*3.3. Effect of Space Holder Content on Morphology and Properties of Composites*

Figure 11 shows the morphology of the samples with different space holder contents (20 wt.% Zr content). Figure 11a,c,e show the macroscopic morphology of the specimens with space holder contents of 50 vol.%, 60 vol.% and 70 vol.%, where the morphology can remain intact after the removal of the space holder by impregnation. However, in the case of space holder content greater than 70 vol.%, some areas of the sintered specimens were difficult to maintain integrity due to the clumping of the space holder during cold pressing and collapse or detachment during impregnation, so porous specimens with space holder content greater than 70 vol.% were not explored in this paper. Figure 11b,d,f shows the enlarged shapes of specimens with 50 vol.%, 60 vol.% and 70 vol.% space holders. After removing the NaCl space holder by immersion, the macroscopic pores basically maintain the original shape of the NaCl particles, and with the increase of the space holder, the pores are more frequently connected, and the pore wall thickness gradually decreases.

**Figure 11.** *Cont*.

**Figure 11.** Macroscopic morphologies of porous materials with different contents of NaCl space holder (**a**,**b**) 50 vol.%; (**c**,**d**) 60 vol.%; (**e**,**f**) 70 vol.%.

This section introduces the relative density data according to the literature [30] investigation to better study the effects of different space holder contents on material properties [30]. The relative density is the ratio of the apparent density of the porous material to the theoretical density when the material is densified. Table 2 shows the mass, volume, apparent density and theoretical density of the 20Zr samples with different space holder percentages.

**Table 2.** The mass, volume, apparent density and theoretical density of the 20Zr samples with different space holder percentages.


Relative density is also another manifestation of the density of the material, which can be calculated by the following equation [31]:

$$R = \frac{\rho\_P}{\rho\_s} \tag{5}$$

where *R* is the relative density, *ρ<sup>P</sup>* is the apparent density of porous materials and *ρ<sup>s</sup>* is the theoretical density of materials when they are dense. Table 3 shows the porosity, intergranular porosity and relative density of the composites with different space holder contents. It illuminates that with the increase of space holder content, the number of intergranular pores decreases gradually, and the porosity of the material is closer to the volume fraction of the space holder. This is due to the reduction of metal powder, the powder gap caused by cold pressing and the Kirkendall voids formed by the in situ reaction is also reduced [32], and the pores of porous materials are mainly formed by space holders.

Figure 12 shows the compressive stress–strain and energy absorption capacity curves with different relative densities (20Zr). It can be found that with the increase of porosity, the elastic strain limit and the slope of the curve decrease, and the yield stress of materials also decreases gradually. The plateau region in the curves is longer and flatter with the decreases in relative density. It is because porous materials with lower relative density (or higher porosity) have more pore structures. When the pore wall collapses and deforms under a compression load, there is enough space inside to bear the deformation of the pore wall. From the energy absorption capacity curve, it can be concluded that the energy

absorption performance of the porous material has a positive correlation with the relative density, because when the relative density is higher, there are more matrix materials in the porous material, and the compressive performance of the material will be better. Therefore, with the decrease in relative density, the energy absorption capacity also decreases.

**Table 3.** The porosity, intergranular porosity and relative density of the composites sintering at different space holder percentages.


**Figure 12.** (**a**) Compressive stress–strain and (**b**) energy absorption capacity curves of composite materials with different relative densities.

Figure 13 shows the yield stress and plateau stress of the composites with different relative densities. It can be seen that the performance range of porous materials increases with the increase of relative density. This rule is mainly because with the increase of porosity, the space of the pore wall in the same area is smaller, and the thickness of the pore wall is thinner, the supporting capacity to the load decreases greatly, so the performance of the porous material decreases gradually. However, the decline in performance brings a larger specific surface area and lower density.

**Figure 13.** (**a**) Yield stress and (**b**) plateau stress of composites at different relative densities.

By comparing the prepared Al3Zr/2024Al porous composites with other references, the properties of the materials are significantly improved, and the corresponding results are shown in Table 4. It is worth noting that the properties of porous composites prepared by in situ synthesis are better than those of pure aluminium, indicating that in situ synthesis has a unique advantage in solving the poor properties of porous aluminium.


**Table 4.** Compression properties of different porous materials.

To better describe the effect of the relative density of porous materials on the compression properties of porous materials, Gibson and Ashby [6] assume that the pore wall is a dense material, and the compression of porous materials is mainly accomplished by the buckling and compression of the pore wall, and its strength is mainly determined by its relative density. A prediction model is proposed for this assumption, which can be calculated by the following equation [6]:

$$
\sigma = 0.3 \left( \Phi \frac{\rho\_f}{\rho\_d} \right)^{\frac{3}{2}} + 0.4 (1 - \Phi) \frac{\rho\_f}{\rho\_d} \tag{6}
$$

where *σ* is the compressive strength of the porous material, *ρ<sup>f</sup>* is the actual density of the porous material and *ρ<sup>d</sup>* is the theoretical density when the material is fully dense, *Φ* is the volume percentage of the pore wall of the material. Because the porous material prepared by the space holder method is a three-dimensional reticular structure, after the space holder is removed, the whole material is composed of a pore wall, so the *Φ* = 1. Therefore, D.P. Mondal [36] has made some modifications to this model, and the result is the following equation [36]:

$$
\sigma = \mathbb{C}\left(\frac{\rho\_f}{\rho\_d}\right)^n \tag{7}
$$

where *C* and *n* are constant, determined by the properties of the porous material. This equation shows that the relationship between compression properties and the relative density of porous materials is exponential. Applying this equation to this experiment, the relationship between yield stress, plateau stress and relative density is as follows:

$$
\sigma\_y = 535.58 \left( \frac{\rho\_f}{\rho\_d} \right)^{3.01} \tag{8}
$$

$$
\sigma\_p = 743.24 \left( \frac{\rho\_f}{\rho\_d} \right)^{3.45} \tag{9}
$$

where *σ<sup>y</sup>* is the yield stress, *σ<sup>p</sup>* is the plateau stress. However, the pore wall of the actual porous material is difficult to be completely dense, and there will inevitably be some defects in the interior, and its pore structure, such as wall thickness and pore size cannot be the same, and the distribution of pores is also difficult to achieve uniform distribution. But these equations can be used to predict the compressibility of porous materials, which will become a part of the production process route design in actual production.
