**3. Results**

#### *3.1. SEM and EDX Results*

SEM and EDX results for the N8 and N7 outer wires with service lifetimes of 10 and 18 years, respectively, taken from A50-type cables (i.e., without steel cores) as well as for new (0 years of service) wires of an AC50-type cable were discussed earlier in [10,37]. As in the case of A50-type wires, SEM images have shown that the prepared outer-wire crosssections of AC50-type steel core cables are quite suitable for obtaining the EDX spectra and EBSD mapping. The EDX spectra of cross-sectional surfaces from N2-2 and N6 AC50-type samples with service lives of 8 and 20 years, close to the service lives of wires of A50-type cables mentioned above, are shown in Figure 1. According to the results of the analysis of EDX spectra, the chemical composition of the elements of wire samples of both types of different service life from 0 to 20 years has demonstrated no significant difference and is consistent with the composition of the certificate data (Table 3). As expected, the Al content of ~99 wt% prevails in all samples. The EDX spectra show peaks corresponding to the Fe and Si atoms, which, according to the certificate data (Table 3), are the most abundant among impurity atoms, as well as peaks attributed to O atoms due to Al oxidization [10,37]. The EDX spectra also show the presence of peaks of extraneous elements, namely, Ar as a result of argon ion polishing of the surface of the samples and Ni from the walls of the microscope chamber.

## *3.2. EBSD Results*

Distribution EBSD maps of Euler orientation angles *ϕ*1, *Φ*, and *ϕ*2 (correspondingly, angles of intrinsic rotation, nutation, and precession, see Ref. [48] for definition) with superimposed grain boundaries are shown in Figure 2. As grains, regions of the crystal structure were considered the misorientation within which did not exceed 2◦. The colors of the grains on the map correspond to a combination of Euler angles that describe the orientation of the crystal lattice in a given grain.

**Figure 1.** EDX spectra of the AC50 samples (**a**) N2-2 (8 years of service life), (**b**) N6 (20 years of service life).

**Figure 2.** Distribution maps of Euler angles at the center (**<sup>a</sup>**,**b**) and at the edge (**b**,**<sup>c</sup>**) for cross-sections of AC50 samples after (**<sup>a</sup>**,**<sup>c</sup>**) 8 (sample N2-2) and (**b**,**d**) 20 (N6) years of service life. The legend for maps (**<sup>a</sup>**–**d**) is shown in (**e**). Scale for the Euler angle *Φ* is the same as for *ϕ*2.

As a result of the analysis of maps of the distribution of Euler orientation angles in the center and at the edge of the studied thin sections of the cross-sections of the AC50-type samples after operation for 8–20 years (N2-2 and 6), we have constructed histograms of the distribution of grains by size (Figure 3), dependences of the area occupied by grains on their size (Figure 4a), grain-aspect-ratio distribution histogram that is ratio of the maximum grain size to the minimum (Figure 5), and distribution of grain boundary misorientation angle (Figure 6). For the non-exploited AC50 sample (N5, 0 years of service life) and the A50 sample N8 after 10 years of operation, the distribution maps of the Euler orientation angles in the center and at the edge and the distribution histograms constructed for them are presented in [10], while the dependence of the area occupied by grains vs. grain size for these A50 type specimens is plotted in Figure 4b. For the central regions of wire crosssections of A50-type long-service life (up to 62 years) cables, similar EBSD studies were carried out in [37].

**Figure 3.** Histograms of grain size distribution for the centers and edges of cross-sections of outer wires from the AC50 cables after (**a**) 8 years of service (N2-2) and (**b**) 20 years of service (N6). For better visualization, the histograms for sample edges are shifted along the abscissa axes in (**<sup>a</sup>**,**b**).

**Figure 4.** Dependencies of the relative area occupied by grains vs. their size for the cross-sections of outer wires from the (**a**) AC50 and (**b**) A50 cables at the centers of the samples. All dependencies are given on the same scale for comparison. Numbers of samples and their service lives are indicated in the legends of the Figures.

**Figure 5.** Histograms of grain aspect ratio distribution for the centers and edges of cross-sections of outer wires from the AC50 cables after (**a**) 8 years of service (N2-2) and (**b**) 20 years of service (N6). For better visualization, the histograms for sample edges are shifted along the abscissa axes in (**<sup>a</sup>**,**b**).

**Figure 6.** Histograms of grain boundary misorientation angle distribution for the centers and edges of cross-sections of outer wires from the AC50 cables after (**a**) 8 years of service (N2-2) and (**b**) 20 years of service (N6). For better visualization, the histograms constructed for the edges of the samples are shifted along the abscissa axes in (**<sup>a</sup>**,**b**).

One can see from Figure 3a,b that, as in the case of A50-type cables [10], the general nature of the grain size distribution in the center and at the edge of the cross-section of samples of different service life periods does not change, and in all cases, the most frequently occurring grain sizes are of ~2 μm. At the same time, in the entire size range from 0.5 to 6 μm, insignificant differences are observed in the relative frequency of occurrence of grains in the center and near the edge of the samples.

With an increase in the service life of 0 to 18–20 years, the relative area occupied by grains with sizes of ~2 μm changes slightly (within ~±5% of ~26% in N5 wire without operation) in the bulk of AC50 and A50 wires (Figure 4a,b). At the same time, the area occupied by grains with sizes 4–6 μm increases slightly from ~0.5–1% to ~1–2%.

As for the A50-type samples [10,37], the grain aspect ratio distribution histograms in the AC50 type samples (Figure 5a,b) weakly vary depending on the period of operation and position, remaining practically unchanged in the center and at the edges of the crosssections of the wires and after various periods of operation. This invariance of the aspect ratio shows that the grain shape in the A50- and AC50-type samples is practically the same inside the cables and in their near-surface layers and remains the same during operation.

Recently [37], angle-distribution histograms of grain-boundary misorientation, which were constructed for the bulk regions of A50 wires (centers of cross-sections) with different service lives, have shown that the number of high-angle grain boundaries with misorientation in the range of 50–60◦ decreases when the service life is long (down to 0.5–0.9% in the sample with a service life of 62 years from 1.5–2.5% in the unexploited sample N5 (0 years)). This decrease is accompanied by an increase in the number of low-angle boundaries with a misorientation angle of less than 15◦ (up to 1.9–28% in the sample with a service life of 62 years from 1.7–22% for N5 (0 years) wire). It has been suggested in [37] that such a distribution of the misorientation angle of grain boundaries is caused by the alignment of the crystal lattice of grains along one common direction. Meanwhile, at shorter service lives of A50 wires, a similar process of reducing the number of high-angle boundaries with a misorientation in the range of 50–60◦ is initially observed after 10 years of operation (sample N8, 0.4–0.8%) [37] in comparison with the non-operated cable (sample N5, 1.5–2.5%). With a further increase in the service life to 18 years (A50 sample N7), the number of high-angle boundaries with a misorientation of 50–60◦ increases again, up to 0.8–1.2%, although not recovering to the value in the N5 wire (0 years) [37]. This growth, respectively, can be associated with the destruction of grain alignment along the general direction.

