PSI - Issue 83

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

243

4. Results and discussion The fatigue strengths estimated from the performed SL tests were calculated using Eq. (1), and the resulting values are summarized in Table 2. The scatter between repeated SL tests remained limited for all investigated relative densities. The relative standard deviations were 7.69%, 4.76%, 6.04%, and 2.98% for RD values of 12.5%, 25%, 37.5%, and 50%, respectively. These values are acceptable for fatigue characterization of additively manufactured lattice materials, where specimen-to-specimen variability is inherently expected. The lowest scatter was observed for the 50% RD lattice, suggesting that the densest structure provided the most repeatable step-loading response among the tested configurations.

Table 2. Estimated fatigue strength at one million cycles by SL method.

RD (%)

Average (MPa)

Relative Standard Deviation (%)

Test 1 (MPa)

Test 2 (MPa)

Test 3 (MPa)

Case

1 12.5

5.07 24.27 57.15 116.68

4.52 24.59 59.07 120.69

5.25 22.49 64.18 113.73

4.95 23.78 60.13 117.03

7.69 4.76 6.04 2.98

2

25

3 37.5

4

50

To evaluate the accuracy of the SL-derived fatigue strengths, the original S-N data were evaluated at one and two million cycles. The comparison is presented in Fig. 3 and Table 3. In Table 3, the normalized magnitudes of SL/ S N@1M and SL/ S-N@2M is calculated as the ratio of estimated fatigue strength from SL method to S-N curve at one and two million cycles, respectively. At one million cycles, the S-N fatigue strengths at 50% survival probability were 5.75, 27.37, 64.31, and 121.40 MPa for RD values of 12.5%, 25%, 37.5%, and 50%, respectively. The corresponding SL estimates were 4.95, 23.78, 60.13, and 117.03 MPa. Therefore, the SL/S-N ratios were 0.86, 0.87, 0.93, and 0.96, with differences of 13.95%, 13.13%, 6.50%, and 3.60%, respectively. These values demonstrate that the SL method gives conservative estimates at one million cycles and that the accuracy improves with increasing RD with a clear trend. For lower-density gyroid lattices, the load-bearing walls are thinner and the structure can be more sensitive to local stress concentrations, surface irregularities, and process-induced imperfections. Under these conditions, the earlier loading blocks may contribute more significantly to progressive damage accumulation before failure occurs in the final block, causing a larger deviation from the S-N-derived strength. In contrast, the 37.5% and 50% RD lattices exhibit a denser and more continuous load-bearing network, which reduces the normalized influence of the preceding loading blocks and leads to better agreement with the S-N based fatigue strengths reported by Foti et al. (2025).

S-N (1M cycles)

S-N (2M cycles)

SL

S-N (1M cycles)

S-N (2M cycles)

1.10

140

121.40

117.03 115.67

1.05

120

1.02

1.01

1.01

1.00

100

0.98

0.96

0.95

80

0.93

64.31

60.13 59.08

0.90

60

SL/S-N

0.87

0.85

40

0.86

27.37

23.78 24.29

Fatigue Strength (MPa)

0.80

20

5.75

4.95 4.88

0.75

0

0

12.5

25

37.5

50

62.5

0

12.5

25

37.5

50

62.5

Relative Density (%)

Relative Density (%)

(a) (b) Fig. 3 Comparison between S-N-based fatigue strengths and SL estimates at one and two million cycles: (a) absolute fatigue strength; (b) normalized SL-to-S-N fatigue-strength ratio.