Sub-Microstructure of Surface and Subsurface Layers after Electrical Discharge Machining Structural Materials in Water

The material removal mechanism, submicrostructure of surface and subsurface layers, nanotransformations occurred in surface and subsurface layers during electrical discharge machining two structural materials such as anti-corrosion X10CrNiTi18-10 (12kH18N10T) steel of austenite class and 2024 (D16) duralumin in a deionized water medium were researched. The machining was conducted using a brass tool of 0.25 mm in diameter. The measured discharge gap is 45–60 µm for X10CrNiTi18-10 (12kH18N10T) steel and 105–120 µm for 2024 (D16) duralumin. Surface roughness parameters are arithmetic mean deviation (Ra) of 4.61 µm, 10-point height (Rz) of 28.73 µm, maximum peak-to-valley height (Rtm) of 29.50 µm, mean spacing between peaks (Sm) of 18.0 µm for steel; Ra of 5.41 µm, Rz of 35.29 µm, Rtm of 43.17 µm, Sm of 30.0 µm for duralumin. The recast layer with adsorbed components of the wire tool electrode and carbides was observed up to the depth of 4–6 µm for steel and 2.5–4 µm for duralumin. The Levenberg–Marquardt algorithm was used to mathematically interpolate the dependence of the interelectrode gap on the electrical resistance of the material. The observed microstructures provide grounding on the nature of electrical wear and nanomodification of the obtained surfaces.


Introduction
Electrical discharge machining is known technology of changing shape and size conductive and non-conductive materials [1][2][3][4]. Despite plenty of works devoted to the research of electrical discharge machining parameters optimization [5][6][7], there is almost no works devoted to the effect of electrical discharge machining on surface and subsurface layers of structural materials, in particularity to anti-corrosion steels of austenite class [1,8] and aluminum alloy (2024) [9,10].
The thickness of recast layer depending on die-sinking electrical discharge machining factors was researched for tool-, forming medium carbon steel SKD-61 (X40CrMoV5-1) with a copper tool electrode in [11]. The minimum recast layer thickness of 3.72 µm was achieved at operational current of 1 A and operational voltage of 30 V when time of pulse on and time of pulse off were of 50 and 12 µs correspondingly. The authors, in their work, recklessly propose to remove the layer after electrical discharge machining without setting themselves tasks concerning the specific application of the final product. However, an eroded layer with a surface type can be a definite advantage for some applications [12][13][14]: It creates a pleasant tactile texture of evenly distributed convexes of injection-molding plastic parts such as computer cases or other housings.

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The formed eroded layer contributes to reduced surface wear due to its improved exploitation properties (microhardness, wear resistance).

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The convexed surface favors the removal of injection-molded plastic products from the mold.
The surface layer of tool AISI H13 steel (SKD-61, X40CrMoV5-1) after die-sinking electrical discharge machining with a copper tool electrode was improved (microhardness) by adding nitrogen-containing components into a deionized water medium [15]. The formed nitrides and recast layers were detected at the minimum depth of 31.0 ± 4.6 µm with pulse time on and off equal to 100 µs, correspondingly. The maximum depth was 53.2 ± 5.5 µm at pulse time on and off of 500 µs. The microhardness of the surface layer was 800-920 HV 0.025 (the maximum value corresponds to pulse time on of 100 µs, pulse time off of 150-203 µs). The hardness dramatically decreases up to the value of 280-390 HV 0.025 at a depth of 12 µm.
The research of hot work Cr12 (X200Cr12, SKD1) steel recast layer after electrical discharge machining in a hydrocarbon medium with a copper tool electrode showed that the thickness of the recast layer is constant at a pulse duration of 200-300 µs and copper of tool electrode concentration grows [16]. The solidified submcrostructure of surface and subsurface layers was defined as a dense and fine dendritic outermost sublayer, a coarse dendritic intermediate sublayer, and an innermost. The predominant chemical composition of the surface and subsurface layers contains (Fe,Mn) 3 AlC carbide, which shows the carbonization of the layers due to the decomposition of the dielectric medium and the precipitation of carbides, which increased the microhardness of the surface to 574 HV.
Thus, surface and subsurface layers' parameters and submicrostructure research for the wide range of structural materials is an actual scientific and technical problem. Some popular structural materials-especially anti-corrosion steels of austenite and martensitic classes, non-ferrous, and aluminum alloys in particular-required more attention to predict their properties in the conditions of real exploitation and were not covered by previously conducted studies.
The study aims to research the physical nature of wear and phenomena of electrical discharge machining of two structural materials with a brass wire tool electrode in a water medium in the conditions of electrical discharge wear, classification of wear, and observed defects, nanomodification of machined surfaces through optic and scanning electron microscopy, spectroscopy, surface roughness parameters, and discharge gap. The conducted work improves understanding of electrical discharge machining of conductive and non-conductive materials to predict the parameters of surface and near-surface layers of machined surfaces. Based on previously conducted studies, deionized water was chosen as a dielectric medium [18]: to exclude the influence of specimens' carbonization due to working liquid decomposition under discharge pulses; 2.
to avoid the formation of explosives in the presence of water or hydrogen, such as aluminum carbide, during electrical discharge machining specimens in hydrocarbons.
The scientific novelty of the work is in the new data on physical phenomena that occurred between electrodes and water medium in the presence of plasma heat, classification of the obtained machined surface defects, new data on nanomodification of the machined surfaces, interpolation model of the obtained dependencies of the discharge gap on electrical properties of the material. The practical significance of the work is developing the scheme of surface and subsurface layers' structure that is used for engineering work to predict the behavior of the layers under the load. The tasks of the study are the research of the surface topology of two structural materials, such as austenite anti-corrosion X10CrNiTi18-10 (12kH18N10T) steel and AA2024 (D16) duralumin, after wire electrical discharge machining with a brass wire tool electrode in a water medium, discharge gap, classification of the observed surface defects, traces of destruction, and research of the chemical content of surface and subsurface layers ( Figure 1). on electrical properties of the material. The practical significance of the work is developing the scheme of surface and subsurface layers' structure that is used for engineering work to predict the behavior of the layers under the load. The tasks of the study are the research of the surface topology of two structural materials, such as austenite anti-corrosion X10CrNiTi18-10 (12kH18N10T) steel and AA2024 (D16) duralumin, after wire electrical discharge machining with a brass wire tool electrode in a water medium, discharge gap, classification of the observed surface defects, traces of destruction, and research of the chemical content of surface and subsurface layers ( Figure  1).

