3.1. Quasi-Static Uniaxial Compression Results
A major problem that occurred while producing samples was to achieve an acceptable stage of foaming. From
Figure 5, it is evident that the precursors at the bottom of the sample are not fully foamed; they still have the bar shape. Precursor bars have not been joined at the outer alumina skin, which was still not broken. It was nonhomogeneous foaming with the low-temperature at one part of the mold, which is not acceptable. Samples H2 and H3 had the same problem during the production as sample H1. Samples H4 and H5 had the outer skin without irregularities and cracks,
Figure 6.
Table 1 shows the values of mass and volume of the reinforcements themselves, the total mass of reinforced samples, the volume of the aluminum foams, densities and relative densities of the aluminum foams. Volume of the reinforcements,
Vr (cm
3), was determined by the equation:
where
mr (g)—mass of the reinforcement and
ρs (7.85 g/cm
3)—density of the steel. Volume of the aluminum foam,
Vf (cm
3), was determined by the equation:
where
Vm (567.4503 cm
3)—volume of the mold. The equation used for determining the density of the aluminum foam,
ρf (g/cm
3), was:
where
mp (430 g)—mass of the precursor. The relative density,
ρr, was determined by the equation:
where
ρAl (2.7 g/cm
3)—density of the aluminum.
There are small differences in the relative densities of the samples, which means that the values of absorbed energy can be compared with each other for all samples (with the exception of samples H4 and H5), regardless of whether they are reinforced or not, and regardless of the type of the reinforcement applied.
Figure 7,
Figure 8,
Figure 9 and
Figure 10 show stress–strain curves for all types of used reinforcements and non-reinforced foams, with a plotted point on each curve according to which the absorbed energy is determined. The compression behavior of aluminum foams reinforced with steel wire elements is shown in
Figure 7. There were initial problems while producing these samples where the foaming process was not successful (samples H1, H2 and H3). Samples H4 and H5 stood out in particular. They have absorbed less energy than the first three samples, but their curves are closer to the ones of the “ideal” absorbers—they have a long flat stress–strain plateau, which is explained with lower densities of these samples. Generally, curves are similar but not overlapping.
Figure 8 shows stress–strain curves of aluminum foams reinforced with cylindrical wire mesh. O3 sample had an almost “ideal” force—deformation curve. The curves of O1 and O2 samples are overlapping, and they absorbed almost the same amount of energy. Stress–strain curves of aluminum foams reinforced with steel meshes are shown in
Figure 9. Surprisingly, curves are almost completely overlapping, which is important for the replicability of aluminum foam behavior. Stress–strain curves for non-reinforced aluminum foams are shown in
Figure 10. While curves do not look “ideal”, they are still overlapping in the linear plasticity region.
Figure 11 shows the compression behavior for all 14 samples. The majority of the curves look similar under low deformation. As the deformations increase, the difference becomes more prominent. The initial load causes elastic deformation, but the starting line in most cases is not straight and has a lower slope than the one corresponding to the actual Young’s modulus of aluminum because some cells begin to locally yield even at very low loads. According to Gibson–Ashby model [
5], bending takes place in the quasi-linear stage. When the stress reaches the compression limit, the cell collapse occurs, which initiates the densification of the foam until the final deformation of the densification. In the horizontal curves in
Figure 7,
Figure 8 and
Figure 11, the cell walls are gradually deformed, while in the case of inhomogeneous distribution of deformations, there is local densifying, i.e., inhomogeneous density distribution along the sample, which requires an increase in load for further compression and the horizontality of the curve is lost.
Table 2 shows obtained results plateau stress (
Rplt), plateau stress at the end of the plateau (
R130), strain at the end of the plateau (
Aplt-E), specific energy absorption (
Ev) and specific energy absorption efficiency (
Eeff) of each sample. Specific energy absorption and its efficiency are two properties of aluminum foams that are codependent and important for the production of aluminum foams. Absorbed energy can be high, but with the low-efficiency of the foam, which is not preferable.
The mean value of specific energy absorption for the H series samples was 4.01 MJ/m3 (without samples H1, H2, and H3, which were not taken into consideration due to the nonhomogeneous structure and poor foaming process), which is significantly lower (55.31%) compared to non-reinforced aluminum foams. The efficiency of the H4 sample is 71.58% and of the H5 sample is 73.14%, which is still high, considering the problems with the production of the H series of samples. It is interesting to notice that the H4 sample had an almost “ideal” stress–strain curve, alongside with O3 sample. The reason for this is the fact that the H4 and H5 samples have a slightly lower density and begin to compress at lower stresses, which ultimately results in a reduced possibility of energy absorption.
