Electric Field Effect on Surface Layer Removal during Electrolytic Plasma Polishing

E.V. Parfenov1*, R.G. Farrakhov1, V.R. Mukaeva1, A.V. Gusarov1, R.R. Nevyantseva1,

A. Yerokhin2

1Ufa State Aviation Technical University, 12 Karl Marx Street, Ufa, Russia2University of Manchester, Oxford Road, Manchester, M13 9PL, UK

Abstract

In this paper, electric field distribution in the electrolyser during electrolytic plasma

polishing (EPPo) is analysed. The analysis takes into account field distribution in the electrolyte

and the voltage drop in the vapour gaseous envelope (VGE), providing strong bridging to the

surface properties using the results of 3D scanning. A numerical approach is used for simulation

of the field in the electrolyte which is treated as a linear conductive medium, taking into account

a non-linear voltage drop in the thin vapour gaseous envelope formed around the anode. The

resultant current density distribution from the electrolyte can be used for evaluation of material

removal profile via Faraday’s law and current efficiency. The results of 3D scanning show a

good correspondence with the theoretical results. The average thickness of the surface layer

removed after 15 min of EPPo treatment reaches 20-40 μm, with the surface roughness Ra

decreasing from 0.3-0.5 to 0.06-0.08 μm, providing a mirror-like surface finish. The removed

layer profile change around the sample cross-sectional perimeter exhibits high peaks of the

volume loss at the edges, which is consistent with the theoretical profile. The study reveals

several important features of the EPPo process mechanism. Firstly, the mechanism is

predominantly electrochemical with a rough estimate of the current efficiency at 30%. The VGE

essentially provides surface oxide removal by hydrodynamic flows and shifts the anodic reaction

balance from water electrolysis to the metal dissolution. Secondly, despite presence of plasma

discharge in the VGE, it does not cause damage to the surface, due to its diffused type and low

intensity. Thirdly, the VGE provides a uniform treatment, especially at higher voltages, because

the negative differential resistance of the VGE balances out the current density distribution over

a complex shape of the sample, providing a uniform removal of the surface layer. However, this

works only for the surface features of size larger than the VGE thickness (>3-5 mm); otherwise,

the feature becomes exposed to the electrolyte without the VGE shielding and is rapidly

dissolved because of the inrush of the current density. Finally, the proposed approach contributes

to understanding of the mechanisms underlying electrolytic plasma processing and provides a

reliable tool for modelling these non-linear processes.* Corresponding author. E-mail: pev_us@yahoo.com, tel. +7 347 272 1162

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Keywords: electrolytic plasma polishing, stainless steel, electric field simulation, vapour gaseous

envelope, 3D scanning, treatment uniformity

1. Introduction

Electrolytic plasma processes (EPP) cover a wide range of applications in surface

engineering [1]. These include oxidising treatments, primarily plasma electrolytic oxidation

(PEO), and non-oxidizing treatments, e.g. case hardening and cleaning [2, 3]. A distinct feature

of the non-oxidising EPPs is a thin vapour gaseous envelope (VGE) formed around the working

electrode when a high voltage, leading to intensive ohmic heating of the electrolyte, is applied

[4]. This results in either a rapid heating of the working electrode, which is used for nitriding

and/or carburising (PEN/PEC), or intense surface cleaning used for polishing and/or coating

removal (EPPo/EPCS) [5-7]. In this study, we shall focus on the anodic EPPo of a stainless steel.

The vapour gaseous envelope has the highest electrical resistance in the circuit; therefore,

the majority of the voltage drop occurs across it. The VGE is a quasi-stationary object, since it

exists only during the electrolytic plasma process. Moreover, it is also a non-linear object; this

follows from the EPP current-voltage characteristics (CVC) exhibiting a negative differential

resistance (NDR) region corresponding to the operational regime [1]. This occurs because

growing voltage increases the specific amount of heat liberated in the vicinity of the working

electrode, making the VGE thicker, so decreasing the current. Another source of non-linear NDR

behaviour is a glow discharge which appears in the VGE due to the high electric field.

Depending on the EPP type, the VGE thickness varies in the range from 0.01 to 5 mm, resulting

in the values of electric field of up to 106 V·cm–1, which is close to the breakdown values in

vapour-gaseous media [1, 8, 9]. Although the importance of VGE is generally recognised,

limited theoretical studies exist dating back to 1980s [10, 11].

Recent trends in the EPP research show increasing interest to the assessment of the

treatment uniformity [5]. This includes electric field analysis for the electrolyte as a conductive

medium. Theoretical studies of electric fields in both the electrolyte and the VGE for a

cylindrical coaxial system was carried out in [8] and [12] for PEN/PEC and EPPo processes,

respectively. This is a 1D field problem, and more complex shapes have not so far been

considered. The voltage drop in the electrolyte is often neglected, with that in the VGE assumed

to be equal to the total applied voltage and the current density at the working electrode being

averaged and considered constant [4, 13]. While the former is fair for the majority of EPPs with

a VGE, the latter holds only when using the simplest electrode shapes and layouts.