Equipment and Machining Factors
A two-axis wire electrical discharge machine ARTA 123 Pro (JSC "Scientific Industrial Corporation "Delta-Test", Fryazino, Moscow Oblast, Russia) (Table 1, Figure 2) was chosen in the experiments for machining in deionized water. The machine body is made of gray cast iron that showed excellent thermal and compensating vibration properties.

Equipment and Machining Factors
A two-axis wire electrical discharge machine ARTA 123 Pro (JSC "Scientific Industrial Corporation "Delta-Test", Fryazino, Moscow Oblast, Russia) (Table 1, Figure 2) was chosen in the experiments for machining in deionized water. The machine body is made of gray cast iron that showed excellent thermal and compensating vibration properties. trial Corporation "Delta-Test", Fryazino, Moscow Oblast, Russia), with a tensile strength of 1000 N/mm 2 . The computer numerical control (CNC) program was prepared manually. The first set of experiment factors were chosen following recommendations [21][22][23] and experience in machining structural materials ( Table 2). The electrode tool has a negative bias, and a workpiece is positive. Electrical discharge machining was accomplished with flushing to provide better performance and machining stability [24]. The path offset was not taken into account during machining [1,21].
(a) (b)   The machine is placed in a thermo-constant room to reduce ambient temperature influence on the experimental results. The specimens were immersed in deionized water for 10 min before electrical discharge machining to avoid dimensional fluctuations of the temperature difference between the environment and the working medium. The level of the medium was established at 1-2 mm above workpiece height. The upper wire tool guide was established above 2-5 mm from the dielectric level [19,20]. The wire tool electrode was made of CuZn35 brass with a diameter d w of 0.25 mm, Artacut (JSC "Scientific Industrial Corporation "Delta-Test", Fryazino, Moscow Oblast, Russia), with a tensile strength of 1000 N/mm 2 . The computer numerical control (CNC) program was prepared manually. The first set of experiment factors were chosen following recommendations [21][22][23] and experience in machining structural materials ( Table 2). The electrode tool has a negative bias, and a workpiece is positive. Electrical discharge machining was accomplished with flushing to provide better performance and machining stability [24]. The path offset was not taken into account during machining [1,21].

Materials to Be Machined
Two structural materials typical for the aerospace industry and tool production were chosen for the experiments, such as anticorrosion chrome-nickel X10CrNiTi18-10 (12kH18N10T) steel of austenite class (Table 3) and 2024 duralumin (D16, Table 4). The thickness of the samples was 20 mm (Figure 3a). Five samples for each experimental set were produced to research a machined surface and measure the discharge gap (Figure 3b,c). It should be noted that chromium content provides anticorrosion properties of the steel when nickel is responsible for its austenite class that improves its machinability and extends the exploitation properties. The titanium addition hampers chromium carbides' formation and forms refractory carbides of titanium in reaction with carbon. This type of chromiumnickel steel dominates the modern rolled metal market [25][26][27][28]. Duralumin is used mainly in a quenched state and is classified as a durable thermo-hardened construction material for the aerospace industry and unsuitable for welding [29,30].