The grain boundary misorientation angle distribution histograms for the bulk regions (centers of cross-sections) of the outer wires of AC50 cables (Figure 6 for samples with a service life of 8 and 20 years, see also [10] for a non-exploited sample) show an evolution similar to A50-type wires with comparable service lives up to the 18 years described above. Initially, with an increase in the service life from 0 years (sample N5 [10,37]) to 8 years (N2-2), there is a decrease in the number of high-angle boundaries with a misorientation in the range of 50–60◦, although somewhat less than in the A50 wire after 10 years of operation (from 1.5–2.5% in sample N5 (service life of 0 years) down to 0.75–1.2% in sample N2-2 (8 years, AC50) and 0.4–0.8% in sample N8 (10 years, A50)), i.e., the grains probably tend to line up along one direction. With a further increase in the service life of AC50-type wires up to 20 years (sample N6), there is an increase in the number of high-angle boundaries with a misorientation of more than 15◦, in particular, with a misorientation in the range of 50–60◦ to 1.1–1.8% (in comparison to 0.8–1.2% in the A50 wire N7 (service life of 18 years)), which presumably indicates an increase in the number of grains with an arbitrary orientation of the crystal lattice.

The grain boundary misorientation angle distribution histograms for near-surface layers of wires (edges of cross sections) of the outer wires of AC50 cables (for samples with a service life of 8 and 20 years, see Figure 6; for an unused sample, see [10]) are similar to the histograms obtained for the centers of cross-sections. At the edges, there is only a slight decrease in the number of high-angle boundaries with a misorientation in the range of 50–60◦ compared to the centers of the sections (respectively, for the edge and center, 1.0–1.9% and 1.5–2.5% in sample N5 (0 years), 0.75–1.0% and 0.75–1.2% in sample N2-2 (8 years), and 0.95–1.6% and 1.1–1.8% in sample N6 (20 years)), i.e., the misorientation of the grains practically does not change either in the bulk or in the near-surface layers of the AC50 wires. A completely opposite situation is observed in the wires of the A50-type wires. In addition to the drop in high-angle grain boundaries after 10 years of service, as discussed above, the absence of a rigid steel core in A50 cables results in a noticeable difference in histograms obtained from the center and from the edge of the cross-section. At the edge of the section, i.e., in the near-surface layer of the A50 wires, the number of high-angle boundaries with misorientations in the range of 50–60◦ is noticeably reduced (respectively, ~0.1% and 0.4–0.8% at the edge and in the center of the cross-section of sample N8 (10 years) [10]), which probably indicates that in the near-surface layer of the A50 wires, the crystal lattice of grains tends to align along one common direction more strongly than in the bulk regions of the wires.

Thus, the analysis of EBSD maps obtained from the centers and edges of the crosssections of the samples (Figure 2 and Refs. [10,37]) shows that the distribution histograms of the misorientation angle of the grain boundaries (Figure 6) are the most sensitive to

changes in the microstructure, whereas the grain-size distribution histograms (Figure 3) are less sensitive. Compared with AC50 wires, in wires taken from A50 type cables without a steel core in a layer at a distance of ~150 μm from the surface, there is a tendency towards greater grain alignment. The presence of a steel core in AC50-type cables leads to a significant change in grain misorientation in AC50-type wires compared to A50 wires after a comparable service life of up to 20 years in power lines. Grain misorientation in near-surface layers (near the edge of the wire cross-section) and in the bulk of AC50 wires varies slightly for samples of the same service life, although depending on the duration of operation in a manner similar to the A50-type wires (initially, there is a tendency to align the crystal lattices of grains with a service life of 8 to 10 years, with an increase in the duration of operation up to 18–20 years, the arbitrariness of grain orientation increases). In the wires of both types of cables, the aspect ratios of grains in near-surface layers and in the bulk of the wires practically do not change (Figure 5), indicating the invariance of the grain shape in both regions of the samples.

#### *3.3. Results of Densitometric Measurements*

Systematic determination of the density *ρ*d of wires from used A50- and AC50-type cables of approximately the same service life, carried out by densitometry, has shown that the density of the aluminum part of the AC50 cable is somewhat higher than that of the A50 one, despite the fact that the service life of AC50 wires is somewhat longer. For instance, the integral density *ρ*d of aluminum wire of sample N6 (AC50) is 0.05% higher than that of N7 (A50), with a service life of 20 and 18 years, respectively.

To elucidate the possible reasons for this difference, we determined the density *ρ*dL of the near-surface layer of the samples under study (see Formula (2)). Figure 7 shows examples of such distributions of the true density defect (cf. Formula (3), in %) over the cross-section for the studied samples of A50 wires (from [10]) and for AC50 ones after 18 and 20 years of operation, respectively, where *T*etch is the thickness of the removed layer, determined by Formula (1), and Δ*ρ*dL/*ρ*dL is the value of the defect in the density of the near-surface layer relative to the density of the entire cross-section of the wire. As follows from the analysis of dependences, the absolute value of the density defect decreases as much as the near-surface layer is removed, i.e., the deviation of the integral density *ρ*dL of the surface layer decreases with respect to the density in the bulk of the wire. The main change in the density defect in wires of both types is observed in a relatively thin layer about 10 μm thick, that is, the lowest value of the layer density is observed in a narrow near-surface layer. Such a change in density indicates that defects of a void nature (nano and micropores, microcracks) are concentrated just in this narrow near-surface layer. After the removal of this layer (~10 μm) in both types of wires, an insignificant decrease in the absolute value of Δ*ρ*dL/*ρ*dL continues until a layer of ~30 μm is removed from the surface.

**Figure 7.** Dependence of the value of the density defect in the near-surface layer of samples N7 (A50, service life of 18 years) [10] and N6 (AC50, service life of 20 years).

Thus, within the statistical spread of the experimental values Δ*ρ*dL/*ρ*dL, both types of wires show the presence of two characteristic values of the thickness of near-surface defect layers (NSDLs), in which there appears to be a noticeable decrease in density compared to the bulk of the wires. In narrow near-surface layers less than ~10 μm thick, the density is the lowest due to the high concentration of void defects and demonstrates the greatest changes with distance from the surface in depth, and at depths from the surface of ~10 to ~30 μm, it weakly increases until stabilization, apparently due to the reduction in the number of defects. It is also worth noting that the absolute value of the density defect of the nearsurface layer in wires from cables with a steel core (AC50) is somewhat less (by ~0.1–0.2%) than for A50 wires, and, as follows from Figure 7, this difference is most noticeable in a narrow near-surface layer ~5–10 μm thick. The smaller absolute value of the NSDL-density defect in AC50 wires probably reflects a smaller number of void defects in these wires due to the softening effect of the steel core.

