*3.4. Electrical Conductivity*

The electrical conductivity for parallel connection of conductors can be calculated using the rule of mixture:

$$
\sigma\_{\varepsilon f} = \sigma\_{Al} f\_{Al} + \sigma\_{\mathbb{C}u} f\_{\mathbb{C}u} = \sigma\_{Al} (1 - f\_{\mathbb{C}u}) + \sigma\_{\mathbb{C}u} f\_{\mathbb{C}u},
$$

The effective conductivity of aluminium–copper-clad conductors, calculated using theoretical conductivities for aluminium and copper constituents, is represented by the dashed line in Figure 7. In reality; however, the effective conductivity was about 10% lower than the ideal theoretical value, and was in the range of 55% to 60% IACS. The low initial conductivity could be explained by the Fe high content in the solid solution and is in line with results published in [18].

The electrical conductivity measured after deformation shows strong dependence on the severity of the deformation. The conductivity after one pass dropped from the initial value to 36.1% ± 3.6% IACS for a thin sheath and to 60.5% ± 2.4% IACS for a thick sheath. The conductivity decreased further after two deformation passes, more when using Route BC than when using Route A.

**Figure 7.** Effective conductivity versus thickness of copper cladding after deformation.

Short annealing at 200 ◦C restored conductivity to a greater extent than prolonged annealing at 120 ◦C, especially for samples deformed by one or two passes along Route BC, as seen in Figure 8. It should be noted that conductivity after annealing of samples with the thick sheath exceeded the theoretical values (~68%IACS), represented by the dashed line in Figure 7 and reached ~75% IACS. Connectivity of samples with thin sheath was worse due to defects introduced by SPD and leads to the conclusion that the cladding thickness has the lower limit on the benefits offered by this cladding technique.

**Figure 8.** Effective conductivity after deformation and two annealing schedules for different thicknesses of copper cladding (the dashed line shows the theoretically predicted level of conductivity).
