# Comparison of Structural, Microstructural, Elastic, and Microplastic Properties of the AAAC (A50) and ACSR (AC50/8) Cables after Various Operation Periods in Power Transmission Lines

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}cross-section, hereinafter referred to as AC50) with the cross-section of the stranded conductor of ~50 mm

^{2}, which were in operation for 0–20 years in the Volgograd region of Russia. Using the techniques of X-ray diffraction, electron backscattered diffraction, densitometry, and the acoustic method, the structural and microstructural features of the wires have been compared and found to be correlated with their elastic-microplastic properties. It has been ascertained that the presence of a steel core in AC50 leads to a decrease in the defectiveness of the near-surface layer of their aluminum wires. Compared with A50 cables, the development of void defects in the near-surface layer of Al-wires of AC50 cables slows down (by ~1 year with a service life of ~10 years and by ~3 years with a service life of ~20 years).

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Samples

^{2}, the diameter of individual aluminum wires is 3 mm, the estimated cable weight is 135 kg/km. Steel-aluminum cables designated as AC50 were also investigated. They contain six Al wires with a diameter of 3.2 mm, whirled around a steel core with the same diameter of 3.2 mm. The cross-sections of the AC50 cable according to the passport are 48.2 mm

^{2}(Al) and 8.04 mm

^{2}(steel), the estimated weight of the cable is 195 kg/km. It should be noted that the values of the diameters of the wires studied, measured experimentally, differ from the nominal values and range from 2.85 mm to 3.03 mm and from 3.20 mm to 3.24 mm for A50 and AC50 wires, respectively (Table 2).

#### 2.2. Experimental Details of Measurements and Analysis

#### 2.2.1. Experimental Details of EDX, SEM, and EBSD

^{2}in size, approximately in the center of the cross sections and near their edges at a distance of ~150 μm from the outer surface of the wires, i.e., in positions corresponding to the internal bulk and near-surface layers of wires, respectively. The EDX analysis was carried out on an area of 500 × 500 μm

^{2}in cross-section to obtain averaged values of the sample composition. During the analysis, the spectrum was continuously accumulated while the area was scanned by an electron beam.

#### 2.2.2. Experimental Details of Densitometric Measurements

_{d}of the samples (hereinafter also referred to as “densitometric density” or “integral density”). To accurately determine the density, samples of aluminum wires 80 mm long and weighing about 1.5 g were used, and distilled water was used as the liquid. The dependence of the density on the temperature of such a liquid is known with the required accuracy. So, the relative error δρ

_{d}/ρ

_{d}in determining the density did not exceed 1 ∙ 10

^{−4}. To study the surface-layer influence, the wires were investigated after different periods of service life, and the distribution of the change in density over the cross-section of the wires (density defect Δρ

_{dL}/ρ

_{dL}) was obtained. Chemical etching was carried out in a 20% NaOH aqueous solution. During etching, the thickness of the removed layer was determined as [10]:

_{0}and m

_{0}are the radius and mass of the sample in the form of a cylindrical rod before polishing, respectively, and m

_{i}is the mass of the sample after polishing the ith layer.

_{dL}) and the value of the density defect Δρ

_{dL}/ρ

_{dL}in polished layers were calculated with the formulas [10]:

_{d}

_{0}is the density of the sample before polishing, while ρ

_{di}is that after polishing of the ith layer.

_{etch}≈ 20 μm. This provided information on the distribution of the density defect over the cross-section of the sample with a decrease in its radius.

#### 2.2.3. Experimental Details of XRD Measurements and Analysis

_{α1,2}radiation from a copper anode after a K

_{β}-filter in the form of a Ni-foil and a linear position-sensitive semiconductor X-ray detector LYNXEYE (Bruker AXS, Karlsruhe, Germany) with an opening angle of 5°. The temperature in the chamber where the holder with the sample was installed was kept equal to 314 ± 1 K during the measurements. The measurements were carried out using the method of θ-2θ scanning in the range of diffraction angles 2θ = 6–141° with a step of Δ2θ

_{step}= 0.02°. The regimes were used either with sample rotation around an axis coinciding with the axis of the diffractometer goniometer or without rotation, when the X-ray beam was incident on the long side of a cylinder-like sample (see illustration in [10]). Owing to XRD patterns obtained with rotation, the influence of the averaged effects of preferential orientation was estimated. XRD patterns measured without rotation were used to obtain the parameters of XRD reflections (observed Bragg angle (2θ

_{obs}), observed full width at half-maximum intensity (FWHM

_{obs}), maximum (I

_{max}), and integral (I

_{int}) intensities of a reflection) for quantitative analysis of the structural and microstructural parameters of the Al material of the studied samples. Using the EVA program [40], the XRD patterns were corrected for the contribution of the background and Cu-K

_{α2}radiation, and the values of the above reflection parameters were determined. The obtained observed Bragg angles 2θ

_{obs}of the reflections were adjusted with the angular corrections Δ2θ

_{zero}(detector zero shift) and Δ2θ

_{displ}(displacement due to the mismatch of the sample surface with the focal plane of the diffractometer; see [10]), which were determined from additional XRD measurements of the samples, immersed to surface level in NaCl powder, certified with XRD powder standard Si640f (NIST, Gaithersburg, MD, USA). X-ray phase analysis was performed by means of the EVA program using the Powder Diffraction File-2 (PDF-2) powder database [41].

_{B}obtained after angular corrections and the Miller indices hkl of the reflections, the parameters a of the cubic unit cell of the wire Al material were calculated, corresponding to each individual XRD reflection. In this case, the estimated standard deviation (e.s.d.) δa of the parameter a was calculated analytically from δ2θ

_{B}(e.s.d. of the Bragg angle), which was taken as half of the step Δ2θ

_{step}with which the XRD pattern was measured (i.e., δ2θ

_{B}= 0.01°). The average value of the parameter a was determined using the Celsiz program [42], which performs refinement using the least squares method.

_{x}(g/cm

^{3}) determined from XRD data (hereinafter “X-ray density” or “XRD density”) was calculated from the ratio of the mass of the unit cell of the crystalline Al phase to the volume of the unit cell as:

_{cell}(Å

^{3}) = a

^{3}is the volume of the Al cubic unit cell, Z = 4 is the number of formula units in the Al unit cell, A

_{r}= 26.9815384 a.m.u. (atomic mass units) is the tabular value of the atomic mass of Al, and C

_{a.m.u.}= 1.660539066 10

^{−24}g/a.m.u. is the conversion factor from a.m.u. to grams.

_{x}/ρ

_{x}were also calculated. In these calculations, in expression (5), p = a or ρ

_{x}for any reflection from the sample (either the average value of the unit cell parameter or density of a sample), and p

_{0}is either the value of the unit cell parameter a

_{0}or the density ρ

_{x0}of the Al material in the bulk of a new sample (0 years of service).