Additionally, the densitometry method was used to study the relative change in the integral density (defect Δ*ρ*d/*ρ*d of the integral density) of A50 samples in the range from 0 to 54 years (Figure 8). The values of the integral density Δ*ρ*d were determined for the wires after 0, 8, 18, 35, and 54 years of operation (see Table 2 for sample numbers). It has been established that the most dramatic change in the integral density *ρ*dL is observed in the range from 0 to 20 years of operation. An increase in service life of more than 20 years also leads to a further slight decrease in the density of the wire material. However, when analyzing the data, it should also be taken into account that, as was shown in [10,37], a noticeable amount of Al2O3 oxides are formed on the surface of the wires, the density of which (~3.7 g/cm3) is significantly higher than the density of aluminum (~2.7 g/cm3). That is why it can be assumed that the true absolute value of the integral defect of aluminum wire without the aluminum oxide contribution is greater due to the formation of void microdefects, i.e., with a service life of more than 20 years, the density fitting curve without taking into account the contribution of aluminum oxides will go lower in the graph of Figure 8.

**Figure 8.** Dependence of the integral value of the density defect in A50 wires on the service life during operation up to 54 years.

#### *3.4. Results of XRD Investigations*

Figure 9a–c presents the measured XRD patterns of AC50 samples with service lives from 0 to 20 years. For A50-cable wires with comparable service lifetimes of up to 18 years, the XRD patterns can be found in [10,37]. The XRD reflections of the cubic Al crystalline phase at angular 2*θ* positions corresponding to Bragg angles are schematically shown in Figure 9d by vertical bars whose heights are proportional to the intensities of the reflections according to the PDF-2 card 01-073-9843 [49].

**Figure 9.** XRD patterns detected from wires of AC50 cables after (**a**) 0 (N5), (**b**) 8 (N2-2), and (**c**) 20 (N6) years of exploitation. (**d**) schematically presents the XRD pattern of Al according to PDF-2 card 01-073-9843 (the height of each bar represents the intensity of the corresponding XRD reflection according to the PDF-2 card). Insets in (**<sup>a</sup>**–**<sup>c</sup>**) present the 2*θ* diffraction angle range 21–43◦ on a larger scale, exhibiting the weak reflections attributed to δ\*- and δ-Al2O3. The Bragg angle positions of the δ\*- and δ-Al2O3 reflections are shown according to PDF-2 cards 00-056-1186 and 00-046-1215, respectively, using different symbols. The Miller indices *hkl* of the observed reflections are indicated.

As in the case of wires from the A50-type cables [37], the XRD patterns of the AC50 wires contain all the Al reflections with an enlarged 022 reflection intensity that indicates the polycrystalline nature of the wires with a noticeable effect of preferential orientation along the [011] crystallographic direction (see Figure 9a–d for comparison). As for the A50 wires, the intensity of the 111 reflection for the AC50 wires with a service life of up to 8 years remains the highest despite the presence of a preferential orientation along the [011] direction (Figure 9a,b), whereas the preferential orientation along [011] develops more strongly for wires after 20 years of operation, the 022-reflection intensity becomes the highest.

Quantitative ratios of the intensities of reflections 022 to 111 and 002 to 022, which characterize the preferential orientation of Al wires from AC50 and A50 cables, are given in Table 4 and are graphically shown in Figure 10. As one can see, both types of wires show the identical tendency to grow for the preferential orientation along the [011] crystallographic direction. Nevertheless, in AC50 type wires (with a steel core), the preferential orientation is more pronounced at all service lives, although the difference in preferential orientation between the AC50 and A50 wires decreases as the service life increases to 20 years. At the same time, the ratio of maximum intensities of XRD Al 022 and 111 reflections (*I*max022/*<sup>I</sup>*max111) increases by ≈2.2 times in A50 wires with an increase in service life

from 8 to 20 years compared with ≈2.0 times in AC50 wires with an increase in service life from 10 to 18 years. Such a decrease in the rate of amplification of the effects of preferential orientation can be attributed to the stabilizing effect of the steel core in AC50 wires. In addition, it is likely that the stronger influence of the effects of preferential orientation in AC50 wires is due to the fact that in the starting state of AC50 wire (0 years of operation), the preferential orientation along [011] is already more pronounced than in A50 wire without operation, which is probably due to the peculiarity of the technological process in the production of aluminum wire of various batches for A50 and AC50 wires.

**Table 4.** XRD analysis results of A50 and AC50 wires (temperature of measurements is *T* = 314 ± 1 K). Sample numbers and sample service life (years) are given according to Table 2. Table data from PDF-2 for crystalline Al phase are shown for comparison.


**Figure 10.** Dependence of the *<sup>I</sup>*max022/*<sup>I</sup>*max<sup>111</sup> ratio on the service life *t* of the Al wires from the AC50 and A50 cables. Lines connecting the experimental points are guides to the eye only.

As in the case of the A50 wires [37], the XRD patterns of the AC50 wires after operation (Figure 9b,c) show the formation of very weak reflections attributed to δ\*- and/or δmodifications of Al2O3 [51,52] (δ-phase, space group *P*41212 (92), PDF-2 card 00-056-1186; δ\*-phase, space group *P*222 (16), PDF-2 card 00-046-1215). With a service life of up to 20 years, δ\*-/δ-Al2O3 reflections in AC50 wires after operation develop more strongly compared to those in A50 ones (without a steel core), apparently due to the oxidizing effect of the steel core, which is enhanced by possible damage to aluminum wires when rubbing against the steel core. Whereas the ratios *q* of the integrated intensity *I*int of the 121 δ\*- (and/or 212 δ-) Al2O3 reflection to *I*int of the Al reflection with the highest intensities (with Miller indices *hkl* = 111 for service life up to 10 years and 022 after 18 years) in A50 wires are, respectively, 0.21(5)% and 0.5(1)% for samples N8 (service life of 10 years) and N7 (18 years), this value *q* amounts to 0.53(3)% and 0.9(1)% for the AC50 wires N2-2 (10 years) and N6 (20 years), respectively, see Figure 11.

**Figure 11.** The fraction *q* of the Al2O3 crystalline phases in wires from A50 and AC50 cables with an exploitation duration of up to 20 years, which is estimated as *q* = *<sup>I</sup>*intAl2O3/*<sup>I</sup>*intAl · 100%, where *<sup>I</sup>*intAl2O3 is the integral intensity of the 121 *δ*\*-(212 *δ*-) Al2O3 reflection and *<sup>I</sup>*intAl is the integral intensity of the strongest Al reflection.