Materials to Be Machined
Two structural materials typical for the aerospace industry and tool production were chosen for the experiments, such as anticorrosion chrome-nickel X10CrNiTi18-10 (12kH18N10T) steel of austenite class (Table 3) and 2024 duralumin (D16, Table 4). The thickness of the samples was 20 mm (Figure 3a). Five samples for each experimental set were produced to research a machined surface and measure the discharge gap ( Figure  3b,c). It should be noted that chromium content provides anticorrosion properties of the steel when nickel is responsible for its austenite class that improves its machinability and extends the exploitation properties. The titanium addition hampers chromium carbides' formation and forms refractory carbides of titanium in reaction with carbon. This type of chromium-nickel steel dominates the modern rolled metal market [25][26][27][28]. Duralumin is used mainly in a quenched state and is classified as a durable thermo-hardened construction material for the aerospace industry and unsuitable for welding [29,30].     A Fischer Sigmascope SMP10 instrument (Helmut Fischer GmbH, Sindelfingen, Germany) controlled the specific electrical resistance ρ (Figure 3d, Table 5). The device measures the material electric conductance in Siemens and the percentage of the control sample's electrical conductance made of annealed bronze in the range of 1-112%. The measured values are converted to Ω·mm 2 m . The linear thermal expansion coefficient, thermal conductivity, melting points are presented in Table 5 [31][32][33][34].

Characterization of the Samples
The surface roughness parameters such as arithmetic mean deviation (R a ), 10-point height (R z ), maximum peak-to-valley height (R tm ), mean spacing between peaks (S m ) of the surface samples were controlled by a high-precision profilometer, Hommel Tester T8000 (Jenoptik GmbH, Villingen-Schwenningen, Germany), with a resolution of 1-1000 nm; a measurement error is of 2%.
The Dektak XT stylus profilometer (Bruker Nano, Inc., Billerica, MA, USA) obtained linear and 3D diagrams with a vertical accuracy of 5 Å (0.5 nm), the radius of the stylus is 12.5 µm.
The cross-sections were prepared using Opal 410, Jade 700, and Saphir 300 sample equipment (ATM, Haan, The Netherlands) and the standard probe techniques. An epoxy resin with quartz sand provided pouring of the samples as a filler was used.
X-ray photoelectron spectroscopy (XPS) was used to study the chemical composition of subsurface layers. The analysis was performed using Thermo Scientific's K-ALPHA X-ray photoelectron spectrometer (Thermo Fisher Scientific Inc., Bremen, Germany) equipped with an Avantage Data System (version 5.0).
The discharge gap is calculated by the next equations [8,35] where ∆ is a measured distance of the cut between two machined surfaces, mm; d w is a diameter of the wire tool, mm. The effective (recommended) offset of the wire tool electrode path is calculated by the equation The Levenberg-Marquardt algorithm (increasing exponential approximation and Boltzmann (Sigmoidal) approximation over a dataset) [36], which is an optimization method aimed at solving the least-squares problems and an alternative to Newton's method, was used to mathematically interpolate the dependence of the interelectrode gap on the electrical resistance of the material. SciDAVis 2.4.0 (Scientific Data Analysis and Visualization, Slashdot Media, San Diego, CA, USA) software was used to interpolate and analyze the obtained dependencies.

Machining Factors and the Discharge Gap
The stable machining process was achieved, but the wire consumption exceeds the expected value during the first set of experiments for X10CrNiTi18-10 (12kH18N10T) steel. The wire rewinding speed was reduced by 30% during the second group of experiments. Electrical discharge machining 2024 (D16) duralumin showed that the wire is broken, and no effective discharges were achieved. The second group of the experiments showed a stable processing character with increased operational voltage and rewinding speed combined with shortened pulses. Figure 4 shows the measured slot width l for two types of materials, including the wire radius d w of 0.25 mm. The effective discharge gap ∆ DB following Equation (1) is in the range of 45-60 µm for X10CrNiTi18-10 (12kH18N10T) steel and the range of 105-120 µm for 2024 (D16) duralumin. The minimal value is associated with a stable mode. The recommended value for the offsets of the wire tool path ∆* DB will be 175 µm and 235 µm correspondingly. method, was used to mathematically interpolate the dependence of the interelectrode gap on the electrical resistance of the material. SciDAVis 2.4.0 (Scientific Data Analysis and Visualization, Slashdot Media, San Diego, CA, USA) software was used to interpolate and analyze the obtained dependencies.

