PSI - Issue 75

Alberto Campagnolo et al. / Procedia Structural Integrity 75 (2025) 564–571 Alberto Campagnolo, Giovanni Meneghetti/ Structural Integrity Procedia (2025)

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fatigue testing was varied between 0 and 0.8, as reported in (Yonezawa et al. 2020). During the fatigue tests, the local strain amplitude was monitored using a strain gauge fixed at approximately 2 – 2.5 mm from the HFMI groove edge; this allowed to define the number of cycles N f to technical crack initiation at 5% strain drop, while a run-out condition was defined at 3 million cycles. All specimens reaching the failure condition exhibited crack initiation at the weld toe. The experimental results were originally reported in terms of the number of cycles N f as a function of the applied nominal stress range Δσ . To apply the Peak Stress Method (PSM) to HFMI-treated longitudinal stiffeners following Eq. (2), a three dimensional finite element (FE) model was developed, incorporating the finite notch radius ( ρ > 0) characteristic of the treated weld toe. By taking advantage of the triple geometrical symmetry, only one-eighth of the joint was modelled, see Fig. 2 . The material was assumed to behave as linear elastic and isotropic, characterized by a Young’s modulus E = 206000 MPa and a Poisson’s ratio ν = 0.3. The model employed a free-mesh of 10-node tetrahedral elements (SOLID187 from the Ansys® element library). A global mesh size d global = 2 mm was used throughout the model, while a local refinement with d = 0.05 mm was implemented within the crescent-shape structural volume to ensure numerical convergence. A nominal stress range Δσ = 1 MPa was applied to the model, as schematically illustrated in Fig. 2. Upon solving the FE model, the averaged strain energy density, denoted as ∆ ̅ , was computed within the defined structural volume. The resulting ratio Δσ eq,peak / Δσ , as calculated from Eq. (2), has been reported in Table 1. Table 1: Material, welding process, geometrical parameters and testing conditions of HFMI treated steel welded joints. Reference Material σ y [MPa] Welding process t [mm] 2α [°] z [mm] depth [mm] ρ HFMI [mm] Nominal load ratio R # data Δσ eq,peak /Δσ 4. Calibration of PSM-based design curves for HFMI treated steel joints The fatigue test results originally reported in terms of nominal stress range Δσ (Yonezawa et al. 2020) have been converted into the corresponding equivalent peak stress range Δσ eq,peak by using Eq. (2). Then, the experimental results were grouped according to different ranges of the nominal load ratio R as proposed by IIW Recommendations (Hobbacher 2016), the material yield stress being the same for all considered data (see Table 1) and in the range 550 ≤ σ y < 750 MPa. For each group, the data were plotted individually and then fitted with fatigue curves assuming a fixed slope of k = 5 , in agreement with experimental observations reported in the literature (Yildirim and Marquis 2012) and incorporated into the IIW recommendations for HFMI-treated joints (Marquis and Barsoum 2016). Starting from the mean fatigue curves (50% survival probability), the intrinsic scatter T σ , as defined between survival probabilities of 2.3% and 97.7% and found to be 1.90 in (Campagnolo et al. 2022), has been superimposed. This procedure enables the determination of the corresponding PSM-based FAT class. The resulting design curves and associated FAT classes are presented in Figs. 3a – e, which include also the PSM scatter band for as-welded steel joints (blue dashed lines) for comparison purposes. It is worth noting that the PSM scatter bands for HFMI treated joints reported in Fig. 3a and 3d had been first calibrated in (Campagnolo et al. 2022) and, therefore, they have been furtherly validated here, all experimental results falling inside the relevant scatter bands. On the other hand, the PSM scatter bands for HFMI-treated joints reported in Figs. 3b,c,e, have been calibrated here for the first time by fitting them on the experimental results available from (Yonezawa et al. 2020). The resulting FAT classes are 392 MPa for R ≤ 0.15 (Fig. 3a), 259 MPa for 0.15 < R ≤ 0.28 (Fig. 3b), 225 MPa for 0.28 < R ≤ 0.40 (Fig. 3c), 228 MPa for 0.40 < R ≤ 0.52 (Fig. 3d) and 174 for R > 0.52 (Fig. 3e), representing improvements of 151%, 66%, 44%, 46% and 12%, respectively, compared to FAT 156 for the corresponding as welded joints (Meneghetti and Campagnolo 2020). (Yonezawa et al. 2020) SBHS 500 575 semi automatic CO 2 arc welding 12 135 10 0.3 3 0 ≤ R ≤ 0.15 0.15