Enhancing Computed Tomography-Based Pore Mesh Models Through Matching with Microscope Cross-Section Images

Three samples of additive manufactured AlSi10Mg were produced on a Trumpf TruPrint1000 (TRUMPF, Ditzingen, Germany). The samples are of cuboid shape with a conic end to ease separation from the build platform, with a length and width of \(10\, \textrm{mm}\) and a height in build direction of \(15\, \textrm{mm}\). The two most common types of internal defects in AM, gas porosity and Lack-of-Fusion defects, were induced into the material by altering the energy density during production. Two parameter sets were changed to induce specific types of porosity into the material, while the third sample was produced with standard parameters to compare the induced porosities to common production porosities. The adjusted parameters of the parameter sets are shown in Table 1. The altered parameters increase the occurrence of specific defects, but are not excluding the occurrence of other defects, e.g. the parameter set ’LoF’ produces mostly Lack-of-Fusion defects, but gas porosity can still occur within the material and can subsequently be detected via CT scanning. Other types of internal defects can be forced within an AM process, but the two selected defect types are the most common [1]. The hatching pattern angle was not changed after each layer, which produces pores in distinct columns parallel to the building direction (see Fig. 2). These columns help in matching the porosity detected by both data sources. After manufacturing, all three specimen were CT scanned on a V|Tome|x M (Waygate Technologies, Hürth, Germany). The samples were scanned at a resolution of 10 \(\upmu \)m. The resulting 2D image stacks (between 1933 and 1994 images) were binarized via Otsu’s thresholding method [17] and reconstructed into 3D models using the Marching-Cubes algorithm [18, 19].

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After the non-destructive data acquisition the samples were embedded in resin in a CitoPress (Struers, Copenhagen, Denmark), then ground and polished on a Tegramin 30 (Struers, Copenhagen, Denmark) to achieve surfaces suitable for imaging. The abrasive metallographic preparation process is detailed in Table 2.

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High-resolution images were captured using a VHX 5000 (Keyence, Osaka, Japan) optical microscope. Figure 2 shows the images of the cut sections of the samples with different processing parameters. The different level of porosity can be clearly seen, also notable are the different pore sizes comparing the “GP" parameters and the “LoF" parameters (see Fig. 2b and c). The microscopic image was thresholded using Otsu’s method [17] to differentiate the pores from the surrounding material. Subsequently, the pores were labeled using the Python library scikit-image [19], allowing for individual pore identification. Some shape distortion might arise during sectioning and polishing. The measured pore size from metallography might not perfectly represent the original pore.

The metallographic image was imported into the 3D CT data to identify the corresponding slicing plane within the 3D reconstruction. The 3D model was sectioned along this slicing plane, and the resulting cut surface was exported for further analysis. A Nearest Neighbor search [20] was performed to match pores between the metallographic images and the CT cut surfaces, with a threshold set for maximum distance to prevent false matches. The threshold was set to eight pixels, corresponding to a circle with a radius of 38 \(\upmu \)m centered on each CT pore’s centroid. This threshold allows a matching of most of the pores detected via CT (see Table 3), while excluding spurious defects introduced by metallographic sample preparation. A match between CT and MS pores was declared if the centroid of a CT pore coincided with an MS pore either at the same location or within the specified eight-pixel radius. Figure 3 shows the results of the matching process between both surface datasets. Figure 3b shows a section of the surface, indicating the good match between pores for pores larger than 30 \(\upmu \)m. The centroids of both datasets don’t match perfectly, due to a constant offset. This offset does not influence the results of the area comparison, since it is below \(8\,\)pixels. The contour matches were further processed to calculate and compare their respective cut surface area.

Differences between the two data sources for the matched pores were analysed, focusing on discrepancies in the calculated cut section area. Systematic deviations in pore area measurements between CT-derived pores and metallographic data were identified as shown in Fig. 4.

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For all parameter sets, on average the pore area detected by CT is lower than for the same pores detected by metallography. To estimate the global difference, a linear regression was conducted using pores with less than a \(20\,\%\) area deviation between the two data sources. The area deviation constraint ensures that the regression is not influenced by outliers. Only a subsection of pores is used for the calculation of the correction factors, mainly due to the large scatter in cut section areas measured from both data sources. The coloured areas in Fig. 4 show the complete pore dataset for all three parameter sets, while the pores used for the regression are displayed as coloured markers. The linear regression shows an underestimation of the pore area by the CT data source for all parameter sets.

To quantify the deviation, a global areal correction factor \(k_A\), based on the linear regression was used for each parameter set. The area-based correction factor was then converted into a volume-based factor \(k_V\), based on the assumption that the pores are spherical or approximately spherical. For pores from the parameter sets “Std" and “GP", the roundness \(R = P^2/(4\pi A)\) with the pore perimeter P and the pore area A is equal or less than 1.2 for more than \(93\,\%\) of the pores. This is only true for \(44\,\%\) of the pores from the parameter set “LoF". The assumption of circularity and subsequent sphericity seems only valid for the parameter sets “Opt" and “GP".

Further processing is also done on the parameter set “LoF", to see the effect of the rescaling and smoothing workflow on pore shapes that deviate from spheres. This might influence the accuracy of the global correction factor. The values for the areal and volumetric correction factors, as well as the percentage of datapoints used for the linear regression are shown in Table 3.

