## 3 Results and Discussion
### Geometric Distortions and Warpage  
Concerning the main tests of this research, both horizontally and vertically built specimens displayed a visible amount of shrinkage. Generally, the shrinking was more pronounced in dimensions that were aligned with the vertical direction of the build, meaning a significant impact on the thickness of horizontally printed specimens and the length of vertically printed specimens. Shrinkages up to 22.93% and 16.62% were verified in thickness and length, respectively. In addition, horizontally built specimens presented a defined warpage tendency, with specimens that were closer to the top/open surface of the crucible displaying higher warping values. The bottom specimens shrank but displayed little warping. One explanation for this could be the fact that each specimen was subject to a different weight load on top of it. Another effect was that during shrinking, the support sand above a specimen flowed downwards, and the glass microspheres in the surroundings were affected by this flow of powders. This effect was accumulated in some areas of thecrucible, and the displacement of the center glass powders became larger as the number of specimens below the specimen under consideration increased, promoting warping. This influence of build orientation on warping can be observed in Figure 6A,B, which show batches 8h and 8v. The influence of the sand percentage in the reduction of warping is also clear in Figure 6C. Regarding the holding time (\(\Delta_{hold}\)) analysis in [35], in Figure 7A, in the horizontal specimens, the shrinkage variations were not very significative, being the maximum mean shrinkage value obtained in the thickness (15.7%), for a \(\Delta_{hold}\) of 8 h. In vertically printed specimens (Figure 7B), a \(\Delta_{hold}\) of 1 h resulted in the shorter specimens, while the longer specimens were obtained for a \(\Delta_{hold}\) of 8 h. Considerable variations on the average shrinkage were detected for the width (4%) and thickness (7.61%), possibly due to problems inherent to the printing process. The most notable shrinkages happened, as expected, in the vertical directions, i.e., along the thickness of horizontally built specimens and along the length of vertically built specimens. Figure 6: Representative example batches of specimens and their relative positions inside the crucible. (**A**) Horizontal specimens. (**B**) Vertical specimens. (**C**) Horizontal specimens with 60% sand in weight. Figure 7: Average geometric distortion (shrinkage) of specimens under variable sintering hold time (\(\Delta_{hold}\)). (**A**) Horizontally built specimens. (**B**) Vertically built specimens. Absolute values of each measure are in mm, and relative variation from CAD model is a percentage. Negative values indicate an increase in size. Concerning the influence of sand percentage (%\({}_{sand}\)) on horizontal specimens' geometrical distortions, the shrinkage was indeed reduced to nearly zero, as intended, in specimens with sand percentages over 40% (Figure 8). It can also be seen that the standard deviations that were very pronounced in some cases were minimized, possibly because the glass microspheres were now limited by the sand particles and could not flow. The same happened in the vertical specimens, as the specimens with 60% sand even expanded (length shrinkage of \(-\)0.77%), which was possible considering that the apparent density of the glass microspheres was superior to the apparent density of the sand used as support powder. Even though they were printed horizontally, the specimens of batch 60%h, printed with 60% sand mixed in the build powder, did not warp. When measuring dimensions along the length of each vertically printed specimen, the width and thickness decreased, from the base of the crucible/specimen to the top. Naturally, the sand percentage had an impact on the mass, volume, and density. As the sand percentage increased, the glass microspheres were stopped from shrinking and flowing.