Patricia Garcia-Muñoz
email: garciamunoz@unistra.fr

Christophe Lefèvre

Didier Robert

Nicolas Keller
email: nkeller@unistra.fr

Christophe Lefevre

Ti-substituted LaFeO3 perovskite as photoassisted CWPO

Keywords: Ti-substituted LaFeO3 perovskite, photoassisted CWPO, photocatalysis, mineralization, water treatment, advanced oxidation process

teaching and research institutions in France or abroad, or from public or private research centers.

UV-A light. Thus, the photoassisted CWPO with Ti-substituted LaFeO3 catalysts may overcome some drawbacks of single AOPs by combining higher rates at complete mineralization.

1-INTRODUCTION

Over the last decades, water treatment usually based on mechanical, physical, chemical or biological processes [1] had to face with the increase in both the volumes and the concentrations of polluted water streams, and in the decrease in biodegradability of the pollutants to be removed. In addition to the implementation of increasingly stringent and constraining environmental govern regulations, the heterogeneity of targets and of water matrix compositions and loads, as well as the emergence of biorecalcitrant pollutants has created a strong incentive for the development of new cost-effective, sustainable and high efficiency technologies or for the intensification of already existing technologies aiming at the abatement of pollutants in order to meet ever stricter legislation requirements.

Advanced Oxidation Processes (AOPs) have been successfully applied for the removal in water of a large panel of refractory compounds that are not degraded by conventional treatments [2][3][4][5][6][7][8][9][10]. These promising treatments are based on the generation of oxidative radicals HOx° (HO° and HOO°) that react with the pollutant and subsequently with the reaction intermediates, leading to their oxidation and in fine to their removal from water. A wide variety of AOPs have been studied in detail such as, ozonation, photolysis, photocatalysis, Fenton process or Catalytic Wet Peroxide Oxidation (CWPO), Catalytic Wet Air Oxidation (CWAO), ...etc. Among them, the Fenton process, or its analogous heterogeneous CWPO, and photocatalysis, have gained special attention due to their high efficiency and relatively low cost [6].

Both processes operate through different reaction mechanisms and under different working conditions. In a typical Fenton process, the generation of HOX° is achieved by the decomposition of H2O2 in the presence of metallic ions, in most of the cases iron. Despite a relatively high initial reaction rate, the Fenton AOP suffers mainly of the necessity to work at acidic pH and of the generation and precipitation of sludge due to the complexation of iron with short-chain acids. This results in a continuous loss of active phase and to the formation of wastes that strongly reduces the viability of the process. The heterogenization of the Fenton process by incorporating the active phase in a catalytic solid, known as CWPO, overcomes these issues, but decreases the process ability to achieve a complete mineralization of the pollutant an effluent and strongly reduces the reaction rates when compared to the homogeneous Fenton counterpart. Performing CWPO under light in the so-called photo-assisted CWPO or heterogenized photo-Fenton process is a promising strategy allowing the catalyst reactivity to be increased, although the constraints of acidic conditions and the incomplete mineralization are still important drawbacks [11,12]. By contrast, heterogeneous semiconductor photocatalysis is an AOP using the redox surface properties developed by an irradiated semiconductor material with adequate band gap for performing surface reactions between the adsorbed reactants and the HOX° oxidizing species produced from the electron and hole photogenerated charges. While the photocatalytic process can achieve a total mineralization of the refractory pollutants and enables working in a wide pH range value, it suffers unfortunately from far lower reaction rates than homogeneous AOPs like Fenton, and consequently from longer process durations [6].

Therefore, an approach for achieving simultaneously a higher reaction rate and a higher mineralization degree with no loss of active phase with time consists in the combination of both photoassisted CWPO and photocatalysis processes. While physical mixtures of catalysts have been used [13][14][15][16], the design of a single phase catalyst enabling both processes to take place remains an interesting strategy scarcely investigated. The key-parameter remains that a unique catalyst needs to perform efficiently the decomposition of hydrogen peroxide into HOX° while acting simultaneously as heterogeneous photocatalyst under similar operating conditions.

In this frame, only few works have been reported on the combination of both photo-assisted CWPO and photocatalysis AOPs. ZnFe2O4 spinel ferrite was employed by Cai et al. [17] as visible lightassisted heterogeneous Fenton catalyst for the degradation of Orange II in water. While the photocatalyst displayed ability to split H2O2 and allowed a total Orange II removal with a low leaching of iron species (0.02%), only a 60% TOC removal was achieved. Similarly, Mechakra et al. [18] used natural iron oxide (containing mainly a-Fe2O3) for degrading the Linuron herbicide in water under UV and solar light, although only an 80% COD reduction was obtained at complete Linuron removal.

