**3. Results**

### *3.1. Scanning Electron Microscopy*

The gyroid structures present both partially melted powder particles on the surfaces (Figure 2a,b) and the stair effect (Figure 2c,d), typically observed in AM parts (due to the layer-wise manufacturing) [36–48]. While the minimum electron beam spot size of EBM machine is about 200 μm, the melt pool is commonly wider, and the smallest possible sheet thickness that can be resolved in EBM is about 200 μm [28]. The wall thickness of the WT specimens was smaller than that of MT, as can be observed in Figure 2a,b.

WT structures have quite small sheet thickness, as the beam energy used to manufacture them is rather low. The production of such thin structures is at the limits of the machine capabilities, since the powder particle size is between 75 and 125 μm. Consequently, some holes were present in the sheets (Figure 2b,d). Thicker sheets of the MT structures have visibly higher roughness but no through-holes. WT samples have the holes predominantly in the areas where the surface is parallel to the build plane. This is well-known in PBF techniques, where such problems occur in overhanging elements and thin structures normal to the build direction [48].

**Figure 2.** SEM images of (**<sup>a</sup>**,**<sup>c</sup>**)—MT specimen; (**b**,**d**)—WT specimen.

### *3.2. X-ray Computed Tomography*

XCT was used to describe inner structure, evaluate wall thickness, and reveal the difference between the designed structure and the manufactured specimen. The wall thickness of WT and MT EBM structures evaluated from XCT reconstructions is presented in Table 2. The wall thickness distribution in the two specimens is presented in Figure 3a. Note that for both specimens, the targeted wall thickness was 0.2 mm. The actual mean wall thickness was about 0.4 mm and 0.25 mm for MT specimen (bulk-melt mode with contours) and WT specimen (Wafer-mode), respectively. It is clear that for thin-walled structures, the contour-enabled bulk melt mode is not optimal and leads to a larger than desired wall thickness.

**Table 2.** Summary of the results of the quantitative image analysis of XCT data. (Measurement errors cannot be estimated; the error intervals represent the variance of all the measured values).


The reason for the difference between thicknesses of the designed and MT manufactured structures lies in additional thickness caused by two contours and, probably, wider than expected melt pool. Since the surface of the gyroid is curved, it is impossible to evaluate roughness by traditional methods. It is known that arithmetic roughness (Ra) for vertical struts of the EBM-manufactured structures is about 40 μm, while the mean value of the maximum height of the surface profiles of vertical struts (Rt) is 212 μm [28]. Comparison of a designed 3D model and as-manufactured samples performed with the standard

VGStudio function named 'Nominal/Actual Comparison' characterizes the manufacturing accuracy and supplements the wall thickness analysis, Figure 3b. Nominal/Actual Comparison is also an alternative way to describe roughness of the manufactured specimens in qualitative terms. The value of average surface roughness is comparable with the sheet thickness that is quite typical for EBM-manufactured porous structures [49].

**Figure 3.** Evaluation of the parameters based on the XCT data analysis: (**a**) Wall thickness distribution; (**b**) Deviation distribution obtained from Nominal/Actual Comparison analysis.

It makes no sense comparing zero-thickness model used for designing WT samples and 0.25 mm thick reconstruction. Therefore, a model with the desired thickness was used for the Nominal/Actual Comparison. The average wall thickness of the MT specimen based on the 0.2 mm model was about 0.4 mm. A comparison with initial model and, additionally, with 0.4 mm thick model was performed to evaluate surface roughness more precisely.

The deviation of the structure was estimated from both sides of the walls. The searching distance was 0.3 mm, which is quite large in comparison with the average wall thickness. The positive deviation is caused by the presence of contours in MT samples, melt pool 'swelling' into the surrounding powder bed, and the presence of powder particles partially merged with the surface. There are sharp peaks of the relative frequency at the negative deviations followed by rapid drops (indicated by arrows). They may be attributed to the surface elements detected from the opposite side of the wall, and this will be typical for porous lattices with any unit cell design.

