3.1. Porosity content
Figure 3 depicts the porosity content of composite and pure Al specimens. As predicted, the porosity content is higher for the composite specimens than for the pure Al specimens. This is because the reinforcing particles prevent the rearrangement of the powder particles and the contact between matrix neighbor particles in the initial phase of the sintering process and hence, interfere in the consolidation process. The figure exhibits that the amount of porosity for both the composite and pure Al samples increases with increasing the matrix particle size.
For pure Al, according to the literature [27, 28], densification of pure metals occurs in three steps during the SPS process. The first step is the rearrangement of the powder particles, the second step includes the local plastic deformation and the creation of the sintering neck, and the third step is the extensive sintering by mass transport. Almost all of the above steps can be affected by changing particle size. In the first step, the reduction of particle size increases the number of contact points between adjacent particles per unit volume of the sample. Therefore, the rearrangement of particles (relative motion of powder particles) occurs more easily with larger particles. In the second step, the effect of particle size on the formation of the sintering neck and localized plastic deformation should be investigated.
The tensile strength of the sintering neck is the parameter that indicates the extension of the sintering neck between adjacent particles. The following equations can be used to calculate the tensile strength of the sintering neck as a function of particle size [28]:
$$\frac{1}{{R}^{{\prime }}}=\frac{1}{{R}_{1}}+\frac{1}{{R}_{2}}$$
3
$$\sigma =\frac{\gamma }{{R}^{{\prime }}}$$
4
where R' is the equivalent radius of curvature, R1 and R2 are the radii of the contacted particles, \(\sigma\) is the tensile stress of the sintering neck, and \(\gamma\) is the surface tension. The ratio of R' for pure Al particles with an average size of 20, 45, and 63 µm is about 1:2:3. Thus, the tensile strength ratio would be about 3:2:1, i.e., the tensile stress of the sintering neck between small particles is three times higher than that for large particles. Since the growth and expansion of the sintering neck causes the shrinkage of the pores, the larger tensile strength of the small particles can be considered an effective factor for their lower porosity content. The electric field applied during sintering in the SPS process enhances the phenomena of mass transport by Joule heating [29]. Therefore, for the third step of sintering, the influence of particle size on Joule heating should be determined. According to the Joule equation:
The amount of heat generated (Q) is directly proportional to the square of current (I), resistance (R), and time. Increasing the size of the particles increases the pore volume between the particles, which in turn decreases the crosssectional area for the passage of electrons (i.e., current) through the particles. Therefore, the amount of heat generated is less in larger particles than in small particles. It can be concluded that, except for the first step, a decrease in matrix particle size results in a lower porosity content.
For composite specimens, the matrix to reinforcement particle size ratio (PSR) is the most important factor affecting the densification behavior during the sintering process. It has been shown that decreasing the PSR value, especially near unity, leads to the higher density of the composite specimens [30]. Regarding the size of the reinforcing particles (both SiC and metallic glass particles) and the matrix, the PSR value decreases when the grain size of the matrix is increased.
The porosity content of the HC20 and HC45 samples also differs only slightly, but a remarkable increase in porosity content is observed for the HC63 sample. Considering the size of the matrix and reinforcing particles, the PSR for the HC20 and HC45 specimens is within the indicated optimal range of 1/3 to 3 [31].
3.2. Distribution of the reinforcing particles
Figure 4 illustrates the spatial distribution of the reinforcing particles in the composite samples. The FMG and SiC particles are indicated by different colors in the corresponding EDS maps. Relatively homogeneous distribution of the reinforcing particles occurred in the HC20 and HC45 samples (Figs. 4a and b). However, the HC63 sample shows a heterogeneous distribution of SiC and FMG particles in the matrix. Moreover, some microscopic voids are visible in the interface between particles and the matrix. In previous studies [30], it was demonstrated that the size difference between the reinforcing particles and the matrix is a key factor in the distribution of the particles in the matrix. When the size of the reinforcing particles is much smaller than the size of the matrix powder, the reinforcing particles tend to agglomerate in the matrix particles [32].
It is also clear from the figures that agglomeration and the formation of voids at the interfaces were more likely to occur in the SiC particles for all samples. This can be attributed to the metallic nature of the FMG particles and the better interfacial properties (compared to the SiC particles) between them and the Al matrix. The strong FMG/matrix interfacial bonds cause the FMG particles to move and distribute in the metallic matrix of the composites.
Quantitative evaluation of the distribution of reinforcing particles can be done using a parameter named λinter (interparticle distance). λinter is defined as the average distances of an individual particle to its nearest neighbor. To compare the degree of homogeneity of distribution, a statistical parameter called the coefficient of variation, COV [33], was employed. This parameter is defined as the ratio of the standard deviation (𝜎𝑚) to the mean (m). Generally, COV can vary between 0 and 1, and degree of inhomogeneity increases as its value gets closer to 1. Figure 5 presents the COV value of different composite samples which calculated from the corresponding FESEM images (Fig. 4).
The XRD patterns of the composite samples are displayed in Fig. 6. The XRD pattern shows sharp Bragg peaks which belong to aluminum and SiC (Fig. 6(a)). Figure 6(b) shows broad halo at 2θ = 44° in the XRD patterns, characteristic for the amorphous structure of the FMG particles consolidated. As it can be seen from Fig. 6(a), no peaks corresponded to the interfacial products detected in the patterns of the composite samples. Also, there is no remarkable difference between the patterns in terms of the intensity and width of the crystalline peaks as well as their position. Therefore, the values of dislocation densities stored in the matrix of all composite samples are close to each other (Fig. 7).
The stored dislocation density in the matrix of the composite upon cooling from the processing temperature is influenced by the type (which indirectly determine the type of matrix/interface region) and size of the reinforcing particles [34–36]. Therefore, the same reinforcement conditions in all composite samples result in almost the same stored dislocation density in the matrix. All the patterns resemble sharp Bragg peaks with almost the same intensity belonging to aluminum and SiC, and a broad halo for FMG particles around 2θ = 44°. Moreover, no peaks relating to interfacial products existed in the patterns of the sintered samples.
3.3 Mechanical properties
The Brinell hardness values for the various samples are shown in Fig. 8. As predicted, the hybrid composite samples have higher hardness values than the pure Al samples. It is also found that the hardness of the pure Al samples decreases as the size of the matrix powder particles increases. The hardness of P63 is much lower than the other two pure Al samples. For the composite specimens, the hardness of the HC20 and HC45 specimens are about the same, but the hardness of the HC63 specimen is much lower than the other two.
Figures 9 and 10 show the typical stressstrain relationships under compressive mode for pure Al and composite samples, respectively. The collected data of stressstrain curves are shown in Table 1. For the pure Al specimens, similar trends can be observed in the hardness, yield strength, and compressive ductility values, which were positively affected by the reduction in the particle size of the matrix powder.
Table 1
Compressive mechanical properties of different consolidated samples.
Sample code

