PSI - Issue 83

Amir Hossein Mirzaei et al. / Procedia Structural Integrity 83 (2026) 239–245

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where σ f -1 is the stress level of the block immediately preceding failure, ∆ σ is the stress increment between two consecutive blocks, N b is the number of cycles assigned to each block, and N f is the number of cycles sustained in the last block before fracture.

σ f

. . .

σ s

Δσ

Maximum stress

σ 0

N b, f-1

N f

N b, 1

N b, 2

Loading history

Fig. 1. Schematic illustration of the SL testing parameters.

It should be emphasized that this approach is commonly used to estimate fatigue strength at a specified finite life, and in some studies it has also been used as an approximation of the fatigue limit when sufficiently long block lengths are employed. It is worth noting that fatigue strength is defined as the stress magnitude associated with a material's failure at a specific, finite fatigue life while fatigue limit represents the stress threshold below which a material is expected to have an effectively infinite life, meaning no macroscopic fatigue failure is predicted to occur. Nicholas reported that block sizes on the order of 3×10 6 to 4×10 6 cycles can provide a practical estimate of the long life fatigue threshold. Accordingly, the interpretation of the SL result depends strongly on the selected value of N b : short blocks tend to reflect fatigue strength at a finite life, whereas longer blocks move the estimate closer to the engineering fatigue limit. A key assumption behind this method is that the damage introduced in the earlier blocks remains limited, so that the final block governs the estimation. However, this assumption may not always hold, especially when the loading history itself influences the material response through progressive damage accumulation or possible history-dependent strengthening effects. For this reason, the SL method should be viewed as an efficient engineering approximation whose accuracy depends not only on the material, but also on the chosen initial stress, stress increment, and, most importantly, the number of cycles in each block. 3. Experiments 3.1. Materials Solid-based gyroid lattice coupons were manufactured from Ti-6Al-4V by powder bed fusion–laser beam (PBF LB) using an EOS M290 system. The specimens were produced with the standard processing parameters prescribed for this alloy, namely a laser power of 280 W, a scan speed of 1200 mm/s, a hatch spacing of 0.14 mm, and a layer thickness of 0.03 mm. The hatch region was scanned in a zig-zag pattern, with a 67° rotation between successive layers, followed by contour exposure. Four nominal relative densities were considered: 12.5%, 25%, 37.5%, and 50%. Each lattice specimen contained five unit cells of 4 mm in each spatial direction, resulting in cubic samples with overall dimensions of 20 mm × 20 mm × 20 mm. After fabrication, all specimens were subjected to post-processing heat treatments. First, a stress-relief treatment was carried out in vacuum at 650 °C for 3 h before removal from the baseplate. Subsequently, the specimens were annealed in vacuum for 2 h at 940 °C, followed by Hot Isostatic Pressing (HIP) treatment in Argon at 100 MPa with a 2 h soak time at 925 °C and then slow cooling of -10 °C/min. These procedures were applied to all samples in order to reduce residual stresses and to ensure a consistent material condition prior to fatigue testing (Foti et al., 2025).