A thorough investigation of the XRD patterns measured from samples of various life time periods showed that reflections corresponding to the same Miller indices *hkl* are systematically shifted, which corresponds to a change in the cubic unit cell parameter of the wire Al material, even after applying the angular corrections for zero shift and displacement, as described in Section 2.2.3. As an example, Figure 12 shows a reflection with a Miller index of *hkl* = 133 for the studied A50 and AC50 wires with a service life of 0 to 18–20 years.

**Figure 12.** Part of the XRD patterns in the vicinity of the *hkl* = 133 reflection for several A50 and AC50 samples.

Cubic unit cell parameters *a* of the Al material of the A50 and AC50 wires, averaged over all observed reflections and calculated by the *Celsiz* [42] program using the leastsquares method, are presented in Table 4 and graphically shown in Figure 13a against the service life duration. The corresponding X-ray densities *ρ*x and density defects Δ*ρ*x/*ρ*x of the Al material of A50 and AC50 wires, which are calculated with Formulas (4) and (5), respectively, are shown in Table 4 and Figure 13b.

**Figure 13.** The dependences of (**a**) the Al cubic crystal unit cell parameter *a* and (**b**) density *ρ*x calculated from the XRD data on the service life *t* of the Al wires of overhead power transmission lines. At the right axis of (**b**), the scale of the corresponding density defect (reduction of density) Δ*ρ*x/*ρ*x (where Δ*ρ*x = *ρ*x − *ρ*x 0 years, *ρ*x 0 years is the mean density of the A50 wire N5-2 (service life of 0 years)) of the Al wires is shown. The horizontal line in (**a**) indicates the tabulated value of the Al cubic unit cell parameter *a* according to the PDF-2 card 01-071-4008 [50] and that in (**b**) exhibits the corresponding calculated *ρ*x value. The lines running through the experimental points are guides to the eye only. In the graphs (**<sup>a</sup>**,**b**), the duration of the delay of changes of the *a* and *ρ*x parameter values for A50 and AC50 wires are shown for two service life points.

As one can see from Table 4 and Figure 13a,b, the unit cell parameter and density Al of the material of the wires from the A50 and AC50 cables in the initial state (service life of 0 years) are almost the same (within e.s.d. to within the fourth decimal place, namely, *a* = 4.05026(12) Å and 4.05032(10) Å and *ρ*x = 2.6973(2) g/cm<sup>3</sup> and 2.6972(2) g/cm3, respectively, at an XRD measurement temperature of 314 ± 1 K). The values of these parameters are noticeably differ from the tabulated Al values (*a* = 4.05069 Å and *ρ*x = 2.6964 g/cm3) at a temperature of 312.3 K, which is close to the temperature of the XRD measurements in this work. As previously noted [37], a decrease in the average unit cell parameter and, accordingly, an increase in the Al density of the wire material can be associated with the incorporation of a small number of Fe and Si atoms into the Al structure, which, according to the manufacturer's passport [39] and EDX results (Figure 1a,b and Ref. [37]), are present in the wire composition in amounts up to 0.20 wt.% and 0.08 wt.% (see Table 3), respectively.

When the service life *t* of cables of both types in overhead power lines increases, both the cubic unit cell parameter *a* and the X-ray density *ρ*x of the wire Al material alter almost linearly over the studied time intervals up to 20 years (Figure 13a,b), with lattice parameter *a* increasing and *ρ*x decreasing for wires from cables of both types. Although the nature of the tendencies of changes in the structure parameters of wires from AAAC (A50) and ACSR (AC50) cables over time is the same, ye<sup>t</sup> the rate of temporal change of the characteristics of A50 and AC50 wires is different. The presence of a steel core in AC50 cables leads to a decrease in the stretching rate of the unit cell parameter *a* of the Al wire material from 1.26(4) · 10−<sup>4</sup> Å/year in A50 wires down to 1.07(3) · 10−<sup>4</sup> Å/year in AC50 wires with a service life of up to 20 years. At the same time, the rate of decrease in the density *ρ*x of the A50 and AC50 wires (i.e., the rate of degradation of Al wire due to the

formation of void defects) decreases in absolute value from −2.52(8) · 10−<sup>4</sup> g/cm3/year to −2.13(7) · 10−<sup>4</sup> g/cm3/year, respectively. As a result, after about 11 years of service, the unit cell parameter *a* and density *ρ*x of the Al material of AC50 type wires are the same as in Al wires from A50 type cables after 10 years. With a long service life of ~20 years of operation, the gain for AC50 wires is already ~3 years (see Figure 13a,b), i.e., the structure parameters of AC50-wire Al material after about 23 years of service are the same as those of A50-wire Al material after 20 years. Thus, the presence of a steel core in an ACSR (AC50) cable delays the structural degradation of the Al material of the cable wires.

The average sizes *D*0 of crystallites, averaged over all *Dhkl* values obtained from the *FWHM*corr of each observed Al reflection with the Miller indices *hkl* according to the Scherrer equation in the framework of the model of zero contribution of microstrains (model *ε*s = 0), reveal close values in wires of both types, namely, within *D*0 = 109(16)–138(16) nm for unused wires (0 years of service life), 139(41)–136(29) nm and 126(33)–120(23) nm for A50/AC50 wires after 10/8 years and 18/20 years of operation, respectively (Table 4, see also Supplementary Materials (SM) Figure S1).

However, the XRD-data analysis by means of the WHP and SSP techniques (see WHP and SSP plots in Figure S2 in SM for AC50 samples and Ref. [37] for A50 wires) shows that, whereas average microstrain *ε*s is zero or very close to zero for unused wires of both types (service life of 0 years) and the average crystallite sizes *D* are slightly larger in unused AC50 wires (in A50 (N5-2) wires, *ε*s = 0.010(14)%, *D* = 111(14) nm and *ε*s = 0%, *D* = 109(6) nm according to WHP and SSP, respectively, compared with *ε*s = 0.007(11)%, *D* = 141(17) nm (WHP) and *ε*s = 0%, *D* = 138(16) nm (SSP) in AC50 (N5) wires), microstrains in the wires after operation evolve accompanied with a notable increase in the size of crystallites (see Table 4 and Figure 14). Moreover, in wires from cables without a steel core (A50 type cables), absolute values of average microstrain *ε*s and average crystallite sizes *D* grow after 10–18 years of operation, noticeably larger than in wires from AC50 cables (with a steel core) after 8–20 years of service in overhead power lines (cf. *ε*s = 0.031(2)% and 0.034(3)%, *D* = 246(55) nm and 302(54) nm according to WHP and SSP techniques, respectively, for A50 wires and *ε*s = 0.025(3)% and 0.029(3)%, *D* = 167(13) nm and 219(19) nm according to WHP and SSP techniques, correspondingly, for AC50 wires).

