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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1. Introduction Fatigue approaches based on local parameters have proved to be reliable for the fatigue lifetime assessment of welded structures (Radaj and Sonsino 1998; Radaj and Vormwald 2013; Giannella et al. 2022a). Among them, the notch stress approach (Radaj et al. 2006; Fricke 2012; Radaj and Vormwald 2013), those based on the Notch-Stress Intensity Factors (NSIFs) (Lazzarin and Tovo 1998; Lazzarin et al. 2004; Radaj et al. 2006), including the averaged Strain Energy Density (SED) criterion (Livieri and Lazzarin 2005; Lazzarin et al. 2008) and the Peak Stress Method (PSM) (Meneghetti and Lazzarin 2007a; Meneghetti 2012, 2013; Meneghetti and Campagnolo 2020), along with the critical plane approach (Sonsino 1995; Susmel 2009; Carpinteri et al. 2009) and the Theory of Critical Distances (TCD) (Susmel 2008, 2009; Baumgartner et al. 2015) deserve to be mentioned. In this context, the Peak Stress Method (PSM) is a numerical method to rapidly estimate the NSIFs at the toe and root sides of a welded structure, such locations being assumed as sharp V-notches ( ρ = 0 mm) with opening angles 2 α equal to 135° and 0°, respectively, by using coarse mesh pattern. The PSM has been paired with the fatigue criterion based on the averaged SED, as described in (Meneghetti and Lazzarin 2011). For further details on the PSM or the averaged SED criterion, the reader is encouraged to consult previous publications (Lazzarin et al. 2008; Meneghetti and Campagnolo 2020), since only the primary equations and parameters will be mentioned here for brevity. Accordingly, the fatigue assessment of welded components under multiaxial loading conditions is performed on the basis of the equivalent peak stress range (Eq. (1)). Such damage parameter has been defined in (Meneghetti and Campagnolo 2020) by considering an equivalent uniaxial stress state, under plane strain condition, able to generate the average SED existing at the weld toe or weld root under a general mode I+II+III stress state. σ̄ θθ,θ=0, peak , τ̄ r θ,θ=0, peak and τ̄ θz,θ=0, peak are the moving averages of the mode I, mode II and mode III peak stresses, respectively, calculated on three adjacent vertex nodes belonging to the weld toe or the weld root lines. Such peak stresses are calculated from linear elastic 3D FE analyses where coarse mesh patterns of 10-node tetrahedral elements are employed (Campagnolo et al. 2019; Meneghetti et al. 2022). • f w1 , f w2 , f w3 are parameters defined in (Meneghetti and Lazzarin 2007b; Meneghetti 2012, 2013) as functions of the FE type and the global element size d , the size of the SED-based control volume R 0 and the notch opening angle 2α. • c w1 , c w2 , c w3 are parameters which account for the mean stress effect. There is no mean stress effect in as welded joints, therefore c w = 1 for any value of the nominal load ratio R . Conversely, for stress-relieved joints, c w depends on the nominal load ratio R according to the expression derived in (Lazzarin et al. 2004). Once the equivalent peak stress has been calculated at the critical location of the welded component by using Eq. (1), the resulting value is compared with the appropriate reference design curve to estimate the fatigue life of the considered component. For this purpose, the local biaxiality ratio λ must first be determined as a function of the peak stresses, following the formulation given in Eq. (2). 2 2 2 2 w2 w2 r , 0,peak w3 w3 z, 0,peak 2 2 w1 w1 , 0,peak c f c f c f  =  =  =   +   =   , (2) then, the appropriate fatigue design curve is selected based on the value of λ following the recommendations provided by (Meneghetti and Campagnolo 2020): • if λ = 0, the PSM-based fatigue design scatter band is characterised by Δσ eq,peak,A,50% = 214 MPa, an inverse slope k = 3 and a scatter index referred to probability of survival of 2.3-97.7% equal to T σ = 1.90; • if λ > 0, the PSM-based fatigue design scatter band is characterised by Δσ eq,peak,A,50% = 354 MPa, an inverse slope k = 5 and a scatter index referred to probability of survival of 2.3-97.7% equal to T σ = 1.90. 2 2 2 2 2 2 , 0,peak r , 0,peak  = z, 0,peak eq,peak  =  c f w1 w1 w2 w2 w3 w3 c f c f  =  =  +   +   , (1) where: •