**3. Results**

#### *3.1. Radiographical Evaluation of the Freeze Foaming Process*

By acquiring two 2D pictures per second (500 ms exposure time) a real-time observation and analysis of the foaming process is possible. Due to the superposition of structural phenomena, the thickness of the sample was reduced to 5 mm for radiographically evaluations. To qualify the changes between the steps, manual tracking is conducted by overlaying each picture with a grid, and following the movement of distinct points in the sample. The resulting coordinates can be converted to changes in actual values for the size or height of the foam, and can be correlated with the pressure at the moment of picture acquisition. This method of evaluation was applied for three different sample temperatures and a pressure reduction rate of 50 and 10 mbar/s, respectively. As an example, the plotted results for 10 mbar/s are shown in Figure 3, as experiments at different pressure reduction rates behave similarly.

**Figure 3.** Percentage growth as a function of pressure for 5, 23, and 40 ◦C, at 10 mbar/s.

Independent of the initial suspension temperature, foaming starts between 450 and 550 mbar. However, the growth, as well as the pressure at which the foaming stops, are highly influenceable by the initial temperature. A lower temperature leads to an inhibited foaming, which results in a lower overall growth. Even though the foaming process itself continues up to lower pressures, the lower foaming rate cannot be compensated. For example, a suspension with a pressure reduction rate of 10 mbar/s and an initial temperature of 5 ◦C stops foaming at 15 mbar, while a 40 ◦C suspension already stops at 35 mbar. Suspensions undergoing 50 mbar/s exhibit a very similar behavior. Looking at foaming rates over pressure, the highest suspension temperature also results in the highest growth rates values at higher pressures (Figure 4).

**Figure 4.** Foaming rate as a function of pressure for different temperatures at 10 mbar/s.

Samples with an initial temperature of 23 ◦C exhibit a lower maximum at lower pressures while 5 ◦C samples showed an almost constant foaming rate and, therefore, no identifiable maximum.

To evaluate and verify the findings from the radiographical evaluation, the results were compared to data obtained from the freeze dryer at IKTS (Table 1) [24]. Apart from 5 ◦C suspensions, their findings support the trend identified at the ILK. For suspensions with an initial temperature of 5 ◦C, the IKTS identified a foaming rate maximum at pressures between 40 and 60 mbar. However, the freeze dryer is equipped with an additional condenser, which is not available in the in situ device. It is not possible, so far, to achieve the foaming rate maximum and finish the pressure-induced foaming process.


**Table 1.** Comparison of the pressures of beginning, end, and maximum of foaming at temperatures of 5, 23, and 40 ◦C by in situ μCTs (ILK) and by freeze dryer (IKTS) [24].

Through analysis of radiographic images, edge effects on the foaming process can be verified. Figure 5 illustrates their impact on a 10 mbar/s sample at 23 ◦C. Both edges, as well as the center, were manually tracked using the method described earlier, and the local growth rates were determined. As expected, the edges exhibit a much slower growth when compared to the center. Possible reasons include wall friction, as well as a drying of the suspension. This behavior is especially observable in suspensions with an initial temperature of 40 ◦C, which also develops a compact layer on top of the suspension.

**Figure 5.** Edge effects on foaming at 23 ◦C (10 mbar/s).

#### *3.2. CT Evaluation of the Freeze Foaming Process*

To examine the developmental stages of foaming, μCT and the improved testing device is used to create a virtual and reconstructed volume (VGStudio 2.0, Volume Graphics GmbH, Heidelberg, Germany) of the foam's structure. During the CT measurements, the sample is rotated 360◦, and after an angle of 0.25◦, one image is taken. Those pictures can be reconstructed with the program "Phoenix datos", which is generating a 3D model. This model can be imported into "VGStudioMax 3.0" (Volume Graphics GmbH). In this program, it is possible to perform various analyses, such as defect analysis or foam structure analysis. A region of interest (ROI) is selected, and a surface determination is performed automatically. A threshold value is determined to be able to separate material from background. The porosity can be determined from this data.

In order to acquire sufficient CT data, given that Freeze Foaming is a fast process, the exposure time is reduced from 500 to 250 ms. In addition, the number of images for the holding steps is reduced from 1440 to 720. The following parameters were selected for the evaluation of the foam structure: Threshold—80%, Accuracy—Fast; Direction of analysis—Right; Analysis mode—Background; Features—Advanced cell properties.

The first step was a complete foaming at two pressure reduction rates (10 mbar/s and 50 mbar/s). The results and their porosities are shown in Figure 6.

**Figure 6.** Cross-sections and porosities of completely foamed suspensions at two pressure reduction rates and three temperatures.

Increasing the pressure reduction rate from 10 to 50 mbar/s results in only a slight increase in porosity (Figure 6, right). However, the orientation of the pores seems to be significantly influenced by the pressure reduction rate. Suspensions foamed at 50 mbar/s exhibit vertically elongated pores, while those foamed at 10 mbar/s are oriented more horizontally. Due to the higher reduction rate inflicted on the process-induced air, the velocity of the inflating bubbles increases, thus forming vertical pores. In both cases, this is especially visible for 23 ◦C samples. Samples with an initial temperature of 40 ◦C show a decrease in porosity during foaming, due to their low viscosity, and the foam collapses before freezing by reaching the triple point.