**Figure 14.** Comparison of dependences of (**a**) average crystallite size *D* and (**b**) absolute value of average microstrain *εs*, calculated by the WHP and SSP techniques, on the service-life duration *t* for Al wires from the cables of the AC50 and A50 types.

Thus, the use of a steel core in the AC50-type cable (the cross-sectional area of the aluminum components of the cable remains practically the same, ~50 mm2, as in A50-type cable without the steel core) slows down the changes in the average parameters of not only the structure (the cubic unit cell parameter *a* of the Al material and its density *ρ*x), but also of the microstructure (the average size *D* of crystallites and absolute value of average microstrain *ε*s in them) of the Al material of cable wires.

It is to be expected that the steel core will affect not only the average characteristics of the wires but also their NSDLs. In order to investigate how the presence of a steel core in a cable affects the state of NSDLs of wires from that cable, XRD profiling of the structural and microstructural characteristics of AC50 wires in comparison with A50 wires was carried out by means of the method described in [10]. As noted in experimental Section 2.2.3, the essence of XRD profiling is that each Bragg angle 2*θ*B of the reflection with Miller indices *hkl* corresponds to the X-ray penetration depth *Thkl* pen in accordance with Formula (6), determined by the linear absorption coefficient *μl* and the X-ray density *ρ*x of the material (Al in the case of the wires under study). If the samples were powder or there was no profile dependence on the depth of penetration of X-rays, then the structural and microstructural characteristics obtained from the analysis of reflections, i.e., at all depths from the sample surface, would have close values statistically disordered for different reflections within e.s.d.

Figure 15a,b presents a comparison of the distributions of the values of the cubic unit cell parameter *a* and the XRD mass density *ρ*x of the wire Al material, which are calculated from the structural data with Formula (4), along with the penetration depth *T* = *Thkl* pen of X-rays, which is estimated with the Formula (6) from the Bragg angles 2*θ*B of the observed reflections, for wires from AAAC (A50) and ACSR (AC50) cables.

**Figure 15.** Distribution of (**a**) the cubic unit cell parameter *a*(*T*) and (**b**) the XRD mass density *ρ*x(*T*) of the wire Al material along the depth *T* from the surface of the A50 and AC50 wires. Samples are numbered according to Table 2 and their service lifetimes are shown in (**a**). The symbols for (**b**) are the same as shown in (**a**). At the right sides of (**<sup>a</sup>**,**b**), the axes are shown corresponding, respectively, to the lattice defect Δ*a*/*a* and the density defect Δ*ρx*/*ρ<sup>x</sup>*, which are estimated with respect to the bulk of the non-exploited sample of A50 type (N5-2, 0 years of operation). The approximation lines in (**<sup>a</sup>**,**b**) are drawn according to the exponential decay law. In (**b**), the thicknesses *<sup>T</sup>*layer of the NSDL are estimated for AC50 wires from the intersection of the distribution curves for AC50 samples of different non-zero service lives with the curve corresponding to a non-used sample (N5-2, service life of 0 years). The inset in (**b**) presents the extrapolations of the distribution curves of AC50 wires to depths of 200 μm from the surface for samples. The shown estimates of the total thickness *<sup>T</sup>*layersat of the NSDL for wires are obtained from the intersection with tangents drawn at the points when the distribution curves reach a plateau (when *ρ*x reaches the value *<sup>ρ</sup>*xsat = 99.99% of the density estimated from the distribution curve at a depth of 200 μm).

As one can see from Figure 15a,b, the cubic unit cell parameter *a* and the density *ρ*x of the Al material of wires with different service life lengths from cables of both types are not the same at different depths *T* from the surface of the wires, but show smooth dependences *a*(*T*) and *ρ*x(*T*), which are fairly well described by approximation curves that correspond to the exponential decay law. To simplify the perception, the fitting curves are not shown in Figure 15b for the experimental points corresponding to the A50 wires. An analogue of Figure 15b with all fitting curves is given in SM Figure S3.

Since the XRD density *ρ*x is inversely proportional to the cube of the parameter *a* (*ρ*x ~1/*a*3, see Formula (4)), it is satisfactory to consider the dependences *ρ*x(*T*) alone. For wires from cables of both types, the density *ρ*x is maximum and practically does not change at a sufficient distance from the surface in the bulk of the wires. Near the surface, *ρ*x is minimum, which is the result of the formation of defects of a void nature in the near-surface layers [10] (i.e., of the formation of NSDLs).

The main changes in the structure and density of the wire Al material occur in the near-surface layer with a thickness of *<sup>T</sup>*layer = 36.4–39.1 μm for A50 wires or a bit smaller, *<sup>T</sup>*layer = 35.9–38.2 μm, for AC50 wires, which were determined from the intersection of the approximation curves *ρ*x(*T*) referring to wires after operation with the fitting curves of unused wires of the corresponding type (see Figure 15b for AC50 samples and Ref. [10] for A50 wires). The approximation curves *ρ*x(*T*) of the unoperated A50 (N5-2) and AC50 (N5) wires are very close. At depths *T* from ~25 μm for both wires, the density defect is Δ*ρ*x/*ρ*x ≈ −0.05% and practically does not change. When approaching the surface, only a slight drop in density is observed in the wires of both types ( Δ*ρ*x/*ρ*x ≈ −0.2% at a depth of *T* ≈ 12.5 μm). Thus, NSDL with almost the same negative density defect (i.e., with a decrease in density due, apparently, to defects of a void nature), which does not exceed ~0.2% in absolute value at a depth of *T* ≈ 12.5 μm, already exists in wires from unused cables of both A50 and AC50 types.

As follows from the definition of the *<sup>T</sup>*layer value (see above), in A50 and AC50 wires after operation at a depth equal to *<sup>T</sup>*layer ~35.9–39.1 μm from the surface, the density defect is the same as in non-operated wires ( Δ*ρ*x/*ρ*x ≈ −0.05%). However, after operation, the density of the near-surface layers noticeably decreases the greater the closer the layer is to the surface, and in A50 wires (from AAAC cables without a steel core), this decrease in density is significantly greater than in AC50 wires. For example, in A50 wires at depths of *T* ≈ 12.5 μm, the density defect reaches Δ*ρ*x/*ρ*x ≈ −0.68% and −1.17% for wires after 10 (sample N8) and 18 years (N7) of operation in comparison with Δ*ρ*x/*ρ*x ≈ −0.48% and −1.04% for AC50 wires after service life durations of 8 (sample N2-2) and 20 years (N6), respectively, i.e., the density defect in AC50 wires is less in absolute value by ~30% and ~10% after ~10 and ~20 years of operation. Thus, the use of a steel core in AC50-type ACSR cables leads to less degradation (smaller decrease in the density) of near-surface layers with a thickness of at least ~25 μm (as can be seen from Figure 15b, the largest deviations of the approximation curves *ρ*x(*T*) for A50- and AC50-type wires start at depths from the surface of less than ~25 μm).