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Electric field modelling is routinely used for the analysis of electrochemical processes,

simulation and structural optimisation of electrolysers, especially in Al reduction, fuel cells and

batteries, anodic coatings and other applications [14-16]. The nonlinearity of EPPs could be a

reason why the electric field has not so far been deeply explored for this group of processes.

Therefore, the aim of this study is to investigate electric field distributions in the

electrolyte and the vapour gaseous envelope, and bridge associated results with surface

characteristics obtained after electrolytic plasma polishing of stainless steel components.

2. Theoretical

2.1. General approach

This research attempts to join the results of theoretical and experimental studies of EPPo

treatment of a stainless steel. Firstly, a 2D analysis of longitudinally invariant electric field

distribution is carried out. Consequently, a current density distribution along the sample

perimeter is obtained and translated into the weight loss and surface profile change. Secondly, an

experimental study of the EPPo with the analysed layout is performed at different voltages

corresponding to the treatment range boundaries and providing similar average current densities.

Further, changes in the actual surface profile of the sample are assessed using a 3D scanner and

compared to the theoretical estimates, to reveal the VGE role in the material removal.

2.2. Electric field modelling

2.2.1 Assumptions

The following assumptions can be adopted:

1) the problem is solved for the case of a bubble boiling in the VGE during anodic

EPPo under potentiostatic conditions;

2) the electrolyte is agitated; therefore, its temperature T is independent on spatial

coordinates;

3) the electrolyte is considered as a linear homogeneous conductive medium with

constant specific conductivity γ;

4) the plasma discharge is distributed uniformly over the VGE, with no filamentation

or micro-discharging occurring;

5) the system nonlinearity is determined by the resistance of the VGE;

6) the VGE thickness changes in the range of 0.1 to 2.0 mm, which is significantly

less than the interelectrode distance (100...200 mm);3

7) the problem is solved for a longitudinally invariant field which corresponds to a

common case of processing long workpieces.

The above assumptions allow the electrolyte temperature to be used as a constant,

depending on the CVC of the process; therefore, instead of a multiphysics problem of the heat-

and mass transfer in the electromagnetic field, a stationary problem of a current density

distribution could be solved at this stage.

2.2.2 Boundary problem

The 2D field distribution in the conductive medium (electrolyte) is obtained by

numerically solving Laplace equation ∇2 φ=0 in Castesian coordinates (x , y , z) with respect to

the electric potential φ [17]. Based on assumption (7), the 2D problem (Fig. 1) is solved for the

longitudinally invariant field φ=φ (x , y ). A rectangular plate anode is placed in the centre of the

system at position (x¿¿1; y1)¿ and the cathode with size of x3× y3 forms the perimeter of the

system. Dirichlet boundary conditions φ=0 and φ=U are adopted at the cathode and anode

respectively. Therefore the non-uniformity of current density can be assessed along the perimeter

of the workpiece cross-section parallel to the xOy plane.

The Laplace equation adapted to this case

∂2 φ∂ x2 +

∂2φ∂ y2 =0

can be solved using finite difference or finite element method for a mesh covering the area of

interest so that for each node with coordinates (i , j) of the mesh the potential φ i , jis calculated.

This solution can be achieved using any electric field modelling software, e.g. COMSOL, ElCut

and others.

2.2.3 System non-linearity

The system non-linearity is formalised in an integral form as a non-linear CVC obtained

experimentally for the average anode current density:

δ= f (U , T )

This determines the current I :

I=δ ∙ s,

where s is the surface area of the anode.

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2.2.4 Modelling approach

The modelling approach takes into account the electric field in the electrolyte and the

VGE, and consists of the following three steps.

The first step is dedicated to the solution of the electric field problem with respect to the

distribution of potential φin the electrolyte. This solution corresponds to a given value of voltage

U without taking into account the voltage drop over the VGE. The result is a matrix m× n of

potentials φ i , j. The resulting potential distribution helps obtaining the electric field E⃗ using a

gradient operator:

E⃗=−∇ φ

and further the current density δ⃗ via Ohm’s law:

δ⃗=γ E⃗,

where γ is the specific conductivity of the electrolyte.

Both E⃗ and δ⃗ are obtained as numerical derivatives and stored as paired matrixes m× n of

their projections (e.g. δ ( x ) i , j and δ ( y )i , j) to x and y axes.

The integration of the current density over the cathode surface sc provides current

through the electrolyte:

I ¿=∮sc

❑

δ⃗ d⃗s

which for the chosen mesh and four sides of the cathode becomes

I ¿=(∑j=1

n

|δ ( x ) 1 , j|∆ y+∑j=1

n

|δ ( x ) m, j|∆ y+∑i=1

m

|δ ( y ) i ,1|∆ x+∑i=1

m

|δ ( y )i , n|∆ x) ∙ z3

where z3 is the longitudinal size of the system along axis z. This value is different from I .

The second stage is dedicated to the analysis of the equivalent circuit of electrolyser (Fig.

2). In this circuit, current I can be calculated for given values of voltage U , electrolyte

temperature T and anode surface area according to the CVC formalised above. The resulting

value of I is much smaller than that of I ¿ obtained in the first step.