Machining Factors and the Discharge Gap
The stable machining process was achieved, but the wire consumption exceeds the expected value during the first set of experiments for X10CrNiTi18-10 (12kH18N10T) steel. The wire rewinding speed was reduced by 30% during the second group of experiments. Electrical discharge machining 2024 (D16) duralumin showed that the wire is broken, and no effective discharges were achieved. The second group of the experiments showed a stable processing character with increased operational voltage and rewinding speed combined with shortened pulses. Figure 4 shows the measured slot width l for two types of materials, including the wire radius dw of 0.25 mm. The effective discharge gap ΔDB following Equation (1) is in the range of 45-60 µm for X10CrNiTi18-10 (12kH18N10T) steel and the range of 105-120 µm for 2024 (D16) duralumin. The minimal value is associated with a stable mode. The recommended value for the offsets of the wire tool path Δ*DB will be 175 µm and 235 µm correspondingly.
Optical microscopy of the formed kerf on the X10CrNiTi18-10 (12kH18N10T) steel specimen shows the absence of fused layers of the kerf edge, a uniform distribution of the workpiece texture ( Figure 4a). The edges of the kerf on the duralumin specimen demonstrate increased roughness, possibly indirectly related to the high electrical conductivity of aluminum, which means more intense and dense radial channels between the electrodes, increased machining productivity at roughing (Figure 4b).

Roughness Parameters and Surface Topology
3D profiles of the machined surfaces are in Figure 5, and measured roughness parameters are in Table 6. Both samples have a typical "shagreen" type of surface with the spaced convexes of deposed recast (secondary) material. The formed flakes of secondary material are up to 35 µm for X10CrNiTi18-10 (12kH18N10T) steel and up to 45 µm for Optical microscopy of the formed kerf on the X10CrNiTi18-10 (12kH18N10T) steel specimen shows the absence of fused layers of the kerf edge, a uniform distribution of the workpiece texture (Figure 4a). The edges of the kerf on the duralumin specimen demonstrate increased roughness, possibly indirectly related to the high electrical conductivity of aluminum, which means more intense and dense radial channels between the electrodes, increased machining productivity at roughing (Figure 4b).

Roughness Parameters and Surface Topology
3D profiles of the machined surfaces are in Figure 5, and measured roughness parameters are in Table 6. Both samples have a typical "shagreen" type of surface with the spaced convexes of deposed recast (secondary) material. The formed flakes of secondary material are up to 35 µm for X10CrNiTi18-10 (12kH18N10T) steel and up to 45 µm for 2024 (D16) duralumin. The size of flakes strongly depends on the electrical conductivity of materials and used electrical factors of machining (higher voltage corresponds to more profound geometry when operational current is responsible for the density of discharge and, consequently, erosion wells). The obtained profiles are further discussed in Section 4.2.
Metals 2021, 11, x FOR PEER REVIEW 8 of 22 2024 (D16) duralumin. The size of flakes strongly depends on the electrical conductivity of materials and used electrical factors of machining (higher voltage corresponds to more profound geometry when operational current is responsible for the density of discharge and, consequently, erosion wells). The obtained profiles are further discussed in Section 4.2.

Characterization of the Samples
The machined surfaces have the following defects-mechanical rupture (1) occurred at the end of the operation and thermal traces of short circuits (2) (Figure 6).

Characterization of the Samples
The machined surfaces have the following defects-mechanical rupture (1) occurred at the end of the operation and thermal traces of short circuits (2) ( Figure 6).

Characterization of the Samples
The machined surfaces have the following defects-mechanical rupture (1) occurred at the end of the operation and thermal traces of short circuits (2) (Figure 6).  The SEM-images of the eroded surfaces at the place of wire tool penetration demonstrate three types of defects related to the thermal chemical nature of the material destruction that occurred during electrical discharge machining-thermal cracks formed during cooling the deposed material of secondary structure (1), flakes of the secondary structure formed from the components of the electrodes and dielectric medium (2), main recast and the heat-affected sublayer of primary material (3) (Figure 7). The obtained eutectics are further discussed in Section 4.2.
Metals 2021, 11, x FOR PEER REVIEW 9 of 22 The SEM-images of the eroded surfaces at the place of wire tool penetration demonstrate three types of defects related to the thermal chemical nature of the material destruction that occurred during electrical discharge machining-thermal cracks formed during cooling the deposed material of secondary structure (1), flakes of the secondary structure formed from the components of the electrodes and dielectric medium (2), main recast and the heat-affected sublayer of primary material (3) (Figure 7). The obtained eutectics are further discussed in Section 4.2.

