**4. Discussion**

The investigation results show that the sheet-based gyroid structures present an interesting combination of morphological properties and quasi-static mechanical behavior. Thin-wall gyroid structures obtained in EBM-manufacturing using different Themes were expected to have identical geometrical and mechanical properties due to initial settings. In the current research, the complex shape of the final gyroid samples was largely affected by the choice of the Themes, and fused powder particle distribution influencing the surface roughness and effective wall thickness. Such rough beaded surfaces are typical for AM lattice structures. Suard et al. investigated the influence of the fabrication angle on the surface roughness of EBM struts [49]. They reported that for a vertical strut, the roughness does not significantly fluctuate, while the roughness of oblique and horizontal struts increases on the down-facing surfaces. This was assumed to be due to the partial overmelting and reduced cooling, which lead to the 'leakage' of the melt and formation of the stalactite-like micro-columns and blobs (in our case indicated by white arrows in Figure 4a). It was established that for significant overhanging angles (more than 45◦ from horizontal), a greater number of partially molten powder particles are attached to the downward surfaces [51]. Moreover, Yang et al. demonstrated that sheet-based Ti-6Al-4V gyroids manufactured by LPBF have different surface morphology between up- and down-facing surface areas [38].

For the MT specimens, the beads are formed mainly on surfaces parallel to the building direction. Thus, the vertical walls had effective thickness up to 0.5 mm, while the oblique and horizontal walls had a thickness of 0.25 mm, Figure 4c. Typically, in the beam-like structures, there is an increase of the surface irregularities in struts produced by EBM with direction diverging from vertical [49]. However, in sheet-based structures, vertical walls are thicker, as it seems that the contours of the Melt Theme strongly influences resulting thickness of the oblique and horizontal walls. WT specimens possess quite uniform thickness for oblique and vertical wall areas, Figure 4d. Since holes are systematically present in the horizontal walls, no thickening in the WT was observed.

For porous samples, three types of compression failure are known [5]. The first type is layer-by-layer failure. This type is characterized by the collapse of cells in planes perpendicular to the manufacturing and loading direction: each layer collapses into the one below. The second type is brittle fracture of the cell walls and propagation of cracks through the lattice. Commonly, the fracture starts at a pre-existing defect, such as an internal pore of a surface irregularity. A crack can fork perpendicularly to its direction of propagation through the walls of the cells, implying that crack propagation through the structure is likely tortuous. The third type is diagonal shear. In some cases, combined diagonal shear and layer-by-layer failure occurs, for example, for sheet-based gyroid manufactured by SLS from maraging steel [6]. The compressive failure mode of the gyroid lattice is related to the size of its constituent cells.

The different stress values of the MT and WT specimens can be explained by the different relative density, while the different shape of the stress-strain curves is most probably due to the influence of the through-holes and smaller wall thickness in the WT samples, favoring Euler instability of the walls under compressive load. Such instability has a statistical character, as it occurs in single walls separately (or in groups of walls favorably oriented with respect to the load axis).

Interestingly, compression tests revealed that despite the difference in wall thickness and material volume, the two types of specimens have similar quasi-elastic gradient (around 1.5 GPa). Following a Gibson-Ashby law [52,53]:

$$E = E\_0 \times \left(1 - P\right)^n \tag{5}$$

One can calculate the shape factor *n* using the known porosity values *P* and the Young's modulus of Ti6Al4V (*E*0 = 110 GPa). Corresponding values are *n* ~ 2.3 for WT and *n* ~ 3.2 for MT samples. Since *n* = 2 corresponds to a cellular structure of compacted overlapping pores and *n* = 3 to a cellular structure of compacted non-overlapping pores [52], we can observe that thinning the walls not only causes an increase of porosity but also makes elastic behavior of the samples more similar to a strut-like cellular structure. The MT structure even tends to the elastic behavior of a cellular structure of overlapping spheres (*n* = 4).

Importantly, the values of the quasi-elastic gradient satisfy the limits of the elastic moduli for human cortical bone [54]. Moreover, the specific energy absorption at 50% strain for the two structures is quite similar, showing that EBM WT structures are as strain tolerant as MT.

It was demonstrated by Yang et al. that L-PBF Ti-6Al-4V gyroid sheet-based structures under compression load behave as bending-dominated structures [38], while Al-Ketan et al. [6] and Kelly et al. [35] showed stretching dominated deformation for the sheet-based gyroids made of maraging steel and Ti-6Al-4V, respectively. The linear elastic regime is driven by the bending of the inclined cell walls or by the stretching of the vertical cell walls.