Application of Kirchhoff’s voltage law (KVL) divides the applied voltage U between the

electrolyte and the VGE into U 1 and U 2 , corresponding to equivalent resistances R1 and R2 in

the circuit. Following assumption (3), R1 is a linear element conforming to Ohm’s law at any

current:

R1=UI ¿ =

U 1

I.

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R2 is a non-linear element, but its voltage drop can be obtained from the KVL:

U2=U −I R1 .

Now having U2, the voltage drop over the electrolyte can be obtained as

U1=U −U 2 .

This value is different from that used for the boundary problem solution.

On the third stage we balance voltage drops over the electrolyte used in steps one and

two, thus, balancing currents I and I ¿. Following the similarity principle held for the linear

element in the system, the electric field values for the electrolyte can be corrected using the

similarity coefficient:

k=U 1

U

Because the VGE thickness is significantly less than the mesh step, the potentials and current

density projections can also be corrected as

φ 'i , j=k ∙ φ i, j ;

δ '(x )i , j=k ∙ δ ( x ) i , j;

δ ' ( y )i , j=k ∙ δ ( y ) i , j .

Integrating the corrected current density over the cathode surface area as in step one,

currents I and I ¿ can be balanced, and the non-linear problem solved.

2.3. Removed layer thickness assessment

2.3.1 Theoretical assessment via electric field modelling (EF technique)

Theoretical evaluation is made according to Faraday’s law using the results of the current

density integration over the anode surface area described above. Assuming that the anodic

dissolution is the dominant process at the potentials of EPPo, and taking into account the sample

chemical composition (Table 1), the following anodic reactions can considered:

Fe0−2e→ Fe2+¿¿ (-0.44 V)

Fe2+¿−e → Fe3+¿¿ ¿ (0.77 V)

Cr0−3 e→ Cr3+¿ ¿ (-0.74 V)

Further, the mass of the dissolved component can be evaluated as

m= 1F

∙ Mz

∙δ ∙ s ∙ t ∙ η

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where Faraday constant F=96484 C·mol–1; valence number z=3 for both species; M is the molar

mass for iron and chromium respectively; δ – anode current density; t – treatment time, η –

current efficiency.

The total weight loss can be estimated using the proportions of the elements in the steel:

∆ m=0.13 ∙mCr+0.87 ∙mFe .

Further estimation of the removed layer thickness via the weight loss is described below.

2.3.2 Experimental assessment via weight loss (WL technique)

Fig. 3 shows a sketch of the parallelepiped sample a× b ×c in size with the removed

layer h shown. The surface layer is removed from all sides, except for the top due to the VGE

shielding and two round holder attachment places with diameter d . Therefore, the treated surface

area is:

s=2ac+2 bc+ab−π d2

2.

Then the removed layer thickness can be obtained from the weight loss:

h=m1−m2

ρ ∙ s,

where m1 – the sample weight before the treatment, m2 – the sample weight after the treatment; ρ

– steel density. For the EPPo process, the current efficiency was studied before, yielding the

values from 20 to 35% [18]. The average values of electric current recorded during the

treatments allow these values to be validated.

2.3.3 Experimental assessment via 3D scanning (3D technique)

Fig. 4 shows stereolitography (STL) models of the sample before and after the treatment

with the cross-sections showing loss of thickness. The cross-sections can be analysed at different

z positions: e.g. 10, 20, 30 and 40 mm from the bottom of the sample. The STL models can be

aligned using Magics software supplied with the 3D scanner and further processed in MATLAB

in order to obtain the profile change as follows.

For the chosen positionz, the STL points found within a belt ± 1 mm wide are marked as

belonging to the cross section. Next, their Cartesian coordinates (x , y ) are converted into polar

coordinates (r ,α) (with the origin shifted to the cross-section centre) and sorted with ascending

α . Thus, a random order of the points chosen by the 3D machine is changed to the order along

the cross-section. Further, a difference between cross-sections before and after the treatment in

the polar coordinates is converted back into Cartesian:

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x=r cos α ,

y=rsin α ,

and the origin is shifted to the lower left corner of the cross-section ((x1; y1) in Fig. 1). Finally,

the profile is straightened along the cross-section perimeter and further compared to that

obtained by other techniques.

3. Experimental

3.1. Electric field modelling

In this study, the solution was obtained by finite differences method using originally

developed program in MATLAB environment. The program solves the Laplace equation for a

uniform mesh. Each node with coordinates (i , j) has the potential φ i , jaccording to the following

finite difference Laplace equation:

φi+ 1, j+φ i−1, j−2 φi , j

(∆ x)2 +φi , j+1+φ i , j−1−2 φi , j

(∆ y )2 =0

where ∆ x=∆ y – mesh step. A multi-mesh approach was used, where the results of the analysis

with a coarse mesh become an initial approximation for the analysis with the finer mesh. The

initial mesh step was chosen as ∆ x1=∆ y1=1cm, and after 6 iterations of the mesh refining the

final mesh step was ∆ x6=∆ y6=0.033 cm.