_{s}in them) was carried out using the SizeCr program [43] in accordance with the method described in [10,37] and analyzed in detail in [43]. Using the SizeCr program, based on the observed ratio FWHM

_{obs}/B

_{int}(where B

_{int}= I

_{int}/I

_{max}is the integral width of a reflection), the reflection’s type (Gaussian, or Lorentzian, or pseudo-Voigt (pV)) was determined for each reflection, and, depending on the type of reflection, a correction of FWHM

_{obs}for instrumental broadening was made, see [10,37,43]. As a rule, the observed XRD reflections were pV-type ones. That is, they were characterized by the ratio 0.637 < FWHM

_{obs}/B

_{int}< 0.939. The values FWHM

_{corr}(FWHM

_{obs}corrected for instrumental broadening according to reflection type) were used to calculate the microstructural parameters. The microstructural characteristics of Al wire materials (average crystallite size D and absolute value of average microstrain ε

_{s}) were determined by the graphical methods WHP (Williamson–Hall plot) [44] and SSP (Strain–Size plot) [45] adapted to the observed pV type of XRD reflections. The points of the WHP and SSP graphs, corresponding to every XRD reflection hkl, were calculated using the SizeCr program, utilizing the coefficients K

_{Scherrer}= 0.94 and K

_{strain}= 4 of the Scherrer and Wilson–Stokes equations, connecting the corresponding FWHM

_{corr}components with crystallite size D

^{hkl}and microstrain ε

_{s}

^{hkl}values, respectively (see [43,44,45]). In the absence of microstrains (model ε

_{s}= 0), the SizeCr program calculated the sizes D

^{hkl}

_{0}of crystallites for each observed reflection as well as the mean-square-root value D

_{0}for all reflections. When setting a fixed value of D

^{hkl}, the values of the microstrain ε

_{s}

^{hkl}corresponding to each observed XRD reflection hkl were calculated.

_{l}= 48.657 cm

^{2}/g is the linear absorption coefficient of Al in the case of Cu-K

_{α1}radiation (after correcting for the Cu-K

_{α2}contribution), and θ

_{B}is half of the 2θ

_{B}Bragg angle (after accounting for angular corrections). The structural and microstructural characteristics of the sample material, which were calculated for each reflection with Miller indices hkl, correspond to the material’s state averaged along the crystallographic direction [hkl] over the volume of the near-surface layer with a thickness equal to the penetration depth ${T}_{\mathrm{pen}}^{hkl}$. As a result, analysis of different reflections detected at different Bragg angles 2θ

_{B}makes it possible to obtain profiles of changes in structural and microstructural parameters with depth from the surface.

#### 2.2.4. Experimental Details of Acoustic Measurements

_{d})) makes it possible to study microprocesses that can take place in samples when external conditions change.

^{−6}to ~3 ∙ 10

^{−4}. The modulus of elasticity was determined using the formula [47]:

_{d}determined by the densitometric method was used), and f is the oscillation frequency of the rod-shaped wire samples close to 100 kHz. Upon studying the E(ε) dependence, microplastic deformation diagrams σ(ε

_{d}) were constructed, which made it possible to evaluate the properties of the material in the “stress—inelastic strain” coordinates customary in mechanical tests, when the value of the amplitudes of vibrational stresses σ = E ∙ ε (Hooke’s law) is plotted along the ordinate axis, and the nonlinear inelastic deformation ε

_{d}= ε ∙ (ΔE/E)

_{h}is plotted along the abscissa axis, where (ΔE/E)

_{h}= (E − E

_{i})/E

_{i}is the amplitude-dependent defect of Young’s modulus. The quantities E

_{i}and δ

_{i}measured at small amplitudes ε when both E and δ are yet independent of ε are called amplitude-independent Young’s modulus and amplitude-independent decrement of elastic vibrations, respectively.

## 3. Results

#### 3.1. SEM and EDX Results

#### 3.2. EBSD Results

_{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.

#### 3.3. Results of Densitometric Measurements

_{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.

_{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 Δρ

_{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 Δρ

_{dL}/ρ

_{dL}continues until a layer of ~30 μm is removed from the surface.

_{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 near-surface 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.

_{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 Δρ

_{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 Al

_{2}O

_{3}oxides are formed on the surface of the wires, the density of which (~3.7 g/cm

^{3}) is significantly higher than the density of aluminum (~2.7 g/cm

^{3}). 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.

#### 3.4. Results of XRD Investigations

_{max}

^{022}/I

_{max}

^{111}) 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.

_{2}O

_{3}[51,52] (δ-phase, space group P4

_{1}2

_{1}2 (92), PDF-2 card 00-056-1186; δ*-phase, space group P222 (16), PDF-2 card 00-046-1215). With a service life of up to 20 years, δ*-/δ-Al

_{2}O

_{3}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-) Al

_{2}O

_{3}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.

_{x}and density defects Δρ

_{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.

_{x}= 2.6973(2) g/cm

^{3}and 2.6972(2) g/cm

^{3}, 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/cm

^{3}) 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.

_{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, yet 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

^{−4}Å/year in A50 wires down to 1.07(3) ∙ 10

^{−4}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

^{−4}g/cm

^{3}/year to −2.13(7) ∙ 10

^{−4}g/cm

^{3}/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.

_{0}of crystallites, averaged over all D

^{hkl}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).

_{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).

^{2}, 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.

_{B}of the reflection with Miller indices hkl corresponds to the X-ray penetration depth ${T}_{\mathrm{pen}}^{hkl}$ in accordance with Formula (6), determined by the linear absorption coefficient μ

_{l}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.

_{x}of the wire Al material, which are calculated from the structural data with Formula (4), along with the penetration depth T = ${T}_{\mathrm{pen}}^{hkl}$ of X-rays, which is estimated with the Formula (6) from the Bragg angles 2θ

_{B}of the observed reflections, for wires from AAAC (A50) and ACSR (AC50) cables.

_{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.

_{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).

_{layer}= 36.4–39.1 μm for A50 wires or a bit smaller, T

_{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 Δρ

_{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 (Δρ

_{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.

_{layer}value (see above), in A50 and AC50 wires after operation at a depth equal to T

_{layer}~35.9–39.1 μm from the surface, the density defect is the same as in non-operated wires (Δρ

_{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 Δρ

_{x}/ρ

_{x}≈ −0.68% and −1.17% for wires after 10 (sample N8) and 18 years (N7) of operation in comparison with Δρ

_{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).

_{x}(T) to large depths from the surface shows that, for wires of both types, the estimated density ρ

_{x}

^{200μm}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 ρ

_{x}

^{bulk}of the wires in the bulk.

_{x}

^{T}

^{layer}at a depth of T

_{layer}for A50 and AC50 wires after operation is ~99.6% of ρ

_{x}

^{200μm}(i.e., of ρ

_{x}

^{bulk}). Most of the XRD mass density ρ

_{x}drop is occurring in a layer with a thickness equal to T

_{layer}from the surface ($\frac{{\rho}_{\mathrm{x}}^{12.5\mathsf{\mu}\mathrm{m}}-{\rho}_{\mathrm{x}}^{T\mathrm{layer}}}{{\rho}_{\mathrm{x}}^{12.5\mathsf{\mu}\mathrm{m}}-{\rho}_{\mathrm{x}}^{200\mathsf{\mu}\mathrm{m}}}\xb7100\%$ ~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 T

_{layer}from the surface of the wires.

_{layer}

^{sat}from the surface where the density ρ

_{x}

^{sat}is 99.99% of the value ρ

_{x}

^{200μm}(which is taken as the value of ρ

_{x}

^{bulk}). 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 $\frac{{\rho}_{\mathrm{x}}^{12.5\mathsf{\mu}\mathrm{m}}-{\rho}_{\mathrm{x}}^{\mathrm{sat}}}{{\rho}_{\mathrm{x}}^{12.5\mathsf{\mu}\mathrm{m}}-{\rho}_{\mathrm{x}}^{200\mathsf{\mu}\mathrm{m}}}\xb7100\%$≈99% criterion for all studied samples of both types, in the near-surface layer of thickness T

_{layer}

^{sat}, almost the entire observed decrease in the XRD mass density ρ

_{x}occurs in comparison with the values of density ρ

_{x}

^{bulk}in the bulk of the wires.

