## 3 Results and Discussion
### Tensile Strength Analysis
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Composite** & **Microhardness** & \multicolumn{2}{c}{**Ultimate**} & \multirow{2}{*}{**Yield Strength**} & \multirow{2}{*}{**Elongation (\%)**} \\
**Specimen** & **(HV)** & & & \\  & & **(MPa)** & & \\ \hline C0 & 128.1 & 371.5 & 243.6 & 18.2 \\ C1 & 142.5 & 388.1 & 259.4 & 17.2 \\ C2 & 149.4 & 421.4 & 277.1 & 16.5 \\ C3 & 164.4 & 467.6 & 303.1 & 14.4 \\ C4 & 156.7 & 401.5 & 268.5 & 15.1 \\ C5 & 165.2 & 456.2 & 297.3 & 14.2 \\ C6 & 174.1 & 485.7 & 312.1 & 11.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mechanical Properties of Copper hybrid composites. Figure 14: Variation of yield strength and ultimate tensile strength of Cu alloy and Cu-(3, 6, 9) wt.% WC-Gr hybrid composites. Based on the continuum mechanics, the excellent bonding between the reinforcement and the matrix helps to enhance the tensile behavior of the materials. The yield strength of the materials is enhanced due to the discontinuously reinforced ceramic particulate based on the shear-lag model [28]. The theoretical yield strength of the developed composite (\(\sigma_{yc}\)) can be determined based on the theoretical strength of the matrix (\(\sigma_{ym}\)), the volume fraction of the reinforcement (\(v_{p}\)) and aspect ratio of the ceramic particulate (\(s\)) shear-lag model, as shown in Equation (1) [29]. \[\sigma_{yc}=\sigma_{ym}[\left\{v_{p}\Big{(}1+\frac{s}{2}\Big{)}\right\}+\big{(} 1-v_{p}\big{)}] \tag{1}\]  
The yield strength and UTS of the composite materials also increased due to the presence of ceramic reinforcement acting as a resistance to plastic deformation and crack propagation [30]. An earlier study by [PERSON] et al. [26] indicated that adding 10 wt.% SiC and 10 wt.% WC in the soft aluminum 6061 alloy matrix enhances the yield strength and UTS by 30.76% and 38%, respectively, with the reduction of maximum ductility by 86%. In the present study, it was experienced that the addition of 9 wt.% of SiC along with 1 wt.% of graphite enhanced the ultimate tensile strength by 26%, and the addition of 9 wt.% of WC along with 1 wt.% of graphite enhanced the ultimate tensile strength by 30%. Moreover, the thermal mismatch between the copper matrix and the ceramics reinforcements would probably be another reason for improving the tensile properties. The mismatch among the coefficients of thermal expansion (CTE) generates a rise in the dislocation density in the composites. Therefore, it resulted in prismatic punching of the dislocations at the interface, which led to the work-hardening of the composites [31]. The formation of these dislocation densities is proportional to the surface area of the reinforcement. The homogenous dispersion of the reinforcements tends to increase the surface area, resulting in higher work hardening in the fabricated composites. The introduction of ceramic reinforcement like SiC and WC in the copper C87600 alloy matrix enhanced the tensile properties of the materials; however, the ductility of the materials was reduced. The effect of ceramic reinforcement on the percentage elongation of the developed copper-based hybrid metal matrix composites is shown in Figures 15 and 16. The base copper C87600 alloy showed a percentage elongation of 18.2%; however, by adding 9 wt.% SiC and 1 wt.% graphite to the copper matrix, the ductility of the materials is reduced to 14.4%. Similarly, the ductility of the materials is decreased to 11.5% for Cu-9%WC-1%Gr composites in comparison with the base copper alloy. The 9%SiC-1%Gr reinforced copper composites had witnessed a 21% reduction in the elongation percentage in comparison to the base alloy, whereas the decrease in the percentage elongation was found to be 36% for the Cu-9%WC-1%Gr composites. The addition of these hard and stiff particulates resulted in the increment of brittleness that subjected to the decline in the ductility of the composite. A higher decrease in ductility was observed by the addition of WC particulate as compared to SiC particulates. Similar results were also reported by [PERSON] et al.