*2.1. Samples*

To compare the structural, microstructural, elastic, and microplastic properties of two types of uninsulated cables, namely, A50 (AAAC) and AC50 (ACSR), individual aluminum wires of overhead power-line cables were studied after different periods of operation, see Table 2. Hereinafter, wires of the A50-type cables will be referred to as "A50-type wires" or "A50 wires" for short, and wires of the AC50-type cables will be referred to as "AC50-type wires" or, for short, "AC50 wires".

**Table 2.** Samples of cables of overhead power lines with different service life, which were selected for research (samples A50 are from [10,37]) 1.


1 Additionally, samples of the A50 type that do not have an AC50 counterpart in service life (N3, 35 years of service life (same as in Refs. [10,37]) and N10, 54 years) were investigated in some experiments.

The nominal characteristics of the A50 and AC50 types of cables according to the manufacturer's passport (Interstate Technical Standard GOST 839-2019) [1]) are summarized in Table 1. The A50 cable consists of seven separate Al wires and, according to the cable passport, has a cable conductor cross-section of 49.5 mm2, 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<sup>2</sup> (Al) and 8.04 mm<sup>2</sup> (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).

In manufacturing the aluminum wires of the above cables, cold-drawn aluminum of grade A7E (GOST 11069) [39] was used. Table 3 shows the chemical composition of the aluminum alloy according to the manufacturer's quality certificate.

**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.


All the Al wires are manufactured using the same technology from aluminum of the same grade, and the results of XRD studies [37] revealed that the unexploited A50 and AC50 wires (respectively, N5-2 and N5) showed almost the same structural and microstructural parameters. That is why, in the study by different methods of a series of A50-type samples of different length service lives, the results obtained on N5 AC50-type wire were considered as related to the initial state (service life of 0 years), unless otherwise indicated.

Samples of the optimal length for the studies will be specified in the description of each method. They were cut from the outer wire of the tested cables and washed in an ultrasonic acetone bath to remove external impurities and protective grease. Under the term "outer wires", we mean Al wires under the influence of the atmosphere and also other wires (either exclusively Al wires in the case of A50 cables or, in addition, steel core in the case of AC50 ones).

It should be noted that from the available samples, wires of A50 and AC50 types with the maximum possible service life were selected for comparison. However, there is a difference of 2 years between the service life of the samples after operation (10 and 8 years or 18 and 20 years for samples A50 and AC50, respectively, see Table 2). Taking into account the long expected service life of 45 years in accordance with the manufacturer's standard [1], it can be expected that this difference will be insignificant when comparing their properties.

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

All details of the experiment and analysis of the results of EDX, SEM, EBSD, XRD measurements, and densitometric and acoustic investigations are detailed in [10,37]. Therefore, this article provides only a brief description of the experimental equipment, measurements, and their analysis.

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

To study samples by SEM, EDX, and EBSD by use of a JSM 7001F scanning electron microscope (JEOL, Tokyo, Japan) equipped with an INCA PentaFETx3 system for EDX microanalysis and with an HKL Nordlys detector (Oxford Instruments, Abingdon-on-Thames, UK) to obtain EBSD maps, polished cross sections of wire samples with a diameter of 2.85–3.24 mm were prepared (see Table 2). For the preparation of polished cross sections, a MultiPrep8 machine (Allied, San Francisco, CA, USA) was used with a gradual reduction in the abrasive grain for mechanical grinding of the section. The final polishing of the section surface was carried out with an argon-ion beam using a 1061 SEM Mill system of ion milling and polishing (Fischione, Export, PA, USA). The EBSD maps were taken with a step of 0.5 μm in areas of 100 × 100 μm<sup>2</sup> 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<sup>2</sup> 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

The densities of wire samples were determined by hydrostatic weighing on a Shimadzu AUW 120D analytical balance using an SMK-301 attachment (Shimadzu Corporation, Kyoto, Japan). This method, called the densitometric method, employs weighing a sample in air and in a liquid as well as determining the density of the liquid used at a given temperature. This method makes it possible to obtain the integral densities *ρ*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 δ*ρ*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 Δ*ρ*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]:

$$T\_{\text{etch}} \approx R\_0 \cdot \left(1 - \sqrt{\frac{m\_i}{m\_0}}\right),\tag{1}$$

where *R*0 and *m*0 are the radius and mass of the sample in the form of a cylindrical rod before polishing, respectively, and *mi* is the mass of the sample after polishing the *i*th layer.

The layer density (*ρ*dL) and the value of the density defect Δ*ρ*dL/*ρ*dL in polished layers were calculated with the formulas [10]:

$$
\rho\_{\rm dL} = \frac{(m\_0 - m\_i) \cdot \rho\_{\rm di} \cdot \rho\_{\rm d0}}{m\_0 \cdot \rho\_{\rm di} - m\_i \cdot \rho\_{\rm d0}},
\tag{2}
$$

$$\frac{\Delta\rho\_{\rm dL}}{\rho\_{\rm dL}} = \frac{\rho\_{\rm dL} - \rho\_{\rm d0}}{\rho\_{\rm dL}},\tag{3}$$

where *ρd*0 is the density of the sample before polishing, while *ρdi* is that after polishing of the *i*th layer.