_{layer}(~50–70% reduction in density ρ

_{x}) and T

_{layer}

^{sat}(~99% reduction in density ρ

_{x}). The thickness T

_{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 T

_{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 T

_{layer}

^{sat}of NSDL, where almost all void defects are concentrated, is significantly (3–4 times) greater than T

_{layer}for wires from cables of both types. In A50 wires, the value of T

_{layer}

^{sat}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 T

_{layer}

^{sat}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 T

_{layer}

^{sat}. At the same time, the AC50 sample N2-2 after 8 years of operation has a T

_{layer}

^{sat}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.

_{x}of the Al material are not exclusive characteristics which demonstrate smooth dependences on the depth T (=${T}_{\mathrm{pen}}^{hkl}$ 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).

_{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 D

^{hkl}and the absolute value of microstrain ε

_{s}

^{hkl}after making the appropriate correction of FWHM

_{obs}for instrumental broadening (see [37,43]), corresponding to an hkl reflection.

^{hkl}and ε

_{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 = D

^{hkl}

_{0}within the model of the absence of microstrains (ε

_{s}= 0) for the A50 and AC50 wires under study (Figure 17a,b).

^{hkl}

_{0}, calculated in the zero microstrain approximation (ε

_{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 D

^{hkl}

_{0}around the approximation curves is rather large, which makes it difficult to obtain sufficiently accurate quantitative characteristics, although the trends in D

^{hkl}

_{0}(T) are rather apparent.

^{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 D

^{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 D

^{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 D

^{hkl}

_{0}. For wires of both types, the approximation curves for D

^{hkl}

_{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 D

^{hkl}

_{0}near the surface than in the case of A50 wires without a core, while the sizes D

^{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 D

^{hkl}

_{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).

_{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 (ε

_{s}= 0), while the crystallite sizes at large depths T ≥ 15 μm are fixed and equal to the crystallite size D

_{12.5μm}at a depth of T ~12.5 μm.

_{s}

^{hkl}distributions obtained for AC50 wires with different service lifetimes under the above assumptions. Similar estimates of the ε

_{s}

^{hkl}distribution for A50 wires with various service lifetimes can be found in [10].

_{s}

^{hkl}over depth T from the surface for NSDLs of AC50 and A50 wires shows that the microstrains ε

_{s}

^{hkl}estimated under the assumption of crystallite sizes fixed at D

_{12.5μm}at a depth T ~12.5 μm become constant in value (“saturated”, ε

_{s}

^{sat}) already at depths of T ~15 μm. An example of evaluating the value of ε

_{s}

^{sat}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 ε

_{s}

^{hkl}(T), one can conclude that the values of ε

_{s}

^{sat}for AC50 wires are smaller than for A50 wires with a comparable service life. Figure 19 shows ε

_{s}

^{sat}vs. service life t for both wire types. As can be seen, the form of the ε

_{s}

^{sat}(t) dependences is very similar for both types of wires. Yet, for AC50 wires, the dependence ε

_{s}

^{sat}(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).

_{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 D

^{hkl}

_{0}(T) and ε

_{s}

^{hkl}(T) in NSDL will acquire a form close to bell-shaped.

#### 3.5. Results of Acoustic Studies

_{d}), for three studied samples with the same service life are shown in Figure 20a and Figure 21a (A50, samples N8, 10 years of service life) and Figure 20b and Figure 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.

_{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

^{−8}obtained for specimens with the lowest δ

_{i}value for all investigated wires.

_{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).

_{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).

_{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.

## 4. Discussion

_{x}(t), Figure 13b) are linear or close to linear (fraction of aluminum oxide q(t), Figure 11). Thus, the difference of 2 years between the compared parameters for wires of different types does not play a role because the dependences for the wires of different types differ well from each other, and the values of these parameters for a wire of the same type with a difference of 2 years are close. The same can be said about the time dependences of other parameters (Figure 16 and Figure 19), particularly about the dependence of the deformation characteristics of wires on their service life (Figure 22).

_{x}(T), Figure 15a,b), then, taking into account that according to determined values of the rate of change of these quantities with time (see Section 3.4), in 2 years they will change only by ~1 · 10

^{−4}Å and ~2 · 10

^{−4}g/cm

^{3}, respectively. Moreover, the parameter a of the Al unit cell will increase, and the density ρ

_{x}will decrease. As a result, if we scale the values of a and ρ

_{x}of A50 wires (service life of 10 years and 18 years) to the values for AC50 wires (service life of 8 years and 20 years) by substraction/addition of the corresponding quantity for 2 years, then the difference between the dependences a(T) and ρ

_{x}(T) for different types of wire will change only slightly. All trends remain, and numerical values are virtually unchanged (up to the fourth digit after the decimal point). As an illustration, the SM Figure S3 shows an example of the dependencies of ρ

_{x}(T) Al wires on A50 cables, reduced to the same service life as the AC50 cable wires. Obviously, this conclusion also applies to the profile dependence of the densitometric density ρ

_{dL}of NSDL (density defect Δρ

_{dL}/ρ

_{dL}, Figure 7).

^{2}cross-sectional area of their aluminum component as ACSR (AC50) cables (Table 1). The most significant difference in their design is the replacement of an additional central aluminum wire in AAAC (A50) cables with a steel core wire of approximately the same diameter in ACSR (AC50) cables. As can be expected, the presence of a steel core in ACSR (AC50) type cables, which is much stiffer than the Al wires of these cables, will reduce the influence of at least some of the above factors, such as stretching and abrasion of wires, in ACSR (AC50) type cable wires compared to AAAC (A50) cable wires. As a result of using the steel core, changes in the structure, microstructure, and, as a result, in the physical properties of AC50 wires will occur more slowly.

_{d}measured by densitometric technique decreases according to a law close to the exponential-decay law. The greatest drop in ρ

_{d}is observed in a narrow near-surface layer up to ~10 μm (~80–85% of the total reduction), the smallest value of ρ

_{d}being near the surface. Taking into account the absence of light chemical elements in sufficiently large quantities according to the results of the EDX microanalysis (Table 3 and Section 3.1), obviously, it indicates the presence of defects of a void nature (nano and micropores, microcracks) in the narrow near-surface layer, the concentration of these defects increasing when approaching the surface. Deeper inside a wire, ρ

_{d}grows weakly until stabilization at depths from ~10 μm to ~30 μm from the surface, apparently due to a decrease in the number of defects. Such a change in the density and in the number of defects is expected since it is the surface of a wire that is affected by the environment and neighboring wires in the first place.

_{dL}/ρ

_{dL}(calculated by Formula (3)) is somewhat smaller (by ~0.1–0.2%) in absolute value than in an A50 wire (Figure 7), i.e., the integral density ρ

_{dL}in this thin layer in the AC50 sample obtained by densitometric measurements of the wire after etching (Formula (2)) is slightly higher than that in the A50 wire. Moreover, the integral density ρ

_{d}of the entire AC50 wire is ~0.05% higher than that of the A50 wire.

