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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1. Introduction The PSM for variable amplitude (VA) uniaxial and multiaxial local stresses was formulated for the first time in a previous investigation, to which the reader is referred (Campagnolo et al. 2022). For the sake of brevity, only a brief reference to the main steps and equations is made in this study. In the context of the Notch Stress Intensity Factor (NSIF) approach for the fatigue design of welded joints, both the weld toe and weld root are modelled as sharp V-notches having a tip radius equal to zero (ρ = 0) and a specified opening angle 2α (Lazzarin and Tovo 1998). Making use of the averaged Strain Energy Density (SED) fatigue design criterion (Lazzarin et al. 2008), Meneghetti and Lazzarin (Meneghetti and Lazzarin 2007) proposed the Peak Stress Method to evaluate the equivalent peak stress Δσ eq,peak , which is the damage parameter that can be rapidly assessed by using linear elastic FE analysis with relatively coarse meshes (Campagnolo et al. 2022): Δ , =√Δσ , , 2 +Δσ , , 2 +Δσ , , 2 (1) Eq. (1) shows that the equivalent peak stress is a combination of pure mode I, mode II, and mode III constant amplitude equivalent peak stresses, defined as follows (Campagnolo et al. 2022): Δ , , = 1 ∙ 1 ∙ Δ , =0, , ; (2.a) Δ , , = 2 ∙ 2 ∙ Δ , =0, , ; (2.b) Δ , , = 3 ∙ 3 ∙ Δ , =0, , ; (2.c) Wherein σ θθ,θ=0,peak , τ rθ,θ=0,peak and τ θz,θ=0,peak are the opening (mode I), in-plane shear (mode II), and out-of-plane shear (mode III) peak stresses, respectively, evaluated at the fatigue crack initiation locations (i.e. the weld toe and/or weld root) by means of linear elastic FE analysis performed with relatively coarse FE meshes according to the PSM (Meneghetti and Campagnolo 2020; Meneghetti et al. 2022). When using 3D 10-node tetra finite elements, a particular technique has to be used to smooth the noisy distribution of the peak stresses along the weld toe and weld root lines of 3D FE model, owing to the uneven distribution of the number of finite elements sharing the FE nodes lying there (Meneghetti and Campagnolo 2020). The f wi coefficients appearing in Eq. (2) take into account the FE type and size, the material fatigue sensitivity where the SED has to be averaged and the notch opening angle (typically 2  =0° at the weld root and 2  =135° at the weld toe) (Meneghetti and Campagnolo 2020). The f s1 , f s2 , f s3 coefficients of Eq. (2) translates the spectrum of the peak stresses into the corresponding constant amplitude equivalent peak stresses (Campagnolo et al. 2022) by combining the CA formulation of the PSM with the Linear Damage Rule by Palmgren-Miner (Palmgren 1924; Miner 1945). As a result, the ‘constant amplitude equivalent peak stress’ of a given stress mode (I, II or III) causes the same fatigue damage of the corresponding VA spectrum. Eventually, to evaluate the fatigue lifetime of the welded structure, the equivalent peak stress (Eq. (1)) must be compared with the proper PSM-based fatigue design scatter band, which depends on the local biaxiality ratio defined as follows: = Δσ , , 2 +Δσ , , 2 Δσ , , 2 (3) Table 1 summarizes the criteria for selecting the proper fatigue design curve as a function of the value of λ (Eq. (3)) and of the main plate or tube thickness t , as well as the relevant endurable stresses and slopes of the fatigue design curves (Meneghetti and Campagnolo 2020). The PSM formulation for VA local stresses has been successfully validated previously against a large bulk of experimental data from welded joints made of structural steel (Campagnolo et al. 2022; Vecchiato et al. 2023) and in