PSI - Issue 66

Venanzio Giannella et al. / Procedia Structural Integrity 66 (2024) 71–81 Venanzio Giannella et al./ Structural Integrity Procedia 00 (2025) 000 – 000

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mechanics calculations (Lazzarin and Tovo 1998; Livieri and Lazzarin 2005; Meneghetti 2008; Meneghetti et al. 2014; Giannella et al. 2019, 2021; Shlyannikov et al. 2021). Therefore, the significantly longer experimental fatigue lives of the transverse joints compared to the estimates provided by the PSM could be explained by an exceptionally long crack propagation phase, that is inherently excluded by the PSM approach. This assumption can be furtherly supported by analyzing a general expression of the crack driving force ΔK I : I K a  =  , (3) where α represents the shape factor, Δσ is the nominal stress range and a is the crack size. The axial load applied to the plate of a transverse joint ( ΔF ) is carried by the specimen through two parallel load paths, as sketched in Figure 4: the green path crosses the weld bead and the tube and carries the load fraction ΔF tube , while the red path crosses the plate net-section and carries the load fraction ΔF plate . The ratio ΔF tube /ΔF plate is affected by the relative stiffness of the corresponding paths. The initiation of a fatigue crack at the tube-side weld toe and the subsequent propagation through the tube generate a stiffness drop of the green path. As a consequence, ΔF tube diminishes while ΔF plate increases to keep the total applied load range ΔF as constant throughout the test. The crack driving force ΔK I can be calculated by substituting Δσ tube corresponding to ΔF tube (green path of Figure 4) inside Eq. (3). As the crack propagates, the crack size a increases, while Δσ tube decreases because of the reduction in stiffness. Consequently, the rise in the crack driving force ∆ is mitigated, along with the associated growth rate. This phenomenon is not considered by the PSM and can be addressed through crack propagation simulations.

 F

 F

 F tube

 F plate

 F =  F tube +  F plate

Fig. 4. Loading paths which carry the axial load applied to the plate ( Δ F ): the green path crosses the weld bead and the tube (ΔF tube ) while the red path crosses the net-section of the plate ( ΔF plate ). Reproduced with permission from Pelizzari J, Campagnolo A, Dengo C, Meneghetti G (2024) Fatigue lifetime assessment of weld ends with idealized or real geometry in steel joints for off-road vehicles using the Peak Stress Method. Int J Fatigue 178:107964 .

4. Crack propagation simulations The fatigue crack propagation phase in both transverse and longitudinal joints has been investigated by FE analyses performed using Abaqus® as solver and FRANC3D® as pre- and post-processor (see (Giannella 2021; Giannella et al. 2022b) for similar simulations). To do so, linear elastic 3D FE models of the joint geometries including the idealized weld ends were generated in Abaqus® and subsequently discretized with 10-node tetrahedral elements. A semi-circular initial crack having depth a i = 0.1 mm, in agreement with the LEFM approach of the IIW Recommendations (Hobbacher 2016), has been introduced in the experimental crack initiation location, namely the tube-side weld toe for the transverse joints and the plate-side weld toe for the longitudinal joints, see Figure 2. It is worth noting that the propagation of a single initial crack has been analyzed for sake of simplicity, even if multiple crack initiation locations were observed during the experimental tests (see for example Figure 2a,c and Ref. (Pelizzari et al. 2024)), therefore no symmetry has been exploited in the definition of the FE model. Loading and constraint conditions have been applied to the FE models to simulate the actual conditions occurring during experimental tests. Figure 5 shows the FE mesh pattern adopted for the longitudinal geometry along with the boundary conditions, the mesh pattern used for the transverse geometry being similar. The parameters of the Paris law according to Eq. (4) have been found in the literature (Pedrosa et al. 2022) with