3.2. EPPo treatment

Rectangular samples 20 ×5×60 mm in size made out of 20X13 stainless steel (Table 1)

were used for the experiments. A hole, 5 mm in diameter, was made near the top of the sample in

order to attach a screw holder. During the EPPo the samples were immersed into the electrolyte

to the depth of 50-70 mm from the top so that the VGE was completely enclosed in the

electrolyte. The electrolyser was a 30 litre stainless steel bath with a stainless steel cooling coil

arranged into a cubic form 21 ×21×21 cm in size and served as the cathode. A modular DC

power supply (12 modules MeanWell SPV-1500-48) providing up to 600 V and up to 30 A with

a PC based control system was used in the potentiostatic mode. The average voltage and current

values were recorded by the power supply monitor at a rate of 1 s–1 and the instantaneous values

were recorded for 0.2 s by a PC data acquisition board L502 (L-Card) at the sampling frequency

of 100 kHz and a rate of 1 s–1. An appropriate voltage divider (1:100) and current probe (30 A)

with instrumental amplifiers were used for scaling the signals.8

According to the CVC of the process [19], three voltage levels providing similar average

anodic current densities were used: 350, 250 and 9 V (Fig. 5). The first two correspond to the

boundaries of the EPPo regime providing extreme values of the VGE thickness. The third one

corresponds to the electrolysis without the vapour gaseous envelope, and it was used as a

reference for the electric field distribution in the electrolyte.

All the experiments were carried out at the same temperature of 70 °C maintained with

± 1°C accuracy by a heating and cooling systems operated under TRM202 (OWEN)

microcontroller regulation, with stirring by aeration. The electrolyte consisted of 5% aqueous

solution of (NH4)2SO4. The treatment time was 15 min.

3.3. Surface characterisation

The sample weight was measured before and after EPPo treatments using A&D analytical

balance GR-200 with the accuracy of 0.1 mg. The samples were ultrasonically cleaned in

isopropyl alcohol for 5 min before the measurements. The surface roughness Ra was measured

by a profilometer 283 using the track length of 0.25 mm and the ranges 0-0.1, 0-0.3 and 0-1 μm

with 5% accuracy of the range. The surface morphology was analysed with a JEOL JSM-6390

scanning electron microscope. The 3D stereolitography model was obtained by a 3D scanner

ATOS II XL with the accuracy of ± 5 μm.

4. Results

4.1. Electrical field distribution

Fig. 6 shows 2D modelling results of the potential and electric field distribution in the

electrolyte. The contour lines in the figure represent the equipotential lines with a constant step

of U 1

15. The arrows represent electric field vectors at the mesh nodes. This figure corresponds to

the field distribution in the linear part of the system, so the picture does not depend on the

voltage applied to the electrolyte, and it depends only on the electrode layout which did not

change through this study.

To assess the system non-linearity, the following CVC equation for the anode current

density δ (A cm–2) was obtained by regression analysis using the least squares method:

δ=b0+b1~U +b2

~T+b3~U ~T +b4

~U 4+b5~T3,

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where the voltage (Volts) and temperature of the electrolyte (°C) were normalized to range

[−1;1]:

~U =U −300100

;~T=T−7020

.

This decreases the estimation variance. The coefficients of the regression are shown in Table 2.

This regression is obtained by over 600 experimental points derived from different EPP

processes with the VGE in similar 5% ammonia salt water electrolytes [4, 18, 20-22]. Fig. 7

shows the response surface for the CVC with the experimental points proving that the regression

tendency does not depend significantly on the treated substrate, but strongly depends on the

electrolyte temperature and voltage. The coefficient of determination R2 shows a good degree of

approximation. Analysis of the coefficients in Table 3 supports the non-linearity of the CVC.

Moreover, the negative values of b1, b2 and b5 mean that with the decrease of both voltage and

temperature the current density grows nonlinearly.

Fig. 8 shows distributions of the absolute values of current density and potential for EPPo

at different voltages taking into account the system nonlinearity. The calculation results for these

cases are shown in Table 3. As follows from the figure and the table, the current density

distribution does not change significantly among the cases selected because the average current

densities were chosen to be similar during the experimental design. The shape of the current

density distribution does not depend on the VGE presence in this model because the boundary

conditions keep the normal projections of δ unchanged. Since the thickness of the VGE is less or

compatible to the mesh step in this model, the current density distribution within the VGE

becomes a separate problem which can be solved further having these results as a starting point.

Unlike current density, the potential distribution does change with the presence of the VGE. In

this model, the last mesh step to the anode has a voltage drop of U 2. The values of the voltage

drop over the electrolyte and the VGE are shown in Table 3. These explain the difference

between potential distributions shown in Fig. 8: the higher the voltage, the thicker the VGE and

the higher the voltage drop across it.

4.2. Electrical characteristics of the EPPo process

Evolution of electrical characteristics throughout the EPPo treatment is shown in Fig. 9.

Since the process is carried out in the potentiostatic DC mode, the voltage does not change

during the treatment. The current differs among these cases, but it still constitutes the

approximate value of 10 A providing the average current density of ~0.33 A·cm–2, as intended by

10

the experimental design. The average current values I are presented in Table 4. Slow current

fluctuations occur due to the electrolyte heating during the process and occasional switching on

the cooling pump decreases the electrolyte temperature. This result emphasises the strong

temperature influence on the current; this is reflected in the CVC of the process provided in Fig.

