PSI - Issue 57

Alberto Visentin et al. / Procedia Structural Integrity 57 (2024) 524–531 Alberto Visentin et al./ Structural Integrity Procedia 00 (2023) 000 – 000

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1. Introduction According to a worst-case hypothesis, the Notch Stress Intensity Factor (NSIF) approach takes both the weld toe and weld root as sharp V-notches with a certain opening angle 2α and a null tip radius ( ρ = 0 ). Meneghetti and Lazzarin (2011) proposed the Peak Stress Method (PSM) to apply rapidly the averaged Strain Energy Density (SED) fatigue criterion using linear elastic FE models with coarse FE meshes. The reader is referred to previous publications for details about the PSM (Meneghetti and Lazzarin 2007; Meneghetti 2012, 2013) and the averaged SED approach (Lazzarin and Zambardi2001; Livieri and Lazzarin 2005; Lazzarin et al. 2008), which are not recalled here for sake of brevity. Dealing with arc-welded structures subjected to variable amplitude (VA) multiaxial loadings, the PSM fatigue damage parameter, called equivalent peak stress range, is defined for VA mixed mode I+II+III local stress state acting at the weld toe or weld root as follows:

2

2

2

(1)

eq,peak eq,peak,II eq,peak,III  =  + + eq,peak,I

where the mode I, mode II, and mode III constant amplitude equivalent peak stresses are defined as:

eq,peak,I  =    s1 w1 f f

eq,peak,II  =    s2 w2 f f

eq,peak,III  =    s3 w3 f f

;

;

(2)

, 0,peak,max

r , 0,peak,max  =

z, 0,peak,max  =

 =

In previous expressions: • σ θθ,θ=0,peak ǡ τ r θ,θ=0,peak ǡ ƒ d τ θz,θ=0,peak ƒ r ‡ the mode I (opening), mode II (sliding) and mode III (tearing) peak stresses, respectively, calculated at the weld toe or weld root from linear elastic 2D or 3D FE analyses with coarse mesh patterns, and the subscript ‘max’ indicates the maximum value of the peak stress range in the relevant VA spectrum, according to the guidelines given elsewhere (Campagnolo et al. 2019; Meneghetti et al. 2022). • f wi ( i = 1, 2, 3 being the local stress mode) is a coefficient to estimate the averaged SED and it is defined in (Meneghetti and Lazzarin 2007; Meneghetti 2012, 2013) as a function of the finite element type, the mean element size adopted to generate the free-mesh pattern d , the material structural volume size R 0 of the SED approach and the V-notch opening angle 2α. • f si ( i = 1, 2, 3 being the local stress mode) is a coefficient to evaluate the constant amplitude peak stresses (for mode I, II and III equivalent to corresponding stresses spectra (Campagnolo et al. 2022) thanks to the LDR by Palmgren-Miner (Palmgren 1924; Miner 1945). The proper PSM design scatter band to use in combination with the design stress Δ σ eq,peak Eq. (1) is dictated by the local biaxiality ratio: 2 2 eq,peak,II eq,peak,III 2 eq,peak,I  + =  (3) and the selection criteria are summarized in Table 1 as a function of λ (Eq. (3)) while Fig. 1 reports the scatter bands valid for pure mode I local stresses (λ = 0, Fig. 1a) and multiaxial local stresses (λ > 0, Fig. 1b) (Campagnolo et al. 2022).

Table 1 : Criterion for selecting the reference PSM-based fatigue design curve for steel arc-welded joints (Meneghetti and Campagnolo 2020)

λ Eq. (3)

Δσ eq,peak,A,50% [MPa]

Δσ eq,peak,A,97.7% [MPa]

Δσ eq,peak,A,2.3% [MPa]

k [-]

T σ [-]

Figure

N A [cycles]

λ = 0 λ > 0

214 354

156 257

296 488

3 5

1.90 1.90

1a 1b

2 ∙ 10 6 2 ∙ 10 6