Soltani and Lee reported that the heterogeneous photo-Fenton catalytic degradation of toluene in water under visible light led to 85% mineralization for a complete toluene removal under visible light on a Ba-doped BiFeO3 perovskite with an optimum 0.12 Ba/Bi molar ratio [19]. Substitutional Ba within the perovskite structure improved the photo-Fenton catalytic degradation in weakly acidic conditions, due to the efficient redox cycling of iron species, and to the presence of abundant oxygen vacancies resulting from the distortion (or from the induced metastability) of the flexible perovskite structure when partially substituted. Also, Garcia-Munoz et al. proposed that the presence of both ilmenite and rutile semiconductor phases within a natural ilmenite mineral (FeTiO3 with ca. 15% of rutile TiO2) enabled to obtain higher rates and mineralization yields under solar light than those obtained in the separate processes, with a complete phenol and H2O2 conversion for a TOC conversion of 95%, with a negligible 0.5% iron leaching [20].

Lanthanum ferrite (LaFeO3) perovskite is an interesting p-type semiconductor with a narrow band gap of 2.65 eV and one of the most common ABO3 perovskite type oxides investigated for being applied as gas sensor, electrode for solid oxide fuel cells, optoelectronic and magnetic materials or heterogeneous catalysts [21]. The transition metal B-cation presents redox characteristics that allow significant mobility of oxygen, thus conferring activity in redox reactions [22] to the perovskite material. In addition, the material takes great advantage of its composition versatility, i.e. A1-xA'xB1-yB'yO3±d with the possibility of A-and/or B-cation partial substitution and the consequent geometric and charge constraints [22], for modifying its textural, structural and electronic properties, and consequently for tuning its redox and catalytic properties. Therefore, the incorporation of divalent or trivalent cations into La or Fe sub-lattices has been investigated. Cation-substituted ferrites have been mostly applied as photo-Fenton catalysts, using e.g. Cu-doped LaFeO3, or Fe-, Mn-, Co-or Cu-based lanthanum perovskite, the Fe-based one being the most active in the oxidation of acetic acid in water [23,24]. LaFeO3 and doped-LaFeO3 perovskites were not extensively studied as photocatalysts [21,25].

The effect of the partial substitution of La with divalent Ca or monovalent Li ions [26,27], and of Fe with Zn or Mn [28,[START_REF] Dong | Photocatalytic activities of LaFe1-xZnxO3 nanocrystals prepared by sol-gel auto-combustion method[END_REF] has been investigated. Parrino et al. synthesized Cu-substituted LaFeO3 with enhanced activity in the gaseous propanol degradation under solar light [25]. Although its low activity under visible light was improved through band-gap engineering by cation incorporation [27,[START_REF] Rashmi | [END_REF], the results remained far from complete mineralization, whereas LaFeO3/AgBr, LaFeO3/TiO2 or LaFeO3/SnS2 heterojunction photocatalysts led very recently to enhanced performances under visible light compared to the bare LaFeO3 photocatalyst, thanks to a Z-Scheme mechanism or to inter-conduction band electron transfer [15,31,32].

Here, we report for the first time on the synthesis via a simple sol-gel method of reusable Tisubstituted LaFeO3 catalysts for use in water treatment, that combine both photo-assisted CWPO and photocatalysis processes in order to simultaneously improve the reaction rates and the TOC conversion at circumneutral pH conditions in comparison to the single AOP counterparts, while reducing the iron release into the water for improving the catalyst stability. The removal of 4-Cl-Phenol in water was selected as test reaction under UV-A light, since 4-Cl-Phenol is a model pollutant widely used in AOP studies as being representative of industrial wastewater refractory pollutants.

2-MATERIALS AND METHODS

Materials

Analytical grade chemicals were used without further purification. 4-Cl-Phenol (>99%) and H2O2 (>30%) were purchased from Sigma Aldrich. La(NO3)3 hexahydrate, Fe(NO3)3 nonahydrate and citric acid hydrate (C6H8O7xH2O,99.5%) were purchased from Sigma Aldrich. Commercial Aeroxide© TiO2 P25 was obtained from Evonik.