7.

Fig. 10 shows voltage and current waveforms for the studied conditions. Only slight

voltage ripples are provided by a well stabilised power supply. In both high voltage cases,

significant current fluctuations, constituting up to 40% of corresponding DC values, can be

observed. This can be attributed to the fluctuations in the VGE which is an unstable non-

stationary object. For the low voltage case, no significant current fluctuation can be seen because

the voltage drop occurs only in the electrolyte which is a linear stationary medium in this study.

4.3. Surface properties

Surface plane SEM images of the studied samples are presented in Fig. 11. Before the

treatment (Fig. 11d), the surface clearly shows scratches generated by mechanical finishing to

the desired initial roughness Ra ranging 0.3 to 0.5 μm (Table 4). The EPPo treatment removes

these topological features and provides a smooth and glossy surface finish shown in Fig. 11a-b.

The Ra values range from 0.06 to 0.08 μm. The higher the voltage, the lower the polishing effect

occurs. The weight loss increases with the voltage decrease, following the increase in current.

Fig. 11c shows the surface morphology of the sample treated at 9V. Unlike other

samples, this one is covered by a thin grey oxide layer which can be easily scratched. It consists

of a sponge-like structure constituted by spherical pores interconnected with each other. Its

roughness decreases slightly because the oxide layer fills the initial profile of the mechanical

treatment. This sample has the smallest weight loss.

4.4. Sample shape change

Fig. 12 shows the profile change for the corner marked in Fig. 4. The right lines represent

the flat face a× c and the top lines represent the side of the sample b× c (see Fig. 3). As seen

from the figures, the smallest profile change occurs in the case of treatment at 9V. Further,

treatments at 350 and 250 V provide deeper profile changes. The profile lines appear almost

parallel, except for the corners. As follows from the figures, for the EPPo treated samples, the

material loss at the corners is higher compared to the case without the VGE. The local value

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there can go up to 0.1-0.2 mm. Also, the material loss at the sample sides is generally higher than

on the flat faces.

5. Discussion

5.1. Estimation of the removed layer thickness from electric field

Results of electric field modelling presented in Fig. 8 allowed evaluation of current

density and removed layer thickness around the cross-sectional perimeter to be carried out

(Fig. 13). The current density involution around the perimeter exhibits four peaks corresponding

to the sample corners. The peak height reaches three-fold values of the minimum current density.

The flat face has the minimal values of the current density; the sides also have local minima, but

these are almost twice higher than those on the faces. The highest current density is observed for

the treatment carried out at 250 V; this follows from the CVC of the EPPo process. The model

average current density (Table 3) is close to the experimental values (Table 4). A higher model

value occurs in the case of treatment at 250V (shown in italic in Table 3), which is due to the

CVC regression variance. When considering a specific process, rather than a wide variety of

those as in this study, the regression can be elaborated using a common approach of least

squares. The values of removed layer thickness hEF estimated based on the electric field follow

the values of δ (Fig. 13).

The average values of thickness estimated by the weight loss hWL are shown in Fig. 14 as

a reference and corresponding values of hEF are presented for comparison. For the sample treated

at 350 V, a very good agreement between hWL and hEF can be seen. For the sample treated at 250

V, hEF is larger because of an overestimated model current density, and the ratio of the removed

layer estimates is equal to that of corresponding current densities (≈0.6). This comparison is

valid because the model current efficiency values obtained from the previous studies correspond

to the experimental ones obtained from the measured values of DC current and weight loss (see

Tables 3 and 4).

An exception appears for the treatment at 9V where the hEF is almost three fold higher

than hWL. At this voltage, no VGE is formed and the experimental current efficiency is almost

three fold lower than its EF estimate counterpart. This occurs due to the treatment carried out

without the VGE. These conditions appear to correspond to the potential range of passivation for

the stainless steel [23]. Therefore, the prevailing anodic reaction from the metal dissolution

changes to the water electrolysis:

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2 H2O →O2+4 H+¿+4e ¿

The oxygen, which intensive liberation was observed experimentally, reacts with the substrate

metals providing oxides, e.g. FeO and Cr2O3, covering the surface in a sponge-like manner

where the spheroidal cavities could be formed by the liberated oxygen (Fig. 11c). This

mechanism explains the minimal weight loss and the lowest current efficiency observed for the

sample treated at 9V. Therefore, the removed layer thickness hEF (as in Fig. 14) could be further

corrected by using the appropriate current efficiency.

5.2. Estimation of the removed layer thickness from 3D scans

The 3D scans shown in Fig. 12 were also convoluted along the perimeter to provide

experimental estimates of removed layer thickness h3 D shown in Fig. 15 for the middle of the

sample (z=30 mm).