_{x}of the wire Al material, calculated from structural data, decreases (see Formula (4) and Figure 13b). Obviously, this also leads to a decrease in the integral density ρ

_{dL}of NSDL and the integral density ρ

_{d}of the entire wire, measured by densitometry. The same causes lead to the formation of microvoids (microcracks) with a higher concentration of them near the surface due to the effect of fretting, which leads to a decrease in the ρ

_{dL}in NSDL and the integral density ρ

_{d}of the entire wire. In the presence of a steel core, the influence of many of the above listed factors (sagging, vibrations, etc.), leading to a reduction in the integral density of the NSDL and the whole wire, is reduced. As a result, the integral densities ρ

_{dL}of NSDL in the AC50 wire and the ρ

_{d}of the entire AC50 wire degrade (decrease) less than in the A50 wire.

_{dL}in NSDL and ρ

_{d}of aluminum wires of an AC50 type cable after operation compared to an A50 cable without a steel core.

_{d}of wire and ρ

_{dL}of wire NSDL obtained by the densitometric method are integral quantities averaged, respectively, over the densities of all wire or wire NSDL components, the higher density ρ

_{dL}in NSDL of the Al wires of the AC50 cable compared to the A50 cable, at least at depths up to ~5–10 µm (and, accordingly, a lower value in terms of the absolute magnitude of the negative density defect Δρ

_{dL}/ρ

_{dL}, see Figure 7) can be due to a larger proportion of Al oxides formed in the NSDL of wires of the AC50 cable (Figure 11), probably as a result of the oxidizing action of the steel core. These aluminum oxides (δ- and/or δ*-Al

_{2}O

_{3}) are characterized by a higher nominal calculated XRD density (~3.7 g/cm

^{3}) [51,52] compared to Al (~2.7 g/cm

^{3}) [50]. Hence, the observed integral density ρ

_{dL}of NSDL and, consequently, the total integral density ρ

_{d}of the Al wires of an AC50 type cable will be higher than that of an A50 cable. However, it should be noted that alumina crystallites formed in NSDLs of wires are much denser and harder than aluminum crystallites. It enhances the influence of the fretting effect and, as noted above, leads to the opposite effect of a decrease in density due to the formation of void defects. Since in AC50 wires, probably due to the oxidizing effect of the steel core, the proportion of aluminum oxides is higher compared to A50 wires, the influence of both effects in AC50 wires will arise competitively. On the one hand, due to the greater proportion of aluminum oxides with a higher XRD density than the XRD density of aluminum, integral densities ρ

_{d}and ρ

_{dL}increase. On the other hand, due to the greater influence of fretting, more voids are formed and the integral densities ρ

_{d}and ρ

_{dL}decrease.

_{B}corresponding to different X-ray-penetration depths has confirmed the presence of NSDLs in Al wires of both types and made it possible to obtain their quantitative characteristics. All trends indicated by the results of density measurements discussed above are also confirmed. As a result of the smooth expansion of the Al lattice (an increase in the unit cell parameter a of the wire Al material) while approaching the sample surface, the X-ray density ρ

_{x}calculated from the structural data decreases (see Formula (4)). This decrease in ρ

_{x}with decreasing depth T from the surface occurs according to an exponential decay law similar to the dependence of the densitometric density ρ

_{dL}of the near-surface layer on the thickness T

_{etch}of the layer removed by etching, although flatter (cf. Figure 7 and Figure 15b).

_{x}(T) obtained from the analysis of XRD reflections corresponding to different X-ray penetration depths (i.e., different depths from the wire surface), two characteristic thicknesses of NSDLs of the wires were estimated. One of the characteristic thicknesses obtained from XRD studies (Section 3.4) is close to the characteristic NSDL thickness of ~30 μm obtained from densitometric measurements. In particular, the characteristic thickness T

_{layer}, corresponding to the density ρ

_{x}

^{T}

^{layer}~99.6% of the density ρ

_{x}

^{bulk}in the bulk of wire, is T

_{layer}= 36.4–39.1 μm for A50 wires and T

_{layer}= 35.9–38.2 μm for AC50 wires of different service life lengths (Figure 16).

_{layer}, i.e., in a smaller thickness of that part of the NSDL where the main drop of the X-ray density ρ

_{x}occurs (~50–70% of the total decrease from ρ

_{x}

^{bulk}) when approaching the surface. Although the second characteristic thickness T

_{layer}

^{sat}, which corresponds to the density ρ

_{x}

^{sat}~99.99% of ρ

_{x}

^{bulk}and thus to the entire thickness of the layer from the surface, where almost the entire observed decrease in the X-ray mass density ρ

_{x}(~99%) occurs, is practically the same for A50 and AC50 type wires after 18–20 years of operation (115 µm–119 µm) and ~1.5 times more after 8–10 years of service for AC50 wire (with steel core) than for A50 wire without steel core (160 µm vs. 96 µm, respectively). At the same time, in wires without operation, the value of T

_{layer}

^{sat}of the total thickness of NSDL in AC50 wire was, on the contrary, ~2.5 times less compared to A50 wire (respectively, ~56 μm vs. ~22 μm, see Figure 16). It is possible, however, that such a non-smooth (irregular) dependence of the total thickness of T

_{layer}

^{sat}of NSDL in AC50 wires on the cable-operation duration t, in contrast to the almost linear increase in T

_{layer}

^{sat}for A50 wires, is not due to the presence of a steel core in AC50 wires, but to the peculiarities of manufacturing the cables under study.

_{x}and density defect Δρ

_{x}/ρ

_{x}depending on the depth T from the surface (Figure 15a,b) is another peculiarity obtained from the analysis of XRD reflections from wires, which indicates a notable effect of the steel core in cables AC50 and A50 of the same cross section of ~50 mm

^{2}of the Al component of the cables. For unused wires and at depths T ≈ 25 μm–36 μm from the wire surface after operation for both types of cables, the approximation dependences ρ

_{x}(T) practically coincide. On approaching the surface, the approximation curves ρ

_{x}(T) begin to diverge for operated wires of different types, and the closer to the surface they get, the greated. Moreover, in the presence of a steel core, the decrease in ρ

_{x}(T) and in Δρ

_{x}/ρ

_{x}is smaller. For example, near the surface (T ≈ 12 μm) of wires from cables of the AC50 and A50 types, respectively, after 8 years–10 years of operation, the density defect Δρ

_{x}/ρ

_{x}decreases in absolute value by ≈9 and ≈14 times compared to the value established for the depth from the surface T

_{layer}. After 18 years–20 years of operation, this difference is ≈21 and ≈23 times for AC50 and A50 wires, respectively.

_{x}in the NSDLs of the cable wires when approaching the surface from the depth of the wire occurs more gently. This flatter course of ρ

_{x}(T) in NSDLs of AC50 wires indicates that the degradation (“aging”) of the AC50 wires from cables with steel cores is slower. The quantitative characteristics of wire degradation were obtained by analyzing the wire parameters averaged over all observed reflections, i.e., over the NSDL with a thickness of ~35.5 μm (Figure 13a,b). In the presence of a steel core (ACSR (AC50) cable), the rate of expansion of the crystal lattice and, thus, that of decrease in the X-ray density ρ

_{x}of the Al material of wires in NSDL with a thickness of ~35.5 μm is ~1.2 times lower (−2.13(7) ∙ 10

^{−4}g/cm

^{3}/year for AC50 wires in comparison to −2.52(8) ∙ 10

^{−4}g/cm

^{3}/year for A50 ones, see Section 3.4). As a result, the delay in the degradation of the lattice and ρ

_{x}of the Al material of the AC50-type wires ranges from ~1 year after a service life of ~10 years up to ~3 years after ~20 years of operation.

