# Production and Characterization of Cu/CNT Nanocomposites
## 3 Results and Discussion
### Strengthening Mechanisms
This increase in dislocation density can be attributed to the mismatch of strains at the MWCNT/matrix interfaces due to the difference in thermal expansion coefficients between MWCNTs, and the Cu matrix will block the movement of dislocations. Other authors [7; 17; 18] have also reported dislocation strengthening as one of the most common mechanisms acting on these nanocomposites. Figure 11: _Cont._  
Figure 10: **(a,c)** IPF maps and **(b,d)** [001], [010] and [100] IPFs and [001], [011] and [111] PFs of Cu and Cu/CNT nanocomposites, respectively. The contribution of the different strengthening mechanisms related to yield strength was quantitatively calculated to fully understand the microstructure's effects on the mechanical properties of the nanocomposites. Based on the available literature and the obtained microstructures, the reinforced yield strength should be derived from the sum of the yield strength of the matrix and the strengthening mechanisms [18]. The improvement in the yield strength of the nanocomposites could be attributed to the following mechanisms: (i) load shear strengthening (\(\Delta\sigma_{LT}\)) [18; 25; 26], (ii) grain refinement strengthening (\(\Delta\sigma_{gb}\)) [18; 25; 27], (iii) Orowan strengthening (\(\Delta\sigma_{O}\)) [17; 18; 25; 28], and (iv) dislocation strengthening (\(\Delta\sigma_{Dis}\)) [17; 18; 25; 28]. The yield strength (\(\sigma_{ys}\)) can be determined by Equation (1):  
\[\sigma_{ys}=\sigma_{0}+\Delta\sigma_{gb}+\Delta\sigma_{LT}+\Delta\sigma_{Dis}+ \Delta\sigma_{Or} \tag{1}\]  
The strength increase by a load transfer from the CNTs and Cu matrix was calculated by the shear-lag theory developed by [PERSON] and [PERSON] [26]. [PERSON] and [PERSON]'s modified shear-lag model [26] is the most typically used to characterize the load transfer mechanism. Based on this model, the load transfer (\(\Delta\sigma_{LT}\)) can be obtained by Equation (2):  
\[\Delta\sigma_{LT}=\sigma_{M}\left[\frac{V_{CNT}\Big{(}S_{eff}+2\Big{)}}{2}+(1 +V_{CNT})\right] \tag{2}\]  
where \(V_{CNT}\) is the volume fraction of the CNTs, \(\sigma_{m}\) is the matrix yield strength, and \(S_{eff}\) is the effective aspect ratio of the CNTs (the value of 1.32 was used in this work). Based on the results obtained by the microstructural characterization, it was found that \(\Delta\sigma_{LT}\) can be 57.2 MPa. For the grain refinement strengthening (\(\Delta\sigma_{gb}\)), using the Hall-Petch equation [28], it was calculated to be 8.1 MPa. Regarding the Orowan strengthening (\(\Delta\sigma_{Or}\)), the value was estimated using the equation reported by [PERSON] et al. [28]. The (\(\Delta\sigma_{Dis}\)) contribution was achieved as 2 MPa. This mechanism results in the thermal mismatch between the CNTs and the Cu matrix. The different contribution of these strengthening mechanisms is present in Figure 12. Based on the estimated values, the load transfer mechanism contributes more to improving the mechanical properties of the nanocomposites. These results are consistent with the results obtained in the microstructural characterization, where it was observed that in this work, the increase in dislocation density and grain size differences were not significant between the matrix and the nanocomposite.