## 3 Results
### Evolution of Mechanical Properties
#### 3.4.2 Pronounced Strain Hardening Behavior  
Strain hardening behavior of the composite was analyzed and plotted in Figure 5b by measuring the strain hardening exponent (\(n\)) using Hollomon equations:  
\[\sigma=K\epsilon^{n}, \tag{1}\]  
\[n=d(ln\sigma)/d(ln\epsilon), \tag{2}\]  
where \(\sigma\) is stress, \(\epsilon\) is strain, and \(K\) is a constant [52]. The plot shows strain hardening behavior depending on the microstructure of the composite. It reveals two stages of strain hardening, e.g., an initial high rate due to hard reinforcements (\(n_{1}\) = 0.4112) and a later more homogeneous deformation due to particulate matrix involvement interaction (\(n_{2}\) = 0.3048), with an overall strain hardening rate observed as 0.3515. It is reasonable that particulate matrix involvement interaction (\(n_{2}\) = 0.3048) influences the serrated plastic flow and promotes uniform deformation and superior ductility by delaying localized failure.  
Serrated plastic flow appears either due to displacive phase transformation or the initiation of dislocation plasticity events [53; 54]. As the XRD ruled out the possibilities of displacive phase transformation, dislocation plasticity events likely govern the mode of plastic deformation in Al\({}_{3}\)BC/Al composite. Furthermore, such serrated flow resembles Type-B serrations, which seemingly pronounce dislocation interaction involvement during SGB deformation [53; 54]. Vickers hardness was measured to determine the individual strength of the phases and their influence on the overall strength of the composites (Table 2). It shows significantly higher hardness for Al\({}_{3}\)BC (CG) of \(H_{Al3 BC}\) = 22 \(\pm\) 7 GPa, compared to FG-Al matrix, \(H_{Al}\) = 3 \(\pm\) 1 GPa, and AlB\({}_{2}\), \(H_{AlB2}\) = 2 \(\pm\) 0.5 GPa. The measured \(H_{Al3 BC}\) values are identical to the measured hardness values of Al\({}_{3}\)BC from other published reports, e.g., \(H_{Al3 BC}\) = 24 \(\pm\) 1 [55], \(\sim\)26 [21], respectively. Surprisingly, the hardness of the FG-Al matrix within the composite surpasses that of conventional Al (\(\sim\)1 GPa) [18; 19; 20]. [PERSON]'s model predicted the theoretical [PERSON]'s modulus (E\({}_{\text{Th}}\)) of the composite [56]:  
\[E_{Th}=f_{p}E_{p}+f_{m}E_{m}, \tag{3}\]  
where \(f_{p}\) and \(f_{m}\) are the volume fraction of the particles and the matrix and \(E_{p}\) and \(E_{m}\) correspond to the [PERSON]'s modulus of Al\({}_{3}\)BC (326 GPa) [18; 19] and FG-Al (52 GPa), as measured using nanoindentation, respectively. The measured [PERSON]'s modulus of FG-Al matches the literature value of \(\sim\)56 GPa [21]. The fitted [PERSON]'s modulus \(E_{Th}\) = 224 GPa matches the experimental [PERSON]'s modulus of the Al\({}_{3}\)BC/Al composite (\(E\) = 12 GPa). Furthermore, bulk modulus (\(G\) = 80 GPa) and shear modulus (\(B\) = 196 GPa) were calculated from the empirical equations [57].  
The hardness (\(H_{Th}\)) of the Al\({}_{3}\)BC/Al composite was theoretically predicted using the ROM [58]:  
\[H_{Th\_up}=f_{p}H_{p}+f_{m}H_{m}, \tag{4}\]  
\[H_{Th\_low}=f_{p}H_{p}+f_{m}H_{m}^{-1}, \tag{5}\]  
where \(H_{p}\) and \(H_{m}\) are the Vickers hardness, and \(f_{p}\) and \(f_{m}\) correspond to the mass fraction of Al\({}_{3}\)BC particle and Al matrix (obtained using the XRD patterns), respectively. Notably, the AlB\({}_{2}\) phase was ignored due to low contributions in hardness (\(H_{AlB2}\) = 2 \(\pm\) 0.5 GPa) and mass fraction (low \(V_{f}^{AlB_{2}}\) = 10 \(\pm\) 0.1 wt.%). Such significantly improved mechanical properties surpass those of deformed Al alloys (Table 2).