied to post-process the experimental results summarised in Tab. 1. Independently from the definition adopted to calculate the relevant stress states, the MWCM was applied using multiaxial fatigue software Multi-FEAST© (www.multi-feast.com) . Initially, the accuracy of the MWCM in estimating the fatigue lifetime of the tested FS welded joints was checked by applying this approach in terms of nominal stresses. The calibration constants in Eqs 4 and 5 were estimated using the fully-reversed uniaxial and torsional fatigue curves reported in Tab. 1, obtaining: A