The thickness of each removed layer ranged from a few microns near the wire surface to ~5 μm after the thickness of the removed layer reached *T*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

Samples for XRD measurements were cut in the form of a cylinder ~25 mm long and ~3–3.2 mm (Table 2) in diameter and glued onto a low-background single-crystal Si(119) holder. XRD measurements were carried out on a D2 Phaser powder diffractometer (Bruker AXS, Karlsruhe, Germany) in the Bragg–Brentano *θ*-*θ* geometry with Cu-*<sup>K</sup>*α1,2 radiation from a copper anode after a *<sup>K</sup>*β-filter in the form of a Ni-foil and a linear positionsensitive 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*-2*θ* scanning in the range of diffraction angles 2*θ* = 6–141◦ with a step of <sup>Δ</sup>2*θ*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 (2*θ*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*α<sup>2</sup> radiation, and the values of the above reflection parameters were determined. The obtained observed Bragg angles 2*θ*obs of the reflections were adjusted with the angular corrections Δ2*θ*zero (detector zero shift) and <sup>Δ</sup>2*θ*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].

Using the Bragg angles 2*θ*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.) δ*a* of the parameter *a* was calculated analytically from δ2*θ*B (e.s.d. of the Bragg angle), which was taken as half of the step <sup>Δ</sup>2*θ*step with which the XRD pattern was measured (i.e., δ2*θ*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.

The density of the Al material *ρ*x (g/cm3) 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:

$$\rho\_{\text{x}} = \frac{C\_{\text{a.m.u.}} Z \cdot A\_{\text{r}}}{V\_{\text{cell}} \cdot 10^{-24}},\tag{4}$$

where *V*cell (Å3) = *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−<sup>24</sup> g/a.m.u. is the conversion factor from a.m.u. to grams.

Using the expression:

$$\frac{\Delta p}{p} = \frac{p - p\_0}{p},\tag{5}$$

the defect of the unit cell parameter, Δ*a*/*<sup>a</sup>*, and the X-ray density defect, Δ*ρ*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).

The determination of microstructural parameters (average size *D* of coherent scattering regions, which are also called crystallites, and absolute value of average microstrain *ε*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 *Dhkl* and microstrain *<sup>ε</sup>shkl* values, respectively (see [43–45]). In the absence of microstrains (model *ε*s = 0), the *SizeCr* program calculated the sizes *<sup>D</sup>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 *<sup>D</sup>hkl*, the values of the microstrain *<sup>ε</sup>*s*hkl* corresponding to each observed XRD reflection *hkl* were calculated.

The penetration depth *Thkl* pen of X-rays for each reflection with Miller indices *hkl* (see [46] and illustration in [10]) was estimated as:

$$T\_{\text{Pen}}^{\text{hkl}} = \frac{\sin(\theta \text{B})}{2 \cdot \mu\_1 \cdot \rho\_\text{x}},\tag{6}$$

where *μ*l = 48.657 cm2/g is the linear absorption coefficient of Al in the case of Cu-*K*α<sup>1</sup> radiation (after correcting for the Cu-*K*α<sup>2</sup> contribution), and *θ*B is half of the 2*θ*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 *Thkl* pen. As a result, analysis of different reflections detected at different Bragg angles 2*θ*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

Acoustic resonant methods are based on the analysis of steady oscillations of samples in the form of rods, the length of which is much greater than their transverse dimensions. The determination of elastic and microplastic properties (elastic modulus *E* and decrement *δ* of elastic vibrations and microplastic deformation diagrams *<sup>σ</sup>*(*<sup>ε</sup>d*)) makes it possible to study microprocesses that can take place in samples when external conditions change.

Acoustic properties were studied with the composite oscillator technique applied to aluminum samples in the form of rods ~25 mm long. This length corresponds to the resonant frequency of a polycrystalline aluminum sample of about 100 kHz. Young's modulus *E* (also called the "modulus of elasticity" or "elastic modulus") and elastic vibration decrement *δ* were measured in the range of amplitudes of vibrational deformation *ε* from ~1 · 10−<sup>6</sup> to ~3 · 10−4. The modulus of elasticity was determined using the formula [47]:

$$E = 4\rho \cdot l^2 \cdot f^2,\tag{7}$$

where *l* is the sample length, *ρ* is its density (for calculations of *E*, the density *ρd* 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 *<sup>σ</sup>*(*<sup>ε</sup>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 *εd* = *ε* · (Δ*E*/*E*)h is plotted along the abscissa axis, where (Δ*E*/*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 ye<sup>t</sup> independent of *ε* are called amplitude-independent Young's modulus and amplitude-independent decrement of elastic vibrations, respectively.

Note that the measurements were performed at moderate amplitudes, i.e., the dislocation structure of the material did not change.