Comparison of Fig. 13 and Fig 15 shows a good agreement between the theoretical and

experimental estimates of the profiles. Both estimates provide high peaks corresponding to the

sample corners where the current density significantly exceeds its average value. Also, for the

sample sides, the removed layer thickness is generally higher than that on the faces. These results

support the hypothesis that electrochemical mechanisms dominate over the plasma-assisted

sputtering mechanism of material removal during the anodic EPPo treatment. This is also

supported by the SEM images (Fig. 11a,b) where no discharge craters typical for the DC plasma

electrolytic oxidation, cathodic electrolytic plasma cleaning and electrical discharge machining

are observed [24-26]. This underlines the main difference between the cathodic and anodic

electrolytic plasma processes. In the former, the metal cathode is intensely bombarded by the

cations existing in the VGE, which facilitates cathode heating, sputtering and thermionic

emission, sustaining plasma discharge in the VGE at relatively low voltages [27]. In the latter,

the yield of primary electrons from the electrolytic cathode is much lower [28], and the midpoint

voltage required to initiate the full glow discharge is significantly higher (420 V [27]).

Therefore, within the voltage range of the treatments considered in this study, the effects

associated with plasma sputtering and other non-faradaic processes appear to be insignificant.

The difference between the theoretical hEF (Fig. 13) and experimental h3 D (Fig. 15)

profiles appears as follows. Firstly, the sample treated at 250V exhibits a higher average value of

hEF compared to that of h3 D (Fig. 14) due to the CVC regression variance as discussed above.

The difference between the average values of hWL and h3 D for the samples treated at 350 and

250V (Fig. 14) is similar: 35-40%, and the profiles in Fig. 15 also follow these numbers, except

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for the peak values which obviously have a higher variance than the flat face parts. Another

difference appears for the sample treated at 9V which exhibits the thickness gain (negative h

values) due to the oxide layer formation. This effect is particularly noticeable on the flat faces,

whereas for the sides of the sample the thickness loss is still significant, reaching 30-40 μm. This

means that the passivation is stronger at the sites with lower local current densities, whereas the

sides are also subjected to anodic dissolution. Thus, the mechanism underlying EPPo treatments

of stainless steels includes formation of anodic oxide films on the metal surfaces followed by

oxide removal by hydrodynamic effects associated with the VGE occurring at higher voltages.

Therefore, the presence of the VGE is essential for sustaining anodic dissolution on the metal

surface, thereby providing cleaning and polishing effects.

Another important aspect underpinning VGE effects is the average current density over

complex shape surfaces. As seen from Fig. 15, in the case of VGE assisted treatments at 250 and

350 V, the difference in removed layer thickness between the faces and the sides of samples is

significantly less compared to that obtained for the treatment without the VGE. This can be

explained by the presence of NDR in the CVC of the studied system. Increases in local current

densities in certain sites makes the VGE thicker due to the ohmic heating, which decreases its

conductivity, causing a reciprocal decrease in the current density. Despite the fact that theoretical

current density is higher at the sides of the sample than at the faces, the VGE levels off the

current density, and the resulting thickness of removed layer becomes even. Nevertheless, this

levelling effect does not occur at the corners which appear to be severely dissolved, much more

than the theory predicts. This indicates that the levelling effect does not take place at the sites

which penetrate the whole depth of the VGE. For these sites, the current density becomes too

high (as follows from comparison of currents I and I ¿ in Table 3), and the actual thickness of

removed layer exceeds significantly the both theoretical and average values. This observation is

also supported by the difference between the treatments conducted at 250 and 350V. In the latter

case, the VGE is thicker and the corner peaks become significantly smaller than those

corresponding to the former treatment.

5.3. Removed layer thickness variation along the sample

Comparison of cross-sectional profiles (Fig. 15) at different z positions (Fig. 4) provides

information on the variation of the VGE effect over the sample height. As follows from the 3D

measurements, the profiles do not notably change with z (Fig. 16). This supports the hypothesis

that the VGE thickness is even over the whole anode height, also supporting the initial

assumption (7). However, since the bubbles in the VGE go up, some variance should still be 14

expected. Fig. 17 presents the average values of the removed layer thickness calculated from

those profiles and variations in the surface roughness Ra.

For the sample treated at 350V, material removal and resultant surface roughness are

fairly uniform. However for that treated at 250V, there is a notable difference (20-25%) between

corresponding top and bottom values. This implies that the VGE becomes thinner at the bottom

and this causes a slight decrease in the resulting surface roughness. From such comparison it

follows that increasing applied voltage to 300-350 V would be beneficial for the VGE uniformity

and reduction of excessive dissolution at the corners.

For the sample treated at 9V, a difference in removed layer thickness with height can also

be observed: it is zero or negative at the bottom and positive at the top. The bottom part receives

the highest local current density leading to a higher oxygen yield and resulting in more metal

oxides formed. The oxygen bubbles go up and form a discontinuous VGE which shifts the

balance between oxygen liberation and metal dissolution, so that a non-oxidised region appears

at the top of the sample. This is also consistent with the distribution of surface roughness which

remains unchanged at the top and decreases at the bottom of the sample due to preferential

growth of oxide film in the valleys of the original topology formed at the sample preparation

stage. Consequently, the removed layer thickness increases at the top, approaching the values

obtained by the weight loss method.