Extrapolation of the approximation curves *ρ*x(*T*) to large depths from the surface shows that, for wires of both types, the estimated density *<sup>ρ</sup>*x200μ<sup>m</sup> at depths of ≥200 μm does not change with an accuracy of a thousandth of a percent, and the dependence *ρ*x(*T*) almost reaches a plateau, which can be related to the mass density *<sup>ρ</sup>*xbulk of the wires in the bulk.

Estimates show that the density *ρ*x *T*layer at a depth of *<sup>T</sup>*layer for A50 and AC50 wires after operation is ~99.6% of *<sup>ρ</sup>*x200μ<sup>m</sup> (i.e., of *<sup>ρ</sup>*xbulk). Most of the XRD mass density *ρ*x drop is occurring in a layer with a thickness equal to *<sup>T</sup>*layer from the surface ( *ρ*12.5μ<sup>m</sup> x − *ρ T*layer x *ρ*12.5μ<sup>m</sup> x − *ρ*200μ<sup>m</sup> x ·100% ~70% for most samples (N8 (A50 type, 10 years of service life), N7 (A50 type, 18 years), and N6 (AC50 type, 20 years)) and ~50% for AC50 sample N2-2 after 8 years of operation). Apparently, this significant drop of *ρ*x evidences that most of the defects of a void nature after the operation of cables of both types are formed in a layer of wires with a thickness equal to the value of *<sup>T</sup>*layer from the surface of the wires.

We have also made estimations of the depth *<sup>T</sup>*layersat from the surface where the density *<sup>ρ</sup>*xsat is 99.99% of the value *<sup>ρ</sup>*x200μ<sup>m</sup> (which is taken as the value of *<sup>ρ</sup>*xbulk). In the inset of Figure 15b, these estimates are shown graphically for AC50 samples and were given in [10] for A50 wires. According to the *ρ*12.5μ<sup>m</sup> x − *ρ*sat x *ρ*12.5μ<sup>m</sup> x− *ρ*200μ<sup>m</sup> x·100% ≈99% criterion for all

studied samples of both types, in the near-surface layer of thickness *<sup>T</sup>*layersat, almost the entire observed decrease in the XRD mass density *ρ*x occurs in comparison with the values of density *<sup>ρ</sup>*xbulk in the bulk of the wires.

Figure 16 presents a comparison of the thickness estimates obtained for both characteristic near-surface layers, namely, *<sup>T</sup>*layer (~50–70% reduction in density *ρ*x) and *<sup>T</sup>*layersat (~99% reduction in density *ρ*x). The thickness *<sup>T</sup>*layer of NSDL, where most void defects are concentrated, increases to 39.2(1) μm in A50 wires after a service life of 10 years (sample N8), then remains practically unchanged (39.1(1) μm) in sample N7 after 18 years of operation. Perhaps due to the influence of the steel core, the thickness of the *<sup>T</sup>*layer of a similar NSDL in AC50 wires is a bit less, reaching 35.9(1) μm in sample N2-2 after 8 years of operation and slightly increasing to 38.2(1) μm in sample N6 after 20 years of service. After the operation of wires in cables of overhead transmission power lines, the thickness *<sup>T</sup>*layersat of NSDL, where almost all void defects are concentrated, is significantly (3–4 times) greater than *<sup>T</sup>*layer for wires from cables of both types. In A50 wires, the value of *<sup>T</sup>*layersat increases almost linearly with service life duration from 55.8(1) μm (N5-2, service life of 0 years) to 96.3(1) μm (N8, 10 years) and 114.7(1) μm (N7, 18 years). In AC50 wires (with steel core), the value of *<sup>T</sup>*layersat also increases, though non-linearly, from 21.6(1) μm (N5, 0 years) to 160.0(1) μm (N2-2, 8 years) and 119.1(1) μm (N6, 20 21.6(1) μm (N5, 0 years) to 160.0(1) μm (N2-2, 8 years) and 119.1(1) μm (N6, 20 years). As one can see, NSDL is already present in non-operated wires. The difference in its thickness by almost 2.5 times may be associated not with the type of wires but with the features of their manufacture and with experimental inaccuracies. Samples after 18 and 20 years of operation (respectively, A50 sample N7 and AC50 sample N6) are characterized by similar values of the *<sup>T</sup>*layersat. At the same time, the AC50 sample N2-2 after 8 years of operation has a *<sup>T</sup>*layersat value that is ~1.5 times greater than that of the A50 sample N8 after a comparable 10 years of service. This difference may also be related to the features of operation and inaccuracies of the experiment.

**Figure 16.** Comparison of dependences of thicknesses of the NSDLs, at which there is a ~50–70% (*T*layer) and ~99% (*T*layersat) drop in XRD mass density, on the service life *t* of the wires from the overhead power line cables of A50 and AC50 types (respectively, without and with steel core).

The unit cell parameter *a* and the calculated X-ray density *ρ*x of the Al material are not exclusive characteristics which demonstrate smooth dependences on the depth *T* (= *Thkl* pen in the case of the *hkl* reflection) from the surface from which the diffracted X-rays come. There are the microstructural parameters too. As shown above, there is a microstrain in the Al crystallites. Average size *D* of crystallites and absolute values of average microstrain *ε*s were estimated by WHP and SSP techniques using all the observed XRD reflections (see Table 4, Figure 14, and SM Figure S2).

At the same time, with an increase in the X-ray penetration depth *Thkl* pen, not only the values of the Bragg angles 2*θ*B of XRD reflections regularly change, which determine

the value of the unit cell parameter *a* (i.e., the value *ρ*x), but also their *FWHM*obs, from which one can estimate the size of the crystallite *Dhkl* and the absolute value of microstrain *<sup>ε</sup>*s*hkl* after making the appropriate correction of *FWHM*obs for instrumental broadening (see [37,43]), corresponding to an *hkl* reflection.

Since it is impossible to determine two values, *Dhkl* and *<sup>ε</sup>*s*hkl*, from one reflection at once, in order to identify patterns of trends in changes in microstructural parameters, we first estimated the values *D* = *<sup>D</sup>hkl*0 within the model of the absence of microstrains (*<sup>ε</sup>*s = 0) for the A50 and AC50 wires under study (Figure 17a,b).

