**3. Results**

In this section, the results obtained from the fatigue tests will be disclosed. All the numerical evidence are reported in Appendix A subdivided by cell type. For each cell type, Wohler curves will be provided and discussed. The Wohler curves relate the amplitude of the load, *σa*, for each sample and the number of cycles at which the specimen breakdown occurs. Subsequently, images of broken specimens will be shown to provide insights on the failure mechanism.

#### *3.1. Rhombic Dodecahedron*

The graph in Figure 4. reports the Wohler curves for all the rhombic specimens tested. At equal *σ<sup>a</sup>* (load amplitude), the greatest fatigue life was that of specimens with a smaller cell size, 5 mm, and higher density, 30%. The second longest endurance was produced by cells with a 7 mm cell size and 30% relative density. The lowest fatigue life was witnessed from specimens with a 5 mm cell size and 25% relative density. The most relevant aspect of this graph was the effect of cell size. Increasing cell size, while maintaining fixed the relative density of the specimen (i.e., same amount material per cubic centimeter), noticeably reduced the fatigue life as reported by the comparison between 7\_30 and 5\_30 cells.

**Figure 4.** Wohler curves for rhombic dodecahedron specimens.

The effect of relative density was less stable in all the tested stress amplitudes. As reported in Appendix B, in the main effect graph in Figure A1, the effect of the relative density was not monotonous. While at higher loads the increase of the relative density seemed to provide a higher fatigue life, this was not true for lower loads (60% and 20% of the yield stress). This aspect will require further dedicated analysis in the future.

The photos of the rhombic specimens before the fatigue test are shown in Figures 5 and 6. while pictures of specimens after the test are shown in Figure 6.

The failure occurred along a 45◦ plane with respect to the *Z*-axis and started from a corner of the specimen. The deformation evidenced before the failure was almost absent; the connections broke internally one by one along the plane until the resistant section became insufficient and caused the collapse of the specimen. From the images, it was possible to observe that the breaking of the specimens subjected to higher loads (80% and 60% of *σ*02) was clearer and more similar to the one from the static compression tests. On the other hand, the rupture of the specimens subjected to lower loads (40% and 20% of *σ*02) was more irregular and acted through several fractures' planes simultaneously, causing the final separation of the specimen into more than two pieces. This difference was particularly marked for the 7 mm cells, as visible in Figure 6. For cells with a lower relative density, such as 5-25, irregular fractures were already present for higher loads, such as 60% of *σ*02.

**Figure 5.** Lateral view of the Rhombic dodecahedron AlSi10Mg specimens for fatigue test: (**a**) Rhom-5-25, (**b**) Rhom-5-30 and (**c**) Rhom-7-30.

**Figure 6.** Rhombic cells subjected to fatigue test: (**a**) cell size 5 mm, relative density 25%, max load 80% *σ*02; (**b**) cell size 5 mm, relative density 25%, max load 60% *σ*02; (**c**) cell size 5 mm, relative density 25%, max load 40% *σ*02; (**d**) cell size 5 mm, relative density 30%, max load 80% *σ*02; (**e**) cell size, 5 mm relative density 30%, max load 60% *σ*02; (**f**) cell size 5 mm, relative density 30%, max load 40% *σ*02; (**g**) cell size 7 mm, relative density 30%, max load 80% *σ*02; (**h**) cell size 7 mm, relative density 30%, max load 60% *σ*02; (**i**) cell size 7 mm, relative density 30%, max load 40% *σ*02.

#### *3.2. Octet Truss*

The graph in Figure 7 reports the Wohler curves for all the tested Octet truss specimens. In accordance with the present results, the longest fatigue life was shown by the 5-30 specimens, followed by the specimens 7-30 and 5-25 with intersecting behaviors.

Similar to the case with Rhombic cells, Octet truss curves for 5-30 and 7-30 were almost parallel to each other, with the 7-30 case shifted to lower cycles. This behavior suggests a clear negative effect of increasing of the cell size with same relative density.

As for the 7-30 vs. 5-25 trend, relative density played a beneficial effect at higher loads (80% and 60% of *σ*02) and reported a dissimilar trend at lower loads (40% and 20% of yield stress). Additionally, in this scenario, further analyses are required to deeply investigate the effect of this parameter. It is important to note that specimens 5-30 and 5-25 reached the imposed fatigue limit (1.5 × <sup>10</sup><sup>7</sup> cycles) without breaking with a *<sup>σ</sup><sup>M</sup>* equal to the 20% of yield stress.

The photos of the Octet specimens before the fatigue test are reported in Figure 8 while pictures of specimens after the test are in Figure 9.

**Figure 7.** Wohler curves for Octet truss specimens.

**Figure 8.** Lateral view of the Octet truss AlSi10Mg specimens for fatigue test: (**a**) Octet truss 5-25, (**b**) Octet truss 5-30 and (**c**) Octet truss 7-30.

The fracture of the specimen was, in part, similar to that evidenced during compression tests. The failure occurred along a 45◦ plane with respect to the *Z*-axis and started from a corner of the specimen. Deformation before the failure was almost absent; the connections broke internally one by one along the plane until the resistant section became insufficient and caused the collapse of the specimen. The failure mode of the 5-25 specimens subjected to all loads was more irregular compared to the others and acted simultaneously on several planes causing the final separation of the specimen into more than two pieces. Similarly, the 7-30 specimens subjected to higher loads (80% and 60% of *σ*02) also failed in a similar manner to that seen for the compression tests; on the other hand, the failure mode of the same cells when subjected to lower loads (40% and 20% of *σ*02) was more irregular and acted on several planes simultaneously, causing final separation of the specimen into more than two pieces.

**Figure 9.** Octet cells subjected to fatigue: (**a**) cell size 5 mm, relative density 25%, max load 80% *σ*02; (**b**) cell size 5 mm, relative density 25%, max load 60% *σ*02; (**c**) cell size 5 mm, relative density 25%, max load 40% *σ*02; (**d**) cell size 5 mm, relative density 30%, max load 80% *σ*02; (**e**) cell size 5 mm, relative density 30%, max load 60% *σ*02; (**f**) cell size 5 mm, relative density 30%, max load 40% *σ*02; (**g**) cell size 7 mm, relative density 30%, max load 80% *σ*02; (**h**) cell size 7 mm, relative density 30%, max load 60% *σ*02; (**i**) cell size 7 mm, relative density 30%, max load 40% *σ*02.