Chemical Nanomodification of the Surface Layer
The chemical analyses of the sample surface after electrical discharge machining by X-ray photoelectron spectroscopy are presented in Figures 8 and 9. Both of the surface layers have the presence of the chemical components of the wire tool and complex compounds of secondary order (metastable solid solution and/or eutectics).

Chemical Nanomodification of the Surface Layer
The chemical analyses of the sample surface after electrical discharge machining by X-ray photoelectron spectroscopy are presented in Figures 8 and 9. Both of the surface layers have the presence of the chemical components of the wire tool and complex compounds of secondary order (metastable solid solution and/or eutectics). Metals 2021, 11, x FOR PEER REVIEW 10 of 22 (e) (f)  Both samples show metallic Zn and copper oxide samples responsible for metallic grey and black sediment on the machined surfaces (Figures 8a,b, and 9a,b). Zn is bound in oxide (usually matte white film) (Figures 9a) at the duralumin sample. The quantity analyses confirmed their slight presence of wire tool electrode material (less than 4 at %). Both samples show metallic Zn and copper oxide samples responsible for metallic grey and black sediment on the machined surfaces (Figures 8a,b and 9a,b). Zn is bound in oxide (usually matte white film) (Figure 9a) at the duralumin sample. The quantity analyses confirmed their slight presence of wire tool electrode material (less than 4 at %).
C-C, C-O, C=O (Figures 8f and 9e) bonds correspond to the atmospheric contamination and precipitation of carbides during directed rapid heating and slow cooling (typical for welding, plasma or laser treatment). For the samples of X10CrNiTi18-10 (12kH18N10T) steel, it is~58 at % and, for the samples of 2024 (D16) duralumin, it is~40 at %. Figure 10 shows the cross-sectional surface of an X10CrNiTi18-10 (12kH18N10T) steel sample to research the near-surface layers' chemical composition and distribution spectrum of the chemical elements in the near-surface layers of the sample. The near-surface layer has recast material presence and formed flakes of secondary material (solid solutions and eutectics) and cracks (Figure 10a). The chemical elements of wire penetrated the machining surface at a depth of more than 6 µm, the content of workpiece material elements grows and achieves proportions of the main material at a depth of 4 µm. EDS graphs were also plotted for other chemical elements, but their percentage is so tiny that it seems insignificant and does not have a principal character for the overall picture of the near-surface layer of the sample depletion. The obtained data are further discussed in Section 4.2.
C-C, C-O, C=O (Figures 8f and 9e) bonds correspond to the atmospheric contamination and precipitation of carbides during directed rapid heating and slow cooling (typical for welding, plasma or laser treatment). For the samples of X10CrNiTi18-10 (12kH18N10T) steel, it is ~58 at % and, for the samples of 2024 (D16) duralumin, it is ~40 at %. Figure 10 shows the cross-sectional surface of an X10CrNiTi18-10 (12kH18N10T) steel sample to research the near-surface layers' chemical composition and distribution spectrum of the chemical elements in the near-surface layers of the sample. The near-surface layer has recast material presence and formed flakes of secondary material (solid solutions and eutectics) and cracks (Figure 10a). The chemical elements of wire penetrated the machining surface at a depth of more than 6 µm, the content of workpiece material elements grows and achieves proportions of the main material at a depth of 4 µm. EDS graphs were also plotted for other chemical elements, but their percentage is so tiny that it seems insignificant and does not have a principal character for the overall picture of the near-surface layer of the sample depletion. The obtained data are further discussed in Section 4.2.

Dependencies of Interelectrode Gap on Electrical Properies
Dependencies of the interelectrode gap optimum values of X10CrNiTi18-10 (12kH18N10T) steel and 2024 (D16) duralumin after electrical discharge machining with a brass wire tool electrode in a water medium on specific electrical resistance ρ, linear thermal expansion coefficient α × 10 6 , thermal conductivity λ, and melting point Tm are shown in Figure 12. The obtained trend lines for two materials with different electrophysical properties agree with the theoretical data presented in [37]. It should be noted that the data were obtained for a structural material-a conductive aluminum-based composite (75-95%) with the addition of semiconducting silicon carbide. The values of the interelectrode gap decrease, and the electrical discharge machining productivity (material removal rate) increases with an increase in the electrical resistance of the material being machined.