**Figure 17.** Distribution of the crystallite size *D* = *<sup>D</sup>hkl*0 estimated in the framework of zero microstrain assumption *(*model *εs* = 0) in the Al wires along the depth *T* from the surface of the (**a**) A50 and (**b**) AC50 wires. Sample numbers according to Table 2 and their service lifetimes are shown in (**<sup>a</sup>**,**b**). The approximation lines in (**<sup>a</sup>**,**b**) are drawn according to the exponential-decay law.

As one can see from Figure 17, wires from cables of both types (with and without a steel core) demonstrate identical trends of a smooth change in the crystallite size *D* = *<sup>D</sup>hkl*0, calculated in the zero microstrain approximation (*<sup>ε</sup>*s = 0) for different reflections corresponding to different depths *T* from the surface. It is worth noting that, obviously due to the lower precision of determining the parameters of the microstructure compared to the parameters of the structure, the scatter of the experimental points *<sup>D</sup>hkl*0 around the approximation curves is rather large, which makes it difficult to obtain sufficiently accurate quantitative characteristics, although the trends in *Dhkl*0(*T*) are rather apparent.

The sizes of crystallites *<sup>D</sup>hkl*0 in non-exploited A50 (N5-2) and AC50 (N5) wires change slightly and almost linearly at different depths *T* from the surface (if one considers the approximation lines at experimentally achievable depths up to *T* ~35.5 μm; see Figure 17a,b). For the A50 N5-2 wire (service life of 0 years), the experimental values of *<sup>D</sup>hkl*0 corresponding to different reflections (i.e., to different depths *T* from the surface) give an average crystallite size of 109(16) nm, while for the AC50 wire N5 (0 years), the experimental points corresponding to different *T* are scattered around an almost straight horizontal line corresponding to a larger average value of 138(16) nm (model *ε*s = 0 in Table 4). Approximation curves of operated samples for experimental values of *<sup>D</sup>hkl*0 obey the exponential decay law or the nearly linear drop law in the case of AC50 wires, i.e., in both cases, the farther from the surface (within ~35.5 μm thick NSDL), the smaller *<sup>D</sup>hkl*0. For wires of both types, the approximation curves for *Dhkl*0(*T*) in wires with a service life of 8–10 years go higher than for wires with a longer service life of 18–20 years. The presence of a steel core in AC50 type wires leads to a smaller crystallite size *<sup>D</sup>hkl*0 near the surface than in the case of A50 wires without a core, while the sizes *<sup>D</sup>hkl*0 of crystallites are almost the same far from the surface (compare 185 nm and 208 nm near surface at a depth *T* of ~12.5 μm for AC50 and A50 wires after 8 (sample N2-2) and 10 (N8) years of exploitation, respectively, and ≈100 nm for both wires at *T* ~35.5 μm with, correspondingly, 141 nm and 173 nm at *T* ~12.5 μm and

≈90 nm at *T* ~35.5 μm for AC50 and A50 wires after 20 (N6) and 18 (N7) years). As a result, the amplitude of variation of the *Dhkl*0(*T*) approximation curves in NSDL at depths from the surface *T* ~12.5 μm to ~35.5 μm for AC50 wires is noticeably smaller than for A50 wires (respectively, ≈74 nm and ≈62 nm in AC50 wires with service lives of 8 (N2-2) and 20 (N6) years compared with ≈94 nm (N8, 10 years) and ≈91 nm (N7, 18 years) in A50 wires).

As in [10] for wires of the A50 type, we have estimated the distribution of the absolute value of microstrain *ε*s in crystallites at depths up to *T* ~12.5 μm for AC50 wires under the assumption that there are no microstrains near the surface at depths up to *T* ~12.5 μm (*<sup>ε</sup>*s = 0), while the crystallite sizes at large depths *T* ≥ 15 μm are fixed and equal to the crystallite size *<sup>D</sup>*12.5μm at a depth of *T* ~12.5 μm.

Figure 18 shows the *<sup>ε</sup>*s*hkl* distributions obtained for AC50 wires with different service lifetimes under the above assumptions. Similar estimates of the *<sup>ε</sup>*s*hkl* distribution for A50 wires with various service lifetimes can be found in [10].

**Figure 18.** Distribution of microstrain *ε*s = *<sup>ε</sup>*s*hkl* along the depth *T* from the surface of the AC50 wire. The microstrain *<sup>ε</sup>*s*hkl* is estimated under the assumption of a fixed crystallite size equal to the crystallite size *<sup>D</sup>*12.5μm near the surface (at a depth of *T* ~12.5 μm). Sample numbers according to Table 2 and their service lifetimes are shown. The inset shows an example of estimation of the average microstrain *<sup>ε</sup>*s*sat* in the NSDL at depths *T* ≥ 15 μm, if the crystallite size is fixed and equal to the crystallite size *<sup>D</sup>*12.5μm.

An analysis of the obtained distributions of *<sup>ε</sup>*s*hkl* over depth *T* from the surface for NSDLs of AC50 and A50 wires shows that the microstrains *<sup>ε</sup>*s*hkl* estimated under the assumption of crystallite sizes fixed at *<sup>D</sup>*12.5μm at a depth *T* ~12.5 μm become constant in value ("saturated", *<sup>ε</sup>*ssat) already at depths of *T* ~15 μm. An example of evaluating the value of *<sup>ε</sup>*ssat is given in the inset in Figure 18 for AC50 N2-2 wire with a service life of 8 years and in [10] for A50 wires. Upon comparing the distribution profiles *<sup>ε</sup>*s*hkl*(*T*), one can conclude that the values of *<sup>ε</sup>*ssat for AC50 wires are smaller than for A50 wires with a comparable service life. Figure 19 shows *<sup>ε</sup>*ssat vs. service life *t* for both wire types. As can be seen, the form of the *<sup>ε</sup>*ssat(*t*) dependences is very similar for both types of wires. Yet, for AC50 wires, the dependence *<sup>ε</sup>*ssat(*t*) is shifted to smaller values, i.e., the presence of a steel core in AC50 type cables reduces the absolute value of microstrain in the wires of this type of cable compared to A50 wires without a core. The results obtained confirm the trends and even the numerical values of absolute values of average microstrain *ε*s obtained by the WHP and SSP techniques for microstrains averaged over NSDL with a thickness of ~35.5 μm (see Figure 14b).

**Figure 19.** Microstrain *<sup>ε</sup>ssat* calculated under the assumption of a fixed crystallite size equal to the crystallite size *<sup>D</sup>*12.5μm near the surface (at a depth of *T* ~12.5 μm) depending on the service life *t* of the Al wires of the overhead power lines of the A50 and AC50 types (correspondingly, AAAC and ACSR types, without and with steel cores).