Synthesis of Ti-modified LaFeO3

Ti-modified LaFeO3 materials were obtained by modifying a classical sol-gel Pechini synthesis. In this method, Lanthanum nitrate hexahydrate and iron nitrate nonahydrate were dissolved in 30 mL distilled water at 108.3 g/L and 133 g/L, respectively, and the metallic ions undergo complexation by subsequent addition of citric acid at 70 g/L, corresponding to a stoichiometric molar ratio in respect of the metallic ions. Controlled amounts of TiO2 Aeroxide P25 were further directly introduced under stirring into the aqueous sol, corresponding to nominal amounts of 5, 10, 15, 20, 30 and 50 wt.% in respect of the theoretical amount of LaFeO3 perovskite obtained. The resulting suspensions were maintained at 80°C for 2 days (2°C/min heating rate) in order to induce the complete gel formation.

The calcination of the dried gel was performed using a heating cycle as reported by Gosavi et al. [33] with heating rates of 5°C/min, consisting in holding the temperature at 600°C for 2 h, before to further maintaining a temperature plateau at 700°C or 800°C for 2 h if necessary.

Without considering the titania phase, the stoichiometric reaction forming the LaFeO3 perovskite structure is as follows (Eq.1) [34]:

!"($% & ) & (6* + % + -.($% & ) & (9* + % + 0 1 * 2 % 3 (* + % → !"-.% & + 60% + + 3$ + + 6* + % [Eq.1]
Non-modified lanthanum ferrite powders were synthesized as reference materials by following the same protocol without any addition of titania, with a similar calcination procedure at 600-800°C.

Characterisation techniques

X-ray diffraction (XRD) pattern have been recorded at room temperature in a θ/θ mode on a Brucker D8 Advance diffractometer equipped with a monochromatic copper radiation source (Kα = 1.54056 Å) with a scan step of 0.02°. Some patterns have been investigated by Rietveld refinement with the Fullprof software for which the modified Thompson-Cox-Hasting function was chosen to generate the line shape of the diffraction peaks. Instrumental broadening has been previously

determined by measuring the scattering from corundum (NIST standard SRM 1976b) [35,36].

The surface area measurements were carried out on a Micrometrics Tristar 3000 using N2 as adsorbent at -196 °C with a prior outgassing at 250°C overnight to desorb the impurities or moisture.

The iron and titanium contents in the catalysts were determined by Inductively coupled plasma optical emission spectroscopy (ICP-OES) carried out on an Optima 7000 DV spectrometer (Perkin Elmer).

X-Ray Photoelectron Spectroscopy (XPS) characterization was performed on a ThermoVGMultilabESCA3000 spectrometer (Al Kα anode at hλ = 1486.6 eV). The energy shift due to electrostatic charging was subtracted using the adventious sp2 carbon C 1s band at 284.6 eV.

Contributions with Doniach-Sunjic shape [37] and a' S-shaped' Shirley type background [38] were used.

Typical reaction procedure

The experiments were carried out in a batch beaker-type glass reactor at atmospheric pressure, at room temperature and using H2O2 as main oxidant. 50 mg of catalyst was dispersed under stirring in a 100 mL aqueous solution of 4-chlorophenol at 25 mg/L concentration, corresponding to an initial organic carbon concentration of 14.8 ppm and to a catalyst load of 0.5 g/L. Prior to irradiation, the suspension has been stirred for 1h in the dark to ensure the establishment of the adsorption/desorption equilibrium. After adding hydrogen peroxide at the stoichiometric concentration corresponding to a complete mineralization of the initial pollutant (125 mg/L), the suspension was exposed to a 60 W/m 2 irradiance UV-A light centered at 365 nm, provided by Philips 24W/10/4P lamps. At each time interval, 15 mL of solution has been sampled and then filtered through 0.20 μm porosity filter to remove the photocatalyst powder if any, before the concentration of 4chlorophenol has been determined by UV-Visible spectrophotometry by monitoring the disappearance of the main absorption peak at λ=224 nm [39]. Total Organic Carbon measurements were performed using a Shimadzu TOC-L analyzer to determine the organic carbon load. Hydrogen peroxide concentration was measured by colorimetric titration using the TiOSO4 method [START_REF] Eisenberg | Colorimetric Determination of Hydrogen Peroxide[END_REF] and the Fe leached during time-course of reaction was quantified by the ortho-phenanthroline method [START_REF] Sandell | Colorimetric Determination of Traces of Metals[END_REF].