_{x}(namely, from the unit cell volume of the Al material in NSDLs of wires (Formula (4)) directly indicates that the cables are less stretched because of vibrations due to wind and, possibly, temperature fluctuations of the surrounding atmosphere, which are the main reasons for the higher density ρ

_{x}in NSDL of Al wires from AC50 cables compared to A50 ones. Due to the stabilizing effect of the steel core, the wires of an AC50 cable are less affected by vibrations and stretches. As a result, the Al lattice of the wire material of AC50 cable expands less, and accordingly, the X-ray density ρ

_{x}estimated from XRD structural data decreases less compared to A50 wires.

_{s}formed in the Al crystallites of NSDL of wires of AC50 cables after service in comparison with that of A50 cables (Figure 14b). Moreover, apparently, the same reason is associated with a lower value of microstrains ε

_{s}

^{sat}observed at depths T below the wire surface in AC50 wires after operation compared to A50 ones (Figure 19). In this case, directly at a depth from the surface down to T ≈ 12.5 μm, the wires of both types are apparently relaxed (ε

_{s}= 0), which seems to be the natural state of the surface of the wires.

_{x}

^{bulk}in the bulk of the wire at depths T of 200 μm and more (and, accordingly, the value ρ

_{x}

^{sat}= 0.9999 ∙ ρ

_{x}

^{bulk}), which are estimated by extrapolation from the approximation curves ρ

_{x}(T) for unexploited samples A50 and AC50, are close to each other. Quantitative estimation by approximating curves ρ

_{x}(T) gives ρ

_{x}

^{bulk}= 2.6987(2)g/cm

^{3}and 2.6970(2) g/cm

^{3}for A50 and AC50, respectively. These ρ

_{x}

^{bulk}values also agree satisfactorily with the average density values in NSDL of wires ρ

_{x}= 2.6973(2) g/cm

^{3}and 2.6972(2) g/cm

^{3}(Table 4). Therefore, the X-ray densities ρ

_{x}estimated for NSDLs of wires and their bulk agree satisfactorily for the two types of zero-service-life wires. These estimated values of ρ

_{x}are larger than the tabular calculated X-ray density of Al material at a temperature of 312.3 K, which is close to the temperature of XRD measurements in this work (ρ

_{x}= 2.6964 g/cm

^{3}according to PDF-2 card 01-071-4008). As discussed in Section 3.4, this discrepancy may be because of the inclusion of a few Si and Fe atoms in the Al structure, which are present in the composition of wires according to EDX (Table 3, Figure 1a,b and Ref. [37]).

_{x}of the Al material averaged over NSDL of 35.5 μm thick (i.e., averaged over the near-surface layer with a thickness of about 1st characteristic thickness T

_{layer}of NSDL from the wire surface, see Figure 13b) and the integral density ρ

_{d}of entire wire (Figure 8) obtained from densitometry measurements is observed. Moreover, for A50 wire from the AAAC type cable, the average X-ray density defect Δρ

_{x}/ρ

_{x}(NSDL characteristic) and the defect of the integral (densitometric) density of the entire wire increase in absolute value from ~0% for unused wire to practically the same value ≈ −0.17% after 18 years of operation. In the case of AC50 wires from the ACSR cable, the average defect of the X-ray density of NSDL wire is also ~0% for unused wire and Δρ

_{x}/ρ

_{x}= −0.162(1)% after 20 years of operation, i.e., somewhat less in absolute value than for A50 wire with a comparable service life. Thus, although the tendency to decrease the density ρ

_{x}of the NSDL with a thickness of T

_{layer}~35.5 µm is the same for both types of cables, for AC50 wire the decrease is less than for A50 wire, which once again emphasizes the stabilizing effect of the steel core in AC50 cables.

_{x}in NSDL of a thickness from the surface of about T

_{layer}~35.5 µm, the XRD density ρ

_{x}

^{sat}= 0.9999 ∙ ρ

_{x}

^{bulk}at depths T = T

_{layer}

^{sat}(~100 µm–160 µm for wires after operation ~10–20 years) does not decrease but increases with an increase in service life from 0 to ~20 years. Figure 23 shows the obtained values of the density ρ

_{x}

^{bulk}and the unit cell parameter a

^{bulk}of the Al material in the bulk, recalculated from ρ

_{x}

^{bulk}using Formula (4) depending on the service life t. For both kinds of wires, the initial value (t = 0 years of operation) of ρ

_{x}

^{bulk}is close to the tabular value ρ

_{x}of pure Al powder at a temperature approximately equal to the temperature of XRD measurements in this work. As can be seen, the dependences ρ

_{x}

^{bulk}(t) for wires of both types qualitatively resemble the dependences of the fraction q(t) of the Al

_{2}O

_{3}phases in the wires (Figure 11). For wires of the A50 cables, the dependences ρ

_{x}

^{bulk}(t) and q(t) are close to linear in the interval from 0 to 18 years, with the density ρ

_{x}

^{bulk}increasing from the initial value by ≈0.4% to ρ

_{x}

^{bulk}= 2.7092(2) g/cm

^{3}after 18 years of service. In the presence of a steel core (the AC50 cables), ρ

_{x}

^{bulk}increases from the initial value to almost the same value ρ

_{x}

^{bulk}= 2.7091(2) g/cm

^{3}after 8 years of service, slightly decreasing to ρ

_{x}

^{bulk}= 2.7085(2) g/cm

^{3}after 20 years of operation.

_{d}obtained in densitometric investigations is a characteristic of the entire wire volume (NSDL and bulk, including all crystalline and non-crystalline phases), which is measured experimentally. On the contrary, the X-ray densities ρ

_{x}

^{bulk}in the bulk of the wires are estimated from the approximation dependences of the X-ray densities ρ

_{x}(T) down to large depths T ~200 μm from the surface, where the experimental values of ρ

_{x}are calculated from the experimental values of the unit cell parameter a of the Al material in the NSDL of wires at depths T from ≈12.5 μm to ≈35.5 μm. Along with a possible partial overestimation of the value of ρ

_{x}

^{bulk}due to experimental errors in determining the Bragg angles 2θ

_{B}of the observed Al reflections and, accordingly, the individual values of the X-ray density ρ

_{x}corresponding to these reflections, another physical reason for the increase in the X-ray density of ρ

_{x}

^{bulk}in the volume (in the bulk) of wires can be considered. The increase in the density ρ

_{x}

^{bulk}in the bulk of the wires corresponds to the compression of the lattice in the bulk and correlates with the increase in the proportion of aluminum oxides δ- and/or δ*-Al

_{2}O

_{3}(Figure 11), with higher mass densities ~3.7 g/cm

^{3}than ~2.7 g/cm

^{3}of aluminum. Presumably, the formed aluminum oxide crystallites compress the Al lattice of the wire material, the values of ρ

_{x}

^{bulk}increasing consequently.