It should be noted that both considered cases (the absence of microstrains (*<sup>ε</sup>*s = 0, Figure 17a,b) and a fixed crystallite size equal to the size of crystallites near the surface of the samples (Figure 18)) are limiting. If, for example, the size *D* of crystallites from the surface to the depth first increases and then decreases, then, in accordance with the formulas for calculating the parameters of the microstructure (see [10,43]), the absolute value of microstrain *ε*s also first increases and then decreases. As a result, in this case, the dependences *Dhkl*0(*T*) and *<sup>ε</sup>*s*hkl*(*T*) in NSDL will acquire a form close to bell-shaped.

Thus, the XRD study of wires from A50 and AC50 cables of different service life lengths from 0 to 20 years revealed the features of changes in the structural and microstructural parameters of NSDL of wires (characteristics averaged over the NSDL with a thickness of ~35.5 μm in accordance with the values of the Bragg angles of the observed reflections and the profiles of these characteristics in depth from the surface of the wire) depending on the presence of a steel core in the cables of overhead power lines from which these wires are extracted.

#### *3.5. Results of Acoustic Studies*

To study the quite probable scatter of experimental data of the acoustic study along the wire segment, samples with a length of ~25 mm were cut from different sections of the wire (as a rule, there were three pieces for each service life). This scatter can be caused both by the different deformation prehistory of wire sections during cable manufacture and by its operation duration. As an example, the results of the measurements of the amplitude dependence (i.e., dependence on the amplitude of vibrational strain *ε*) of both the Young's modulus *E*(*ε*) and the decrement of elastic vibrations *δ*(*ε*), as well as the dependence of oscillatory stress on the amplitude of the nonlinear inelastic deformation, *σ*(*ε*d), for three studied samples with the same service life are shown in Figures 20a and 21a (A50, samples N8, 10 years of service life) and Figures 20b and 21b (AC50, N6, 20 years of service life). It can be seen from the Figures that the data obtained from pieces cut from different sections of wire of the same service life noticeably differ from each other. The greatest difference (several times) is observed for the values of *δ* and *σ*. The Young's modulus *E* turns out to be structurally sensitive only in the third or fourth significant decimal place, and, apparently, this sensitivity is determined mainly by the presence of defects and the microplastic properties of a particular piece.

**Figure 20.** Dependences of the Young's modulus *E* and decrement *δ* on the amplitude of vibrational deformation *ε* for Al wires of (**a**) A50 type after 10 years of service before (N8\_1,2,3) and after (N8\_1) etching and (**b**) AC50 type after 20 years of service (N6\_1,2,3). The measurements were taken at room temperature.

**Figure 21.** Diagrams of microplastic deformation *<sup>σ</sup>*(*<sup>ε</sup>d*) of Al wires of (**a**) A50 type after 10 years of service before (N8\_1,2,3) and after (N8\_1) etching and (**b**) AC50 type after 20 years of service (N6\_1,2,3). The measurements were taken at room temperature.

We have made an attempt to reveal the effect of operating time on the studied parameters. To do that, one sample with the smallest value of the amplitude-independent decrement *δ*i was selected for each material (A50 and AC50) and service life. In such a wire piece, the plastic deformation and, consequently, defect formation, which can occur during the manufacture of the cable, are apparently less than in the other wire areas. When these

values are the minimum, the effect of unfavorable factors (wind, snow sticking, etc.) on the decrement, leading to the appearance of additional defects and their evolution during operation, should be more apparent. The obtained data are summarized in Table 5 and, for explicitness, are shown in Figure 22 in the form of dependences on the operating time, the Table and Figure show the values of the elastic modulus *E*, amplitude-independent decrement *δ*i, and microplastic flow stress *σ*s = *σ* measured at inelasticstrain amplitude *ε*d = 4 · 10−<sup>8</sup> obtained for specimens with the lowest *δ*i value for all investigated wires.

**Table 5.** Samples of cables of overhead power lines' Young's modulus *E*, amplitude-independent decrement of elastic vibrations *δ*i, and microplastic flow stress *σ*s of the aluminum samples prepared from wires of overhead power lines with different service life and selected according to the criterion of the smallest value of the amplitude-independent decrement *δ*i. For each sample, the number of studied pieces cut from wires of the same service life is indicated.


**Figure 22.** Dependences of Young's modulus *E*, amplitude-independent decrement *δ*i, and microplastic stress *σ*s for Al wires on operating time *t*. The measurements were taken at room temperature.

When looking at Figure 22, the first thing that catches the eye is the noticeable effect of the steel core. The use of this core in AC50 type samples maintains a low level of amplitude-independent decrement *δ*i and a high level of stress *σ*s of microplastic flow in comparison with the wires of the A50-type cables without a steel core. At the same time, as expected, the values of *δ*i and *σ*s differ insignificantly for A50 and AC50 unused samples (0 years of service life).

As for the dependences of *δ*i and *σ*s on the operating time (Figure 22), these parameters change much less for the wires of a steel core (ACSR) AC50 cable than for those of an all-aluminum (AAAC) A50 cable. One can also note the difference in the behavior of *E*, *δ*i, and *σ*s for wires from the former cable and the latter one, namely the fact that, at approximately the service life, where there is a maximum in the operating-time dependence of *E*(*t*), *δ*i(*t*), and *σ*s(*t*) for one, the minimum is observed for the other one. The presence of a steel core in an ACSR AC50 cable at the beginning of operation for a service life of up to 8 years is favorable for Al wires from the cable (*δ*i decreases while both *E* and *σ*s increase), then there are slight changes for the worse with an increase in service life up to 20 years. On the contrary, in Al wires of an all-aluminum (AAAC) A50 cable, at first, significant unhardening is observed after 10 years of service, then there is a slight improvement in deformation characteristics with an increase in service life up to 18 years. However, it should be noted that the results obtained should be treated with caution since the number of samples studied is small. Nevertheless, the positive role of the steel core for power transmission lines is not in doubt, as it has already been discussed in the review of the available literature in Section 1 (Introduction).

In this paper, apparently, we need to once again pay attention to a result discussed in detail in [10], namely, the fact that the defects are mainly located in the NSDL of the Al wires. Figures 20a and 21a show data for A50 sample N8\_1 (service life of 10 years) in its original state and after etching (N8\_1), when a layer of about 35 μm thick was removed from the surface. In the initial state before etching, this sample had the largest amplitudeindependent decrement *δ*i, the lowest level of microplastic stress *σ*, and the smallest value of Young's modulus *E*. Upon etching, it turned out to have the smallest decrement *δ*i and the largest value of *σ* among all the investigated samples with numbers N8\_*i* (*i* = 1 − 3). Young's modulus of the sample N8\_1' also increased noticeably, i.e., an improvement in the deformation characteristics is observed after the removal of the near-surface layer by etching. Evidently, this indeed means that most of the defects are located in the near-surface layer. Undoubtedly, one can dare to attribute this result to other samples (N8\_2 and N8\_3, N6\_1,2,3 and so on), for which etching was not carried out.
