PSI - Issue 75

Francesco Collini et al. / Procedia Structural Integrity 75 (2025) 375–381 F. Collini et al. / Structural Integrity Procedia 00 (2025) 000–000

376

2

finish, and the presence of stress raisers like defects and / or notches. Over the years, various approaches have been developed to capture these e ff ects in conventionally manufactured parts, ranging from critical plane approaches Socie and Marquis (1999); Stephens et al. (2000); Susmel (2009), to stress invariant approaches Sines and Ohgi (1981); Crossland (1956), energy-based methods Garud (1981); Ellyin (1989); Lazzarin and Zambardi (2001) and defect sensitive approaches Murakami and Takahashi (1998); Beretta and Murakami (2000); Nadot and Billaudeau (2006); Endo and Ishimoto (2006, 2007); Gadouini et al. (2008); Yanase and Endo (2014); Okazaki et al. (2014); Araujo et al. (2019); Machado et al. (2020); Vantadori et al. (2022); Dias et al. (2022). In the case of Additively Manufactured (AM) components, the ability to create complex net-shaped parts introduces peculiar internal defects, poor surface finish, and blunt (and sometimes even sharp) notches, with interactions among these features that are not yet fully and comprehensively understood. Several studies have specifically addressed the multiaxial fatigue behaviour of L PBF components, focusing on the e ff ects of surface conditions, defect size and morphology, and post-processing treatments (Fatemi et al. (2017); Molaei et al. (2022)). Recently (Foti et al. (2023)) reviewed several multiaxial fatigue prediction methods, focusing on their accuracy in correlating fatigue data under various loadings for both as-built and machined surfaces, considering post-processing e ff ects. The review showed that critical plane approaches and fracture mechanics-based (FM) models o ff er promising multiaxial fatigue assessment of AM components. In addition to fully dense components, lattice structures produced via L-PBF have garnered attention because of their high sti ff ness to-weight ratios. However, their fatigue performance is critically a ff ected by process-related defects and geometric notches inherent to their architecture and subjeted to local multiaxial stress states. Collini and Meneghetti (2024) explored the applicability of Linear Elastic Fracture Mechanics (LEFM) principles to predict the fatigue limit of such lattice structures, highlighting the significant role of both manufacturing defects and structural notches in fatigue strength. In the context of predicting the multiaxial fatigue threshold or fatigue limit of a component weakened by cracks, sharp notches, defects, an extension of the Atzori-Lazzarin-Meneghetti diagram (Atzori and Lazzarin (2001); At zori et al. (2003, 2005)) was recently proposed and validated by a large number of experimental data relevant to conventionally manufactured specimens taken from the literature Collini et al. (2025). Basically, the model provides the remote threshold stress range of a component from an equivalent crack size parameter a v eq ∆ w which depends on crack / notch / defect size, geometry, and loading mode and their combination that was defined using the averaged strain energy density criterion in a finite small volume (SED) Lazzarin and Zambardi (2001); Lazzarin et al. (2008). In this paper, the approach is applied for the first time to preliminary multiaxial fatigue test results obtained from L-PBF Ti-6Al-4V specimens weakened by a net-shaped sharp V-notch, as part of a broader experimental campaign currently under investigation. In this section, only the necessary definitions and equations useful for the analysis and discussion of the data will be provided, while the interested reader can find the complete theoretical background in Collini et al. (2025). Consider a sharp V-notched component (with notch tip radius ρ = 0) subjected to several loading modes by applying multiple remote loads ( ∆ σ g and ∆ τ g ), as schematically reported in Figure 1a. According to the SED model, fatigue behavior is governed by the strain energy density ∆ w averaged in a finite circular material volume R c , i , centered in the sharp V-Notch (see, Figure 1a). The ∆ w at the tip of a sharp notch can be expressed as a function of the range of the Notch Stress Intensity Factor (i.e. the parameter that describes the intensity of the singular term of the stress field) K v i (Gross and Mendelson (1972)) for each loading mode (N-SIF) with the following equation (Lazzarin and Zambardi (2001); Lazzarin et al. (2008)): 2. Theoretical framework of the multiaxial Atzori-Lazzarin-Meneghetti diagram

e i E   

c , i    2

3  i = 1

∆ K v i R γ i

∆ w = c w

(1)

where:

• c w , considered the same for all loading modes, is a coe ffi cient accounting for the mean stress e ff ect (Meneghetti and Lazzarin (2007); Meneghetti and Campagnolo (2020));