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TRANSCRIPT
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: [email protected], 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.
2
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.
5
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:
7
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,
9
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
11
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:
12
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
13
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