Figure 4 illustrates the Nominal/Actual analysis of the samples. White arrows in Figure 4a indicate stalactite-like structures on the horizontally oriented parts of the MT walls (areas parallel to the layers, purple color). This effect is quite common in the PBFmanufactured specimens [50]. Interestingly, it is much less pronounced for the WT specimens due to the smaller beam energy used. In the MT samples, clusters of the partially fused powder particles are also present. The white circles highlight the partially melted powder particles attached to the surface of the vertical areas. This effect was not found for WT specimens, presumably because of the smaller electron beam energy input, Figure 4b. The purple area on the lower part of WT specimen indicates larger dimensional deviation in the first layers. This is a known effect due to the incompletely stabilized temperatures in the semi-sintered powder surrounding the melt pool at the early stages of the build, and uneven compensation of the expansion of powder placed under the start plate. Uneven compensation of the powder expansion leads to the situation when during some of the first layers, EBM rake brings no powder for some parts of the working area. Moreover, sample material starts to be deposited only after a few nominal layers leading to the distortions of

the samples that are due to start from the base plate. Additionally, the material adjacent to the start plate can be distorted and have some different microstructure due to diffusion of metal ions from base plate [28].

**Figure 4.** 3D rendering of the CT reconstructions for the Nominal/Actual Comparison of the MT gyroid (**a**) and WT gyroid (**b**). Visualization of the wall thickness for the MT gyroid (**c**) and WT gyroid (**d**). White arrows indicate stalactite-like structures on the horizontally oriented parts of the MT walls (areas parallel to the layers, purple color). The white circles highlight the partially melted powder particles attached to the surface of the vertical areas.

The through-holes are present nearly in each surface of WT samples parallel to base plate, Figure 5. The shapes of the pores are irregular; in some cases, holes are interconnected, Figure 5a,c. Red arrows in Figure 5b indicate the holes visible in the vertical cross-section of the sample. Careful investigation of the wall surfaces shows the tendency of the up-facing walls, Figure 5c, to have lower roughness than the down-facing ones, Figure 5a.

### *3.3. Mechanical Properties*

### 3.3.1. Compression Tests

Stress and energy absorption vs. strain curves for the compression samples are presented in Figure 6. Characteristics of such curves for the WT samples show a larger scatter than those for the MT ones. Most probably this can be explained by the statistical variation of the shape of the hole-type defects in the WT structures (Figure 2a,b), but the intrinsic variation of the wall thickness also contributes to the scatter. The compressive strength, for

instance, can vary by over 30% among samples. The first maximum compressive strength of the WT samples is about twice lower than that of MT samples.

**Figure 5.** 3D rendering of CT-reconstruction of WT gyroid vertical (**<sup>a</sup>**,**<sup>c</sup>**) and horizontal (**b**) views (**a**—bottom view; **c**—top view; **b**—side view).

Conventional cellular structures with uniform density exhibit three deformation regimes during compressive testing [46]: a linear elastic compression, a plateau with approximately constant stress, and a final densification with steeply increasing stress. Sheet-based TPMS structures except gyroid ones are reported to have fluctuations of the curve in the plateau regime [4,6]. The mechanical behavior of our specimens does not fully follow this description. For MT specimens, a single drop and recovery in the strength in the plateau region can be observed, Figure 6a,b. The stress-strain curve of the WT shows a drop in the strength of the structure right after the peak strength is reached. This may be a result of sudden fracture of the wall element in one layer. The following fluctuations in the plateau region can be observed. According to Al-Ketan et al. [6], the fluctuations in strength can take place due to collapse or fracturing events of cell layers, while the recovery is due to local densification of the collapsed layer where the load is transmitted directly to the next layer of cells. The values of the plateau stress were calculated based on the ISO 13314 [34] (see Section 2.5). The plateau stress of WT gyroid is about 15 MPa, whereas it is about 49 MPa for MT gyroids.

