Rtimi

W Elfallah

A A Assadi
email: aymen.assadi@ensc-rennes.fr

A Bouzaza

D Wolbert

J Kiwi

S Rtimi
email: sami.rtimi@epfl.ch

Innovative and stable TiO 2 supported catalytic surfaces removing aldehydes under UV-light irradiation

Keywords: TiO 2 -PES, batch photo-reactor, kinetics, intermediate by-products, GC-MS, L-H isotherms, degradation kinetics

Innovative and stable TiO2 supported catalytic surfaces removing aldehydes under UV-light irradiation

Introduction:

VOCs have been found to be hazardous to the human health and introduce collateral environmental damage. VOCs are discharged into the atmosphere by households and industry, and found in the exhaust gases from animal quartering, and residential cleaning agents. Damaging health effects have been reported on the eyes, nose and throat. They also lead to headaches, loss of coordination and nausea, damages to the liver, kidney and the central nervous system [START_REF] Peter | Aldehyde Sources, Metabolism, Molecular Toxicity Mechanisms, and Possible Effects on Human Health[END_REF]. Moreover, they can induce cancer in animals; and can cause cancer in humans [START_REF] Heck | Starr, Formaldehyde Toxicity-New Understanding[END_REF]. The technologies developed until now to remove VOCs have not been entirely successful and do not meet the regulatory levels becoming more demanding during the last decade. Recently studies report the aldehyde removal by adsorption [START_REF] Gabrielson | Adsorption of aldehydes and ketones on anion exchangers in cyanide form[END_REF], biological treatment [START_REF] Huck | Formation and removal of selected aldehydes in a biological drinking-water treatment process[END_REF] and advanced oxidation processes (AOP's).

Photocatalytic TiO 2 materials have been widely used during the last four decades due to their low cost, photo-activity and stability [START_REF] Assadi | Use of DBD plasma, photocatalysis, and combined DBD plasma/photocatalysis in a continuous annular reactor for isovaleraldehyde elimination-synergetic effect and byproducts identification[END_REF]. TiO 2 is widely used in catalytic processes occurring at the air-solid interface at room temperature and atmospheric pressure [START_REF] Boyjoo | A review on photocatalysis for air treatment: From catalyst development to reactor design[END_REF][START_REF] Robotti | Photocatalytic abatement of NOx by C-TiO 2 /polymer composite coatings obtained by low pressure cold gas spraying[END_REF][START_REF] Curcio | TiO 2 solgel for formaldehyde photodegradation using polymeric support: photocatalysis efficiency versus material stability[END_REF]. TiO 2 (titania) stands out as one of the most active photocatalyst [START_REF] Zhong | Performance of Ultraviolet Photocatalytic Oxidation for Indoor Air Applications: Systematic Experimental Evaluation[END_REF] under UV-radiation. The electrons in the valence band of TiO 2 under light move to the conduction band generating electron (e -)-hole (h + ) pairs. These electrons in contact with air are able to reduce the O 2 forming superoxide ions. Moreover, the holes oxidize water adsorbed on the TiO 2 -surface generating hydroxyl radical (HO°) [START_REF] Rtimi | Innovative transparent non-scattering TiO 2 bactericide thin films inducing increased E. coli cell wall fluidity[END_REF][START_REF] Ochiai | Photoelectrochemical properties of TiO 2 photocatalyst and its app,ications for environmental purification[END_REF]. The later radical species oxidize organic compounds to produce CO 2 [START_REF] Zhong | Photocatalytic air cleaners and materials technologies abilities and limitations[END_REF][START_REF] Assadi | Isovaleraldehyde elimination by UV/TiO 2 photocatalysis: comparative study of the process at different reactors configurations and scales[END_REF][START_REF] Gl | Photocatalytic oxidation of multicomponent mixtures of estrogens (estrone (E1), 17β-estradiol (E2), 17αethynylestradiol (EE2) and estriol (E3)) under UVA and UVC radiation: photon absorption, quantum yields and rate constants independent of photon absorption[END_REF][START_REF] Ay | Immobilisation of titanium dioxide onto supporting materials in heterogeneous photocatalysis: a review[END_REF]. TiO 2 has been also used in chemical synthesis [START_REF] Suciu | TiO 2 thin films prepared by sol-gel method[END_REF][START_REF] Tk | A review of photocatalysts prepared by sol-gel method for VOCs removal[END_REF] and energy conversion [START_REF] Ochiai | Fabrication of a TiO 2 nanoparticles impregnated titanium mesh filter and its application for environmental purification[END_REF].

Many research groups studied the photocatalytic oxidation for indoor and outdoor cleaning under UV and/or solar light. The reaction rate of a photocatalytic reaction depends on the catalyst, the applied light intensity, the concentration of reactants (in our case gaseous effluents), the flow rate and the type of reactor used (batch or continuous) [START_REF] Zhong | Performance of Ultraviolet Photocatalytic Oxidation for Indoor Air Applications: Systematic Experimental Evaluation[END_REF][START_REF] Zhong | Photocatalytic air cleaners and materials technologies abilities and limitations[END_REF]. This paper presents the optimization for the TiO 2 impregnation on two supports: polyester (from now PES) and Glass Fiber Tissue (from now GFT). It reports some properties of these surfaces [START_REF] Nesic | New evidence for TiO 2 uniform surfaces leading to complete bacterial reduction in the dark: Critical issues[END_REF] along the Langmuir Hinshelwood (L-H) isotherm followed during the photocatalytic degradation of the two aldehydes. The first evidence for the degradation kinetics for gas-phase PCO of aldehydes is presented on PES-TiO 2 and GFT-TiO 2 . Butyraldehyde and isovaleraldehyde were chosen as probes due to their abundant presence in exhaust gases from animal process/quartering [START_REF]OECD screening information databases 3-methyl butanal[END_REF].

Experimental Section 2.1. Chemical reagents

Chemicals were Sigma-Aldrich (USA). The isovaleraldehyde (≥ 98%) and butyraldehyde (≥99%) were p.a. reagents and used as received. Both aldehydes belong to the priority group of VOCs pollutants: aromatics (one, two or three rings) alkanes, ketones, alcohol, and chloro-carbons by the French Environment and Energy Management Agency (ADEME).

Apparatus and Analysis:

The batch reactor used was approximately 400 mm high and was able to contain a volume of 1.5 L. The catalytic samples used presented a surface of 330 cm 2 and were attached to the inner wall of the cylindrical reactor. The fluorescent UV-lamp in the photo-reactor was Philips PL-S 9W/10/4P. The outside wall of the reactor was covered with Al-foil during the irradiation experiments to prevent the lamp UVemission to reach the outside of the reactor. A magnetic stirrer and a magnetic barrel allowed the homogenization of the gas phase. During the course of this study a aldehyde samples were injected into the reactor. A magnetic stirrer and some glass spheres were used to homogenize of the inlet gas phase. When the equilibrium was reached, the UV lamp was turned on.

Samples were taken regularly from the reactor for analysis.

The main reaction intermediates present in gas phase were analyzed to suggest at later stages during this study a reaction mechanism. Carbotrap compositions were used to concentrate the pollutiants: Carbopack Y, is used for the selective retention

Catalyst

Glass Fiber Tissue (GFT)

The glass-fiber(GFT) was provided by Ahlstrom Research/Services [START_REF] Zhong | Photocatalytic air cleaners and materials technologies abilities and limitations[END_REF]. This material contained colloidal silica, a variable percentage of titanium dioxide, manganese dioxide nanoparticles and inorganic fibers as shown in Figure 2a. TiO 2 was deposited on the inorganic fibers by impregnation using an industrial-size press as shown in Figure 2b. A mixture of 50-wt% colloidal silica and different wt% of TiO 2 nanoparticles (PC500 Millennium) and manganese dioxide is suspended in pure water. In order to ensure the deposition of 13 g/m 2 of dry TiO 2 on the GFT support.

The suspension was composed of 40% of dry powder and 60% of pure water. The PC500 TiO 2 nanoparticles consisted of anatase 5-10 nm in diameter with and TiO 2 SSA nanoparticles of 300 m 2 /g as shown in Figure 2a. PES-TiO 2 samples were prepared hydrothermal (HT) preparation treatment method. During the HT-preparation, the TiO 2 colloidal suspension was prepared dissolving titanium tetra-isopropoxide (TTIP, Sigma Aldrich) in isopropanol in a 1:3 volume ratio. Then, the solution was transferred into a beaker with 50 ml of 0.1M HNO 3 . This way of preparation lead to a substantial TiO 2 aggregation. To study the effect of these aggregations on the photocatalytic activity, some samples were ultrasonicated for 10 min prior to the PES impregnation; these samples will be called US-TiO 2 -PES along the manuscript. The polyester samples 10x10 cm was immersed into the acid TiO 2 precursor suspension and heated under stirring in a reflux condenser for 2 hours at 80°C. The PES fabric was removed from the suspension, rinsed with demineralized water and treated in ultrasound bath for 2 min to remove the unbounded TiO 2 particles. The last operation was repeated three times and the TiO 2polyester fabric dried for 2 hours in air at 70°C.

The low surface energy of polyester led to poor TiO 2 nanoparticles adhesion. In order to fix a higher amount of TiO 2 on PES, the PES was pretreated by UVC-light to induce a higher density of functional polar groups able to bind TiO 2 nanoparticles [START_REF] Rtimi | Novel FeOx-polyethylene transparent films: synthesis and mechanism of surface regeneration[END_REF]. UVC pretreatment enhances the polarity, roughness and hydrophilicity of polyester improving its bondability and interfacial adhesion. The UVC pre-treatment induced negatively charged functional groups, e.g., carboxylic, percarboxylic, epoxide and peroxide groups due to the atomic and excited-O*. The polyester negative sites bind the slightly positive deposited Ti 4+ /(TiO 2 ) by electrostatic attraction involving chelation/complexation [START_REF] Rtimi | Indoor light enhanced photocatalytic ultra-thin films on flexible non-heat resistant substrates reducing bacterial infection risks[END_REF]. The TiO 2 was deposited immediately after the UVCpretreatment due to the short lifetimes of the polar radical species.

To determine the TiO 2 isoelectric point (IEP), a Colloidal Dynamics Acousto Sizer II (Sydney, Australia) instrument was used. The zeta potential is calculated from the widely used Smoluchowski equation [START_REF] Rtimi | Indoor light enhanced photocatalytic ultra-thin films on flexible non-heat resistant substrates reducing bacterial infection risks[END_REF][START_REF] Fujishima | TiO 2 photocatalysis and related surface phenomena[END_REF] for thin double layers (ka >20). The electro-acoustic determines the dynamic mobility, of the suspensions in 150 ml KNO 3 (0.01M). The pH adjusted with HNO 3 to around 3 and then titrated up to pH 10 or 11 by addition of KOH (0.01 M) 25°C. The colloid was dispersed under vigorous agitation and ultrasonic treatment for 5 minutes (150 watts, 20 kHz).

The Ti-content of the TiO 2 -PES samples was determined in an Orbis PC Micro EDXRF analyzer equipped with a Rh micro-focus X-ray tube (50 kV and 1 mA) and X-ray multiple optic turret with 30 µm poly-capillary X-Ray optics/collimator.

Diffuse reflectance spectroscopy (DRS) was carried out in a Varian Analytical

Instruments Cary 5 UV-VIS-IR spectrophotometer (controlled by the Cary Win UV software) within the wavelength range of 300-800 nm and a resolution of one nm.

The spectral absorption of the samples was plotted in the Kubelka-Munk (KM) units vs. wavelength.

Pollutants degradation conditions

Degradation of isovaleraldehyde and butyraldehyde in the photocatalytic reactor was evaluated for several influent pollutant concentrations (Table 1). The diffuse reflectance spectra (DRS) in Figure 3 show a higher optical absorption for the samples prepared by the HT-method compared to the samples prepared by the US-method. The higher TiO 2 loading on the HT-samples explains these DRS results as determined by (XFR) and can be explained by the different aggregation of the TiO 2 clusters on the polyester surface. This leads to light reflectance in all directions increasing the signal registered in the optical integration sphere.

The rough UV-Vis reflectance data cannot be used directly when accounting for the absorption coefficient of the TiO 2 -impregnated polyester due to the large scattering contribution. Normally, a weak dependence is assumed for the scattering coefficient S on the light diffusion.

In agreement with the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloidal stability, nanoparticle aggregation sets in at pH close to the TiO 2 IEP 6-7

used during the preparation of the TiO 2 colloidal suspensions due to the attractive Van der Waals forces. The TiO 2 single particles present sizes between 40-60 nm.

The hydrodynamic diameter of the aggregates was found to be 170-240 nm and is approximately equivalent to 3-6 primary TiO 2 particles [START_REF] Nesic | New evidence for TiO 2 uniform surfaces leading to complete bacterial reduction in the dark: Critical issues[END_REF], aggregates involve a higher mass of TiO 2 but a lower surface per particle active intervening in the photocatalytic process.

Pollutant degradation

To separate the effects of photocatalysis and adsorption, the VOC with a concentration of several g/m 3 were mixed with air and stirred for 30 min in the dark to reach adsorption-desorption equilibrium at time zero. Subsequently, the mixture was irradiated under UV-light for 180 min to test the photo-activity of PES-TiO 2 . After the experimental conditions became stable, the PCO reaction was initiated and the VOC injected. Under steady-state conditions samples were taken to evaluate the degradation rate and the generation of by-products

Comparison with other photocatalyst (GFT)

The PES-TiO 2 and the (GFT)-TiO 2 samples presented a similar TiO 2 loading as determined by XRF of 0.61 wt%/wt-PES and 0.57 wt%/wt-GFT. PES and GFT did not led to aldehyde degradation in the dark or under light irradiation. Butyraldehyde, removal on GFT was about twice faster compared to PES, it reaches 90% removal in 30 minutes on GFT-TiO 2 as seen in Figure 5a. On PES-TiO 2 about 90% of butyraldehyde was removed within 60 min. The TiO 2 accessibility to lower depths in the GFT glass-wool containing TiO 2 dispersed nanoparticles offer a higher number of active sites per nanoparticle in the glass wool compared to the PES support. [START_REF] Gl | Photocatalytic oxidation of multicomponent mixtures of estrogens (estrone (E1), 17β-estradiol (E2), 17αethynylestradiol (EE2) and estriol (E3)) under UVA and UVC radiation: photon absorption, quantum yields and rate constants independent of photon absorption[END_REF]. Table 2 shows that GFT-TiO 2 leads to a faster butyraldehyde degradation compared with the PES-TiO 2 . Anatase crystals are formed at around 300°C and rutile at around 600°C when heating TiO 2 colloids in the absence of a structure-forming surface like polyester [START_REF] Nesic | New evidence for TiO 2 uniform surfaces leading to complete bacterial reduction in the dark: Critical issues[END_REF][START_REF] Mejía | Preparation, testing and performance of TiO 2 /Polyester for the degradation of gaseous methanol[END_REF]. These temperatures are significantly higher compared to temperatures of around 80°C used in the preparation of TiO 2 -polyester surfaces (see section 2.3.2). This can lead to different crystallographic structures influencing the photocatalytic activity as recently reported [START_REF] Rtimi | Innovative transparent non-scattering TiO 2 bactericide thin films inducing increased E. coli cell wall fluidity[END_REF][START_REF] Nesic | New evidence for TiO 2 uniform surfaces leading to complete bacterial reduction in the dark: Critical issues[END_REF]. These support materials present: a) a different catalytic site accessibility for the aldehyde and b) a distinct light exposure of the TiO 2 sites to the incoming UV-light [START_REF] Gl | Photocatalytic oxidation of multicomponent mixtures of estrogens (estrone (E1), 17β-estradiol (E2), 17αethynylestradiol (EE2) and estriol (E3)) under UVA and UVC radiation: photon absorption, quantum yields and rate constants independent of photon absorption[END_REF].

By-products Identification

The by-products detected during the photocatalytic degradation of butyraldehyde on PES-TiO 2 were determined by GC-MS. The degradation by-products detected were: methanol (2) acetone (3), ethyl acetate (4), acetic acid (5) and propionic acid [START_REF] Boyjoo | A review on photocatalysis for air treatment: From catalyst development to reactor design[END_REF]. Butyraldehyde (1) was also present after 30 minutes. These results are similar to those reported by Assadi et al. [START_REF] Assadi | Photocatalytic oxidation of Trimethylamine and Isovaleraldehyde in an annular reactor: Influence of the Mass Transfer and the relative humidity[END_REF][START_REF] Assadi | Abatement of 3-methylbutanal and trimethylamine with combined plasma and photocatalysis in a continuous planar reactor[END_REF], reporting acetic, propionic, and butyric acids.

Catalyst recyclability

The reusability of the used catalyst is an important factor to investigate since it is a measure for its practical application potential degrading pollutants in the gas phase [START_REF] Pachoalino | Gas phase photocatalytic decontamination using polymer supported TiO 2[END_REF][START_REF] Mejía | Preparation, testing and performance of TiO 2 /Polyester for the degradation of gaseous methanol[END_REF]. The repetitive use of the GFT-TiO 2 photocatalyst up to the 5 th cycle leading to butyraldehyde degradation is shown below in Figure 7. No loss of activity was detected by the photocatalyst during its repetitive recycling as shown in Figure 7. The catalyst was thoroughly washed after each photodegradation cycle and reused. The results reported in Figure 7 show the potential of the GFT-TiO 2 samples for application in air treatment.

Conclusion

Figure 1 .

 1 Figure 1. Schematic of the batch photo-reactor with the central co-axial mercury 9W mercury UV-light source

  of the C 12 to C 20 compounds. By way of Carbopack B C 5 to C 12 , compounds were trapped while the lighter compounds C 2 to C 5 were adsorbed with Carboxen 1003. The initially concentrated aldehydes on different Carbotrap (Supelco) were then pumped by a a Gillian LFS-113 pump under a flow rate of 50 mL/min. Subsequently, a Turbomatrix Perkin Elmer unit was used to thermally desorb these concentrated compounds. Then the gases were analyzed through a transfer line to the GC/MS Perkin Elmer Clarus 500 equipped with a Quadrupole mass spectrometer detector. The GC/MS column consisted of a capillary column FFAP-CB Chrompact 25 m long, 0.15 mm in diameter and a stationary phase's thickness of 0.25 µm. The temperature in the oven, the injection chamber and the detector were 100, 120 and 200 °C respectively.

Figure 2a .

 2a Figure 2a. Scanning electron micrographs (SEM) of the glass fibers (GFT). An industrial type press was employed to impregnate fibers with the TiO 2 suspension, followed by the drying cstep arried out by Ahlstrom Research and Services.

Figure 2b .

 2b Figure 2b. Diagram of the impregnation technique for GFT synthesis "size press" 2.3.2. TiO 2 impregnated PES: TiO 2 loading, spectral absorption and isoelectric point.

Figure 3

 3 Figure 3 shows the spectral absorption of TiO 2 -impregnated polyester prepared by both preparation methods HT or US.

Figure 3 .

 3 Figure 3. Diffuse reflection spectroscopy (DRS) absorption of PES-TiO 2 .

Figure 4a and b show

  Figure 4a and b show the variation of isovaleraldehyde) and butyraldehyde concentrations versus time at different inlet concentrations. The degradation rate first increased with the inlet concentration, due to the availability of the photocatalytic sites at a low concentration range [9, 11].The concentrations of both aldehydes shown in Figures4a/4bdecreased with increasing irradiation time, going from 10 to 3 g/m 3 and from 9 to 0.8 g/m 3 within 15 min irradiation, at inlet concentration values of 10 and 9 g/m 3 respectively. These rates were similar to the values reported for some VOCs[START_REF] Ochiai | Photoelectrochemical properties of TiO 2 photocatalyst and its app,ications for environmental purification[END_REF][START_REF] Zhong | Photocatalytic air cleaners and materials technologies abilities and limitations[END_REF][START_REF] Assadi | Isovaleraldehyde elimination by UV/TiO 2 photocatalysis: comparative study of the process at different reactors configurations and scales[END_REF][START_REF] Gl | Photocatalytic oxidation of multicomponent mixtures of estrogens (estrone (E1), 17β-estradiol (E2), 17αethynylestradiol (EE2) and estriol (E3)) under UVA and UVC radiation: photon absorption, quantum yields and rate constants independent of photon absorption[END_REF]. We suggest that the degradation mechanism of the aldehydes on supported-TiO 2 involve TiO 2 electrons in the conduction band (cb) reacting with adsorbed O 2 on the TiO 2 yielding HO 2 °

Figure 4a .

 4a Figure 4a. Butyraldehyde degradation on PES-TiO 2 as a function of the initial aldehyde concentration) under a Philips UV 9W mercury lamp irradiation (I=30W/m 2 ).

Figure 4b .

 4b Figure 4b. Isovaleraldehyde degradation on PES-TiO 2 as a function of the initial aldehyde concentration under a Philips UV 9W mercury lamp (I=30W/m 2 ) irradaition.

Figure 5a .

 5a Figure 5a. Butyraldehyde photodegradation kinetics on GFT-TiO 2 and PES-TiO 2 samples under a Philips UV 9 W mercury lamp irradiation (I=30W/m 2 ).

Figure 6 .

 6 Figure 6. By-products observed during butyraldehyde degradation by GC-MS on PES-TiO 2

Figure 7 .

 7 Figure 7. Repetitive degradation of butyraldehyde on a GFT-TiO 2 sample under 9W Philips mercury light. Further experimental conditions: I=30W/m 2 , butyraldehyde concentration = 5 g/m 3 .

  Butyraldehyde and isovaleraldehyde degradation mediated by PES-TiO 2 and GFT-TiO 2 under mercury UV-light have been reported in this study. The by-products during the photocatalytic degradation of butyraldehyde on PES-TiO 2 were identified by GC-MS. The GFT-TiO 2 presented a larger photo-activity compared to PES-TiO 2 and this comparison was quantified by the k c values found during in the L-H treatment of the experimental data. A stable degradation performance of the aldehydes by the GFT-TiO 2 samples was observed during repetitive recycling under UV-light irradiation. This catalyst presents an application potential for application in air treatment.

Table 1 .

 1 Experimental Conditions used during the degradation of aldehydes in the batch photo-reactor.

	Parameter	Value & domain
	Gas Temperature	Ambient (293 K)
	Gas Pressure	Atmospheric pressure (1 atm)
	Volume of reactor Isovaleraldehyde Inlet Concentration	1 L 1 to 22 g/m 3
	[Isoval] Butyraldehyde Inlet Concentration [Buty]	1 to 20 g/m 3
	Relative humidity Intensity of UV lamp	40-50 % 30 W/m 2
	3. Results and discussion
	3.1

. TiO 2 loading, IEP and spectral absorption

By X-ray fluorescence (XRF), HT PES-TiO 2 samples were found to have a 0.61 wt%TiO 2 / wt PES loading and the US PES-TiO 2 samples presented a TiO 2 loading of 0.39 wt%TiO 2 / wt PES. The quantity of TiO 2 was not very high as to affect the PES flexibility and/or other mechanical properties.

where I is the light intensity (W/m 2 ), k 0 is a rate constant independent of the light intensity and is the order of I (0 < < 1).

The linearized L-H equation reads:

The plot of 1/r 0 versus 1/[VOC] 0 allows to determine k c and K values by the plot presented in Figure 5b. According to the values reported in Figure 5b, the values of the L-H constants (k c and K) are shown in the Table 2.


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  The effects of catalysts on the conversion of organic matter and bio-fuel production in the microwave pyrolysis of sludge at different temperatures Rui Ma, Xiaofei Huang, Yang Zhou, Lin Fang, Shichang Sun, Peixin Zhang, Xianghua Zhang, Xuxin Zhao To cite this version: Rui Ma, Xiaofei Huang, Yang Zhou, Lin Fang, Shichang Sun, et al.. The effects of catalysts on the conversion of organic matter and bio-fuel production in the microwave pyrolysis of sludge at different temperatures. Bioresource Technology, 2017, 238, pp.616-623. 10.1016/j.biortech.2017.04.103. hal-

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O Hubert

E Hug

Influence of plastic strain on magnetic behaviour of non-oriented Fe-3Si and application to manufacturing test by punching 1

The prediction of core losses in a rotating electrical machine requires generally a numerical approach (finite element or integral method). However the magnetic characteristics obtained through standard Epstein facility and inserted in the numerical programs predict losses which are quite different from the experimental ones. This difference can be partly explained by the presence of plastic strain close to the cutting edge of manufactured motor sheets. Firstly, numerical functions are established to predict the change of the magnetization and loss curves with respect to the plastic strain level. Secondly, a microhardness test is used to measure the local plastic strain directly on the manufactured sheet. Finally we obtain relations between the main magnetic properties and the position on the sheet : profiles of magnetic properties which are determined allow an improvement of the numerical approach.

Introduction

Core losses due to the magnetic rate of flux density in a soft ferromagnetic material depend on phenomena as complex as hysteresis losses and eddy current losses [1][2] .

Thus the prediction of core losses in a rotating electrical machine is difficult and requires a numerical approach (i.e. finite element methods 3 ). But, even if the functions used in the numerical procedures are based on magnetization characteristics obtained through standard Epstein facility, the predicted losses remain smaller than the experimental ones [2][3] .

It has been checked by many authors 4-5-6 that the microscopic shape of a ferromagnetic material has a fundamental role on its magnetic properties . In particular, plastic strains, resulting in the generation of dislocations, cause the magnetic properties of a non oriented (N.O.) 3% Silicon -Iron sheet to deteriorate 3- 7 . Plastic deformation could be caused to a rotating electrical machine sheet during its manufacture and could damage its magnetic properties.

The aim of this work is to reveal the presence of this type of manufacturing damage which could explain the differences between calculated and experimental losses.

Preliminary work consisted of applying the magnetic properties of a plastically deformed sheet to the whole meshed volume [START_REF] Hug | [END_REF] .

In this paper, the approach is now twofold : firstly, the effect of plastic deformation on the magnetic properties of a N.O. 3% Silicon -Iron sheet (0.5 mm thick) has been modelled from experimental measurements carried out with an A.C. 50 Hz supply. This involves a tranformation of classical models. Secondly, the local plastic strain has been directly identified in the manufactured sheet close to the cutting edge. The results lead to the determination of the profile of magnetic properties.

2 Evolution of magnetic properties with plastic deformation

Experimental procedure

Classical techniques for the measurement of magnetic properties (standard Epstein facility) are not suitable for an investigation of strained materials ; a new magnetic circuit has consequently been manufactured. As shown in figure 1 this consists of a ferromagnetic yoke where a magnetic flux φ(t) is created by a field coil. φ(t) is channelled into a tensile-strained specimen so that the effect of plastic deformation can be measured. This magnetic circuit is used with a 50 Hz alternating current. Specimens, which consist of 200mm long, 20mm wide, and 0.5mm thick bands, have been chosen in the rolling and transverse directions (results are averaged to avoid any texture effect). They have been annealed (720°C, 2H, P(O 2 ) = 2.10 -4 Torr) and plastically deformed from 0% up to 20% (plastic deformation level = ε p (%)) at room temperature and constant extension rate. A coil positioned on the deformed sample produces an electromotive force e(t) due to the rate of magnetic flux ; the e(t) and the excitation current i(t) signals are stored and used to produce a hysteresis loop giving the magnetic flux density B(t) as a function of the magnetic field H(t). From Faraday's law, B(t) is proportional to the integrated e(t) function : V(t).

B(t) = ! S . e(t) dt = ! . V(t) S . n (1)
with : α : integrating constant S : specimen cross section n : number of turns of the magnetic flux density coil Ampere's law states that H(t) is proportional to i(t) :

H(t) = i(t) . N L (2)
with : L : medium in-yoke length N : number of turns of the field coil

The maximum magnetic flux density B m is measured as a function of the maximum magnetic field H m . This is the first magnetization curve obtained with the AC supply. The area scanned by the hysteresis loop is also recorded. It is directly proportional to the total core losses (calculated as function of the maximum magnetic flux density level P(B m )). The measures are carried out with around 10% of incertitudes.

Experimental results

For a given H m , we observe, as shown in figure 2, that B m is decreasing as the plastic strain increases. The amplitude of damage varies following two patterns. Below the knee of the magnetization curve, the different curves tend to diverge. Above the knee, the curves converge to the same magnetic saturation limit. P(B m ) curves calculated from the areas of the hysteresis loops and shown in figure 3 vary in a similar way to the first magnetization curves. Firstly we remark the important and out of standard-norm initial level of core losses in the specimens : P = 6 W/kg for B m = 1.4 T. This is due to the sinusoidal field strength H(t), which induces a nonsinusoidal (trapezoidal) magnetic flux density B(t). This type of magnetic excitation increases losses. In undeformed specimens, we observe a parabolic increase of core losses with maximum magnetic flux density. The plastic strain causes at first a divergence of the curves (up to 0.9 Tesla), and then a convergence.

Establishment of the models

This part of the work concerns models developed to find simple relations between the main magnetic properties and plastic strain. In this paper the least squares method is employed for all numerical calculations of parameters in our models. The indicated incertitudes come from these calculations.

Concerning the first magnetization characteristic, the Fröhlich classical model is used [START_REF] Jiles | Introduction to magnetism and magnetic materials[END_REF] (α and β are characteristic constants of the material) :

B m = H m ! + ".H m or B m = (1/ß) . H m (!/ß) + H m (3)
The Fröhlich equation yields:

B m = G . 1 - A A + H m n (4)
where :

G = (1/ß) A = (!/ß) n " 1
The parameters G, A and n are numerically determined from each experimental curve ; they take a particular value for each plastic strain level (illustrated in table 1).

The results of this model ( 4) are shown in figure 2. The evolution of the parameters G, A and n as functions of plastic strain is shown in figure 4. The following relations are used to model this evolution :

G = a 1 (! p + b 1 ) n 1 (5) A = a 2 (! p + b 2 ) n 2 (6) n = a 3 (! p ) n 3 + n° (7)
The different constants a i , b i and n i used in relations (5) ( 6) and ( 7) are numerically determined. They depend on the nature of the material. We find similar values for the exponents n 1 , n 2 and n 3 (≈ 0.3).

Concerning the evolution of core-losses, the Steinmetz classical law [START_REF] Jiles | Introduction to magnetism and magnetic materials[END_REF] , P = ß (B m ) m , is used to model the experimental results (figure 3). ß and m parameters are numerically determined and take a particular value for each plastic strain level (table 1).

ß and m become functions of plastic strain and their evolution versus plastic strain is modelled using the following relations:

ß = ß° - a b +! p n4 (8)
m = m° + c d +! p n5 (9)
The constants in relations ( 8) and ( 9) are numerically determined (figure 5). The exponents are n 4 = 0.34 (± 0.05) and n 5 = 0.86 (± 0.12).

Once the plastic strains are accounted for, B m = f(H m ) and P = f(B m ) become three dimensional functions : B m = f(H m ,ε p ) and P = f(B m ,ε p ).

Discussion

Limits of validity

The different models used show a range of validity induced by the mathematical limits of the functions B m (H m ) and P(B m ). Regarding the first magnetization characteristics, we note first that it does not give any information about the Rayleigh zone ; it may also not be valid below 100 A/m. Moreover, this model indicates a saturation limit G which increases with the plastic deformation level : once the curves have crossed (after 7500 A/m), the model becomes invalid. On the other hand, the model used for core-loss prediction remains very imprecise with respect to the global evolution of losses. This model becomes invalid above 1.4 T where a crossing of P(B m ) curves is observed.

Influence of plastic strain on magnetic properties

From a micromagnetic point of view, the aspect of the first part of the magnetization curves is explained by the Bloch wall behaviour in an alternating field [1][2][3][4][5][START_REF] Jiles | Introduction to magnetism and magnetic materials[END_REF] ; the second part of the curves should be attributed to the rotation of elementary magnetic moments. We observe that plastic strain has a larger influence on the Bloch wall motion than on the rotation of the magnetic moments. The influence on the Bloch wall motion can be explained by an increase of the density of dislocations due to plastic strain. These dislocations act as potential barriers which hinder the Bloch wall motion [5][START_REF] Jiles | Introduction to magnetism and magnetic materials[END_REF][START_REF] Hug | [END_REF] . The behaviour of the core loss curves is very close to that of the first magnetization curves for the same reasons : Bloch wall motion requires more energy when the material is deformed ; in contrast, rotation of the elementary magnetic moments is less affected.

Influence of the small strains

Small strains have a strong influence on the fluctuations of the P(B m ) and B m (H m ) curves. This is illustrated by a rapid change of the main coefficients (A, ß, n, m) at the initial stages of deformation. To confirm this observation, further experiments were carried out under a quasi static supply to measure the variation of coercive field strength H c with plastic strain : this parameter should be very sensitive to microstructural changes [5][START_REF] Jiles | Introduction to magnetism and magnetic materials[END_REF] . As shown in figure 6, we find two stages. Between 0% and 0.4% of plastic strain, there is a rapid linear increase of H c . Above 0.4%, the slope becomes much smaller but the variation remains linear. 0.4% of plastic strain corresponds to the beginning of the real plastic strain hardening since below that, the metallurgical state of the material is characterized by the Lüders strain state [START_REF] Neuhauser | [END_REF] . This first stage of deformation involves marked changes of the microstructural state 9 such as strong increase of the number of high potential barriers 5 , rapid multiplication of the number of dislocations [START_REF] Strudel | in école d'été d'Yravals[END_REF] , influence of Cottrell atmospheres on the behaviour of dislocations 11 . The later strain hardening stage is characterized by slower changes of the microstructural situation and so of the magnetic properties.

3 Application to a punched Non Oriented 3% Silicon -Iron sheet

Manufacturing of rotating electrical machine sheets

The manufacture of rotating electrical machine rotor and stator sheets is often carried out by progressive-die methods requiring the use of high productivity presses. An example of successive stages of stamping is shown in figure 7. This process involves a strong shearing at the cutting-edge and irreversible plastic strain is present after punching. Since as shown earlier in section 2, a direct relationship exists between the plastic strain level and the magnetic properties. The cutting operation should also have a significant effect on the magnetic properties of rotating electrical machine sheets. SCHMIDT 12 showed that relations exist between the change of the first magnetization curve, the increase of core-losses and the cut length for a N.O. 1%

Silicon -Iron sheet. SZYMURA and ZAWADA 13 observed a similar phenomenon for grain-oriented 3% Silicon -Iron.

Measurement of strain after cutting

The aim of the present work is to apply models which have been developed, to a particular example of cutting and a punching test which is close to industrial manufacturing processes has been chosen. In a first approach, two sheets were tested using the magnetic circuit which has been described earlier. Each sheet was punched by three holes. One sheet was annealed (720°C, 2H, P(O 2 ) = 2.10 -4 Torr) to eliminate plastic strains. The results of this test are shown in figure 8 where a significant influence of plastic strain can be seen on the knee of the magnetization curve (decrease of the maximum permeability). This result confirms the effect of plastic strain close to the cutting edge.

Local plastic deformation after cutting cannot be measured directly, so a microhardness test [14][START_REF] Maillard | CETIM[END_REF] has been used since MAILLARD [START_REF] Maillard | CETIM[END_REF] showed that it was possible to find a relationship between the plastic strain in a metal sheet and hardness. In the present work, the hardness was measured in specimens plastically deformed to different amounts. Hardness was measured on the vertical axis section of the "useful deformed part" of the specimens. A Vickers microhardness (HV) test was used because the indentation is small enough (≈ 30 µm diagonally) to allow the measurement of hardness changes over small distances. A HV = f(ε p ) function is obtained, which is used to deduce plastic strain level close to the cutting edge of a punched metal sheet.

Relationship between plastic strain after cutting and after tensile test

Vickers microhardness measurements have been carried out on numerous plastically deformed specimens and the HV = f(ε p ) relation is also valid for any uniaxial tensile test. But the punching test induces a complex deformation state, with strong shearing of the material. This situation meant that a multiaxial criterion had to be used in the three dimensional space of plastic strains. The isotropy of the mechanical properties of the silicon-iron material has first been verified after tensile testing along the rolling, tranverse, and 45° angle directions. As a consequence, we chose the Levy-Mises criterion [START_REF] Adda | Eléments de métallurgie physique -Déformation plastique[END_REF] which expresses the equivalent plastic deformation ε eq p as a function of the principal plastic deformations (ε I p , ε II p , ε III p ) along the three principal directions (x I : traction direction, x II : width direction, x III : thickness direction) :

d! eq p = 2 9 (d! I p -d! II p ) 2 + (d! II p -d! III p ) 2 + (d! I p -d! III p ) 2 (10)
The plastic strain takes place at constant volume and the deformation is homogeneous so that the the following relation is experimentally verified :

dε II p ≈ dε III p ≈ -(1/2) dε I p
The following relations are immediately obtained :

dε eq p = dε I p => ε eq p = ε I p = ε p Uniaxial plastic strain can also be identified to equivalent plastic strain for the particular sheet used : HV = f(ε p ) is equivalent to HV = f(ε eq p ). This relation can then be employed immediately after a microhardness test on the cutting edge of a punched N.O. 3% Silicon -Iron sheet to deduce the local equivalent plastic strain level.

Results : derivation of a HV = f(ε eq p ) law

The results are shown in figure 9. The microhardness value increases rapidly in the initial stages of plastic deformation. The rate of increase then slows down. This curve can be compared with the stress-strain curve of this material.

The fitting law chosen is that used to model the mechanical behaviour of colddrawable materials [START_REF] Maillard | CETIM[END_REF][START_REF] Adda | Eléments de métallurgie physique -Déformation plastique[END_REF] :

HV = HV° + !.(" eq p ) # (11)
δ and α oefficients are numerically calculated. The strain-hardening coefficient is : α = 0.41 (± 0.03). The initial hardness is HV° = 196 (± 3). δ = 19.5 (± 1.2)

Application to a punching test

Experiment

A punching test machine has been made which is coupled with a tension / compression machine. The punching speed is 1 mm/min. The diameter of holes is 5 mm. Experiments were carried out under normal conditions : 20 °C , atmospheric pressure.

Microhardness measurements

The punched sheet was cut along a diameter of a hole and polished on the transverse section. Numerous microhardness tests were made close to the cutting edge on the polished section. The first results consisted of iso-hardness maps (as shown in figure 10). These three-dimensional data (HV, x, y) were transformed to twodimensional ones giving hardness value as a function of the distance from the cutting edge (figure 11). The variation of microhardness can be modelled as follows :

HV = HV° + p (x + q) r (12)
with x the distance from the cutting edge given in mm.

The constants p, q and r are numerically calculated. The exponent r is significantly large (r = 4.9 (± 2.0)), the decrease of HV = f(x) is consequently fast. Incertitudes in this model are important because the dispersion of results is important. (p = 21 (± 5), q = 0.64 (± 0.30) mm).

Development of complete models

From HV = f(x) and HV = f(ε eq p ) a relation ε eq p = f(x) can easily be deduced, giving equivalent plastic deformation level versus distance from the cutting edge :

! eq p = K (x + q) u (13)
This curve plotted in figure 11 gives information concerning the zone affected by the punching in spite of the strong incertainties (K = 2.5 (± 1.3)). Plastic strain is very high at the cutting edge, decreases rapidly (the exponent u is very high : u = 12 (± 4)), and is lower than 0.5% after x=0.5 mm. However, the effect of the small plastic strains on the magnetic properties is not negligible and in practice, the influence zone of the punching extends up to 1 mm from the cutting edge.

On the other hand, knowing the relationship between the change of magnetic

Future developments

The next stage would consist in modelling such a punched sheet via a numerical finite element method with a sufficiently refined mesh. Then, the B m (H m ,x) and P(B m ,x) characteristics of different elements would be affected as function of their mean distance from the cutting edge. This may result in an improvement of the modelling procedures of rotating electrical machines. Of course, many improvements may be possible concerning the global precision of results and models, so that incertitudes of parameters could decrease.

Conclusion

The present work consisted first of an attempt to develop new functions allowing a "plastic strain level" parameter to determine B m (H m ) and P(B m ) curves of a Non Oriented 3% Silicon -Iron sheet. The equivalent plastic strain profile ε eq p = f(x) near the cutting edge of the same punched material were then measured. This last relation has been obtained using a Vickers microhardness test. A mathematical function giving magnetic properties profiles versus distance from the cutting edge followed, which could be introduced into numerical models (mainly finite element modelling) of rotating electrical machines.

  properties and plastic deformation (after a tensile test), the two kinds of profiles of magnetic properties can be deduced : [Magn. Prop.] = f(x). B m (H m ) and P(B m ) curves become B m (H m ,x) and P(B m ,x) three-dimensional functions, which have been plotted in figure12.

Acknowledgements

The authors wish to thank professors M.CLAVEL and M.KANT for their assistance and useful discussions.