_{d}) and XRD (ρ

_{x}) density of samples detected by densitometry and XRD methods. A slight increase in the E modulus for the AC50 from 0 to 8 years of operation can be explained by taking into account the data on the proportion of aluminum oxides shown in Figure 11. For AC50, after 8 years of service, the volume fraction of Al

_{2}O

_{3}oxides in the wire NSDL is almost three times greater than for A50. According to the literature data, the elastic modulus for Al

_{2}O

_{3}is E = 247–380 GPa compared to E ~70 GPa for Al, therefore, the formation of such a layer contributes to the increase in the elastic modulus of the AC50 wire. With an increase in the service life of up to 20 years, it is likely that the formation of defects of a hollow nature (nano and micropores, etc.) in Al wires is decisive for changing the E modulus and leads to its decrease in AC50 wires. In addition, the alignment of the crystal structure of grains in the near-surface layer along one direction and their elongation in the direction of stretching [10] and the crystallographic texture of crystallites along [011], which is enhanced for both types of wires during their operation, can also affect the modulus of elasticity [54].

_{i}, depending on the operating time t (Figure 22), it can be noted that for AC50, the decrement δ

_{i}changes slightly, while for A50, its changes are substantial. The observed change for the A50 is most likely due to more intensive plastic deformation processes caused by a greater load resulting from the absence of a steel core. This is also indirectly confirmed by the results of EBSD for longitudinal sections of A50 wires, according to which the process of changing the shape of the grains to a more elongated one in the direction of the load action takes place in the surface layer [10]. At the same time, the non-monotonic nature of the change in δ

_{i}(t) for A50 correlates with the dependence of the sizes of the crystallites D(t) (Table 4 and Figure 14a). These microstructural changes are associated, among other things, with a change in the dislocation structure of the material, which determines the changes in the decrement δ

_{i}. The same structural changes also affect the change in the microplastic stress σ

_{s}(t) (Figure 22), which demonstrates the positive effect of the steel core in overhead power line cables, leading to the preservation of a high level of σ

_{s}in AC50 wires with a service life of up to 20 years for the studied samples.

## 5. Conclusions

_{d}, which is measured using the densitometric method, and the X-ray density ρ

_{x}, which is calculated from the unit cell parameter a of the lattice of the Al material in NSDL of wires, decrease according to a law close to the exponential-decay law as the depth T from the surface decreases, although more gentle in the case of ρ

_{x}(T) than ρ

_{d}(T). With an increase in the operating time, the ρ

_{x}and ρ

_{d}values at depth ~12.5 μm near the wire surface decrease significantly (density defect Δρ

_{x}/ρ

_{x}≈ −1.1% after a service life of ~20 years in comparison to Δρ

_{x}/ρ

_{x}≈ −0.2% in non-exploited samples and ≈ 0% in the bulk).

_{d}, ~100% of the total decrease in the ρ

_{d}and ~50%–70% of the total decrease in ρ

_{x}, and a ~99% decrease in the X-ray mass density ρ

_{x}, respectively. The difference in the results obtained by the methods of densitometric and XRD profiling is associated with the different sensitivity of the methods to different effects on the wires during operation. In the case of X-ray density ρ

_{x}, which is calculated from structural data, the structural state of the Al material of the NSDL of wire will play a major role. The Al lattice of the NSDL of wire expands when approaching the surface, and, accordingly, the X-ray density ρ

_{x}decreases, which is mainly due to the formation of defects of a void nature in the NSDL of wires under the action of vibrations due to wind, temperature fluctuations of the surrounding atmosphere, and fretting. In the case of densitometric density ρ

_{d}, which is an integral value, an important role is also played by the contribution of other phases, aluminum oxides in particular, the crystallites of which are formed when the service life increases, which, in turn, leads to the formation of a larger number of void defects near the surface because of the fretting amplification.

_{layer}of that part of the NSDL where the main decrease in X-ray density ρ

_{x}(~50–70% of the total drop) occurs when approaching the surface is 1–2% less than that in wires from AAAC-type A50 cables without a steel core. For wires from AC50 cables, a smaller value of microstrains is observed, which are formed at depths T ≥ 15 μm from the wire surface in NSDL after operation, compared to A50 cables, and it is associated with the steel core effect limiting cable vibrations because of wind.

_{x}, which is calculated from XRD data in NSDL with a thickness of ~35.5 μm, with the service life in the presence of a steel core is noticeably lower (respectively, 1.07(3) ∙ 10

^{−4}Å/year and −2.13(7) ∙ 10

^{−4}g/cm

^{3}/year for AC50 wires compared to 1.26(4) ∙ 10

^{−4}Å/year and −2.52(8) ∙ 10

^{−4}g/cm

^{3}/year for A50 wires). As a result, the expansion of the lattice in the NSDL and, accordingly, the decrease in the X-ray density ρ

_{x}of the NSDL Al wire material from A50 type cables without a steel core occurs faster by ~1 year after a service life of ~10 years and by ~3 years after ~20 years of operation.

## Supplementary Materials

_{s}= 0), on the service life duration t for Al-wires of A50 and AC50 type cables of the overhead power lines; Figure S2. WHP and SSP of AC50 wires, without exploitation and after 8 (and 20 years of exploitation.; Figure S3. Distribution of the mass X-ray density ρ

_{x}(T) of the wire Al material along the depth T from the surface of the A50 and AC50 wires.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

A50 | AAAC cable with an Al conductor cross-section of 49.5 mm^{2} |

A7E | grade of cold-drawn aluminum according to GOST |

AAAC | all aluminum alloy aonductor |

AC50 (AC50/8) | ACSR cable with Al conductor cross-section of ~50 mm^{2} and ~8 mm^{2} cross-section of steel core |

ACSR | aluminum conductor steel reinforced |

a.m.u. | atomic mass unit |

EBSD | electron backscattering diffraction |

EDX | energy dispersive X-ray microanalysis |

e.s.d., e.s.d.s. | estimated standard deviation(s) |

FWHM | full width at half-maximum of XRD reflection |

GOST | interstate technical standard |

NSDL, NSDLs | near-surface defect layer(s) |

PDF-2 | Powder Diffraction File-2 |

pV | pseudo-Voigt |

Ref., Refs. | Reference(s) |

SEM | scanning electron microscopy |

SSP | size-strain plot |

SM | Supplementary Materials |

WHP | Williamson–Hall plot |

XRD | X-ray diffraction |

e.g., | Latin” exempli gratia” (for example) |

i.e., | Latin “id est” (that is) |

etc. | Latin “et cetera” (and so on) |

cf. | Latin “confer” (compare) |

2θ | diffraction angle |

2θ_{B} | Bragg angle of XRD reflection corrected to angular corrections (zero shift Δ2θ_{zero} and displacement Δ2θ_{displ}) |

2θ_{obs} | observed Bragg angle of XRD reflection |

A_{r} | tabular value of the atomic mass of aluminium |

a | cubic unit cell parameter of Al |

a_{0} | parameter of the Al cubic unit cell in the bulk of a new (0 years of service) wire |

a^{bulk} | parameter of the Al cubic unit cell in the bulk of wire of non-zero service life |

B_{int} | integral width of XRD reflection |

C_{a.m.u.} | conversion factor of a.m.u. into gram |

D | average size of crystallites |

D_{0} | mean square root value of crystallite size after averaging the D^{hkl}_{0} values over all reflections in framework of model with absence of microstrains (ε_{s} = 0) |

D^{hkl} | size of crystallite corresponding to XRD reflection with Miller indices hkl |

D^{hkl}_{0} | size of crystallite corresponding to XRD reflection with Miller indices hkl in framework of model with absence of microstrains (ε_{s} = 0) |