Dependencies of Interelectrode Gap on Electrical Properies
Dependencies of the interelectrode gap optimum values of X10CrNiTi18-10 (12kH18N10T) steel and 2024 (D16) duralumin after electrical discharge machining with a brass wire tool electrode in a water medium on specific electrical resistance ρ, linear thermal expansion coefficient α × 10 6 , thermal conductivity λ, and melting point T m are shown in Figure 12. The obtained trend lines for two materials with different electrophysical properties agree with the theoretical data presented in [37]. It should be noted that the data were obtained for a structural material-a conductive aluminum-based composite (75-95%) with the addition of semiconducting silicon carbide. The values of the interelectrode gap decrease, and the electrical discharge machining productivity (material removal rate) increases with an increase in the electrical resistance of the material being machined. Interpolating the theoretical data of the source of the dependence of the value of the interelectrode gap on the electrical resistance, we obtain increasing exponential approximation over a dataset [38] using the following dependence where A is an amplitude of −2.657 +/− 0.197 µm; t is e-folding time of 14.898% +/− 0.002 %; y0 is a graph offset of 88.719 +/− 0.268 µm. The scaled Levenberg-Marquardt algorithm was used with a tolerance = 0.0001 from the value at x1 = 5% to the value at x2 = 25 %, agreement criterion χ 2 = 0.0055, determination coefficient R 2 = 0.9999, the number of interpolations was 13. Unfortunately, the method of increasing exponential approximation over a dataset did not converge after 1000 iterations for the data obtained in the current study to provide a similar (exponential) character of dependence of the interelectrode gap optimum values of X10CrNiTi18-10 (12kH18N10T) steel and 2024 (D16) duralumin on specific electrical resistance ρ. The Boltzmann (Sigmoidal) approximation over a dataset [39] was used as an alternative ( Figure 13) Interpolating the theoretical data of the source of the dependence of the value of the interelectrode gap on the electrical resistance, we obtain increasing exponential approximation over a dataset [38] using the following dependence where A is an amplitude of −2.657 ± 0.197 µm; t is e-folding time of 14.898% ± 0.002%; y 0 is a graph offset of 88.719 ± 0.268 µm. The scaled Levenberg-Marquardt algorithm was used with a tolerance = 0.0001 from the value at x 1 = 5% to the value at x 2 = 25%, agreement criterion χ 2 = 0.0055, determination coefficient R 2 = 0.9999, the number of interpolations was 13. Unfortunately, the method of increasing exponential approximation over a dataset did not converge after 1000 iterations for the data obtained in the current study to provide a similar (exponential) character of dependence of the interelectrode gap optimum values of X10CrNiTi18-10 (12kH18N10T) steel and 2024 (D16) duralumin on specific electrical resistance ρ. The Boltzmann (Sigmoidal) approximation over a dataset [39] was used as an alternative ( Figure 13) where A 1 is an initial value of 127.66 ± 4.71 µm; A 2 is an end value of −207.94 ± 276.54 µm; x 0 is a center of x-range of 1.20 ± 0.49 Ω·mm 2 m ; dx is a time constant of 0.38 ± 0.09 Ω·mm 2 m . The scaled Levenberg-Marquardt algorithm was used with a tolerance = 0.0001 from the value at x 1 = 0.05 Ω·mm 2 m to the value at x 2 = 0.73 Ω·mm 2 m , agreement criterion χ 2 = 0.1400, determination coefficient R 2 = 0.9999, the number of interpolations was 29.  Let us rough compare the character of the obtained graphs ( Figure 14). The obtained analytical dependencies require further research and experimental testing to identify stable relationships for various materials. Both functions have the right to exist until the positive or negative value of the derivative of the revealed dependence is proved within abscissas' (ρ) and ordinates' (Δ) positive values (>0).

Submicrostructure of Surface and Subsurface Layers
Both of the surfaces have the presence of thermal destruction under discharge pulses but were subjected to the chemical interaction between components of workpieces made of X10CrNiTi18-10 (12kH18N10T) steel and 2024 (D16) duralumin and brass tool electrode in water (Figures 4-7). The formed sediment during electrical discharge machining can not only change electrical conditions for the discharges in the interelectrode gap but hampers its effectiveness when the quantity of effective impulses is less than idle pulses that addressed to the destruction of the formed sediments and erosion debris that leads to the reduction of the effective discharge gap provoke short circuits [21]. It should be noted that machining of X10CrNiTi18-10 (12kH18N10T) steel, unlike duralumin machining, is accompanied by a series of bright orange flashes and the formation of abundant black dust clouds.
The analysis of the surface 3D profiles ( Figure 5) and measured roughness parameters (Table 6) showed that the surface topology of the samples made of 2024 (D16) duralumin have a more pronounced character. It correlates with the measured discharge gap, known electrical and physical properties of 2024 (D16) duralumin, chosen pulse frequency (f), and duration (D) despite the increased operational voltage (V0) that should provide denser discharges augmentation and current strength (I) that with the identical other conditions forms deeper wells [8].
The classified groups of the defects ( Figure 6) showed that the first group includes residual snag or chip after jumper rupture and vertical wire traces according to the inconstant machining speed of the machine mode in case of the heterogeneous structure of the workpiece. The second one is for visible melting traces related to the wire clip between two electrodes that leads to consequent short-circuits at the end of machining and visible surface color gradients associated with the different tempering temperatures achieving in the interelectrode gap that correlated with the insufficient dielectric flushing and noneffective evacuation of the erosion products. The classification of the defects is presented in Figure 15a.