**Figure 6.** Compressive stress-strain curves for the gyroid samples manufactured in (**a**) MT; (**b**) WT. (Note the different y-axis scales). Energy absorption per unit volume versus strain curves for lattice samples of (**c**) MT; (**d**) WT. (Note the different y-axis scales).

Figure 7 presents photographs of the WT and MT structures at different deformation stages, corresponding to 6%, 18%, 24%, 36%, and 50% of the overall strain. Both WT and MT samples mainly display layer-by-layer deformation behavior. Plastic deformation is also visible in both sample types. Such deformation is more evident in the vicinity of the collapsing layers.

After the first maximum of compressive strength, a deep fall of the stress can be observed (Figure 6a,b). For the MT structure, this fall starts around 15% strain and corresponds to the collapse of the first layer (Figure 7b). The WT structures display several stress maxima and minima because the individual cell walls come into contact with each other after collapsing of a layer. In this case, the first minimum around 7–15% strain corresponds to the collapse of the first layer (Figure 7a). At larger strains, the stress grows again; this region is described by some authors as strain-hardening [46]. The structure becomes stronger because of the densification of the crushed layer. While losing its dimensions, the specimens recover a part of the initial crushing strength before reaching 50% strain [5].

**Figure 7.** Steps of mechanical deformation during compression: (**a**) WT; (**b**) MT. Red arrows indicate places where the structure lost integrity during compression. The encircled layers keep integrity even at the 50% strain.

It is worth mentioning that WT specimens reach first maximum compression stress at 5% of strain, whereas MT specimens reach it at 10%. The yield strain, the compressive offset stress, and the first maximum compressive strength of the MT specimen are twice as large as that for WT specimen. Specific energy absorption at 30% strain for MT porous structure is 1.5 times higher than that for WT structure, see Figure 6c,d and Table 3. However, specific energy absorption at 50% strain for the two structures is quite similar.


**Table 3.** Mechanical properties of the specimens.

### 3.3.2. Tensile Tests

Figure 8 shows the tensile stress-strain curves for MT and WT specimens. The tensile behavior of the samples manufactured using different Themes are similar. Ultimate tension stress (UTS) of the MT specimens is three times higher than that for WT specimens; however, their quasi-elastic gradients for both themes are equal to 1.2 GPa. The tensile failure strain of this type of specimen is about 10%.

**Figure 8.** Tension stress-strain curves: (**a**) MT; (**b**) WT.

### *3.4. Finite Element Analysis*

To analyze the elastic deformation process and the stress distribution during tensile tests, FE simulations were employed. The simulated stress distributions in the elastic region of a tensile test of both MT and WT models are displayed in Figure 9. The simulated stress distributions during a compression test (elastic range) were similar to tensile ones and are not presented here. In this research, a fine mesh has been used and the dependency of the results to the mesh size has been checked.

Interestingly, during elastic deformation of the structure, only the vertical elements of the gyroid wall are affected by mechanical deformation. These elements together have spiral shapes due to the specific design of the gyroid. They are stress-sensitive and reminiscent of elastic springs. This phenomenon matches the description of inclination angles influencing the manufacturability of TPMS described by Yang et al. [38]. As reported, the most frequent surface orientation within the experimental gyroid structure had an inclination angle of 55◦ to the build plane, while the least frequent possess around 0◦ inclination angle. The yielding process of the metal initiates in the vertical areas located parallel to the load direction and more actively continues in the diagonally (55◦) oriented parts. The yielding process finally reaches horizontally aligned saddle points. Therefore, the holes appeared in these areas because of tessellation discrepancy influence on the mechanical behavior only after the whole specimen reaches the yield strain, and they do not affect the quasi-elastic gradient.

**Figure 9.** Simulations of the stress distribution during uniaxial tension (elastic region) of the gyroids with different thicknesses.