E | Young’s modulus (modulus of elasticity, elastic modulus) |

E_{i} | amplitude-independent Young’s modulus |

f | oscillation frequency of wire-samples |

FWHM_{corr} | FWHM_{obs} corrected for instrumental broadening |

FWHM_{obs} | observed full width at half-maximum of XRD reflection |

hkl | Miller indices of XRD reflection |

[hkl] | Miller indices of crystallographic direction |

K_{Scherrer} | coefficient in Scherrer equation |

K_{strain} | coefficient in Wilson–Stokes equation |

I_{max} | maximum intensity of XRD reflection |

I_{max}^{022}, I_{max}^{111}, I_{max}^{002} | maximum intensitie of XRD reflection with Miller indices 022, 111, and 002, respectively |

I_{int} | integral intensity of XRD reflection |

I_{int}^{Al} | integral intensity of the strongest Al reflection |

I_{int}^{Al}_{2}^{O}_{3} | integral intensity of the 121 δ*-(212 δ-) Al_{2}O_{3} reflection |

l | wire-sample length |

m_{0} | mass of the sample before polishing (etching) |

m_{i} | mass of the sample after polishing of the ith layer |

N5, N5-1, etc. | Number 5, Number 5-1, etc. |

p | a parameter of wire Al material (unit cell parameter a or X-ray mass density ρ_{x}) |

p_{0} | a bulk parameter of Al material of a new (0 years of service) wire (unit cell parameter a_{0} or X-ray mass density ρ_{x}) |

q | fraction of the Al_{2}O_{3} crystalline phases in wires |

R_{0} | radius of the wire-sample in the form of a cylindrical rod (before polishing (etching)) |

t | service life duration |

T | depth from the wire surface or or penetratiun depth or temperature (in dependence on context) |

T_{etch} | thickness of the layer removed by polishing (etching) |

T_{layer} | layer thickness corresponding to depth where ~70% of the decrease in the mass density ρ_{x} occurs in comparison to the ρ_{x}^{200μm} value |

T_{layer}^{sat} | layer thickness corresponding to depth where ~99% of the decrease in the mass density ρ_{x} occurs in comparison to the ρ_{x}^{200μm} value |

${T}_{\mathrm{pen}}^{hkl}$ | penetration depth of X-ray radiation, corresponding to XRD reflection with Miller indices hkl |

V_{cell} | volume of the Al cubic unit cell |

Z | number of formula units in the Al unit cell |

Δ2θ_{displ} | displacement correction |

Δ2θ_{step} | 2θ step of XRD scanning |

Δ2θ_{zero} | correcting shift of the zero of the counter |

Δa/a | defect (relative change) of the unit cell parameter a |

(ΔE/E)_{h} | amplitude-dependent Young’s modulus defect (amplitude-dependent variation of E) |

Δρ_{d}/ρ_{d} | defect (relative change) of the mass density ρ_{d} |

Δρ_{dL}/ρ_{dL} | density defect value of the etched layer |

Δρ_{x}/ρ_{x} | defect (relative change) of the mass density ρ_{x} |

δ | (logarithmic) decrement of the sample material ((logarithmic) decrement of elastic vibrations) |

δ2θ_{B} | e.s.d. of Bragg angle 2θ_{B} |

δρ_{d}/ρ_{d} | relative error of integral density ρ_{d} |

δa | e.s.d. of the Al cubic unit cell parameter a |

δ_{i} | amplitude-independent part of the logarithmic decrement δ (amplitude-independent decrement of elastic vibrations) |

ε | vibrational strain amplitude (vibrational deformation) |

ε_{d} | non-linear inelastic strain (non-linear inelastic deformation) |

ε_{s} | absolute value of average magnitude of microstrains |

ε_{s}^{hkl} | absolute value of microstrain corresponding to XRD reflection with Miller inices hkl |

ε_{s}^{sat} | average microstrain ε_{s}^{sat} in the NSDL at depths T ≥ 15 μm if the crystallite size is fixed and equal to the crystallite size at a depth of T ~12.5 μm |

θ | half a diffraction angle |

θ_{B} | half a Bragg angle of XRD reflection 2θ_{B} |

λ | wavelength of Cu-K_{α1} radiation (after correction of Cu-K_{α2} contribution) |

μ_{l} | the linear mass absorption coefficient of material |

ρ | mass density |

ρ_{d} | mass density of material measured by densitometry technique (‘densitometric density‘, ’integral density’) |

ρ_{d0} | density of a sample before polishing (etching) measured by densitometry technique |

ρ_{di} | density of a sample after polishing (etching) of the ith layer measured by densitometry technique |

ρ_{dL} | mass density of the etched layer obtained by densitometry technique |

ρ_{x} | mass density of material calculated according to XRD structural data (‘XRD density’, ‘X-ray density’) |

ρ_{x}^{12.5μm} | XRD mass density at depth of 12.5 μm from the surface |

ρ_{x}^{200μm} | XRD mass density at depth of 200 μm from the surface |

ρ_{x}^{bulk} | XRD mass density in the bulk of the wire-sample |

ρ_{x}^{T}^{layer} | XRD mass density of Al material at a depth of T_{layer} |

ρ_{x}^{sat} | XRD mass density of Al material at a depth of T_{layer}^{sat} |

ρ_{x0} | XRD density in the bulk of a new (0 years of service) Al wire |

ρ_{x 0 years} | mean density of the A50 wire N5-2 (service life of 0 years) |

σ | amplitude of vibrational stress (microplastic deformation, microplastic stress) |

σ_{s} | microplastic flow stress (microplastic stress, micro-flow stress) equal to σ at inelastic strain ε_{d} = 5.0 × 10^{−8} |

Φ | Euler angle (angle of nutation) |

φ_{1} | Euler angle (angle of intrinsic rotation) |

φ_{2} | Euler angle (angle of precession) |

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**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 (

**a**,

**b**) and at the edge (

**b**,

**c**) for cross-sections of AC50 samples after (

**a**,

**c**) 8 (sample N2-2) and (

**b**,

**d**) 20 (N6) years of service life. The legend for maps (

**a**–

**d**) is shown in (

**e**). Scale for the Euler angle Φ is the same as for φ

_{2}.

**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 (

**a**,

**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 (

**a**,

**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 (

**a**,

**b**).

**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).

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

**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 (

**a**–

**c**) present the 2θ diffraction angle range 21–43° on a larger scale, exhibiting the weak reflections attributed to δ*- and δ-Al

_{2}O

_{3}. The Bragg angle positions of the δ*- and δ-Al

_{2}O

_{3}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.

**Figure 10.**Dependence of the I

_{max}

^{022}/I

_{max}

^{111}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.

**Figure 11.**The fraction q of the Al

_{2}O

_{3}crystalline phases in wires from A50 and AC50 cables with an exploitation duration of up to 20 years, which is estimated as q = I

_{int}

^{Al}

_{2}

^{O}

_{3}/I

_{int}

^{Al}∙ 100%, where I

_{int}

^{Al}

_{2}

^{O}

_{3}is the integral intensity of the 121 δ*-(212 δ-) Al

_{2}O

_{3}reflection and I

_{int}

^{Al}is the integral intensity of the strongest Al reflection.

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

**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) Δρ

_{x}/ρ

_{x}(where Δρ

_{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 (

**a**,

**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.

**Figure 14.**Comparison of dependences of (

**a**) average crystallite size D and (

**b**) absolute value of average microstrain ε

_{s}, 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.

