PSI - Issue 75

Alberto Campagnolo et al. / Procedia Structural Integrity 75 (2025) 564–571 Alberto Campagnolo, Giovanni Meneghetti/ Structural Integrity Procedia (2025)

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3

crescent-shape geometry, as depicted in Fig. 1. In this configuration, R 0 denotes the depth of the crescent-shape region along the symmetry axis of the structural volume. The corresponding outer radius of this volume is given by ( R 0 + r 0 ), where r 0 represents the distance from the notch tip to the center of the structural volume. This distance can be expressed as a function of the notch opening angle 2α and the notch root radius ρ (see expressions inside Fig. 1). It is important to highlight that the structural volume is not centered at the geometric notch tip. Instead, it is located at the point along the notch edge where the maximum principal stress occurs, in accordance with the ‘equivalent local mode I’ concept proposed by (Gómez et al. 2007).

r 0 = q− q 1 ρ q = 2π− π 2α

φ

2  ≅ 



HFMI

σ 11,max

depth

Weld root



r 0

R 0

t/2

weld toe

y

R 0 + r 0

Notch bisector line

x

- Fig. 1: The “crescent shape” structural volume (Lazzarin and Berto 2005) to calculate the averaged SED at the radiused weld toe (ρ > 0) of a HFMI treated transverse non-load-carrying (nlc) fillet-welded joint as described in (Campagnolo et al. 2022) . The ‘direct approach’ is applied to evaluate the averaged SED, and afterwards, the equivalent peak stress is calculated according to Eq. (2). Concerning the averaged SED calculation for welded joints having a radiused weld toe, a direct approach is typically adopted. This method relies on linear elastic finite element (FE) analyses in conjunction with Eq. (1), enabling the computation of the averaged SED (measured in N/mm 2 or, equivalently, in MJ/m 3 ) without resorting to NSIF-based formulations.



W

FEM,i

V(R )

(1)

FEM  = W

0

V(R )

0

In Eq. (1), W FEM,i denotes the strain energy (measured in N∙ mm) computed at the integration points of the i-th finite element located within the structural volume V(R 0 ) (measured in mm 3 ), as illustrated in Fig. 1. Lazzarin and co-workers (Lazzarin et al. 2010) demonstrated that a relatively coarse finite element mesh can be employed within the structural volume of radius R 0 without compromising the accuracy of the strain energy evaluation. Subsequently, by introducing the expression for the strain energy density (SED) corresponding to an equivalent uniaxial plane strain condition, it becomes possible to derive the equivalent peak stress within the Peak Stress Method (PSM) framework. This equivalent peak stress offers a convenient damage parameter for fatigue assessment and can be expressed as follows:

2 2E − =  1

2 2 E ΔW 1   −

(2)

→

2

ΔW

eq,peak  =

FEM

FEM

eq,peak