Submicrostructure of Surface and Subsurface Layers
Both of the surfaces have the presence of thermal destruction under discharge pulses but were subjected to the chemical interaction between components of workpieces made of X10CrNiTi18-10 (12kH18N10T) steel and 2024 (D16) duralumin and brass tool electrode in water (Figures 4-7). The formed sediment during electrical discharge machining can not only change electrical conditions for the discharges in the interelectrode gap but hampers its effectiveness when the quantity of effective impulses is less than idle pulses that addressed to the destruction of the formed sediments and erosion debris that leads to the reduction of the effective discharge gap provoke short circuits [21]. It should be noted that machining of X10CrNiTi18-10 (12kH18N10T) steel, unlike duralumin machining, is accompanied by a series of bright orange flashes and the formation of abundant black dust clouds.
The analysis of the surface 3D profiles ( Figure 5) and measured roughness parameters (Table 6) showed that the surface topology of the samples made of 2024 (D16) duralumin have a more pronounced character. It correlates with the measured discharge gap, known electrical and physical properties of 2024 (D16) duralumin, chosen pulse frequency (f ), and duration (D) despite the increased operational voltage (V 0 ) that should provide denser discharges augmentation and current strength (I) that with the identical other conditions forms deeper wells [8].
The classified groups of the defects ( Figure 6) showed that the first group includes residual snag or chip after jumper rupture and vertical wire traces according to the inconstant machining speed of the machine mode in case of the heterogeneous structure of the workpiece. The second one is for visible melting traces related to the wire clip between two electrodes that leads to consequent short-circuits at the end of machining and visible surface color gradients associated with the different tempering temperatures achieving in the interelectrode gap that correlated with the insufficient dielectric flushing and non-effective evacuation of the erosion products. The classification of the defects is presented in Figure 15a. The observation area presented in the SEM-microphotographs ( Figure 7) excludes any mechanical rupture or melting traces. The obtained microphotographs showed nonoxide (oxygen unsaturated) structures-metastable solid solution and thin eutectic [40][41][42][43], by other words, movable and adherent to the surface films of the first order that corresponds to the submicron structure of the material under erosion wear with the presence of formation and removal of brittle secondary structures of the second order (Figure 15b) [44,45].
Stainless steel tends to generate significant internal stresses in the subsurface layer with its low thermal conductivity and a high coefficient of linear expansion (Table 5, Figure 12c,d). At the low intensity of the heat source (spark discharge channel), steel heating occurs in a large zone, while the cooling rate during processing in water is significant (in contrast to processing in air and hydrocarbons), and the steel does not stay in the heating zone for a long time more than 600-700 °C. Nevertheless, precipitation of carbides to the depth of the surface layer (Figure 8e,f), oxidation of chromium (a spongy mass that is the source of cracking) is observed at the depth of 2 µm (Figures 8d and 10b). Titanium (0.8%) in the composition of the steel should prevent the precipitation of chromium carbides.
The elemental analysis of X10CrNiTi18-10 (12kH18N10T) steel sample near-surface layers ( Figure 10) show penetration of brass wire tool components (Cu, Zn) up to the depth of more than 6 µm (observed distance), when the content of iron and chromium increases sharply from the surface to proportions close to the chemical state of the base material of the workpiece at a depth of 4 µm. A similar character is seen in Figure 11 for 2024 (D16) duralumin. The studies [2,11,[15][16][17]19,[46][47][48] show that penetration (adsorption in the recast layer) of the tool electrode material components can reach a depth of 10 µm (from 2.55 up to 50 µm depending on used materials of electrodes, dielectric medium, and experiment factors). At the same time, this uneven distribution of the workpiece and wire elements can be explained by sublimation phenomena of the recast layers (similar to laser ablation during heating with the concentrated energy flows such as laser, plasma, electric discharges, fast energy neutral atoms [49][50][51][52]), when components of workpiece material sublimate primarily [53,54]. More refractory components of the secondary material of the second order, such complex compounds as oxides and stoichiometric solid solutions of oxides [29,[55][56][57][58][59], do not entirely sublimate in a single current pulse and remain in the form of a nano scaffold. Secondarily, the sublimated elements of the workpiece, tool The observation area presented in the SEM-microphotographs (Figure 7) excludes any mechanical rupture or melting traces. The obtained microphotographs showed non-oxide (oxygen unsaturated) structures-metastable solid solution and thin eutectic [40][41][42][43], by other words, movable and adherent to the surface films of the first order that corresponds to the submicron structure of the material under erosion wear with the presence of formation and removal of brittle secondary structures of the second order ( Figure 15b) [44,45].
Stainless steel tends to generate significant internal stresses in the subsurface layer with its low thermal conductivity and a high coefficient of linear expansion (Table 5, Figure 12c,d). At the low intensity of the heat source (spark discharge channel), steel heating occurs in a large zone, while the cooling rate during processing in water is significant (in contrast to processing in air and hydrocarbons), and the steel does not stay in the heating zone for a long time more than 600-700 • C. Nevertheless, precipitation of carbides to the depth of the surface layer (Figure 8e,f), oxidation of chromium (a spongy mass that is the source of cracking) is observed at the depth of 2 µm (Figures 8d and 10b). Titanium (0.8%) in the composition of the steel should prevent the precipitation of chromium carbides.
The elemental analysis of X10CrNiTi18-10 (12kH18N10T) steel sample near-surface layers ( Figure 10) show penetration of brass wire tool components (Cu, Zn) up to the depth of more than 6 µm (observed distance), when the content of iron and chromium increases sharply from the surface to proportions close to the chemical state of the base material of the workpiece at a depth of 4 µm. A similar character is seen in Figure 11 for 2024 (D16) duralumin. The studies [2,11,[15][16][17]19,[46][47][48] show that penetration (adsorption in the recast layer) of the tool electrode material components can reach a depth of 10 µm (from 2.55 up to 50 µm depending on used materials of electrodes, dielectric medium, and experiment factors). At the same time, this uneven distribution of the workpiece and wire elements can be explained by sublimation phenomena of the recast layers (similar to laser ablation during heating with the concentrated energy flows such as laser, plasma, electric discharges, fast energy neutral atoms [49][50][51][52]), when components of workpiece material sublimate primarily [53,54]. More refractory components of the secondary material of the second order, such complex compounds as oxides and stoichiometric solid solutions of oxides [29,[55][56][57][58][59], do not entirely sublimate in a single current pulse and remain in the form of a nano scaffold. Secondarily, the sublimated elements of the workpiece, tool electrode, working medium that form low-temperature plasma cloud [60] in the interelectrode gap are deposed partly at the refractory nano scaffold of the secondary material of the second order [21,61,62].