**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 (

**a**,

**b**), the axes are shown corresponding, respectively, to the lattice defect Δa/a and the density defect Δρ

_{x}/ρ

_{x}, 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 (

**a**,

**b**) are drawn according to the exponential decay law. In (

**b**), the thicknesses T

_{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 T

_{layer}

^{sat}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 ρ

_{x}

^{sat}= 99.99% of the density estimated from the distribution curve at a depth of 200 μm).

**Figure 16.**Comparison of dependences of thicknesses of the NSDLs, at which there is a ~50–70% (T

_{layer}) and ~99% (T

_{layer}

^{sat}) 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).

**Figure 17.**Distribution of the crystallite size D = D

^{hkl}

_{0}estimated in the framework of zero microstrain assumption (model ε

_{s}= 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 (

**a**,

**b**). The approximation lines in (

**a**,

**b**) are drawn according to the exponential-decay law.

**Figure 18.**Distribution of microstrain ε

_{s}= ε

_{s}

^{hkl}along the depth T from the surface of the AC50 wire. The microstrain ε

_{s}

^{hkl}is estimated under the assumption of a fixed crystallite size equal to the crystallite size D

_{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 ε

_{s}

^{sat}in the NSDL at depths T ≥ 15 μm, if the crystallite size is fixed and equal to the crystallite size D

_{12.5μm}.

**Figure 19.**Microstrain ε

_{s}

^{sat}calculated under the assumption of a fixed crystallite size equal to the crystallite size D

_{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).

**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 σ(ε

_{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.

**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.

**Figure 23.**Dependences of the densities ρ

_{x}

^{bulk}and unit cell parameters a

^{bulk}in the bulk of the wires from the cables of AAAC (A50) and ACSR (AC50) types on the service life t of the cables.

**Table 1.**Characteristics of A50 and AC50 overhead power-line cables according to Ref. [1].

Cable Type | Number of Al Wires in Cable | Number of Steel Wires in Cable | Individual Wire Diameter, mm | Cable Section, mm^{2} | Estimated Cable Weight, kg/km | Cable Breaking Strength (≤), N |
---|---|---|---|---|---|---|

A50 | 7 | 0 | 3.0 | 49.5 | 135 | 8198 |

AC50 | 6 | 1 | 3.2 | 56.24 ^{a} | 195 | 17,112 |

^{a}Al/Fe section is of 48.2 mm

^{2}/8.04 mm

^{2}.

Sample, N | 5-2 | 5 | 8 | 2-2 | 7 | 6 |
---|---|---|---|---|---|---|

Type | A50 | AC50 | A50 | AC50 | A50 | AC50 |

Service life t, years | 0 | 0 | 10 | 8 | 18 | 20 |

Wire diameter d, mm | 3.02 | 3.20 | 2.85 | 3.24 | 3.03 | 3.07 |

**Table 3.**Chemical composition of A7E-grade aluminum used by the manufacturer (wt.%) according to Ref. [39]. The lower limit of the Al weight content and the upper limits of possible impurities in the wire material are indicated.

Al | Fe | Si | Zn | Ga | Mg | Cu | Ti + V + Cr + Mn | Other |
---|---|---|---|---|---|---|---|---|

99.59 | 0.20 | 0.08 | 0.04 | 0.03 | 0.02 | 0.01 | 0.01 | 0.02 |

**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.

Observed Preferential Orientation | WHP | SSP | |||
---|---|---|---|---|---|

Sample N/Years | [hkl] | I_{max}^{022}/I_{max}^{111}, %I _{max}^{002}/I_{max}^{022}, % | a, Å/ρ_{x}, g/cm^{3}D _{0}, nm (ε_{s} = 0) | D, nm ε _{s}, % | D, nm ε _{s}, % |

A50 type | |||||

5-2/0 | [011] | 42.0(3) 76.4(7) | 4.05026(12)/2.6973(2) 109(16) | 111(14) 0.010(14) | 109(16)0 |

8/10 | [011] | 69.0(4) 66.1(4) | 4.0515(5)/2.6949(11) 139(16) | 302(54) 0.031(2) | 298(26) 0.031(2) |

7/18 | [011] | 153.8(1.6) 55.6(6) | 4.0525(9)/2.6927(17) 126(33) | 246(55) 0.033(3) | 252(32) 0.034(3) |

AC50 type | |||||

5/0 | [011] | 75.8(9) 68.4(9) | 4.05032(10)/2.6972(2) 138(16) | 141(17) 0.007(11) | 138(16) 0 |

2-2/8 | [011] | 90.9(6) 38.8(4) | 4.0511(4)/2.6956(7) 136(29) | 212(28) 0.026(3) | 219(19) 0.026(3) |

6/20 | [011] | 180.7(2.0) 42.7(5) | 4.0525(8)/2.6929(15) 120(23) | 187(27) 0.029(3) | 167(13) 0.025(3) |

Table data for crystalline Al powder | |||||

PDF-2 card 01-071-4008, [50] T = 312.3 K | no | - - | 4.050694/2.69642 - | - | - |

PDF-2 card 01-073-9843, [49] T = 298 K | no | 24.0 191.7 | 4.04932(2)/2.6992(4) - | - - | - - |

**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.

Sample N | Type | Service Life t, Years | E, GPa | δ_{i} · 10^{5} | σ_{s}, MPaat ε _{d} = 4 ∙ 10^{−8} |
---|---|---|---|---|---|

5-2 (3) | A50 | 0 | 72.78 | 23 | 14 |

5 (1) | AC50 | 0 | 71.84 | 27 | 15 |

8 (3) | A50 | 10 | 71.30 | 133 | 8.0 |

2-2 (3) | AC50 | 8 | 72.87 | 17 | 16 |

7 (1) | A50 | 18 | 71.21 | 85 | 9.0 |

6 (3) | AC50 | 20 | 71.58 | 31 | 13 |

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## Share and Cite

**MDPI and ACS Style**

Levin, A.A.; Narykova, M.V.; Lihachev, A.I.; Kardashev, B.K.; Kadomtsev, A.G.; Prasolov, N.D.; Panfilov, A.G.; Sokolov, R.V.; Brunkov, P.N.; Sultanov, M.M.;
et al. Comparison of Structural, Microstructural, Elastic, and Microplastic Properties of the AAAC (A50) and ACSR (AC50/8) Cables after Various Operation Periods in Power Transmission Lines. *Crystals* **2022**, *12*, 1267.
https://doi.org/10.3390/cryst12091267

**AMA Style**

Levin AA, Narykova MV, Lihachev AI, Kardashev BK, Kadomtsev AG, Prasolov ND, Panfilov AG, Sokolov RV, Brunkov PN, Sultanov MM,
et al. Comparison of Structural, Microstructural, Elastic, and Microplastic Properties of the AAAC (A50) and ACSR (AC50/8) Cables after Various Operation Periods in Power Transmission Lines. *Crystals*. 2022; 12(9):1267.
https://doi.org/10.3390/cryst12091267

**Chicago/Turabian Style**

Levin, Aleksandr A., Maria V. Narykova, Alexey I. Lihachev, Boris K. Kardashev, Andrej G. Kadomtsev, Nikita D. Prasolov, Andrei G. Panfilov, Roman V. Sokolov, Pavel N. Brunkov, Makhsud M. Sultanov,
and et al. 2022. "Comparison of Structural, Microstructural, Elastic, and Microplastic Properties of the AAAC (A50) and ACSR (AC50/8) Cables after Various Operation Periods in Power Transmission Lines" *Crystals* 12, no. 9: 1267.
https://doi.org/10.3390/cryst12091267