Mechanical properties such as compressive offset stress, yield strain, first maximum compressive strength and energy absorption are different for sheet-based gyroid manufactured in Melt Theme and Wafer Theme. However, the quasi-elastic gradients and specific energy absorption at 50% strain of these structures are equal. Thus, WT structures are as strain tolerant as MT ones.

Comparison of the quasi-elastic gradient values (in compression) of the studied gyroid sheet-based samples to the ones reported in the literature are presented in Table 4.


**Table 4.** Ti-6Al-4V sheet-based gyroid properties.

L-PBF-manufactured sheet-based gyroids have quasi-elastic gradient significantly larger than EBM-manufactured ones. This can be attributed to surface roughness of the EBM-produced specimens. The highest value of quasi-elastic gradient in the Table 4 belongs to the specimen with the 50% porosity.

Thin walls allow decreasing the distance between neighboring walls, keeping the ability to effectively remove powder from the structure. In fact, it is essential that porous samples used for the mechanical and flow tests be very thoroughly cleaned from residual powder. The semi-sintered powder remaining inside the structure would influence its permeability and mechanical behavior. Additionally, thorough cleaning is critical for the applications where even slow release of loose powder during the component life is completely unacceptable, as in the case of implants. All TPMS structures used in this study were successfully cleaned with conventional powder recovery system (see e.g., [55]).

Using FE simulation, it was shown that relatively small number of through-holes occurring in thin-walled structures does not influence the elastic behavior of the lattice. In case of the WT structures, through-holes are wider and more abundant in the surface sections having small inclination to the layer plane (Figure 10). Two reasons could be responsible for that: first one, related to technology, and second one, to the design process. Technologically, overhanging elements without supports are always problematic in PBF AM. From the point of view of design, since the 3D model (CAD) for WT samples has zero thickness, the part of the STL file corresponding to this problem area cannot be registered by slicer software. The tangent point represents, therefore, a blind spot, where the electron

beam could be turned off (Figure 10a). Further studies into this phenomenon are needed, and corresponding corrections of the zero-thickness design model should be incorporated in the future.

**Figure 10.** Assumption on the through-holes' appearance: (**a**) CT in vertical cross-sectional view; (**b**) Scheme of manufacturing process in vertical cross-sectional view.

It is interesting that the MT specimens, with porosity of 76% and wall thickness about 0.4 mm, have UTS of about 76 MPa, while L-PBF gyroid with the same porosity and wall thickness of 0.5 mm demonstrates UTS of 60 MPa [35]. Sheet-based gyroid manufactured by L-PBF from Ti-6Al-4V with wall thickness of 0.25 mm and porosity varying from 78 to 87% can possess quasi-elastic gradient from 1.9 to 5 GPa, depending on the unit cell size [35]. The UTS for a gyroid with 6 × 6 × 6 mm unit cell and porosity of 87% was found to be equal to 24 MPa [35], equal to the results of the tensile testing of the WT gyroid (Table 3). However, the tensile strain at failure for EBM gyroid is approximately 10% while tensile failure strain of L-PBF gyroid with wall thickness of 0.25 mm ranges from 1.4% to 2.1%.

Achieving minimal thickness of the TPMS sheet-based lattices would yield many advantages: the structure would be lighter; it would be easier to remove entrapped powder; the cell size could be decreased, thereby allowing larger gradients. At the end of powder bed fusion processes, residual powder is always trapped in the final lattice. In the case of implants, if the powder will not be removed, inflammation and blockage of blood vessels may happen. To ensure efficiency of the dense porous structures in terms of bone cells' ingrowth and mechanical properties, an adequate method for the trapped powder removal is still to be found. We assume that in the case if the gyroid sheet-based structures will be produced using Wafer Theme, the size of the unit cell can be decreased while maintaining the ability of effective powder removal from the structure. Moreover, the Wafer Theme can be implemented for manufacturing functionally graded porous structures with optimized pore size. Finally, such structures satisfy the requirements for medical implants to avoid stress-shielding effect.

In conclusion, TPMS WT structures present a few advantages (high strain tolerance in both tension and compression, relatively high quasi-elastic gradient, relatively low surface roughness), and a few caveats (systematic presence of holes at the saddle points of the structure), but prove to be well adapted to mimic human cortical bone. Therefore, such structures certainly merit more attention and further investigations as potential design geometries for load-tolerant lightweight structures used in biomedicine (implants) and technology.