6. Conclusions

Conjoined theoretical and experimental studies have revealed effects of vapour gaseous

envelope on the electric field distribution and surface layer removal during electrolytic plasma

polishing of stainless steels. The electric field was numerically modelled taking into account the

non-linear voltage drop over a thin vapour gaseous envelope surrounding the anode. Obtained

current density distribution in the electrolyte was corrected using similarity coefficient and

employed for evaluation of removed layer thickness profile. It was shown that unlike cathodic

electrolytic plasma treatments, the EPPo mechanism within the studied voltage range is

predominantly electrochemical, with current efficiency of about 30%.

Low-voltage treatments without VGE cause stainless steel to passivate, with resulting

oxide layers blocking surface polishing. Formation of VGE during high-voltage EPPo processing

promotes oxide removal by hydrodynamic fluxes, which shifts the balance of the anodic

reactions towards metal dissolution. A volume type discharge developed in the VGE provides no

detrimental effects to the surface topology, resulting in a uniform material removal and a mirror-

like surface finish with Ra < 0.1 μm all over the sample. 15

The negative differential resistance of the VGE balances off non-uniform current density

distributions over complex shape samples, providing even material removal. However, this

applies only to the surface features of size larger than the VGE thickness (>3-5 mm). Otherwise,

the VGE shielding is compromised and the feature becomes directly exposed to the electrolyte,

which triggers rapid dissolution due to the inrush of the local current density. Sample corners

represent a typical example of such features, dissolving significantly faster than flat faces.

Nevertheless, this effect can be either diminished via increasing the VGE thickness by increasing

voltage, or used for deburring following machining.

7. Acknowledgements

The authors would like to acknowledge the support received through the funding from

Russian Presidential program for young D.Sc. scientists (project No. MD-2870.2014.8) and from

the Russian Foundation for Basic Research (project No. 16-38-60062) and the ERC Advanced

Grant (#320879 ‘IMPUNEP’). The authors also express their sincere gratitude to Institute of

Physics of Advanced Materials, Nanotech Centre and Department of Casting Machines and

Technologies at USATU for the access to the surface characterisation equipment.

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18

Artwork Captions

Table 1. Composition and properties of 20X13 stainless steel

Table 2. Regression model coefficients of the current-voltage characteristics

Table 3. Electric field modelling results

Table 4. Process parameters and properties of the samples treated at different voltages

Fig. 1. Electrode layout for the electric field analysis

Fig. 2. DC equivalent circuit of the electrolyser: R_1 – electrolyte resistance, R_2 – vapour gaseous envelope resistance

Fig. 3. Sketch of the sample with the removed layer h shown

Fig. 4. Stereolitography models of the sample before and after the treatment with the cross-sections showing loss of thickness and z positions of the cross-sections chosen for the analysis

Fig. 5. Schematic diagram of current-voltage characteristics showing positions of the experimental points

Fig. 6. Modelling results of the electric field and potential distributions in the electrolyte. The contour lines represent the equipotential lines with a constant step of U_1/15. The arrows represent electric field vectors at the mesh nodes

Fig. 7. Regression response surface of the current-voltage characteristics for the EPPo treatment of stainless steel in 5% ammonium sulphate solution

Fig. 8. Absolute values current density (a, c, e) and potential distributions (b, d, f) for EPPo treatments at different voltages U: a, b – 350, c, d – 250 and e, f – 9 V

Fig. 9. Evolutions of average values of voltage, current and electrolyte temperature during EPPo treatments at different voltages U: a – 350, b – 250 and c – 9 V

Fig. 10. Voltage and current waveforms after 1 min of EPPo treatment at different voltages U:

a – 350, b – 250 and c – 9 V

Fig. 11. Surface plane SEM images the samples before (d) and after EPPo treatments during 15 min. at different voltages U: a – 350, b – 250 and c – 9 V

Fig. 12. Changes in cross-sectional profiles of the samples (30 mm from the bottom) after EPPo treatments at different voltages U: a – 350, b – 250 and c – 9 V

Fig. 13. Current density δ (a) and removed layer thickness h_EF (b) obtained via the electric field modelling, for the samples after EPPo treatments at different voltages

Fig. 14. Average values of the removed layer thickness h estimated by different techniques: via weight loss (WL), electric field modelling (EF) and 3D scanning (3D)

Fig. 15. Removed layer thickness h_3D obtained via the 3D scanning of samples at 30 mm from the bottom after EPPo treatments at different voltages

Fig. 16. Removed layer thickness h_3D obtained via 3D scanning of samples at various distances z from the bottom after EPPo treatments at different voltages U: a – 350, b – 250 and c – 9 V

Fig. 17. Average values of removed layer thickness h_3D obtained via 3D scanning and surface roughness Ra at various distances z from the bottom of the sample after EPPo treatments at different voltages U: a – 350, b – 250 and c – 9 V

19

Table 1. Composition and properties of 20X13 stainless steel

Chemical composition (%) Specific weight

(kg·m–3)Analog

C Cr Si Mn S P Fe

0.16-0.25 12-14 <0.6 <0.6 <0.025 <0.03 balance 7660 AISI 420

Table 2. Regression model coefficients of the current-voltage characteristics

b0 b1 b2 b3 b4 b5 R2

0.4793 -0.3377 -0.1459 0.1130 0.2571 -0.1878 0.7803

Table 3. Electric field modelling results

Voltage U (V) 350 250 9

Model anode average current density δ (A cm–2)

