PSI - Issue 83

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

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Table 3. Comparison of the estimated fatigue strengths by SL method and S-N curve data. Case

RD (%)

SL (MPa) 4.95 23.78 60.13 117.03

S-N @ 1M (MPa)

Ratio of SL/ S-N@1M

S-N @ 2M (MPa)

Ratio of SL/ S-N@2M

1 12.5

5.75 27.37 64.31 121.40

0.86 0.87 0.93 0.96

4.87 24.29 59.07 115.67

1.01 0.98 1.02 1.01

2

25

3 37.5

4

50

At two million cycles, the S-N fatigue strengths were 4.88, 24.29, 59.07, and 115.67 MPa for the RD sequence from 12.5% to 50%, and the resulting SL/S-N ratios were 1.01, 0.98, 1.02, and 1.01. These values are close to unity, indicating that the SL estimates remain close to the S-N-derived strengths in the adjacent finite-life range. Assuming that within HCF regime, any lower applied stress than the fatigue limit at 2 million cycles will not result in fatigue failure, the obtained SL predictions are promising. However, a certain conclusion on reliability of these for higher life ranges such as 10 million cycles, would require additional S-N data with the runout condition set to that number of cycles. This is particularly important for certain alloys where finite life failures are observed in HCF regime even after 2 million cycles of loading (e.g., aluminium alloys). The present results remain consistent with the recommendation by Nicholas SL method, which proposed block lengths of 3 to 4 million cycles to estimate the fatigue strength at 10 million cycles. Overall, the SL method can be used as an accelerated tool for fatigue-strength estimation in PBF-LB gyroid lattices, but its accuracy is not independent of relative density. The one-million-cycle comparison provides the clearest density-dependent trend, with lower-density lattices showing larger deviations due to the stronger effect of damage accumulated in previous loading blocks. 5. Summary and conclusion In this study, the Nicholas step-loading method was evaluated as an accelerated approach for estimating the fatigue strength of PBF-LB Ti-6Al-4V gyroid lattice structures. Four relative densities, namely 12.5%, 25%, 37.5%, and 50%, were investigated under compression-compression cyclic loading at a load ratio of 0.1. The fatigue strengths obtained from one-million-cycle SL blocks were 4.95, 23.78, 60.13, and 117.03 MPa, respectively, with relative standard deviations of 7.69%, 4.76%, 6.04%, and 2.98%, confirming acceptable repeatability for fatigue characterization of AM lattice materials. The comparison with the original S-N data showed that the SL method provided conservative estimates at one million cycles, with SL/S-N normalized magnitude of 0.86, 0.87, 0.93, and 0.96 as RD increased from 12.5% to 50%. The corresponding differences decreased from 13.95% to 3.60%, indicating improved accuracy for denser lattices. At two million cycles, the ratios remained close to unity, ranging from 0.98 to 1.02, showing close agreement with the adjacent long-life response. The larger deviation at lower RD can be attributed to stronger previous-block damage in thinner-walled, defect-sensitive lattices. Therefore, the SL method can be considered a practical tool for rapid fatigue-strength assessment of Ti-6Al-4V gyroid lattices, although RD-dependent calibration is recommended for design applications. Funding Sources This project has received funding from the European Union’s Horizon Europe research and innovation programme under grant agreement No. 101119917 METRAMAT Doctoral Network at NTNU. References Li, P., Warner, D., Fatemi, A., Phan, N., 2016. Critical assessment of the fatigue performance of additively manufactured Ti–6Al–4V and perspective for future research. International Journal of Fatigue 85, 130–143. Blakey-Milner, B., Gradl, P., Snedden, G., Brooks, M., Pitot, J., Lopez, E., Leary, M., Berto, F., Du Plessis, A., 2021. Metal additive manufacturing in aerospace: A review. Materials & Design 209, 110008. Foti, P., Heydari Astaraee, A., Bagherifard, S., du Plessis, A., Wan, D., Berto, F., Razavi, N., 2025. Fatigue performance of Ti6Al4V lattices: relative density as a partial quantitative predictor. International Journal of Fatigue 206, 109447.