Cylindrical steel mesh reinforcement contributed the most to the specific energy absorption and its efficiency. O series of samples, observing the mean value for energy absorption (10.53 MJ/m3), absorbed 45.24% more energy than non-reinforced aluminum foams. O2 sample stood out, it individually absorbed the highest amount of energy (12.73 MJ/m3), but the O3 sample had the highest efficiency (71.43%).
Flat steel mesh reinforcement also contributed to the specific energy absorption, compared to the non-reinforced aluminum foams, but not as significantly as the O type of reinforcement (cylindrical steel mesh). Samples from the III series, observing the mean value for energy absorption (9.25 MJ/m3) and absorbed 27.58% more energy than non-reinforced aluminum foams. Generally, their individual values for energy absorption and efficiency were similar, although the sample III3 stood out with the lowest energy absorption in that series of samples (8.22 MJ/m3), which indicated good properties replicability of that series of aluminum composites. Aplt-E of the III series of samples is also approximately close. O and III series of samples absorbed more energy compared to non-reinforced aluminum foams. Adding the reinforcements (except steel wire element) contributed to the higher amounts of specific energy absorption and its efficiency.
3.2. Statistical Analysis and Evaluation
The chi-squared goodness-of-fit test was used, as mentioned in Part 2.3, to evaluate the alternative hypothesis and to compare the expected and observed values to determine how well the predictions fit the data. This statistical tool gives information on how different kinds of reinforcements directly affect energy absorption. The input parameters for statistical analysis are listed in
Table 2, but obtained results from the H series of samples was not taken into consideration for the reasons states earlier. Therefore, only samples that had the same foaming time and similar densities were taken as the base of the statistical approach.
The question arises if the change of reinforcements affects specific energy absorption—null and alternative hypothesis needs to be tested. The null hypothesis, H
0, stated that the population proportions in each category are consistent with the specified values in each category. The alternative hypothesis, H
1, stated that the population proportions in each category are not consistent with the specified values in each category [
23]. The null hypothesis in this paper stated that all groups of samples taken into evaluation (O, III and N) would have the same mean values of specific absorbed energy. The alternative hypothesis stated that the results are going to be different; some samples will exceed predicted results, and some will not.
Table 3 and
Table 4 show the observed and expected values and the chi-squared goodness-of-fit test of energy absorption for all samples divided into three categories. The observed values are the actual results of energy absorption capacities in a sample that belongs to a category. The expected values are the number of observations that are expected to occur if the test proportions were true. Categories with a large difference between observed and expected values contribute more to the overall chi-squared statistic. Data in the chi-squared test consists of
N, which represents the total sample size,
DF, which represents degrees of freedom used to determine the
p-value. Graphical representations of the results are shown in
Figure 12 and
Figure 13.
As shown in
Table 3 and
Table 4, the expected value of all samples was 9,014,444 J/m
3, and the
p-value was 0.00, which is less than the value of α, where the significance level is 0.05. Therefore, the null hypothesis H
0 was rejected and concluded that the data does not follow a distribution with certain proportions. As seen from
Figure 12, samples O1, O2, III1 and III2 were larger than expected values, which was confirmed with obtained experimental results. The highest contributing category to the chi-squared value was the O2 sample, which absorbed the highest amount of energy,
Figure 13.
Table 5 and
Table 6 and
Figure 14 and
Figure 15 show the observed and expected values and the chi-squared goodness-of-fit test of energy absorption concerning mean values in individual categories of samples. That way, it can be seen which type of reinforcement, in general, contributed more to the specific energy absorption.
Table 6 shows that
p-value ≤ α and the null hypothesis H
0 was rejected.
Figure 14 shown that O and III types of reinforcements had larger observed values than expected ones, and they had better results than non-reinforced aluminum foams, which was confirmed with obtained experimental results. N series of samples was the highest contributing category to the chi-squared value by category, and they absorbed the least amount of energy,
Figure 15. III type of reinforcement had the lowest contribution to it because their observed values are closest to the expected ones.