0.33 0.66 0.29

Current 𝐼 (A) 9.79 19.93 8.75

Current I ¿ (A) 340.4 243.2 8.75

Similarity coefficient k 0.029 0.082 1.000

Electrolyte resistance R1 (Ω) 1.03 1.03 1.03

Electrolyte voltage drop U 1 (V) 10.1 20.5 9.0

VGE voltage drop U2 (V) 339.9 229.5 0.0

Model current efficiency (%) 21 31 27

20

Table 4. Process parameters and properties of the samples treated at different voltages

Voltage U (V) 350 250 9

Current I (A) 10.7 12.1 9.1

Anode surface area s (cm2) 29.5 30.0 27.7

Anode average current density δ (A cm–2) 0.36 0.40 0.33

Start weight m1 (g) 43.2484 43.8329 45.8238

End weight m2 (g) 42.8667 43.2063 45.6844

Weight loss m1−m2 (g) 0.3817 0.6266 0.1394

Start average roughness Ra1 (μm) 0.32 0.45 0.44

End average roughness Ra2 (μm) 0.08 0.06 0.39

Experimental current efficiency (%) 21 30 9

21

Fig. 1. Electrode layout for the electric field analysis

22

x3

y3

x2x1

y2

0

y1

x

y

Fig. 2. DC equivalent circuit of the electrolyser: R1 – electrolyte resistance, R2 – vapour gaseous envelope resistance

23

U2U1U

IR2

R1

Fig. 3. Sketch of the sample with the removed layer h shown

24

Fig. 4. Stereolitography models of the sample before and after the treatment with the cross-sections showing loss of thickness and z positions of the cross-sections chosen for the analysis

25

Fig. 5. Schematic diagram of current-voltage characteristics showing positions of the experimental points

26

Fig. 6. Modelling results of the electric field and potential distributions in the electrolyte. The

contour lines represent the equipotential lines with a constant step of U 1

15. The arrows represent

electric field vectors at the mesh nodes

27

Fig. 7. Regression response surface of the current-voltage characteristics for the EPPo treatment of stainless steel in 5% ammonium sulphate solution

28

a) b)

c) d)

e) f)

Fig. 8. Absolute values current density (a, c, e) and potential distributions (b, d, f) for EPPo treatments at different voltages U : a, b – 350, c, d – 250 and e, f – 9 V

29

x (cm)y (cm)

2015

1005

1015

201

10

100φ (V)

1000

x (cm)y (cm)

2015

1005

1015

200

0.1

0.2

0.3δ (

A·cm–2)

0.4

0.5

x (cm)y (cm)

2015

1005

1015

201

10

100φ (V)

1000

x (cm)y (cm)

2015

1005

1015

200

0.2

0.4

0.6δ (

A·cm–

2)

0.8

1.0

x (cm)y (cm)

2015

1005

1015

201

10

φ (V)

x (cm)y (cm)

2015

1005

1015

200

0.10.20.30.40.5

δ (

A·cm–2)

Fig. 9. Evolutions of average values of voltage, current and electrolyte temperature during EPPo treatments at different voltages U : a – 350, b – 250 and c – 9 V

30

c

c

a

b

b

a

Fig. 10. Voltage and current waveforms after 1 min of EPPo treatment at different voltages U : a – 350, b – 250 and c – 9 V

31

a

c

b

c

b

a

a) b)

c) d)

Fig. 11. Surface plane SEM images the samples before (d) and after EPPo treatments during 15 min. at different voltages U : a – 350, b – 250 and c – 9 V

32

a)

b)

c)

Fig. 12. Changes in cross-sectional profiles of the samples (30 mm from the bottom) after EPPo treatments at different voltagesU : a – 350, b – 250 and c – 9 V

33

a)

b)

Fig. 13. Current density δ (a) and removed layer thickness hEF (b) obtained via the electric field modelling, for the samples after EPPo treatments at different voltages

34

9 V 250 V 350 V0

10

20

30

40

50

60

70

WL6.6

WL27.2

WL16.9

EF17.4

EF45.9

EF15.3

3D2.26

3D37.6

3D24.6

h (μ

m)

Fig. 14. Average values of the removed layer thickness h estimated by different techniques: via weight loss (WL), electric field modelling (EF) and 3D scanning (3D)

35

Fig. 15. Removed layer thickness h3 D obtained via the 3D scanning of samples at 30 mm from the bottom after EPPo treatments at different voltages

36

a)

37

b)

38

c)

Fig. 16. Removed layer thickness h3 D obtained via 3D scanning of samples at various distances z from the bottom after EPPo treatments at different voltages U : a – 350, b – 250 and c – 9 V

39

10 25 400

0.1

0.2

0.3

0.4

0.5

z (mm)

Ra

(μm

)

b

а

c

Fig. 17. Average values of removed layer thickness h3 D obtained via 3D scanning and surface roughness Ra at various distances z from the bottom of the sample after EPPo treatments at

different voltages U : a – 350, b – 250 and c – 9 V

40

c

b

a