## 3 Results
### Microhardness of Sintered Samples  
Figure 15 displays the three values of the hardness of the Al-5 Fe40 Al, Al-10 Fe40 Al, and Al-15 Fe40 Al composites determined in the present work, with values of 84.6, 101.1, and 107.2 VPN, respectively. In this case, the hardness also varied almost linearly with an increase in the volume fraction of the reinforcement phase [32]. In addition, the microhardness value of the pure Al utilized as the matrix is presented in the above-mentioned plot. Aiming to compare the hardness values measured in the present work with a theoretical basis, a model that describes the variation of hardness as a function of the reinforcement phase concentration was developed. In this theoretical model, the hardness values of pure Al and those of the Fe50 Al intermetallic compounds (under different processing conditions) were taken from the literature [33]. The composition of the Fe50 Al intermetallic phase was considered since its hardness is similar to that of the Fe40 Al intermetallic phase. Then, the hardness values were modeled as a function of the volume fraction of the reinforcement phase (Fe50 Al), in accordance with the rule of mixtures that is represented by the following equation:  
\[p_{c}=\sum f_{i}p_{i}=f_{1}p_{1}+f_{2}p_{2}+\ldots+f_{n}p_{n} \tag{2}\]  
where \(p_{c}\) is the property of compound; \(p_{1}\), \(p_{2}\),... \(p_{n}\) are the properties of each of the constituents of composite material, and \(f_{1}\),\(f_{2}\),... \(f_{n}\) are the volume fractions of each of the components. However, the property modeled here was hardness. Figure 15 displays the variation of hardness modeled as a function of the volume fraction of the reinforcement phase (Fe50 Al), considering, in all cases, an aluminum (Al) matrix. The three curves presented in this plot were generated by considering the hardness of the Fe50 Al intermetallic compounds reported in previous works that were processed under the following parameters: water quenched, furnace cooled at 100 k/h, and annealed at 673 K for 118 h [33]. In these three curves, the hardness of the Al matrix composite changed linearly with increases in the Fe50 Al reinforcement phase [32]. Figure 15: Vickers microhardness of composite materials Al-5 Fe40 Al, Al-10 Fe40 Al, and Al-15 Fe40 Al compared with the predicted values of hardness of various composites reinforced with Fe50 Al intermetallics under different processing conditions. It was observed that the hardness values of the Al-5 Fe40 Al, Al-10 Fe40 Al, and Al-15 Fe40 Al measured in the present research exhibited higher values than the hardness modeled as a function of the content of the Fe50 Al reinforcement phase [33], as can be observed in Figure 15. The hardening effect observed in the composite produced in the present study is due to the hardening mechanism induced by the solid solution of solute Fe in solvent Al, which promotes the formation of strain fields around solute atoms, which, in turn, interact with the stress fields of dislocations and obstruct dislocation motion. Other reasons that promoted the hardness increase in the sintered specimens were the work hardening effect induced by the plastic deformation during milling, the continuous generation of dislocations, and the interruption of dislocation motion [34]. Figure 16 shows the dependence of hardness on dislocation density. In this case, the dislocation density was estimated from the Al-5 Fe40 Al, Al-10 Fe40 Al, and Al-15 Fe40 Al specimens that were subjected to the ball milling process for 8 h. In this plot, a linear relationship of both variables is depicted. For this analysis, the dislocation density was considered to remain constant during sintering since the predominant material transport mechanism occurs by surface, volume, or grain boundary diffusion, or even by vaporization and re-condensation [35]. In addition, Figure 16 displays a relatively linear increase in hardness with increasing dislocation density. This behavior is reasonable since, during the mechanical milling, the particles experienced a plastic deformation.