PSI - Issue 57

Luca Vecchiato et al. / Procedia Structural Integrity 57 (2024) 518–523 Vecchiato L et al./ Structural Integrity Procedia 00 (2023) 000 – 000

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the present investigation it is applied for the first time to fatigue data taken from the literature and relevant to welded joints made of aluminium alloys. Table 1: Criteria for selecting the reference PSM-based design curve for aluminium arc-welded joints. (Meneghetti and Campagnolo 2020) t [mm] λ Eq. (3) Δσ eq,peak,A,97.7% [MPa] Δσ eq,peak,A,50% [MPa] k [-] T σ [-]

t ≥ 5 mm t ≥ 5 mm

λ = 0 λ > 0 λ ≥ 0

92 92 92

123 123 123

3.8 6.5 6.5

1.80 1.80 1.80

3 mm ≤ t < 5 mm

2. Validation: experimental data taken from the literature Smith and Hirt (Smith and Hirt 1992) fatigue tested 6082 aluminium I-beams with a longitudinal stiffener fillet welded on one flange (Figure 1). All specimens were tested in the as-welded state under CA and VA four-point bending loads such that the welded side of the beam was subjected to tensile stresses. A load ratio R = 0.1 and a testing frequency in the range of 10 to 15 Hz were adopted during CA test. As to VA tests, a sequence of approximately 100 loading cycles extracted from an in-field acquisition on a train has been repeatedly applied to the specimens until failure (Smith and Hirt 1992). The relevant stress-range spectrum is shown in Figure 2. In any case, fatigue crack initiation occurred at the weld toe on the beam side. Fatigue tests were stopped and the corresponding number of cycles recorded when either a 30 mm surface fatigue crack was found or the applied number of cycles was greater than or equal to 4.5∙10 7 in case no fatigue cracks were present. A 3D linear elastic FE simulation has been carried out to analyse the experimental data according to the PSM. In more detail, the specimen geometry (Figure 1a) has been modelled in the Ansys ® Mechanical APDL environment by exploiting the double XY and YZ symmetry (Figure 1b). Then, the 3D model has been free-meshed with 10-node tetrahedral elements (SOLID 187 of Ansys® element library) where a global element size d global = 11 mm has been set for the free mesh generation algorithm. A FE mesh pattern having size equal to the main plate thickness (i.e. 11 mm) would have been necessary according to the PSM guidelines to properly assess the fatigue strength of the weld toe under pure mode I loading by using 10-node tetrahedral elements (Meneghetti and Campagnolo 2020), however a more refined mesh d local = 2 mm has been adopted (Figure 1b) to evaluate the peak stresses as close as possible to the experimental crack initiation point (Figure 1b). Indeed, according to the PSM guidelines for tetrahedral elements (Meneghetti and Campagnolo 2020), the average mode I, II, and III peak stresses ̄ , =0, , ̄ , =0, , and ̄ , =0, must be used in Eqs. (2) instead of the mode I, II, and III peak stresses σ θθ,θ=0,peak , τ rθ,θ=0,peak , and τ θz,θ =0,peak , respectively. In more detail, the average peak stresses are defined as the moving average of the peak stresses evaluated on three adjacent nodes along the weld toe line provided that nodes lying on edge surfaces (e.g. the node on the XY plane of Figure 1b) are excluded from calculations (see (Meneghetti and Campagnolo 2020) for a detailed explanation on the PSM applicability requirements for tetrahedral elements). Symmetry boundary conditions have been applied to XY (u Z = 0) and YZ ( u X = 0), while the lower support has been simulated by constraining the Y-displacements ( u Y = 0) (see Figure 1b). Eventually, a uniform bending stress Δσ g = Δ M f / W f = 1 MPa has been applied to the I- beam cross section, Δ M f and W f being the range of the bending moment and the section modulus, respectively (see Figure 1b). Subsequently, the average peak stress ̄ , =0, has been evaluated by averaging the nodal value of the maximum principal stress Δσ 11,peak , since Δ σ θθ,θ=0,peak ≈ Δσ 11,peak under pure mode I stresses. Then, the relevant f s1 (different from CA to VA loading) and f w1 have been computed and entered into Eq. (2), returning the equivalent peak stress range Δσ eq,peak (Eq. (1)) since only mode I local stresses are present at the crack initiation point (Figure 1). Finally, Eq. (3) was adopted to compute the local biaxiality ratio λ which was λ = 0 because mode II and III local stresses are null.