PSI - Issue 75

Luca Vecchiato et al. / Procedia Structural Integrity 75 (2025) 602–608 Luca Vecchiato et al. / Structural Integrity Procedia (2025)

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Given that welded joints typically exhibit a small notch tip radius, the PSM assumes the sharp V-notch hypothesis [5]. It consists of idealizing both the weld toe and the weld root with a null tip radius ρ = 0 and an opening angle 2 α , equal to 135° for the weld toe and 0° for the weld root [5]. Therefore, because of the null tip radius, the resulting local stress field at the notch tip is singular and its intensity is fully characterized by the Notch Stress Intensity Factors (NSIFs) [6 – 8]. Originally proposed by Meneghetti and Lazzarin in 2007 [9], the PSM is an engineering technique to rapidly estimate the Notch Stress Intensity Factors (NSIFs) using linear elastic FE analyses with relatively coarse mesh. Subsequently, Meneghetti and Lazzarin [10] proposed an extension of the PSM to enable the rapid and efficient computation of the averaged Strain Energy Densitity (SED) [11 – 13], whose value is directly dependent on the NSIFs [12]. Expressly, the SED criterion assumes as a fatigue strength parameter the strain energy density averaged over a circular area centered at the notch tip and having radius R 0 , a material constant whose value is 0.28 mm and 0.12 mm for arc-welded joints made of steel and aluminium alloys, respectively [13]. In practice, the PSM translates the range of averaged SED into an equivalent peak stress range Δ σ eq,peak , which, on a plain specimen under plain strain condition, gives rise to the same amount of averaged SED as that observed at the weld toe or weld root of the analysed structure [4]. According to the last formulation of the PSM [4,14], the following expression is used to define the equivalent peak stress Δ σ eq,peak when VA mixed mode I + III loads are present: Δ , =√Δ 2 , , +Δ 2 , , (1) Δ σ eq,peak,I and Δ σ eq,peak,III being the pure mode I and pure mode III equivalent peak stresses, defined as follows: Δ , , = 1 ∙ 1 ∙ Δ , =0, , (2a) Δ , , = 3 ∙ 3 ∙ Δ , =0, , (2b) Where Δ σ θθ,θ=0,peak,max and Δτ θ z ,θ=0,peak,max are the nodal value of the opening (mode I) and out-of-plane shear (mode III) peak stresses, respectively, evaluated at the tip of the sharp V-notch using linear elastic finite element analysis with a coarse (not convergent) mesh, provided that a minimum mesh density at the notch tip is guaranteed [4]. The coefficients f wi in Eq. (2) incorporate the influence of various factors, such as the type and the size of the adopted finite element, the SED control radius R 0 , and the opening angle 2α [4]. On the other hand, the f si coefficients account for the type of load spectrum and are based on the combination of the constant amplitude formulation of the PSM with the linear damage rule [14]. The reader is referred to the relevant literature [4,14] for a more detailed description of the PSM and the coefficients here introduced. When the notch tip radius is significantly larger than the control radius R 0 , the assumption of a sharp notch is no longer applicable [15]. In this condition, the joint exhibits full notch sensitivity and the following expressions must be used instead of Eqs. (2): Δ , , = 1 ∙ Δ , (3a) Δ , , = 3 ∙√ 1− 2 ∙ Δ , (3b) Where Δ σ ρ,max and Δτ ρ,max represent the maximum mode I and mode III elastic peak stresses, respectively, evaluated at the blunt notch tip. These quantities may be determined either through analytical formulations or by means of FE simulations, provided that sufficient mesh refinement is applied at the notch tip to ensure numerical convergence. The final step in the fatigue assessment involves comparing the equivalent peak stress (Eq. (1)) with the relevant PSM-based fatigue design scatter band. This reference curve is selected according to the local biaxiality ratio, defined as: