domain: spi chim phys

text:
J Martin

A Melhem

I Shchedrina

T Duchanoy

A Nominé

G Henrion

T Czerwiec

T Belmonte

Effects of electrical parameters on plasma electrolytic oxidation of aluminium

Keywords: Plasma Electrolytic Oxidation (PEO), Micro-Arc Oxidation (MAO), Pulsed bipolar current, Aluminium, Fast-video imaging, Micro-discharge

The plasma electrolytic oxidation (PEO) of aluminium alloys is investigated for different electrical working conditions using a pulsed bipolar current supply. A particular attention is paid to the effect of the anodic current density (from 10 to 90 A.dm -2 ) and current pulse frequency (from 100 to 900 Hz) on the resulting oxide layer. Micro-discharges are characterized during the process by means of fast video imaging with a time and a space resolution of 8µs and 0.017 mm 2 , respectively. Correlations are established between the micro-discharge characteristics (surface density, lifetime and size) and the elaborated oxide layers (morphology, growth rate and surface roughness). The highest coating growth rate measured (2.1 µm.min -1 ) is achieved with the combination of the highest current density (75.7 A.dm -2 ) and the highest current pulse frequency (900 Hz). Within these specific current conditions it is concluded that the detrimental effects of numerous micro-discharges are minimized. Results also show that the surface roughness may be largely affected by the presence of long-lived and large micro-discharges which develop over the processed surface.

The strongest micro-discharges (live duration up to 0.3 ms and cross-sectional area up to 1 mm 2 ) are mainly observed with the combination of the highest current density (75.7 A.dm -2 ) and the lowest current pulse frequency (100 Hz).

Introduction

Plasma Electrolytic Oxidation (PEO), also known as Micro-Arc Oxidation (MAO) is a particular technique to produce oxide ceramic coatings on light-weight valve metals (such as Al, Mg, Zr, Ti and their alloys). Growth of the oxide layer takes place at potentials above the dielectric breakdown voltage of the insulating oxide surface layer resulting in the development of a large number of short-lived micro-discharges (MDs) which move randomly over the processed surface [1][2][3]. The resulting coating exhibits improved surface performances in terms of hardness, wear protection and corrosion resistance [4][5][6][7]. Associated with the use of environmentally friendly diluted alkaline electrolytes, PEO process gains a growing interest in various industrial domains (transport, energy, medicine) to replace conventional chromic acid anodizing (CAA) or hard acid anodizing (HAA) [2,8].

Numerous studies on the growth mechanisms of PEO coatings have been carried out. All evidence the key role played by the MDs. Plasma during the PEO process has been investigated by using optical emission spectroscopy [9][10][11][12][13]. In this field, Konjević's research group report several studies on the determination of the electron number densities N e and electron temperature T e in real time with the PEO process [14][15][16][17]. MDs have also been studied by video imaging in order to determine their surface number density, lifetime and size at different stages of the treatment. Yerokhin et al. [18] recorded video images at 24 Hz (41 ms time resolution) when AC PEO processing of aluminium samples. Matykina et al. [19] observed the MDs on titanium with a time resolution of 10 ms, while Mécuson et al. [20] studied the MDs behaviour during bipolar pulse PEO of aluminium using an exposure time of 2 ms. More recently, Melhem et al. [21,22] demonstrated the necessity of improving the time resolution to the microsecond range in order to get a more reliable estimation of the MDs characteristics.

In the present work, MDs were examined during the bipolar pulse PEO treatment of Al alloys using fast-video imaging with a time resolution of 8 µs. Measurements allowed us to investigate the influence of the imposed bipolar current pulse on processed materials. A particular attention was paid to the current density and the current pulse frequency values which are known to have strong effects on the performances of the grown oxide layers [23,24]. The latter were characterized by roughness measurements and by scanning electron microscopy observations of both the top surface and coating cross sections. An attempt is made to draw close correlations between measurements on the MDs and material characteristics to better understand the growing mechanisms of the protective coatings.

Experimental procedure

The experimental set-up consists basically of an electrolysis tank containing an electrolytic solution made of KOH and Na 2 SiO 3 diluted in distilled water in the range of 1 g.l -1 . A cooling device allows us to maintain the temperature of the electrolytic solution below 30 °C (303 K) during the process. The electrolyte electrical conductivity and pH are 2.8 mS.cm -1 and 13, respectively. Two rectangular titanium counter-electrodes (cathodes) face both sides of the sample (anode). The electrode gap between each counter-electrode and the sample is 28.5 mm. A bipolar current pulse generator (Ceratronic® process [25]) working in galvanostatic mode is used to supply both the sample and the counter-electrodes. As reported by Mécuson et al., different shapes of the applied current waveform can be achieved by adjusting the current parameters (rising and fall time, frequency, amplitude, offset) over a wide range of values [10,11,20]. So, the amplitude of the positive (I p ) and negative (I n ) currents, the current pulse frequency (F) and the anodic to cathodic charge quantity ratio (R = Q p /Q n ) can be adjusted to suitable values [20]. In particular, they established that applying a higher negative charge quantity than the positive one (R = 0.89 hereinafter referred to as "soft" regime) to the Al alloy sample greatly improves the resulting oxide layer properties by reducing the detrimental effects of strong arc discharges. With this particular soft regime conditions, the positive current density (J p ) and current pulse frequency (F) are investigated in the range 10 to 90 A.dm -2 and 100 to 1000 Hz, respectively. Two grades of Al alloys were used as substrate in this work. The effect of the positive current density was investigated using 2214 grade Al alloy while 1050 grade Al alloy was used to study the effects of the current pulse frequency. The chemical composition of both Al alloys is given in table 1.

Samples have a rectangular shape of 50 mm  30 mm  6 mm. Prior to be processed, samples are polished with 320 grit SiC abrasive papers, ultrasonically cleaned with acetone and dried.

Samples in 2214 grade Al alloy were processed for 70 min while samples in 1050 grade Al alloy were treated for 40 min.

Video images of the MDs during PEO processing are recorded using a Photron SA1.1 camera which allows us to study the MDs evolution either along the current period or over the processing time. For the present study, the sampling rate is set at 125 000 frames per second (125 kfps) which corresponds to a time resolution of 8 µs. Under these specific recording conditions, the spatial resolution of the camera was set at 0.017 mm 2 which is much lower (by a factor of 15) than the minimum area of MDs that was detected in the experiments.

Automatic image processing is done using an homemade software [26,27] allowing us to follow the MDs surface number density per unit time, the lifetime (ms) and the size (area in mm 2 ) distributions of the MDs on the surface as a function of the processing time.

Top views and cross-sections of the PEO-treated samples were examined by field emission gun scanning electron microscopy (FEG-SEM -Philips XL30) working in backscattered electron mode. Prior to be examined, samples were cut, mounted in resin, polished through successive grades of SiC abrasive papers and finely polished to 1 µm with diamond paste. The centre and the edge of the treated samples were closely examined. The centre of the sample is defined as an investigated area (2 mm  2 mm) centred at the intersection of the two diagonals of the rectangular shape of the sample. Concerning the edge of the sample, the investigated area (2 mm  2 mm) is located at 1 mm from the center of its longest side. In both regions, the coating thickness was determined as the average value of 20 measures taken on cross-section over 20 different positions (each 100 µm). The average mean surface roughness of the coating, R a (µm), was assessed using a Surfscan 3S profilometer with lateral and depth resolutions of 8 µm and 0.1 µm, respectively. Roughness of the samples before PEO treatment is 0.20 µm.

Experimental results and discussion

Establishment of the "soft" sparking regime

In our previous studies, it was established that setting the anodic to cathodic charge quantity ratio R less than 1 leads to a total modification of the growth regime that switches from an "arcs" regime to a "softer" one [20,21]. The latter does not exhibit the strong arcs that were reported as detrimental to the oxide layer properties thus resulting in thicker, more dense and more homogeneous (in terms of thickness over the sample area) layers. The "arcs" to "soft" regime switching time is detected by the drop in the anodic voltage amplitude (Fig. 1) due to the change in the impedance of the substrate/layer system [20,[START_REF] Melhem | 63 rd Gaseous Electronic Conference (GEC) and 7 th Int. Conf. Reactive Plasmas[END_REF]. The dependence of the switching time on the anodic current density and current pulse frequency is plotted in figure 2a and figure 2b respectively. The higher the current density and the current pulse frequency, the earlier the process switches to "soft" regime. Transition appears at 62 min with 25.2 A.dm - 2 at 100 Hz and drops to 14 min with 75.7 A.dm -2 at 900 Hz. It is also worth noting that after 100 min of treatment with the lowest investigated current density (12.5 A.dm -2 ) and pulse frequency (100 Hz), the "soft" regime is not reached. Figure 4 shows the evolution of the surface number density of MDs determined by means of video-imaging as a function of the PEO processing time for the different anodic current densities (Fig. 4a) and current pulse frequencies that were investigated (Fig. 4b). Whatever the electrical conditions used MDs surface density at the beginning of the process (after 1 min treatment time) is higher than 5.10 5 cm -2 .s -1 . As the PEO process goes on, the surface density of MDs decreases nearer to 10 4 cm -2 .s -1 at longer treatment times (up to 50 min). The decrease is much stronger as the current density and the current frequency get higher. It is worth noting that with the specific electrical conditions, (12.6 A.dm -2 ; 100 Hz), the process does not switch to the soft regime. Consequently, the surface density of MDs remains quite high, (1.10 5 cm -2 .s -1 ) even at long treatment times.

Micro-discharges characteristics

The fitting of the experimental data points using a double exponential decay law (solid line in Figure 6 is the distribution in size of MDs recorded at 10 min processing time for three different current density values (Fig. 6a) and three different pulse frequencies (Fig. 6b). It

shows the surface density of MDs as a function of the MDs size. It can be seen that whatever the processing conditions used a large amount of MDs exhibits a small size (area) between 0.5 and 1 mm 2 . Figure 6a illustrates the influence of the current density on the size distribution of MDs. It shows that the large MDs are promoted at high current density. The arithmetic average size calculated from the integration of the size distribution curve is about 0.54 mm 2 , 0.72 mm 2 and 0.76 mm 2 at 12.6, 37.9 and 63.1 A.dm -2 , respectively. At very low current density (12.6 A.dm -2 ) size of the MDs doesn't exceed 2.0 mm 2 . Figure 6b illustrates the effect of the current pulse frequency on the size distribution of MDs. It can be seen that size of the MDs tends to decrease with increasing the current pulse frequency with an average size of 0.77 mm 2 , 0.63 mm 2 and 0.56 mm 2 at 100, 500 and 900 Hz, respectively. Large size MDs are promoted when working at low current pulse frequencies.

Discussion about the elaborated oxide layers characteristics

Figures 7a-f show scanning electron microscopy micrographs of cross-section of PEO layers achieved within different electrical conditions. Micrographs in figures 7a-b were taken at the centre (Fig. 7a) and at the edge (Fig. 7b) of Al2214 sample processed for 100 min at low current density (12.6 A.dm -2 ) and low current pulse frequency (100 Hz). Whatever the location on sample, the oxide layer consists of plates and appears as non-homogeneous with an irregular metal-oxide interface. It is rather thin with large porosities. This morphology, which is characteristic of a PEO discharge regime made of "arcs", can be explained by the fact that no transition from "arcs" to "soft" regime was observed for these specific electrical conditions (see Fig. 2a). Jaspard-Mécuson et al. [20] demonstrated that under "arcs" regime, such thin and damaged coating results from a competition between oxidation and erosion mechanisms which are both assisted by numerous arc discharges. This is consistent with our previous observations regarding the surface number density of MDs which remains high even after long treatment duration for these specific conditions (Fig. 4a). Figures 7c-d show micrographs of Al1050 sample treated for 40 min at high current density 75.5 A.dm -2 and low current pulse frequency (100 Hz). Observations were done at the centre (Fig. 7c) and at the edge (Fig. 7d) of the sample. Whatever the location on sample, micrographs evidence that increasing the anodic current density improves the coating thickness and morphology. This trend is closely connected to the "arcs" to "soft" regime transition which occurs earlier with higher current density leading to an earlier decrease in the MDs surface number density (Fig. 4a). The oxide layer thus elaborated is typical of a PEO treatment under "soft" regime conditions and can be divided into two sub-layers as described in the literature: an outer layer constituted of fine pores and an inner, more compact layer [10,20]. Figures 7c-d also illustrate that the oxide layer in the centre (Fig. 7c) and in the edge (Fig. 7d) of the sample exhibit different morphology. Thickness of the oxide layer is thicker at the edge than at the centre.

Homogeneity of the thickness is also improved at the edges than at the centre where it can be observed some residual large discharge channels and a plate-like layer at the top surface. This variation in the oxide layer morphology is related to the spatial gradient in the MDs number observed previously in the figure 3. At the edge, where MDs are numerous at the beginning of the PEO treatment, oxide layer is thicker and more compact than at the centre where less numerous MDs have been observed. Influence of the current pulse frequency on the oxide layer morphology is illustrated in figures 7e-f that show cross-sections of Al1050 sample processed for 40 min at high current pulse frequency 900 Hz at the centre (Fig. 7e) and at the edge (Fig. 7f). It can be clearly seen that the coatings become thicker and more compact as the working frequency increases which matches the earlier occurrence of the "soft" PEO treatment regime (Fig. 4). It is also accompanied by a more regular oxide layer/substrate interface and a more homogeneous treatment over the sample surface.

The average coating growth rate of the PEO coatings determined under different current densities and different current pulse frequencies is presented in figure 8a and 8b, respectively.

Such average growth rate is calculated by dividing the final layer thickness by the treatment time. In the range of the investigated electrical conditions, the current density seems to have a more pronounced influence on the growth rate than the current pulse frequency parameter. It is also noteworthy that there is an enhancement of the average growth rate with the increase in both the current density and the current pulse frequency. For example, the highest coating growth rate observed (2.1 µm.min -1 ) is achieved with the combination of the highest current density (75.7 A.dm -2 ) and the highest current pulse frequency (900 Hz). In contrast, the lowest oxidation kinetics is attributed to the lowest current density (12.5 A.dm -2 ) and the lowest current pulse frequency (100 Hz). This result is closely correlated to the MDs which become less numerous earlier and earlier as the surface is processed for higher current densities and higher current pulse frequencies. This promotes the occurrence of the "soft" regime transition as described above (Fig. 2 and4). Figures 8a and 8b also illustrate another interesting feature:

irrespective of the electrical conditions used, the average growth kinetics is always higher at the edge of the sample than at the centre. Nevertheless, it can be noted that this spatial gradient in the coating growth rate is more pronounced when working with high current density and low current pulse frequency.

Figure 9 reports on the dependence of the surface roughness of the oxide layers on the current density (Fig. 9a) and current pulse frequency (Fig. 9b). Figure 9a shows that roughness increases with the increase in current density while figure 9b evidences a decrease in roughness with the increase in current pulse frequency. This dependence can be associated with the strength of the MDs in terms of lifetime and size as discussed above which exhibits a similar tendency: MDs last longer and are larger for both higher current density and lower current pulse frequency. Roughness may be at least partly a consequence of the long-lived and large size MDs which have detrimental effects on the growing oxide surface. Within the electrical conditions used, figure 9 shows that roughness measurements exhibit differences between the centre and the edge of the treated samples. Roughness is always higher at the edge of the sample than at the centre. Moreover, such spatial gradient in the roughness is stronger at high current density and low current pulse frequency.

Conclusion

In this study, the effects of the anodic current density (from 10 to 80 A.dm -2 ) and the current pulse frequency (from 100 to 900 Hz) on the resulting oxide layer in the bipolar PEO processing of aluminium alloys have been investigated. Correlations between the microdischarges characteristics (surface density, lifetime and size) and the processed material (thickness, homogeneity and roughness) have been discussed.

 Firstly, results show that fast-video imaging with a time resolution of 8 µs makes it possible to accurately investigate the micro-discharges in real-time over the PEO process.

 Secondly, it has been found that the increase in the anodic current density and the pulse frequency provides a qualitative improvement in the coating growth rate and homogeneity. This is explained by the surface number density of micro-discharges which falls down more rapidly with higher current density and higher frequency, leading to an earlier "soft" regime occurrence.

 Thirdly, results evidence that long-lived and large size micro-discharges (up to 0.3 ms and 1 mm 2 , respectively) observed for high current density and low current pulse frequency are detrimental to the oxide layer roughness. On the contrary, short-lived and small size microdischarges (down to 0.2 ms and 0.5 mm 2 , respectively) measured at low current densities and high pulse frequency appears to have less detrimental effect on the material roughness.

 Finally, within the PEO process parameters investigated, our results indicate a spatial heterogeneity in morphology over the PEO processed sample area which becomes more

Figure 3

 3 Figure3shows the spatial distribution of the MDs over the sample surface (at 75.5 A.dm-2

  figure4a) clearly points out that the decay of the MDs number on the surface results from two

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 :Figure 6 :Figure 7 :Figure 8 :Figure 9 :Figures 1 Figure 6

 12345678916 Figure 1: Variation of the anodic current and voltage over the process time for Al2214 alloy sample processed with J p = 88.4 A.dm -2 and F = 100 Hz. The vertical dash line corresponds to

25

 25

Figure 7 Figure 9

 79 Figure 7

Table 1 :

 1 Chemical composition of 2214 and 1050 Al alloys (wt. %)

	Tables
	Al grade	Al	Cu	Mg	Mn	Fe	Si	Zn	Ti	Cr
	Al 2214	balance	3.9-5 0.5-1.2 0.4-1.2 0.3 0.5-1.2 0.25	0.15	0.1
	Al 1050	balance	0.05	0.05	0.05	0.4	0.25	0.07	0.05	-

Acknowledgments

Financial support of the European Commission under grant agreement n° 270589 is greatly acknowledged. We also greatly acknowledge financial support from the Conseil Régional de Lorraine for granting A. Nominé's PhD work.

pronounced at high current density and low current pulse frequency. Average growth rate and roughness are higher at the edge than at the centre of the samples.

List of references


text:
J Martin

P Leone

A Nominé

D Veys-Renaux

G Henrion

T Belmonte

Influence of electrolyte ageing on the Plasma Electrolytic Oxidation of aluminium

Keywords: plasma electrolytic oxidation (PEO), aluminium, electrolyte ageing, oxide coating, micro-discharges, fast-video imaging

The chemical stability of the electrolyte in Plasma Electrolytic Oxidation (PEO) has been the subject of much systematic investigation. The present study reports on experimental results on the ageing of a usual PEO electrolyte and its effect on the oxidation of the Al2214 aluminium alloy. A solution of potassium hydroxide ([KOH] = 1 g.L -1 ) and sodium silicate ([Na 2 SiO 3 ] = 1.65 g.L -1 ) diluted in deionized water was either aged by running a process during 8 h at most or not. Comparison between materials treated in either solution was made next. Crosschecked experimental results from analytical chemistry, plasma diagnostics and materials science clearly evidence the effect of ageing of the electrolyte on the PEO process behaviour.

The transition from arc to "soft" regime occurs earlier (from 18 min to 13 min processing time) as the electrolyte gets older. The concomitant decrease in the electrolyte electrical conductivity (from 7.5 mS.cm -1 to 6.8 mS.cm -1 ) is correlated with changes in the ionic species content in the electrolyte. Fast video-imaging (125 kfr./s) reveals that the micro-discharge characteristics are also sensitive since they become less numerous per area and unit time (from 22010 3 cm -2 s -1 to 12010 3 cm -2 s -1 ), exhibit shorter lifetime and have smaller sizes as the electrolyte ages. SEM observations of the as-grown coatings combined with roughness measures indicate a decrease in coating thickness ( 20 %) and roughness ( 30 %) while species from the electrolyte accumulate in the outer porous layer simultaneously with a gradual enrichment in -Al 2 O 3 phase in the inner compact layer (from 36 % to 43 %). Finally, within the PEO conditions that were used, it is shown that the ageing phenomenon of the PEO electrolyte starts to influence the process after 2 hours aged.

Introduction

Plasma electrolytic oxidation (PEO) is a surface engineering process suitable for light weight metals (Al, Mg, Ti) and their alloys to form protective ceramic coatings [1]. Based on an electrochemical conversion of the metal surface, the rapid growth of the oxide layer takes place at potentials above the dielectric breakdown voltage of the insulating layer, leading thus to the development of numerous short-lived micro-discharges over the processed surface [2][3][4]. The resulting PEO coating exhibits improved surface performances in terms of adhesion, hardness, wear protection and corrosion resistance. As it uses diluted alkaline electrolytes, the PEO process complies with the present environmental and health regulations. Therefore it gains a growing interest in various industrial domains (transport, energy, medicine) to replace conventional chromic or sulphuric acid anodizing processes.

Researches devoted to improve the efficiency of the PEO process are abundant in the literature and one particular way consists in adjusting the right chemical composition of the electrolyte [1]. Electrical conductivity and basicity of the PEO electrolytes are commonly adjusted by addition of alkaline reagents as potassium hydroxide (KOH) or sodium hydroxide (NaOH) which provide both enhanced growth rate and improved tribological behaviour of the oxide-like ceramic coatings (Al 2 O 3 , MgO, TiO 2 ) [5]. Furthermore, additives such as silicate (Na 2 SiO 3 ) and aluminate (NaAlO 2 ) are widely used in order to reinforce the corrosion resistance and thermal barrier properties of Al and Mg oxides and their compounds [6][7][8][9]. The formation of stable products such as Mg 2 SO 4 , MgAlO 4 , 3(AlO 3 ).2(SiO 2 ) that act as barrier layers prevents corrosion of alloys in the most corrosive environments. In recent years, thorough investigations have demonstrated the positive influence of new electrolyte additives (phosphate, fluoride, borate) on the performance of PEO films formed on magnesium and aluminium alloys [10][11][12][13][14]. Some authors have proposed to incorporate suspended nano-particles (Al 2 O 3 , ZrO 2 , TiO 2 , TiC) in the electrolyte to reduce the porosity of the PEO oxide layer and to improve the wear resistance of the formed coatings [15][16][17][18].

Few works deal with the chemical stability of the PEO electrolytes with the effective ageing time over successive treatments. Ageing phenomena, which could affect the final layer characteristics, are usually neglected. From an industrial point of view, the issue of the chemical stability of the electrolyte is of crucial importance in order to guarantee the highest reproducibility of the sought-after properties with the minimum process intervention.

Regarding conventional anodizing processes such as chromic acid anodizing (CAA) or sulfuric acid anodizing (SAA), ageing of the treatment baths (cleaning, sealing, painting) is controlled empirically by manufacturers who limit the drifts in chemical composition by continuously renewing and tuning the content of chemical reagents. In a recent paper Terleeva et al. [19] evidenced the variations in the elemental composition of a silicatealkaline electrolyte characteristics with ageing time (mainly a decrease in concentration of OH -and Si 4+ and increase in Al 3+ ), expressed in terms of accumulated charge quantity flowing through the investigated electrolyte. Their findings revealed that such variations in the electrolyte have a substantial influence on the PEO coating characteristics such as a decrease in the coating thickness and a substantial increase in the degree of aggregation of electrolyte components (Si, Na, K) at the top most surface of the oxide layer.

However, researches on the ageing of the PEO electrolyte are scarce. In this context, the aims of the present study are mainly to confirm such previous results and to correlate variations of both the electrolyte state and the PEO layer characteristics with the micro-discharge behaviour as the electrolyte gets aged. For this purpose, an experimental investigation of the electrolyte ageing during the PEO treatment of an aluminium alloy is reported. The selected electrolyte consists in a standard PEO electrolyte containing sodium silicate Na 2 SiO 3 and potassium hydroxide KOH diluted in deionized water. The ageing process in the electrolyte has been evidenced by taking into account several criteria based on the process monitoring data (voltage-and current-time responses), the electrolyte chemistry (conductivity and ionic species content), the micro-discharges behaviour (density, spatial distribution, size and lifetime) and the material characterization (layer morphology, roughness, thickness, element composition and alumina phase content). Finally, we shall discuss on correlation between the formation process of the oxide ceramic layer and the characteristics of the micro-discharges appearing at the surface of the processed sample in relation with the ageing process in the PEO electrolyte.

Experimental procedure

The experimental set-up consists basically of a 25 L electrolysis tank filled with the electrolyte. Rectangular samples of dimensions 50 mm  30 mm  6 mm (see Fig. 1) made of commercial 2214 grade aluminium alloy were used as substrate in this study (content in weight %, 3.9 -5 Cu, 0.5 -1.2 Mg, 0.4 -1.2 Mn, 0.5 -1.2 Si, 0.5 Fe, 0.5 Ti, 0.25 Zn, Al as balance). Prior to process, all the samples were ground down to 1200 SiC paper, ultrasonically degreased in acetone, dried in warm air, and then immersed in the electrolyte tank. The sample (anode) is located between two titanium counter-electrode plates (cathodes), of size 200 mm  200 mm  1 mm. The gap between each counter-electrode and the sample is set at 55 mm. Therefore, the active electrode area to electrolyte volume ratio is about 1.6  10 -3 cm - 1 . A cooling device allows the electrolyte temperature to be kept in the range of [15 -25 °C].

All the PEO treatments carried out in this study were conducted using a bipolar pulsed current generator working at 100 Hz within the so-called "soft-regime" corresponding to electrical conditions that are reported in detail in reference [3]. Within such a regime, the anodic (Q p ) to cathodic (Q n ) charge quantity ratio R is set at 0.89 (R = Q p / Q n ) which greatly improves the properties of the as-synthesized oxide layer. Indeed, detrimental effects caused by strong arc discharges are strongly reduced. The anodic and cathodic current amplitudes were steered at 30 A and -20 A respectively throughout each experiment. This corresponds to an anodic (resp. cathodic) current density of 76 A.dm -2 (resp. -50.5 A.dm -2 ). Voltage-time and current-time responses were monitored using a 1 GHz bandwidth oscilloscope (Agilent 54832B) during the entire course of each PEO treatment.

The electrolyte consists of a solution of potassium hydroxide ([KOH] = 1 g.L -1  0.018 mol.L - 1 ) and anhydrous sodium silicate ([Na 2 SiO 3 ] = 1.65 g.L -1  0.014 mol.L -1 ) diluted in deionized water. It has been deliberately aged in this electrolyte during 8 hours by running the process in the same electrical conditions. Every hour, the aged sample recently treated was removed from the electrolysis tank, rinsed, dried and rapidly replaced with an untreated one. After each treatment, a 10 mL electrolyte sampling is operated for further chemical analyses.

Video images of the micro-discharges appearing during processing were recorded using a Photron SA1.1 camera which allows us to track the evolution of their characteristics either along the current period or over the processing time. Fast video recordings were synchronized with the current pulses. For the present study, only the lower half-part of the sample is filmed over an area of 7.5 cm 2 (see Fig. 1 a.). The sampling rate is set at 125 000 frames per second (125 kfps), which corresponds to a time resolution of 8 µs. Within these specific sampling conditions, the spatial resolution of the camera was set at 0.017 mm 2 which is much lower (by a factor of 15) than the minimum area of micro-discharges that was detected in the experiments. We resorted to automatic image processing by using a homemade software that provides the micro-discharge surface density per unit time, their lifetime (ms) and size (crosssectional area in mm 2 ) distribution on the surface as a function of time [20].

Top views and cross-sections of the PEO-treated samples were examined by field emission gun scanning electron microscopy (FEG-SEM -Philips XL30) working in secondary and backscattered electron mode, respectively. Chemical composition and distribution of elements in the synthesized oxide layers were determined by EDX analyses. Prior to be examined, samples were cut, mounted in resin, polished through successive grades of SiC abrasive papers and finely polished to 1 µm with diamond paste. The centre and the edge of the treated samples were closely examined as defined in Fig. 1 b. The central area of the sample is defined as an investigated area (2 mm  2 mm) centred at the intersection of the two diagonals of the rectangular shape of the sample while the edge area of the sample is located at 1 mm from the centre of its longest side. In both regions, the coating thickness was determined as the average value of 20 measures taken on cross-section over 20 different positions (each 100 µm). The average mean surface roughness of the coating, R a (µm), was assessed using a Surfscan 3S profilometer with lateral and depth resolutions of 8 µm and 0.1 µm, respectively.

The phase composition of the layer was investigated by X-ray diffraction measurements (XRD) using a Bruker D8 ADVANCE (Cu-K 1 radiation  = 0.1542 nm) instrument operated in Bragg-Brentano geometry with a step size of 0.005° and a scan range from 10 to 100°. XRD measurements were performed on the surface of the whole processed samples. The relative content of corundum phase (-Al 2 0 3 ) in the oxide layer was deduced from XRD peak adjustment and calculated from the integrated intensity of -Al 2 O 3 peaks compared with the integrated ones of both and -Al 2 O 3 .

At different stages of the ageing process, the electrical conductivity ( el ) of the electrolyte solution was measured using a Hach SENSION conductimetre. The initial conductivity of the electrolyte, measured before the first PEO treatment, was 7.5 mS.cm -1 . As a complement, changes in the ionic species amount in the electrolyte solution with the ageing process were evaluated using the Inductive Coupled Plasma -Atomic Emission Spectroscopy (ICP-AES) analytical technique. Analyses were particularly focused on the content variations of sodium Na, potassium K and silicon Si ions, the three main components of the base electrolyte, and on the aluminium Al ions coming from the partial dissolution of the treated alloy.

Experimental results and discussion

Electrolyte characterization

The variation of the electrical conductivity versus the ageing time is shown in Fig. 2. After 1 hour, quite no significant change in the electrical properties is noted ( el = 7.5 mS.cm -1 ).

Nevertheless, between 1 and 5 hours, a quasi-linear conductivity decrease occurs from 7.5 to 6.8 mS.cm -1 . After 5 hours effective use, the electrical conductivity of the electrolyte seems to keep a constant value at about 6.8 mS.cm -1 . Such changes in the electrical conductivity of the electrolyte are related to chemical changes in the content of dissolved species in the electrolyte. Table 1 lists the content of Na, K, Si and Al ionic species in the electrolyte determined by ICP-AES analysis after 1, 3 and 8 hours of effective use. The content of the base electrolyte elements (Na, K, Si) decreases as the electrolyte ages. Conversely the content of Al ionic species, that are initially absent from the fresh electrolyte, increases with the electrolyte duration of use. Therefore, the electrolyte is depleted in species coming from the potassium hydroxide KOH and sodium silicate Na 2 SiO 3 solution while it is enriched in Al ionic species that are issued from the partial dissolution of the PEO treated aluminium samples. Note that changes in the ionic species content start to be noticeable only after 3 hours, for a rather small small value of the active electrode area to electrolyte volume ratio (1.6  10 -3 cm -1 ). ) to keep the current constant. At this stage, no micro-discharges are observed while a bluish luminescence and an intense gas release are visible all over the sample surface. From 10 s on, the process suddenly enters a second stage (stage II). During this period that ranges from 10 s to around 13-20 min depending on the electrolyte ageing level, the slope of the voltage-time curve reduces to  0.04 V.s -1 . This change occurs at an anodic voltage value hereinafter referred to as the anodic breakdown voltage. Once this anodic breakdown voltage is reached ( 750 V), small orange-red discharges initiate on the sample surface, preferentially at corners and edges of the sample. Fig. 3 shows that the electrolyte age has almost no influence, neither on the anodic breakdown voltage nor on the duration of stage II. The third stage (stage III) is characterized by an abrupt drop in the anodic voltage amplitude. This phenomenon was previously reported during AC PEO of aluminium in "soft" regime conditions [3]. This voltage transition is directly correlated with a change in the optical and acoustic characteristics of the discharges [21]. This voltage transition is also named "arcs" to "soft" regime transition because the micro-discharges progressively change to smaller size and shorter lifetime tiny discharges inducing less detrimental effects on the elaborated PEO layers [4]. Fig. 4 describes the evolution of the "arcs" to "soft" regime switching time as a function of the ageing time. The ageing of the electrolyte influences the development of the "soft" sparking regime since this regime appears earlier with an aged electrolyte. With the less aged electrolyte, the "soft" regime occurs gradually at 18 min, but almost instantaneously at 10 13 min with the older one. Finally, the fourth and ultimate stage of the PEO treatment (stage IV) is observed after about 20 min of processing time (Fig. 3). This stage consists of a constant and lower working voltage amplitude which depends on the ageing time. Indeed, Fig. 4 shows that anodic voltage amplitude is the highest at the beginning of the ageing process of the electrolyte ( 710 V after 1 h of ageing), then it drops significantly between 2-and 4 h and it stabilizes to an almost constant value at  640 V after 5 h. discharges are observed for the most aged electrolyte (Fig. 5 f.) while some discharges are actually detected in the less aged electrolyte, preferentially at the centre of the sample (Fig. 5 c.). This can be explained by considering the fact that the development of the "soft" sparking regime has occurred earlier for the aged electrolyte (at  13 min) than for the fresh one (at  20 min). Moreover, Fig. 5 also shows that samples are non-homogeneously covered by the micro-discharges. At the beginning of the process, micro-discharges are located around the corners and edges of the samples and then gradually, they cover the whole specimen area. This edge effect, which has been already reported in previous works [4,21] occurs for all the samples but it is slightly more pronounced for the sample processed in the fresh electrolyte (Fig. 5 b.) compared to the sample processed in the 8 h-aged electrolyte (Fig. 5 e.). Fig. 6 depicts the time evolution of surface density of micro-discharges per second for three electrolytes aged for 1, 4 and 8 h. The inset highlights the influence of the ageing of the electrolyte during "arcs" regime (i.e. before the development of the "soft" sparking regime).

Voltage-time responses

Micro-discharges characteristics

Whatever the state of the electrolyte, the micro-discharge surface density per second at the beginning of stage II (between 10 s and 5 min) is higher than 3.10 5 cm -2 .s -1 . As the PEO process goes on, the surface density of micro-discharges per second decreases by more than one order of magnitude to reach an almost constant low value (10 4 cm -2 .s -1 ) beyond 20 min, once the "soft" sparking regime is established. The inset of the Fig. 6 highlights that this decrease is much stronger at longer ageing times.

In Fig. 7, the time dependence of other characteristics of the micro-discharges (only during the "arcs" sparking regime) is depicted for various ageing times (1, 4 and 8 h), such as the size (Fig. 7 a.-c.) and the lifetime (Fig. 7 d.-f.) of individual micro-discharges. From size distributions, four categories of species can be distinguished: small, medium, large and very large micro-discharges with cross sectional areas in the ranges of 0.2  0.2 mm 2 , 0.7  0.3 mm 2 , 1.3  0.3 mm 2 and >1.6 mm 2 , respectively. Similarly, four categories of microdischarges lifetime can be identified as short, medium, long and very long micro-discharges in the range of 0.02  0.02 ms, 0.07  0.03 ms, 0.15  0.05 ms and > 0.2 ms, respectively. At 1 min, (i.e. when the PEO process enters stage II), the behaviour of the micro-discharges is similar for the different investigated electrolytes. Indeed, no major differences are observed on the size and lifetime distributions between the sample processed in the fresh electrolyte and the other processed in aged electrolytes (Fig. 7 a. and d.). As the process enters the "arcs" sparking regime (stage III), the relative amount of large-size and long micro-discharges gradually increases. At 8 min, slight differences can be noticed between samples treated in different electrolytes (Fig. 7 b. and e.) as smaller and shorter micro-discharges are detected in the aged electrolyte. At 14 min (i.e. at the end of the "arcs" sparking regime), such differences are more pronounced and easily visible. Indeed the population of micro-discharges with a very large size (> 1.6 mm 2 cross-sectional area) is about 41, 4 and 1 cm -2 .s -1 while that of long duration micro-discharges (0.15  0.05 ms) is about 79, 6 and 0 cm -2 .s -1 in the 1, 4 and 8haged electrolyte, respectively (Fig. 7 c. and f.). Then, results on the characterization of microdischarges demonstrate that contrary to the fresh electrolyte, process in aged electrolytes promotes micro-discharges characterized by a smaller size and a shorter lifetime.

Discussion about the elaborated PEO coatings

Fig. 8 shows the backscattered cross-sectional SEM images of PEO oxide layers grown on Al2214 aluminium alloy. Micrographs were taken at the edge and at the centre of samples processed for one hour in the fresh (Fig. 8a.-b., respectively) and in the 8 h-aged electrolyte (Fig. 8c.-d., respectively). All the synthesized coatings exhibit two distinct regions that are characteristic of PEO layers elaborated in the "soft" regime conditions: a thick compact inner sublayer adjacent to aluminium substrate and a porous outer sublayer [3]. Regardless of the state of the electrolyte, micrographs evidence that the thickness is larger at the edge than at the centre. The homogeneity of the thickness is also improved at the edges where a smoother oxide layer / substrate interface is observed. This trend, already reported by Melhem et al. [21], has been explained recently by demonstrating that the occurrence of the "soft" regime is spatially deferred [4]. Indeed, this regime occurs earlier at corners and edges and then propagates towards the centre which suffers the detrimental "arcs" regime a longer time.

Moreover, micrographs evidence that using a fresh electrolyte leads to thicker oxide layers. This is even more obvious at the centre. Nevertheless, micrographs also show that proportion of the porous outer sublayer in the total coating thickness is larger when a fresh electrolyte is used. The aspect of the topmost surface of the coating elaborated in the fresh electrolyte is more irregular and rugged than that synthesized in the 8 h-aged electrolyte. Residual discharge channels are even visible at the topmost surface of the coating formed in the fresh electrolyte.

From cross-sectional SEM micrographs, average thicknesses of oxide layers were determined at the edge and at the centre. Fig. 9 depicts the thickness variation of the total and outer sublayer as a function of the ageing time of the electrolyte. As previously noted (Fig. 8), the thickness of the total layer is always larger at the edge than at the centre whatever the state of the electrolyte. For the fresh one, the total layer thickness is about 120 µm at the edge and about 95 µm at the centre. Concerning the thickness of the porous outer sublayer, no significant differences were noted between edge and centre. Within the range of the operating conditions used in this study, ageing of the PEO electrolyte has a distinct influence on the oxide coating thickness. Indeed, wherever on the sample, the thickness of the overall oxide layer decreases with the ageing time. It is also noteworthy that this trend is more pronounced at the centre than at the edge, suggesting that fresh electrolyte minimizes the spatial heterogeneity of the coating thickness over the processed surface. Nevertheless, even if the improvement in the overall layer thickness with fresh electrolytes is effective, Fig. 9 also shows that the use of such a fresh electrolyte results in an increase in the thickness of the outer porous sublayer, which is known to give poor mechanical properties and disastrous corrosion resistance [22]. At the edge of the samples, the proportion of the outer sublayer is about 30 % of the total layer thickness for a fresh electrolyte but only 13 % for a 8 h-aged electrolyte. Fig. 10 shows the top view macrographs of half a sample treated for one hour in an fresh electrolyte (Fig. 10 a.) and in the 8 h-aged one (Fig. 10 b.). Dark dots are clearly visible on the surface of the sample processed in the fresh electrolyte. They are preferentially located at edges. Such defaults on the surface are large open pores ( 100 -300 µm in diameter) and correspond to discharge channels. This observation is correlated with the "arcs" regime previously described. Indeed, as already mentioned, the population of long-duration and large-size micro-discharges is larger for the fresh electrolyte than for the 8 h-aged one, suggesting a more damaged surface with large open pores all over the surface. Fig. 11 shows the 3D surface topography measured with a touch probe carried out at the edge of the samples processed for one hour in an fresh electrolyte (Fig. 11 a.) and in an 8 h-aged electrolyte (Fig. 11 b.). The surface of the oxide layer synthesized in the fresh electrolyte is rougher. Deep pits are found on the scanned surface that matches with defaults observed previously in Fig. 10 a. From surface topographies in Fig. 11, the roughness parameter R a (the arithmetic mean value) was calculated at both the edge and the centre of each processed sample of this study. Fig. 12 shows the variation of R a as a function of the ageing time of the PEO electrolyte. The roughness value at the centre of the samples is always lower than the one at the edge, whatever the state of the electrolyte. This corroborates macroscopic observations made on the samples presented in Fig. 10 where large defaults and open porosities are preferentially localized at edges. Moreover, Fig. 12 also evidences that R a decreases with the ageing time of the electrolyte. For example, at the centre of the samples, R a value is about 5 µm with the fresh electrolyte and decreases to about 3.5 µm with the most aged electrolyte. The surface becomes smoother as the electrolyte gets aged. Such a decrease in the surface roughness is much more pronounced after 2 hours while after 5 hours, R a stands at a low and almost constant value. Fig. 13 presents the secondary electrons SEM top view micrographs showing the surface of the layers grown on Al2214 aluminium alloy. Micrographs were taken at the edge and at the centre of samples processed for one hour in the fresh (Fig. 13 a.-b., respectively) and in the 8 h-aged electrolyte (Fig. 13 c.-d., respectively). Surfaces exhibit a typical morphology of PEO coatings with a mixture of "pancake"-like structures (site "A" in Fig. 13 b.) surrounded by and filed with "sponge"-like structures (site "B" in Fig. 13 d.). The presence of "pancake" is a typical feature of PEO layers grown on aluminium in "arcs" regime conditions. Such layers are characterized by a micro-porosity which diameter size ranges from 5 to 20 µm. In contrast, the presence of "sponges" characterized by sharp pores (typ. 0.1 to 1 µm in diameter) is usually a footprint of aluminium substrates processed in "soft" regime conditions [3,4,21]. This "sponge"-like structure is also known to contain silicon [23]. Fig 13 shows that the surface of the oxide coating elaborated in the fresh electrolyte is largely dominated by "pancakes" surrounded by a few "sponges". In contrast, by using the most aged electrolyte, "sponges" are interconnected and cover the whole surface of the layer. Such an observation can be explained by the earlier development of the "soft" regime when the electrolyte is aged, the sample surface being thus much longer submitted to the "soft" regime. Fig. 14 shows the EDX spectra recorded on the topmost surface (i.e. the outer sublayer) of the PEO coatings elaborated in 1, 4 and 8 h-aged electrolytes. Note that the surface area analyzed is about 900 µm 2 (square of size 30 µm  30 µm).The outer sublayer contains Al, Mg, Cu, O, Si, Na, K, C and Au regardless of the state of the electrolyte. Note that Al, Mg and Cu come from the Al2214 alloy substrate while O, Si, Na, and K come from the electrolyte (i.e. from potassium hydroxide KOH and sodium silicate Na 2 SiO 3 dissolved in deionised water).

Detection of C and Au are due to traces of organic impurities and gold metallisation required to enhance SEM observations. The proportion of O and Al in the outer sublayer of the PEO coatings remains almost constant whatever the state of the electrolyte. In contrast, EDX spectra show an increase in the amount of Na, Si and K species contained in the outer sublayer with the increase in ageing time of the electrolyte. This result is consistent with previous SEM observations (Fig. 13) showing that the "sponge"-like structures, which are well-known to incorporate elements from the electrolyte, are denser with an aged electrolyte [23][24][25][26]. Moreover, this progressive enrichment of the outer sublayer could explain to some extent the progressive depletion of the ionic species as assessed previously by ICP-AES (see Table 1). Further investigations should however be conducted to get confirmation of this assumption.

Fig. 15 presents EDX maps of Al, O, Si, Na, and K distributions throughout the total layers synthesized in the fresh electrolyte (column a. in Fig. 15) and in an 8 h-aged electrolyte (column b. in Fig. 15). In addition to the former EDX information, these maps evidence that Si, K and Na species are preferentially located in the outer porous sublayers of the coatings, regardless of the age of the electrolyte, while the inner sublayer is mainly composed of Al and O. Nevertheless, some differences are observed between layers grown in the two electrolytes.

In the case of the fresh one, Si, K and Na are non-evenly distributed throughout the outer sublayer and some traces are also found in the inner sublayer. This is particularly true for Na.

In contrast, these three elements are localized only throughout the outer sublayer of the coating grown in the 8 h-old electrolyte. Moreover, Fig. 15 shows that Cu, initially present in the substrate as the main alloying element, forms an interconnected network exclusively distributed throughout the inner sublayer. Concerning the distribution of this element, no differences are noted between the samples processed in either electrolyte.

The X-ray diffraction patterns of the PEO layers grown for 1 h in various aged electrolytes (1, 4 and 8 h) are depicted in Fig. 16. All coatings are predominantly composed of and phases of crystalline alumina Al 2 O 3 . A weak and broad bump centred at 30-40° is assigned to the presence of an amorphous phase in the outer part of the oxide layer, possibly made of amorphous silica SiO 2 or aluminosilica 3(AlO 3 )2(SiO 2 ), as suggested by the spatial distribution of Si throughout the oxide layer (Fig. 15). In Fig. 16, the appearance of aluminium peaks is due to the diagnostic method based on the use of incident X-ray beam that cross entirely the PEO coating and reaches the aluminium substrate. The peaks of cuprite Cu 2 O, which overlap those of -Al 2 O 3 have been identified. Oxidation of copper, the main alloying element of Al2214 aluminium alloys, does take place during the process. Combined with EDX maps in Fig. 15, XRD results suggest the presence of an inter-connected network of cuprite exclusively located in the inner part of the oxide layers. Fig. 17 shows a selected region of XRD patterns in the range of 43-47°. Some authors have proposed to use the relative intensity of (113) -Al 2 O 3 (at 43.6°) and (400) -Al 2 O 3 (at 45.96°) peaks to judge on the and -alumina content and variations in the overall layer phase composition [27,28]. Fig. 17 shows that such a relative intensity of and -alumina peaks increases noticeably with the electrolyte ageing, suggesting an increase in the proportion of the  phase at the expense of the  one as the electrolyte gets aged. The relative content of -Al 2 O 3 in the coating has been quantified for samples processed in various aged electrolytes. Fig. 18 reports the variation of the -Al 2 O 3 content together with the variation of the intensity ratio (113)  /(400)  as a function of the ageing time of the electrolyte. First of all, a strong correlation is observed between the variation of the calculated -Al 2 O 3 content and the variation of the intensity ratio (113)  /(400)  . It supports the idea of using the intensity ratio (113)  / (400)  to describe the proportions of and -Al 2 O 3 phases in the layer. Fig. 18 also shows that the -Al 2 O 3 content is always lower than 50 %. This agrees with the widelyreported conclusion that, in PEO layers grown on aluminium alloys, the -alumina phase is the main crystalline phase. Moreover, Fig. 17 evidences the influence of the ageing process of the electrolyte on the phase composition of the synthesized layers. Indeed, the -Al 2 O 3 content increases with the ageing time of the electrolyte. With the fresh electrolyte, the -Al 2 O 3 content is about 36 % while it reaches about 43 % with the most-aged electrolyte. This trend can be explained by the earlier development of the "soft" regime as the electrolyte gets aged (see Fig. 4), this regime being known to promote the growth of the -Al 2 O 3 phase [18,29,30]. Moreover, the change in the -Al 2 O 3 increase rate after 2 hours ageing suggests that ageing of the electrolyte is effective after about 2 -3 hours of processing. This result is in good agreement with those obtained previously with chemical analysis of the electrolyte, fast video-imaging and coating morphology characterization.

Conclusion

In this study, evidence and influence of ageing of the electrolyte on Plasma Electrolytic Oxidation (PEO) of Al2214 aluminium alloy has been investigated with the use of various experimental techniques including fast-video imaging, chemical analysis and material science.

The tested electrolyte (KOH+Na 2 SiO 3 ) has been deliberately aged during several hours.

Cross-checked results support the same conclusion: chemical ageing of the PEO electrolyte occurs and alteration becomes effective after 2-3 h. of processing. The progressive depletion in the dissolved species (Na, K and Si) with the ageing of the electrolyte is responsible for the decrease in the electrical conductivity of the electrolyte. Ageing affects the oxide layer characteristics whose thickness becomes thinner and more compact with a reduced outer porous sublayer. In an aged electrolyte, the formation of an amorphous alumina-silicate barrier rich in elements coming from the electrolyte (Na, K and Si) that located throughout the outer sublayer is promoted together with the development of the crystalline -Al 2 O 3 alumina in the inner sublayer. Changes in the material are related to changes in the micro-discharges behaviour. As the PEO electrolyte gets aged, the beneficial "soft" oxidation regime appears earlier, leading to less micro-discharges over the processed surface with smaller sizes and shorter lifetime.

List of figure captions

List of tables Table 1

Sodium, potassium, silicon and aluminium ionic species content into a 1 g.L -1 KOH -1.65 g.L -1 Na 2 SiO 3 PEO electrolyte after 1, 3 and 8 hours effective processing duration.

Fig. 3

 3 Fig. 3 shows the anodic voltage-time responses of the PEO treatments performed in three

Fig. 5

 5 Fig.5shows the spatial distributions of the micro-discharges over the processed surface at

Fig. 1 .Fig. 2 .

 12 Fig. 1. Schematic representation of the processed sample showing (a) the area filmed by fast

Fig. 3 .

 3 Fig. 3. Evolutions of the anodic voltage amplitude as a function of the PEO processing time in

Fig. 4 .

 4 Fig. 4. Variations of the "arcs -to -soft" regime switching time and the anodic voltage

Fig. 5 .

 5 Fig. 5. Pictures of the spatial distribution of micro-discharges over the processed surface at

Fig. 6 .

 6 Fig. 6. Evolutions of the micro-discharges surface number density per second with the PEO

Fig. 7 .

 7 Fig. 7. Size (a.-c.) and lifetime (d.-f.) distributions of micro-discharges recorded at three

Fig. 8 .

 8 Fig. 8. Backscattered SEM micrographs of cross-sections of one-hour PEO processed samples

Fig. 9 .

 9 Fig. 9. Variations of the average total thickness (close symbols) and porous outer sublayer

Fig. 10 .

 10 Fig. 10. Top view macrographs of the PEO treated samples (one half only) in a fresh (a) and

Fig. 11 .

 11 Fig. 11. 3-dimensional images of the surface topography of the PEO coatings formed in a

Fig. 12 .

 12 Fig. 12. Variations of the roughness parameter R a (µm) measured at the edge and at the centre

Fig. 13 .

 13 Fig. 13. Top view scanning electron micrographs (secondary electrons) of the surface of one-

Fig. 14 .

 14 Fig. 14. EDX spectra recorded on the topmost surface of the PEO layers grown in an

Fig. 15 .

 15 Fig. 15. Scanning electron micrographs and EDX element maps (Si, K and Na) of the cross-

Fig. 16 .

 16 Fig. 16. XRD patterns (using Bragg-Brentano geometry) of the PEO coatings synthetized for

Fig. 17 .Fig. 18 .

 1718 Fig. 17. Selected region of XRD patterns where (113) -Al 2 O 3 and (400) -Al 2 O 3 peaks are

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Schematic representation of the processed sample showing (a) the area filmed by fast

Fig. 4 .

 4 Fig. 4. Variations of the "arcs -to -soft" regime switching time and the anodic voltage

Fig. 5 .Fig. 6 .Fig. 7 .

 567 Fig. 5. Pictures of the spatial distribution of micro-discharges over the processed surface at

Fig. 8 .Fig. 9 .

 89 Fig. 8. Backscattered SEM micrographs of cross-sections of one-hour PEO processed samples

Fig. 10 .

 10 Fig. 10. Top view macrographs of the PEO treated samples (one half only) in a fresh (a.) and

Fig. 11 .Fig. 12 .

 1112 Fig. 11. 3-dimensional images of the surface topography of the PEO coatings formed in a

Fig. 13 .Fig. 14 .

 1314 Fig. 13. Top view scanning electron micrographs (secondary electrons) of the surface of one-

Fig. 15 . 3 Fig. 16 .Fig. 17 .

 1531617 Fig. 15. Scanning electron micrographs and EDX element maps (Si, K and Na) of the cross-

ratio (113)  / (400)  of (113) -Al 2 O 3 and (400) -Al 2 O 3 peaks as a function of the ageing time of the electrolyte.

Acknowledgements

We greatly acknowledge the Conseil Régional de Lorraine for granting A. Nominé's PhD work under decision 11CP-769. We are also deeply grateful to the FONGECIF Rhône-Alpes for granting P. Leone's graduate school internship. This work was supported by the French Government through the program "Investissements d'avenir" operated by the French National Research Agency (ANR) and referenced to as ANR-11-LABX-0008-01 (LabEx DAMAS).


A Datas

J Y Fourquet

P Chiron

On least-cost path for realistic simulation of human motion

Keywords: Motion capture, posture, and motion

We are interested in "human-like" automatic motion simulation with applications in ergonomics. The apparent redundancy of the humanoid wrt its explicit tasks leads to the problem of choosing a plausible movement in the framework of redundant kinematics. Some results have been obtained in the human motion literature for reach motion that involves the position of the hands. We discuss these results and a motion generation scheme associated. When orientation is also explicitly required, very few works are available and even the methods for analysis are not defined. We discuss the choice for metrics adapted to the orientation, and also the problems encountered in defining a proper metric in both position and orientation. Motion capture and simulations are provided in both cases. The main goals of this paper are:

• to provide a survey on human motion features at task level for both position and orientation,

• to propose a kinematic control scheme based on these features,

• to define properly the error between motion capture and automatic motion simulation.

Introduction

Human motion generation is highly complex and is concerned with (at least):

• the way the tasks are imposed or characterized • the way the numerous dof of the human kinematic chain are coordinated for a given task • how internal dynamics are taken into account • how interaction with the environment is modeled. The work described here is devoted to the study of intrinsic properties of the task space and of the mapping at kinematic level between task and joint space. The motivation is not to neglect dynamicsessential in whole-body equilibrium for instancebut to describe a simple framework for plausible human-like motion generation, when dynamics are not decisive. The ideas are tested on sitting reach motions, for both translations and rotations task components. Generally, the task is denoted by the evolution in space and time of the location X of dimension m .

A reaching task consists in reaching a location f X from 0 X . The configuration q of the mechanical system is known when the value of all its n independent joints is known. If n m < , the motion problem is under-constrained, sometimes said "illposed" in human movement literature, and this setting is known as kinematic redundancy. Then, a multiplicity of joint velocities produces the same velocity in task space. The problem can be formulated as an optimization problem in configuration space and, inside this category of problems, minimum-norm solutions leads to weighted pseudo-inversion schemes [START_REF] Ben-Israel | Generalized inverse theory[END_REF]. Literature on the human movement analysis is mainly focused on reach motion and translation information. Very few works have studied the questions relative to the orientation of the hand or relative to the paths and motions in task space when reaching and grasping is concerned, or when translation and rotation of the end-effector are both imposed. Questions are numerous: they concern the geometry in task space (shape of paths), significant parameterization [START_REF] Choe | Modeling head and hand orientation during motion using quaternions[END_REF][START_REF] Pierrynowski | Oppugning the assumptions of spatial averaging of segment and joint orientations[END_REF], and the temporal aspects (velocity profile), sequences of reach and grasp [START_REF] Lacquaniti | Coordination of arm and wrist motion during a reaching task[END_REF][START_REF] Fan | Control orientation and arm movement during reach and grasp[END_REF][START_REF] Hesse | Changes in grasping kinematics due to different start postures of the hand[END_REF], simultaneous evolution of translation and rotation [START_REF] Wang | Three-dimensional kinematic analysis of in uence of hand orientation and joint limits on the control of arm postures and movements[END_REF][START_REF] Bennis | Coupling between reaching movement di-rection and hand orientation for grasping[END_REF]...). Since coordination of translation and rotation is the focal point, time-scale and length-scale are obviously concerned. As a result of human motion studies, no "fundamental human motion principle" emerges but optimization principles have proved to be useful guides. In this paper, we focus on seated reaching motions in the horizontal plane and tend to reproduce human motions based on well known Morasso experiments [START_REF] Morasso | Spatial control of arm movements[END_REF]. The simulations are realized with a 24 Degrees of Freedom (DOF) virtual human (see Fig. 1). In the next section, translation paths are studied and a kinematics-based scheme is proposed when task path requires too much joint displacement. Section 3 presents a similar approach for rotations. Finally, the last section discusses the translation and rotation coordination. In every section, motion capture and simulation curves are provided.

Translation constraints

Distance, path and motion in task space

In this case, the location p X is made of the Cartesian coordinates ) , , ( z y x X p = of a specific body (hand, head ...) and the natural way to measure length and distance is to use the Euclidean metric. Various authors have studied the reach motion in free space. In many cases reported in the literature, the observed path, in particular for planar movement, is close to straight lines [START_REF] Flash | The coordination of arm movements: An ex-perimentally con rmed mathematical model[END_REF][START_REF] Soechting | Invariant characteristics of a pointing movement in man[END_REF] and the motion along the path exhibits a bell-shaped velocity profile [START_REF] Morasso | Spatial control of arm movements[END_REF][START_REF] Atkeson | Kinematic features of unrestrained arm movements[END_REF].

This behavior has been associated to integral criteria, first in task-space. Among them, the measures substantiate the minimum hand jerk solution [START_REF] Flash | The coordination of arm movements: An ex-perimentally con rmed mathematical model[END_REF] i.e. the solution ) (t X p that minimizes:

(1) here f t is the total duration of the motion and under the constraints that the derivatives all equal zero at both endpoints. In fact, the Calculus of Variations [START_REF] Gelfand | Calculus of variations[END_REF] enables us to conclude that since there is no coupling between the Cartesian coordinates, the path solution of ( 1 (2)

where the coefficients i a depend on the endpoints value and and on . This solution provides the minimum distance paththe geodesic -in the usual Cartesian metrics covered with a smooth time profile verifying the minimum jerk solution along this straight line. Thus a way to program human-like simulation for a variety of position tasks is to impose a straight line and the law defined in relation (2) on this straight line. In fact, several authors have shown that the reference path is not always a straight path and some of them attempted to define new criteria in order to explain these discrepancies. On the one hand, one may think that evolution has led to render the human locomotor apparatus really efficient and turn him able to follow the most efficient paths in Cartesian space: the straight line. Remark that statistical methods popularized in industrial cycle-time measurement such as MTM implicitly include this fact since the cycle-time in usual workplaces is only related to distance of reach [START_REF] Stegemerten | Methods-time measurement[END_REF][START_REF] Kuhn | Computer-aided workload analysis using MTM[END_REF][START_REF] Laring | Mtm-based ergonomic workload analysis[END_REF][START_REF] Ma | A framework for interactive work design based on digital work analysis and simulation[END_REF]). On the other hand, we know that kinematic chains are not isotropic motion generators in Cartesian space. Thus, intuitively, one can infer that there is a preferred workspace zone in which the path is a straight line, and other zones in which the mechanical constraints induced by the nature of kinematic chains will render really difficult to follow a straight line.

Here, the matter is not so much to ask if the optimization criterion acts in Cartesian space or in Joint Space [START_REF] Engelbrecht | Minimum principles in motor control[END_REF][START_REF] Svinin | On the dynamic version of the minimum hand jerk criterion[END_REF] but rather how to reproduce a trade-off between the task efficiency and the constraints induced by the mechanical structure.

Space mappings and mixed criteria

The relation between the respective first order variations and , or the exact relation between the velocities and , writes as a linear map:

(3) where is the Jacobian matrix associated to the task . This mapping is configuration-dependent and does not provide an isotropic transformation from joint space to task space. The properties of this mapping are enlightened by its singular value decomposition (SVD) [START_REF] Golub | Matrix computations[END_REF]. SVD provides the means to analyze the amount of joint displacement necessary to move in a given direction in task space. SVD of writes:

(4)

where is an orthonormal basis of the tangent vectors to the task space, is an orthonormal basis of the tangent space to the configuration space, is a diagonal matrix with rank the singular values of are arranged such that . The geometrical meaning of this decomposition is : maps a unit ball in the tangent space to the task space into a p-dimensional ellipsoid in the tangent space to the configuration space. This ellipsoid has principal axes with length . Remark that the form a basis for the range of and the form a basis of the kernel of . Thus, a significant difference of value among the implies that the amount of joint displacement consumed for a given norm of task displacement in task space varies with the direction and that some directions in task space are really easier to follow. Thus, on the one hand, one may think that human motion will occur in straight line if the task path does not require a large amount of joint motion. On the other hand, some configurations are such that task displacement in a certain direction requires a really high amount of joint motion: in this latter case, at least one singular value takes a significant smaller value and straight paths are not necessarily efficient.

The motion scheme

The proposed approach consists in choosing straight lines as initial guesses for the Cartesian path and to adapt this guess depending on the SVD. Thus, the simulated movements are built upon optimization in path space under the condition of a reasonable expense in joint space. This program is realized on the basis of a kinematic control scheme where lower singular-values filtering acts when SVD detects that the straight line is too costly at joint level. The control scheme is the following:

(5)

where the main task consists in following the Cartesian path and is a secondary task built upon :

• the projector into the null space of ,

• an n-dimensional vector computed as the scaled gradient of a potential field that enables to take into account inequality constraints such as joint limit avoidance and reference posture adjustment. The main task uses the weighted and filtered pseudoinverse of (Ben-Israel and Greville 2003):

(6) where is the inertia matrix and stands for the filtering matrix [START_REF] Maciejewski | Motion simulation: Dealing with the ill-conditioned equations of motion for articulated gures[END_REF]) computed by : (7)

In this matrix, the respective weight of the components is directly related to the value of . A threshold on value has been computed from captured motions paths [START_REF] Hue | On realistic human motion simulation for virtual manipulation tasks[END_REF], by computing singular values for straight and curved Cartesian paths. If the singular value is upper this threshold, then and is the inertiaweighted pseudo-inverse of , else takes a nonzero value along a continuous profile.

Motion capture and simulation results

Motion capture is based on a sequence of Morasso [START_REF] Morasso | Spatial control of arm movements[END_REF] of reaching movements on the horizontal plane. This experiment exhibits the fact that the hand follows a straight line for several cases but that a curved path appear for some other cases. The hand velocity matches the bell-shaped profile of minimum hand jerk criterion.

In simulation, the same tuning of our control scheme exhibits similar path features (see Fig. 2) : it produces straight lines motions when it is efficient to follow them and it switches to curved paths when kinematics prescribe a locally better path. Comparison of solutions, captured and simulated, are made through the usual Cartesian distance measure through the Linearity Index (LI) [START_REF] Wang | Three-dimensional kinematic analysis of in uence of hand orientation and joint limits on the control of arm postures and movements[END_REF]). The LI is a measure of path curvature. The smaller the LI is, the straighter the path is. For the straight line, the motion capture has a and the simulated . For the curved lines, motion capture has a mean and the simulated LI for this case is equal to 4.027%. The values obtained for these index are significant in both examples.

Rotation constraints

Human manipulation tasks (touch, grasp, carry) are such that the position and orientation of the hand(s) is partially or totally known. If the task presents a symmetry, one rotation can be left free, but in many cases it is desirable to impose the orientation of the hands as the result of the definition of a task.

Distance, path and motion in task space

Intrinsically, rotations are elements of SO(3) (the Special Orthogonal Group of dimension 3), a 3dimensional differential manifold with a Lie group structure. A point in this manifold is computed in coordinates by several choices, through various parameterizations. Among them, some are made of surabondant not independent components (rotation matrices), some other are endowed with a minimal number of components (3-angles systems: Euler, Bryant, Yaw-Pitch-Roll ...) but also with singularities ("gimbal lock"). Axis-Angle representation, unit quaternion, exponential map are formalisms that are really close to the canonical coordinates of SO(3). Here, the following developments mainly use the exponential map formalism [START_REF] Park | Smooth invariant interpolation of rotations[END_REF][START_REF] Murray | A Mathematical Introduction to Robotic Manipulation[END_REF]. We try to follow, as for the translation, the geodesic path in rotation. We first define a least distance path on SO(3), and second interpolate a minimum jerk time-evolution along this path. Let denote a rotation matrix. Since Euler [START_REF] Murray | A Mathematical Introduction to Robotic Manipulation[END_REF], we know that it is possible to transform a rotation matrix (or an orthonormal vector frame) into a rotation (or another vector frame) by defining a vector around which an amount of rotation is performed. The exponential map formalism exploits this axis-angle representation.

Let us denote the skew-symmetric matrix derived from the vector that enables to transform the cross-product in a matrix multiplication . Then writes . The solution of this linear matrix differential equation is where 'expm' stands for matrix exponential and is given for by: expm (8)

In the same way, it is possible to prove the existence of with and such that the motion between two orientations and is given by : . The geodesic on between and is obtained by rotating around with a amount and the equation ( 8) provides a natural way to interpolate on the geodesic. Conversely, one can write where 'logm' stands for the matrix logarithm and is given by : with . Note that can be obtained in various ways (from the rotation matrices or quaternion, for instance) and is given by the formula (with ) :

The distance between two rotations is the length of the shortest path between them. It is then computed along geodesics. In SO(3), this distance between two rotations and is given by: where is the Frobenius norm of the matrix . Then, if varies linearly as a function of the time , the motion is a linear interpolation from to along the geodesic. This simple solution is the one provided by the slerp algorithm [START_REF] Shoemake | Animating rotation with quaternion curves[END_REF] popularized with unit quaternions. It provides a constant velocity evolution on the geodesic. From the physics, such a behavior seems unnatural since it requires infinite acceleration at the beginning and at the end. Remarking that translation and rotation result from the same biomechanical system, it is plausible that the time evolution of the variables obeys the same smoothness properties. Then, again minimizing the jerk along the geodesic is the chosen solution and thus:

space mapping and optimization

Tangent vectors to SO(3) are related to joint velocities by the canonical linear map:

(9)
where is a matrix. Then, the animation problem requires first that and be given and second to provide a generalized inversion scheme for the linear system (9). Again, the norm of the tangent vectors in both spaces can be efficiently computed by SVD which gives a local measure of preferred directions in task space for a given configuration.

Motion capture results

The idea is to experiment a simple rotation without translation of the reference point. We ask the subjects to rotate the pose of the hand between two drawn orientations superposed at the same position. The motion capture results are presented in the figures 3 and 4. The figure 3 shows that the time profile for a simple movement of rotation around the vertical axis is really similar to the minimum jerk profile. The figure 4 represents the time evolution of the rotation (from left to right) at regularly spaced instants. Even if the captured motion is slightly different from the geodesic, the motion appears similar and the maximum measured distance is: .

Combining rotations and translations

Discussion

The task simulation amounts to the definition of the interpolation laws for both the position of a particular point of the hand (the Tool Center Point (TCP)) and the orientation of a body-fixed frame. Such a composite object lives in SE( 3), the Special Euclidean group of dimension 3. The associated differential kinematics writes:

(10) Different possibilities arise in choosing the solution of this linear system. On one side, one may think that translation and rotation follow their own rule, independently in two parallel spaces, 3 for the Cartesian coordinates, SO(3) for the orientation parameters. Intrinsic metric and closed-form geodesics are available in each space. Following this idea leads to obtain a straight line motion in Cartesian space for the TCP and a geodesic in SO(3) for the frame attached to the body. We may think that this independence is dubious. In fact, beyond the fact that this problem is solvable in a well-posed setting with natural metrics, at least two other arguments speak for this solution. Firstly, this decoupling is observed naturally in the motion of bodies : in absence of external forces, the linear and angular velocities keep constant values and the resulting path follows in parallel the geodesics of 3 and SO(3). Secondly, SE( 3) is not the crossproduct of 3 and SO(3) and there is no natural (i.e. no bi-invariant) metric on it [START_REF] Zefran | Planning of smooth motions on se(3)[END_REF]. Thus, choosing a metric in SE(3) requires to weight two mathematical objects of different nature with an unique measure of length. Such a weighting has no intrinsic meaning from the geometric point of view. It amounts to choose a Riemannian metric [START_REF] Arimoto | A riemannian geometry approach for control of robotic systems under constraints[END_REF]) on SE(3) defined by a blockdiagonal matrix W related to the length l by: and

(11) This is equivalent to the choice of a length scale between s and . This choice may be motivated by different reasons and the synchronization of translations and rotations may be viewed as time or/and length scale.

In some captured motions, we observe paths that are fairly far from the geodesics, for the translation or the rotation part, or for both. This is in particular the case for motion in which the amount of rotation is really important, and should require that the translation does not occur along a straight line. Thus, again the geometry of the task space is not the sole decisive factor in the generation of human motion. The way rotation and translation constraints interfere in determining a good path in SE( 3) is not easy to understand. If one applies the filtering scheme illustrated for the translation parameters, it must be kept in mind that the singular values of the global map ( 10) are dependent on the choice of length made in (11).

Motion capture and simulation

The experiment of paragraph 2 is modified in the way depicted at figure 5 and tested with 8 subjects. Each subject has to follow the sequence given by ( 12), and positions and orientation are given in Table 1. ( 12) For illustrating purposes, we focus here on two movements depicted in red in the figures: a first one, from (E) to (A), for which the translation observed is close to a straight line, and a second one, from (D) to (F), for which this translation occurs along a curve really different from a straight line. In both movements, the time and space evolution are studied. The first movement is represented in figures 6 and 7. Contrary to the observations for the pure rotation movement, the figure 6 shows that the time profile may be different from the minimum jerk profile. Moreover, the figure 7 shows that the human movement does not always follow the shortest rotation path. The distance between the shortest path and this movement are LI = 4.16% for the position and for the rotation. The second captured movement is represented in the figures 8 and 9. Here, the rotation time profile is identical to a minimum jerk profile (see Fig. 8) but the rotation does not follow the rotation shortest path (see Fig 9). The differences between the shortest path and the captured movement are LI = 10.16% for the position and for the rotation. Both movements are simulated with the kinematic control scheme described in the section 2. The reference paths are the geodesics in rotation and translation, and these paths are covered with a minimum jerk profile after a length-scale in order to synchronize rotation and translation components. SVD filtering is applied globally on a translation and rotation task in order to take into account the cost in joint space. The results of the first movement are given in the figures 10 and 11; the results of the second one are given in the figures 12 and 13. The simulation of the experiment 3.1 has a deformation about 1.97%. The measured maximum distance for the rotation is:

. For the experiment 3.2, the results are LI = 5.32% for the position and a distance of for the rotation. These simulations are dependent on the tuning of the SVD filtering that amounts to weight rotation and translation on one side, internal kinematic constraints on the other. It is shown that various features can be conserved (SVD deformation in translation, minimum jerk rotation time profile) but that it is difficult to predict which component is prevalent in a given movement.

Much work remains necessary to analyze which metrics are pertinent and how space and time constraints interact.

Conclusion

This work aims at studying the relationships between kinematics, optimization principles and human motion. Metrics and shortest paths have been defined and tested in real and simulation. Many cases arise and some of the key features that appear in the real movements can be reproduced or predicted by a kinematic control scheme with leastcost principles. Shortest paths in the separate metrics, for rotation and translation, are present but are not the only possible paths. Minimum jerk time profile is also present but is sometimes slower than the observed time profile, and much work remains necessary to analyze how space and time constraints interact. This may prove the need for the definition of coupled metrics in SE(3) or for a proper weighting between geometric cost in task space, geometric cost in joint space and internal dynamics constraints. Another approach could be to prioritize translation and rotation tasks in order to filter independently both components of the task.

Fig. 1 .

 1 Fig. 1. Virtual human kinematic structure

  minimum hand jerk impose the following time law along the path:

  Fig. 2. Hand translation paths

Fig. 3 .

 3 Fig. 3. Experiment 2 : Comparizon between time evolution of captured rotation of the hand (red) and the unidimensional minimum jerk curve (black).

Fig. 4 .

 4 Fig. 4. Experiment 2 : Boxes representative of the time evolution of the rotation. White boxes (top) represent the

Figure 5 :

 5 Figure 5: Experiment 3 : position and rotation constraints

Figure 6 :

 6 Figure 6: Experiment 3.1 : (a) -translation part of the global sequence of movements (black) and of the studied movement (red) (b) -Comparison between the time evolution of the hand orientation (red) and the minimum jerk (black).

Figure 7 :

 7 Figure 7: Experiment 3.1 : Boxes representative of the time evolution of the rotation. White boxes (top) represent the captured movement. Orange boxes (down) represent the rotation geodesic.

Figure 8 :

 8 Figure 8: Experiment 3.2 : (a) -translation part of the global sequence of movements (black) and of the studied movement (red) (b) -Comparizon between the time evolution of the hand orientation (red) and the minimum jerk (black).

Figure 9 :

 9 Figure 9: Experiment 3.2 : Boxes representative of the time evolution of the rotation. White boxes (top)

Figure 10 :

 10 Figure 10: Experiment 3.1 (simulation) : (a) -translation part of the global sequence of movements (black) and of the studied movement (red) (b) -Comparizon between the time evolution of the hand orientation (red) and the minimum jerk (black).

Figure 11 :

 11 Figure 11: Experiment 3.1 : Boxes representative of the time evolution of the rotation. White boxes (top) represent the simulated movement. Orange boxes (down) represent the rotation geodesic.

Figure 12 :

 12 Figure 12: Experiment 3.2 (simulation) : (a) -translation part of the global sequence of movements (black) and of the studied movement (red) (b) -Comparizon between the time evolution of the hand orientation (red) and the minimum jerk (black).

Figure 13 :

 13 Figure 13: Experiment 3.2 : Boxes representative of the time evolution of the rotation. White boxes (top) represent the simulated movement. Orange boxes (down) represent the rotation geodesic.

Table 1 :

 1 Hand positions and orientations

	Point	Position X	Position Y Orientation
	A	-25	30	+90°
	B	0	25	+45°
	C	30	29	-45°
	D	-30	0	+90°
	E	0	0	+45°
	F	30	0	-45°