Conclusions
The results of optical and scanning electron microscopy and obtained surfaces' topology reveal the nature of electrical erosion wear processes thermal sublimation and dissociation of the material of the supplied directed concentrated energy flux (discharge channel) and subsequent deposition of secondary structures of the material of the secondary order (complex compounds). Classification of the obtained surface topology of the tool electrode determines the types of wear related to the thermal nature of the material ablation (sublimation) and mechanical destruction of the surface layer of the secondary material.
The main finding is the obtained trend for the discharge gap-electrical resistance following the previously published studies for other structural materials, where: The values of the interelectrode gap decrease and the electrical discharge machining productivity (material removal rate) increase with an increase in the electrical resistance of the material being machined.
Two types of interpolation of the dependence of the electrical properties of two conducting materials on the electrical conductivity based on increasing exponential and Boltzmann (Sigmoidal) approximations are demonstrated. The obtained analytical dependencies of the discharge gap and electrical properties of the materials require further research and experimental testing to identify stable relationships for various groups of materials.
Chemical analyses of the subsurface layer of the tool and samples showed nanomodification of the surface by the components formed from the elements of the material and by used dielectric medium (water) and wire tool electrode at the depth up to 4-6 µm. The compositions should be different for each working fluid and following the chemical interactions between elements that occurred in the presence of heat.
Further research is aimed at developing the method of chemical content prediction for providing functional surface and subsurface layers based on the chemical content of the workpiece, tool electrode, and dielectric fluid and at developing physical and mathematical function of the discharge gap-electrical properties dependencies for theoretical prediction the optimum discharge gap value based on known electrical properties of newly designed conductive materials.  Acknowledgments: The authors thank Gennady P. Terentiev (Nizhny Novgorod State University of Architecture and Civil Engineering) for his contribution to developing structural metallic construction.

Conflicts of Interest:
The authors declare no conflict of interest.