The image analysis method prompts a few comments, suggesting that caution is required before attributing an intrinsic characteristic to a sample on the basis of this technique. Determining the porosity rate of a sample by image analysis is based on the assumption that what we observe on a 2D image is representative of the sample as a whole. Great care must therefore be taken with the sampling. This is essential in order to validate and generalize the results obtained to all of the part being analyzed.

Sections of AlSi7Mg0.6 samples produced by SLM display a random distribution of “small-sized” porosities (diameter ≤ 10 µm), while larger diameter porosities are distributed preferentially according to the laser strategy. As a result, the choice of cutting direction, the area selected, the preparation of the sample, and the area considered for carrying out the count are all parameters that can affect the results obtained.

When measuring the relative density of our samples, we encountered a number of difficulties, mainly regarding the choice of magnification and the way in which the metallographic section of the test sample was produced.

#### 3.1.1. Influence of Magnification

The choice of magnification for image acquisition is important on several levels. First, magnification determines the number of pixels in the image; the smaller the magnification, the smaller the number of pixels that make up the same surface area, as shown in the diagram in

Figure 4. If magnification X40 produces a surface area S made up of a single image, for magnification X160, this will require 16 distinct images. The size of the pixel is very much reduced, thus making it possible to discern the smallest sized porosities, which could not be distinguished with a smaller magnification. In addition, the larger the magnification, the longer the acquisition and processing time for a surface area. Thus, the right compromise has to be reached to provide the desired accuracy in an acceptable time.

To validate the procedure used here, we wanted to examine the influence of magnification on the levels of relative density obtained. To do this, images of the same polished surface of a section of the sample were analyzed at three different magnifications (X40, X80 and X200).

Table 3 summarizes these results.

We observed that, in all three cases, the relative densities obtained were of the same order of magnitude, but tended to decrease as the magnification increased, which could be because the smaller porosities were being taken into account. However, it is important to note here that, in the case of the largest magnification, when scanning the same surface, an image reconstruction was necessary. This step was an additional potential source of error. Given the very small differences found in the same measurement of density, it is sensitive to conclude that magnification may have a significant influence. In this case, therefore, it does not seem necessary to use large magnifications. In the rest of the study, a magnification of X40 will be used.

#### 3.1.2. Representativeness of the Surface Observed

Figure 5 shows microscopic sections taken in both directions (longitudinal and transverse) in relation to the build axis. We can see in the transverse direction relative to the build axis that there are areas where large porosities are concentrated, linked directly with the laser mode used. The choice of surfaces analyzed on this section may therefore have an influence on the estimate for the porosity rate of the section as a whole.

In this case, it is important to check whether measurement variabilities exist according to the zone studied. For example, if measurements are taken only in the area within the dotted lines in the cross-section normal to the building direction in

Figure 5, with magnification X40, the average relative density from all the measurements from the selected zones is 98.52%. However, if the entire surface area is calculated at the same magnification, this gives a relative density of 98.33%. It should be noted here that analysis of the entire surface area would mean defining several partially overlapping zones, which would lead to further approximation.

In the case of the cross section parallel to the building direction, the distribution of the large porosities appears to be more homogeneous. Tests carried out on this section, which were similar to those for the cross section normal to the building direction, therefore showed a less pronounced variation: relative density varied from 98.60% for a calculation limited to the five zones defined in

Figure 5 to 98.67% for measurements across the entire surface area.

In summary, as a result of this series of tests, it is difficult to conclude that the total surface area must be studied in order to estimate the porosity rate for a section. There is therefore a tendency to conclude that the choice of surface area has little influence on the result, provided that the surfaces chosen for observation are uniformly distributed across the entire surface area of the section.

However, determining the relative density of a sample on the basis of calculating the porosity rate by image analysis of a polished section assumes that the 2D image is representative of the volume of the sample. In addition to the direction of the section, it is necessary to check whether the density results are dependent on the positioning of the section studied. To do this, a series of analyses were carried out along build axis z in 0.5 mm steps obtained by successive polishing of the section along a length of 3 mm. The average relative density obtained from 3 images using the procedure previously described varied from 99.3 to 99.7% (

Figure 6), which shows that the position of the section seems to be an influencing factor on the resulting relative density in agreement with the results of De Terris and all [

10].

In order to analyze the differences observed, we considered the geometry of the porosities from tomographic observations with a low resolution of 2.4 μm.

Figure 7 shows a 3D reconstruction of an observed parametric porosity. Clearly, the porosity is not spherical, and its walls are concave (on the right) and convex (on the left). It is therefore obvious that the orientation of the porosity with respect to the observed metallographic section will have an impact on the calculation of the area ratio.

It is clear that the ratio of the area extracted from the porosity to the total area of the image varies according to the section under consideration.

The non-spherical shape of the porosity therefore means that the results of an image analysis are dependent on the orientation of the porosity in relation to the section under consideration. This study is also able to focus on one of the limitations associated with analyzing metallographic sections of porosities: it is difficult to apply this method to determine density.

Finally, we conclude that the analysis of metallographic images can produce information on porosity location, distribution and geometry. In addition, the observation of a section can also make it possible to detect the presence of powder that is not completely melted [

10]. On the other side, tomographic analysis has the added advantage of providing a volume representation of the location and geometry of the porosities, but it has the disadvantage of being more complicated to implement and more costly.

However, with an analysis of metallographic images, calculating the relative density of the part depends on the areas chosen for analysis. This therefore limits the scope of this method for defining parts in terms of material health. As a result, to obtain volume and global information on SLM-produced parts, we used the Archimedes method.