PSI - Issue 77

João Nuno Silva et al. / Procedia Structural Integrity 77 (2026) 657–664

661

Joa˜o Nuno Silva et al. / Structural Integrity Procedia 00 (2026) 000–000

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counted (e.g., rainflow) and represented by an equivalent constant-amplitude stress-range spectrum for design checks at the reference number of cycles. Design values of the fatigue nominal stress ranges are obtained by applying damage equivalent factors ( λ i ) to the equivalent constant stress ranges ∆ σ E and ∆ τ E . When the fatigue action is characterised by an equivalent constant-amplitude stress range but macro-geometric or concentrated load e ff ects are present, a stress-concentration factor k t modifies the design stress range. The fatigue resistance verification uses the relevant detail category, ∆ σ c or ∆ τ c , and the resistance partial factor, γ Mf . Compliance is demonstrated by Equations 13 and 14. Alternatively, verification with respect to the fatigue limit may be performed when a variable amplitude spectrum changing ∆ σ e , 2 , Ed by maximum stress range ∆ σ max , Ed , and the detail category value by the constant amplitude fatigue limit value ∆ σ D or ∆ τ D .

∆ σ e , 2 , Ed ∆ σ C /γ Mf ≤ ∆ τ e , 2 , Ed ∆ τ C /γ Mf ≤

U f ⊥ =

1 . 0 ,

(13)

U f τ =

1 . 0 .

(14)

For multiaxial fatigue, the EN 1993-1-9 standard combines the e ff ects of direct and shear components. If the normal and shear stresses act simultaneously in each loading event, the principal stresses are considered and the corresponding ranges verified by Equations 13 and 14. If they do not co-occur, damage is calculated per Miner’s rule. For parent metal failure (including crack initiation at weld toes), the interaction is calculated by Equation 15. For weld failure with crack initiation at the weld root, the multiaxial interaction is expressed by Equation 16. U f , Multi = j = x , y , z ∆ σ j , e , 2 , Ed ∆ σ j , C /γ Mf m σ + k = xy , xz , yz ∆ τ k , e , 2 , Ed ∆ τ k , C /γ Mf m τ ≤ 1 . 0 (15) U f , Multi = ∆ σ wf , e , 2 , Ed ∆ σ wf , C /γ Mf m σ + ∆ τ wf , e , 2 , Ed ∆ τ wf , C /γ Mf m τ ≤ 1 . 0 (16) Although not a standard, the IIW Recommendations provide a framework for fatigue assessment of welded com ponents. Three assessment routes are distinguished: (a) S–N curve-based procedures using the nominal, structural (hot-spot), notch stress approaches; (b) a fracture-mechanics approach based on fatigue crack propagation; and (c) direct experimental verification on components or assemblies. Fatigue checks are performed with design stress ranges (or spectra) multiplied by the partial factor for fatigue actions γ F , and design resistances obtained by dividing charac teristic resistances by the partial factor for fatigue resistance γ M , following the same principles as Equations 13 and 14 in EN 1993-1-9 standard, with the fatigue class FAT, which may be adjusted to account for e ff ects such as stress ratio, plate thickness, or post-weld treatments. For multiaxial loading conditions, the IIW Recommendations specify an interaction criterion that combines the design stress ranges perpendicular / parallel to the weld and the in-plane shear stress range, expressed in Equation 17. The comparison value is CV = 1.0 for proportional normal–shear loading and CV = 0.5 for uncorrelated components (withCV = 1.0 recommended for semi-ductile aluminium). As a simplified conservative alternative, verification may also be performed using the maximum principal stress range, expressed in Equation 18. In addition, the guideline provides a procedure for variable-amplitude loading. U f , Multi = ∆ σ ⊥ , S , d ∆ σ R , d 2 + ∆ σ ∥ , S , d ∆ σ ∥ , R , d 2 + ∆ τ S , d ∆ τ R , d 2 ≤ CV (17) 2.6. IIW Recommendations

S , d

1 2

∆ σ S , d + ∆ σ 2 S , d

+ 4 , ∆ τ 2

(18)

∆ σ comp , S , d =