# Role of Multi-Scale Microstructure in the Degradation of AI Wire for Power Transmission
## 4 Discussion  
### Strength Degradation Behavior  
For the CPAWs and the AFWs, their strength decreases with the increase of annealing temperature. However, the strength degradation rate of the annealed AFWs is always higher than that of the annealed CPAWs. As a result, the strength degradation behavior of the AFW is different from that of the CPAW, which could provide the rules of microstructure design for Al wire with anti-degradation characterization. The mechanisms behind the strength degradation behaviors of the CPAWs and the AFWs have been discussed in our previous papers [11; 12]. Therefore, the evolution of strength of the CPAWs and the AFWs is briefly discussed in this work. As shown in Figures 3 and 4, there are few dislocations  
Figure 8: Grain widths (**a**) and grain lengths (**b**) of the cold-drawn CPAW, the annealed CPAWs, the cold-drawn AFW and the annealed AFWs. observed in the CPAWs and in the AFWs. Therefore, the strength of CPAWs consists of the strength contributed by the grain-boundaries and the texture. In addition, the strength caused by the texture can be estimated by the following equations, which can be found in our previous works [11; 12]:  
\[M_{S}=\frac{f_{<001>}}{\Omega_{<001>}}+\frac{f_{<111>}}{\Omega_{<111>}}, \tag{4}\]  
\[\sigma_{t}=\sigma_{\rm{YS}}\cdot(1-\frac{M_{0}}{M_{S}}), \tag{5}\]  
where \(M_{S}\) is the orientation factor of the CPAW, \(f_{<001>}\) is the volume fraction of \(<\)001\(>\) texture, \(f_{<111>}\) is the volume fraction of \(<\)111\(>\) texture, \(\Omega_{<001>}\) and \(\Omega_{<111>}\) are the Schmid factors of the \(<\)001\(>\) orientation and \(<\)111\(>\) orientation, which are equal to 0.408 and 0.272, respectively, \(\sigma_{t}\) is the texture strengthening, \(\sigma_{YS}\) is the yield strength of the CPAW, \(M_{0}=3.06\) is the mean orientation factor for polycrystalline Al with random orientation [24]. As a result, firstly, the strength induced by texture of the CPAWs can be calculated based on the statistical results corresponding to the volume fractions of \(<\)001\(>\) texture and \(<\)111\(>\) texture. Then, the grain-boundary strengthening of the CPAWs can also be obtained. For the AFW, its yield strength contains the strength due to the dispersed nano-precipitates, the fine grams and the hard texture. The precipitation strengthening of the AFW can be calculated on the basis of the Orowan-Ashby equation [25; 26]:  
\[\sigma_{p}=\frac{0.13\cdot M_{0}\cdot G\cdot b}{L}\cdot\ln\frac{r}{b}, \tag{6}\]  
where \(\sigma_{p}\) is the precipitation strengthening, \(G\) is the shear modulus of Al (26.0 GPa), \(b\) is the Burgers vector of Al (0.286 nm) [24], \(r\) and \(L\) are the mean radius of the precipitate and the inter-precipitate distance. Our previous work has shown that the average radius and the mean distance of the precipitates of the cold-drawn AFW are 5.2 nm and 77.5 nm, respectively [12]. Thus, the precipitation strengthening in the cold-drawn AFW is calculated to be 110.7 MPa. Then, the residual strength of the cold-drawn AFW caused by the texture strengthening and the grain-boundary strengthening can be achieved by the Equations (4) and (5). Our previous work has revealed that the precipitation strengthening of the AFWs annealed for 8 h at 200 and 250 \({}^{\circ}\)C can be ignored due to the serious growth of precipitates [12]. Thus, the texture and the grain-boundary offer the yield strength of the AFWs annealed at 200 and 250 \({}^{\circ}\)C, which can be calculated by the Equations (4) and (5). Therefore, the evolution of strength caused by various strengthening mechanisms of the CPAWs and the AFWs can be calculated and shown in Figure 9. Obviously, the strength caused by grain-boundary strengthening of the cold-drawn CPAW, the AFW, the CPAW annealed at 90 \({}^{\circ}\)C and the AFW annealed at 200 \({}^{\circ}\)C is nearly constant.