0.2% Yield strength (MPa)

Strain to fracture

P20

68

68

P45

47

48

P63

38

43

HC20

99

59

HC45

103

53

HC63

58

48

The slope of the stressstrain curves is almost the same for all composite specimens after yielding, which is an indication of the same strain hardening capacity of the specimens. There is a positive correlation between the strain hardening rate and the dislocation density of metallic materials [37]. Thus, this behavior is due to the small difference between the stored dislocations after sintering (Fig. 7) and before the compression test. The yield compressive strength and ductility were significantly decreased by about 41% and 19% for HC63 compared to HC20. Since all composite specimens have similar composition and phase characteristics (Fig. 6), these different mechanical properties can only be attributed to the following two factors:
i. Porosity content
The much higher porosity content of the HC63 specimen compared to the other two composite specimens (Fig. 3) results in a preferential path for crack propagation under load, which in turn decreases the ductility of the composite [38]. The mechanism of load transfer to the FMG and SiC particles is also negatively affected in the presence of porosity. Therefore, the strength and hardness of the composite specimen would also decrease.
ii. Distribution of the reinforcing particles
The nonuniform distribution of the reinforcing particles in the matrix composite is the second factor that weakens the mechanical properties of HC63. In other words, the accumulation of reinforcing particles decreases the average spacing between the adjacent reinforcing elements, which leads to the growth of interfacial nucleated cracks and the promotion of fracture.