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To reduce the systematic deviation in pore areas between both data sources, the CT data is modified. This is done by isolating each pore mesh, and then uniformly rescaling the meshes around their respective barycenters. This rescaling increases the pore volume to the target volume \(V_{\textrm{Target}} = V_{\textrm{CT}}/k_V\). The CT pore volume is now equal to the hypothetical metallographic pore volume, which is calculated based on the pore area at the cut section with the assumption of sphericity. The pore shape however is still different due to the Marching-Cubes reconstruction of the CT data, which creates stepwise features in the pores. To reduce this stepping effect, a subdivision algorithm [21] and a smoothing algorithm [22] is used. The subdivision algorithm changes the pore shape and in turn the pore volume. A second rescaling of the mesh is therefore necessary. The rescaling factor for the second rescaling is unknown, it changes based on the pore volume. Small pores close to the resolution limit consist of fewer mesh vertices and faces, resulting in a high curvature change. The subdivision algorithm reduces the curvature changes by repositioning and adding mesh vertices. The vertex repositioning is more pronounced for pores with fewer vertices, therefore the effect on the volume change is stronger at smaller pores. An iterative algorithm is used to optimize the second rescaling factor so that the volume stays equal to the target volume. The necessity of the adaptive second rescaling factor is shown in Fig. 5. Without this second factor, the target volume change is not achieved. The effect of the subdivision algorithm on smaller pores (\(V \le 100\) \(\upmu \)m\(^3\)) is clearly visible. The “LoF" parameter set also shows an increased scatter in the deviation to the target volume compared to the other two parameter sets. The scatter could be caused by the more complex shape of Lack-of-Fusion defects, which are often non-spherical and elongated. Images of two different pores from the datasets “GP" and “LoF" are shown in Fig. 8.

After the subdivision step, the smoothing algorithm [22] is applied. Since the smoothing algorithm used is volume conserving, the volume stays constant. The smoothing algorithm reduces the curvature, creating a more organic pore shape, reducing the artefacts from the Marching-Cubes reconstruction. The parameters used for subdivision and smoothing are shown in Table 4. The subdivision and smoothing workflow is based on the article from Taubin [22], and the parameters used are explained thoroughly there.

A total number of 1174 pores were matched between both data sources in the three parameter sets. All parameter sets show a mean reduction in the area difference between both data sources, as shown in Fig. 6. The workflow and regression was applied for all matched pores, which is why the original average area deviation is larger in Fig. 6 than in Fig. 4, where only a subset of the pores is used for the regression. The size of the datasets is shown in Table 3. For the “LoF" parameter set, the area increase for pores with a cut section smaller than 5000 \(\upmu \)m\(^2\) is larger than intended. The CT cut section area \(A_{\textrm{CT}}\) is larger than the metallographic cut section area \(A_{\textrm{MS}}\). This is also true for the other two parameter sets, but only for a smaller cut section area of 2000 \(\upmu \)m\(^2\) for parameter set “GP" and 500 \(\upmu \)m\(^2\) for parameter set “Opt".

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This might be caused by increasing uncertainty for pores with a small size, i. e. a low voxel count. As discussed in the introduction, CT uncertainty increases for objects close to the resolution limit [11, 13]. For pores with a cut section larger than 5000 \(\upmu \)m\(^2\), the rescaling workflow successfully increased the cut section area to the intended size, closer to the measured area in the metallography. For all parameter sets, the absolute difference between both data sources increases with an increasing cut section area. This indicates, that the area deviation could be further reduced by using a correction factor that changes with the detected cut section area, and considering the parameter set “LoF" also includes the sphericity measure as a factor.

While the sphericity could be included in further datasets, a correction factor based on the size of the cut section area needs to be extracted from metallographic preparation, which is unfeasible for industrial applications, because of the destructive measure. A correlation between the cut section area and the pore volume might be useful to bypass this step.

The effect of mesh smoothing on the pore is investigated by considering the curvature. To compare the result of the pore smoothing workflow to the initial mesh one needs to account for the mesh vertices increase by the subdivision algorithm. This is done by sorting each mesh point by curvature and a subsequent normalization of the x-axis to compare multiple pore meshes. Figure 7 shows that for all three parameter sets, the mean curvature of the smoothed meshes are lower than the mean curvature of the original meshes. To illustrate this change, Fig. 8 shows selected pores from the parameter sets “GP" and “LoF". The smoothing removes most of the stepwise features from the Marching-Cubes reconstruction, while keeping the overall shape of the pore. The red line indicates the cut-section line used for the area comparison with the metallographic image. Pores Figs. 8a and c are unsmoothed pores from the CT data, Figs. 8b and d are the pores after the rescaling and smoothing workflow. Pore Fig. 8a is extracted from the parameter set “GP" and represents a smaller pore, with a volume of \(V_\textrm{a} = 4.75 \times 10^{-5}\, \textrm{mm}^3\) which increased \(29\%\) to \(V_\textrm{b} = 6.07 \times 10^{-5} \, \textrm{mm}^3\) due to rescaling and smoothing. The cut section area increased by \(19\%\). Pore Fig. 8c represents a larger pore, extracted from the parameter set “LoF", with a pore volume \(V_\textrm{c} = 6.51 \times 10^{-4}\, \textrm{mm}^3\), increased by \(24\%\) to \(V_\textrm{d} = 8.08 \times 10^{-4}\, \textrm{mm}^3\). The cut section area also increased by \(19\%\).