#### *3.3. Stages of the Foaming Process*

Given the results of radiographic imaging, five holding stages were identified for analyzing the stages of the foaming progress (at 30, 40, 50, 70, and 100 mbar). The pressure reduction rate was adjusted to 10 mbar/s. Cross-sections of those scans are shown in Figure 7 (5 ◦C) and Figure 8 (23 ◦C). For each evaluation, three CT scans were executed to observe pores, and their development—the suspension (1000 mbar), the holding stage at its target pressure, and the final foam structure (5 mbar). Air bubbles that have been introduced into the mold during suspension filling have a large influence on the foam structure. They grow even larger during foaming, and develop significantly larger pores. Due to their high viscosity, this growth is inhibited in 5 ◦C tempered suspensions. Furthermore, the maximum foaming rate takes place at lower pressures (40–60 mbar) [24]. As a large amount of water evaporates, the pressure reduction rate drops, and the time to reach the target pressure of <5 mbar is too long. This process-induced growth inhibition results in a significantly lower porosity. In general, suspensions with an initial temperature of 5 ◦C exhibit a lower porosity after foaming, due to a higher viscosity and a lower amount of escaping water vapor. On the other hand, suspensions with an initial temperature of 40 ◦C exhibit a viscosity too low to be stable during the CT scan and, therefore, were not monitored.

**Figure 7.** Holding stages (I: 100 mbar, II: 70 mbar, III: 50 mbar, IV: 40 mbar, V: 30 mbar) of a 23 ◦C tempered suspension with a pressure reduction rate of 10 mbar/s ((**a**) suspension; (**b**) holding stage; (**c**) foam).

**Figure 8.** Holding stages (I: 100 mbar, II: 70 mbar, III: 50 mbar, IV: 40 mbar, V: 30 mbar) of a 5 ◦C tempered suspension with a pressure reduction rate of 10 mbar/s ((**a**) suspension; (**b**) holding stage; (**c**) foam).

Using the software VGStudioMax, which allows access to volume-based data, the pore size distributions were determined for each holding stage. An exemplary distribution for a 23 ◦C sample is depictured in Figure 9a. The growth starts slowly, accelerates to a maximum, and then slows down again. The lowest variance in pore size distribution can be found at 50 mbar on a 23 ◦C sample, with a relative curve width (b = d90/d10) of 36.2 (b100mbar = 53.1, b70mbar = 36.2, b40mbar = 153.5, b30mbar = 160.9). When the pressure drops below 50 mbar, the pore size distribution becomes flatter and wider, indicating a ripening process. Figure 9b shows the increasing porosity as a function of the decreasing pressure for the three investigated temperatures. Due to their high viscosity, 40 ◦C foamed samples could not be investigated with regard to holding stages and foam formation, because the foam structures collapsed during the investigation.

**Figure 9.** Pore size distribution of a 23 ◦C sample (**a**) and porosity (**b**) at 5, 23, and 40 ◦C samples of different holding stages; pressure reduction rate: 10 mbar/s.

#### *3.4. Mechanical Properties*

Due to the dependence of porosity and pore size distribution of Freeze Foamed samples on process parameters, mechanical properties should vary as well. To evaluate their behavior under load, cylindrical sintered samples were manufactured and subjected to standardized compression tests. Recorded tension–compression curves are depicted in Figure 10.

**Figure 10.** Compression tests on sintered samples (40 ◦C suspension; 5 ◦C suspension; devolatilized 23 ◦C suspension; 23 ◦C suspension).

The fracture behavior clearly exhibits a dependency on suspension temperature (5, 23, and 40 ◦C) and pretreatment (devolatilized and not devolatilized suspensions during the manufacturing process). Samples with a narrow pore size distribution [24] (5 ◦C and 23 ◦C devolatilized [23]) possess a pronounced maximum of force. On the other hand, specimens with a less uniform distribution of pores [24] (40 ◦C and 23 ◦C not devolatilized) show a more constant force level, and only reach about half the maximum force when compared to more homogeneous samples. Mechanical properties of the samples manufactured using Freeze Foaming are strongly influenced by microporosities inside the struts [23]. However, as the resolution of the CT scans were insufficient to examine their structure, they could not be taken into account here.

Furthermore, in situ compression tests, at selected load levels, were conducted to examine failure phenomenology (Figures 11–13).

**Figure 11.** Recorded force–travel curves of compression tests conducted on an in situ μCT; 5 ◦C.

**Figure 12.** Recorded force-travel curves of compression tests conducted on an in situ μCT; 23 ◦C not devolatilized.

**Figure 13.** Recorded force-travel curves of compression tests conducted on an in situ μCT; 40 ◦C.

For more inhomogeneous samples, material failure starts to occur between 25 N (40 ◦C) and 50 N (23 ◦C) (Figures 12 and 13). The density of fractures constantly rises, with increasing deformation, until a partial structure failure develops at relatively low load levels of 50 N (40 ◦C) and 110 N (23 ◦C not devolatilized). On the other hand, more homogeneous foam structures show a maximum load up to 200 N, even after the first signs of material failure (Figure 11). Detailed examinations show that especially cracks on the surface lead to material failure. This is a sign of an uneven sample surface, and results in a non-uniform load.
