PSI - Issue 75

Alberto Visentin et al. / Procedia Structural Integrity 75 (2025) 593–601 Alberto Visentin, Alberto Campagnolo,Vittorio Babini, Giovanni Meneghetti/ Structural Integrity Procedia (2025)

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1. Introduction According to fatigue assessment methods based on Notch Stress Intensity Factors (NSIFs) (Lazzarin and Tovo 1998), welded joints are idealized as sharp V- notched components. In particular, a tip radius ρ = 0 mm and a notch opening angle of 2α = 135° is typically assumed at the weld toe, while a sharp crack configuration with 2α = 0° is adopted at the weld root. Among these approaches, the Peak Stress Method (PSM) has been introduced as an efficient computational strategy to estimate NSIFs using coarse finite element meshes. This method was later integrated with the averaged Strain Energy Density (SED) criterion to enable fatigue assessment under complex loading conditions, as highlighted in (Meneghetti and Lazzarin 2011; Meneghetti and Campagnolo 2020). A comprehensive description of both the PSM and the SED-based framework can be found in previous literature (Livieri and Lazzarin 2005; Meneghetti and Lazzarin 2007; Lazzarin et al. 2008). In the present work, only the essential equations and parameters are recalled for conciseness. For arc-welded components subjected to constant amplitude (CA) multiaxial loadings, a fatigue design parameter, the so-called equivalent peak stress range, has been defined and formalized in Eq. (1) (Meneghetti and Campagnolo 2020). This parameter is constructed to reproduce, under a plane strain uniaxial condition, the same local SED experienced at the weld toe or root in a general mixed-mode I+II+III loading scenario: In the above formulation: • σ θθ,θ=0,peak , τ rθ,θ=0,peak , and τ θz,θ=0,peak represent, respectively, the opening (mode I), sliding (mode II), and tearing (mode III) peak stresses evaluated at the weld toe or weld root, i.e. the expected crack initiation sites. These stress components are obtained from linear-elastic finite element analyses performed by using relatively coarse meshes of 2D or 3D solid elements. When employing 3D tetrahedral meshes within the PSM framework, a local smoothing procedure must be applied. Specifically, moving average values of the peak stresses, denoted as σ̄ θθ,θ=0,peak , τ̄ r θ,θ=0,peak and τ̄ θz,θ=0,peak , are computed over three adjacent vertex nodes, according to Eq. (2). σ̄ ij, θ=0,peak,n=k = σ ij, θ=0,peak,n=k - 1 + σ ij, θ=0,peak,n=k + σ ij, θ=0,,peak,n=k+1 3 | n=node where ij = θθ , r θ , θz (2) • As discussed in (Meneghetti and Campagnolo 2020), the moving average values of the peak stress components must be substituted into Eq. (1) in place of the corresponding peak stresses σ θθ,θ=0,peak , τ rθ,θ=0,peak , and τ θz,θ=0,peak , respectively. • f wi (with i = 1, 2, 3 corresponding to the local stress modes) is a parameter defined in (Meneghetti and Campagnolo 2020) to account for the interaction between the PSM and the averaged SED fatigue criterion. This parameter incorporates the influence of the finite element type and the characteristic element size d , as well as the material’s structural volume radius R 0 and the V- notch opening angle 2α. • c wi (where i = 1, 2, 3 corresponds to the local stress mode) accounts for mean stress effects when applying the PSM to stress-relieved welded joints. Its value is a function of the local stress ratio R i and was originally derived in (Lazzarin et al. 2004). In the case of as-welded joints, the mean stress sensitivity is neglected, and c wi is set equal to 1 independently of the value of R i . Once the equivalent peak stress range has been evaluated at the critical location of the welded structure using Eq. (1), the resulting value is compared against the appropriate reference design curve to estimate the fatigue life. To enable this comparison, the local biaxiality ratio λ must fi rst be determined as a function of the peak stress components, as defined in Eq. (3). 2 2 2 2 2 2 eq,peak  =  w1 w1 , 0,peak w2 w2 r , 0,peak  = w3 w3 z, 0,peak  = c f c f c f  =  +   +   (1)

2

2

2

2

c f 

c f



+ 



(3)

w2 w2

r , 0,peak

w3 w3

z, 0,peak

c f  = 

 =

=

2

2



w1 w1

, 0,peak

 =

S ubsequently, the appropriate fatigue design curve is selected based on the computed value of λ, in accordance with the criteria outlined in (Meneghetti and Campagnolo 2020), which are not recalled here for sake of brevity. Recent advancements of the PSM include its extension to variable amplitude (VA) multiaxial loading conditions