3-RESULTS AND DISCUSSION

Catalyst characterization

The Fe and Ti atomic contents of the Ti-modified LaFeO3 samples were obtained by elemental chemical analysis (Table 1). It confirmed the presence of titanium inside the materials, with an increase in the Ti at.% content from 2.1% to 14.8% when increasing the nominal TiO2 wt.% content used for the synthesis from 5 to 50%. The increase in the Ti at.% content was accompanied by the concomitant decrease in the Fe at.% content from 23% for the Ti-free material down to 9.6%.

Figure 1 shows the XRD patterns of the Ti-modified LaFeO3 materials calcined at 600°C, 700°C and 800°C. The profile Rietvelt refinement of the diffractograms of selected samples is shown in Figure S1, while the refined cationic distribution in the LaFeO3 structure and the crystallographic data of the refined samples are provided in Table 2 and Table S1, respectively. The XRD patterns of Ti-free materials displayed the most intense diffraction peaks at 2θ = 22.6°, 32.2°, 39.7°, 46.1°, 57.4°and 67.3° corresponding to the diffraction of the (100),( 110),( 111),( 200),( 210) and (220) planes of the LaFeO3 phase, respectively. Further, whatever the titanium content and the calcination temperature, all the patterns could be indexed in the Pbnm orthorhombic unit cell of LaFeO3 (see Table 2, Table S1 and Further, the determination of the cationic distribution within the structures was performed considering that Ti can move to both cationic sites. The Ti/Fe and Ti/La occupations were then separately refined and refinements are presented in Table 2. It has been evidenced that Ti preferentially occupies the La site, so that the materials could be labelled as LaxTiyFeO3. This behavior is rather surprising since La is much bigger than Fe. Similar results were observed by Hou et al. with the substitution of the small size Li + ion into the La-sites of LaFeO3 [27] prepared by sol-gel in the presence of acetic acid, and by Li et al. in the reverse emulsion synthesis of La1-xCa 2+ xFeO3 catalysts [26]. By contrast, Cu 2+ preferentially occupied the Fe 3+ sites in Cu-doped LaFeO3 prepared by hydrothermal or citrate autocombustion synthesis [24,25], while partial substitution of La by Ag and of Fe by Co was achieved in LaFeO3 [42]. An increase in the La-to-Ti substitution ratio was observed with the increase in the nominal TiO2 content, as well as with the increase in the calcination temperature (Table 2). However, the XRD patterns also revealed that the partial substitution of La by Ti led to an increase in the amorphous content of the catalyst.

Figures S1).
The partial substitution resulted in a significative increase in the surface area of the material, whatever the calcination temperature, with e.g. surface areas in the 17-40 m 2 /g range at 800°C vs. 8 m 2 /g for LaFeO3. Further, the Ti-substituted LaFeO3 showed a better resistance to the crystallite growth with the increase in the calcination temperature. Indeed, the significant increase in the mean crystallite size observed for LaFeO3, from 16 nm at 600°C to 23 nm at 800°C, was not observed in the case of Tisubstituted LaFeO3, that maintained smaller mean crystallite sizes whatever the calcination temperature. Similarly, the doping of LaFeO3 by Li or Cu ions was also reported to suppress the growth of large crystallites during the thermal treatments compared to the undoped counterparts [24,25].

The UV-Vis absorbance spectra of different Ti-substituted LaFeO3 catalysts is shown in Figure S2.

Whatever the Ti content, they displayed the usual pattern for LaFeO3 materials [27,[START_REF] Rashmi | [END_REF], with a broad absorption band in the UV-vis range till wavelengths of about 600 nm. This indicated that Ti-substituted LaFeO3 materials, similarly than the LaFeO3 material, could potentially act as photocatalyst within this wavelength range.

The morphology of the Ti-substituted LaFeO3 was affected by the Ti content, as shown in the SEM images of Figure S3. In the Ti-free material, the presence of well-defined grain boundaries of LaFeO3 with a prismatic structure was evidenced (A-B), while the incorporation of titanium provoked an agglomeration of the structure (C-D), also responsible for an increase in the mesoporosity. This effect was all the more pronounced that the titanium content was increased (E-F).

XPS analysis of the surface shown in Figure S4 in the case of the pristine LFO-800 and of the LFTi10-800 catalysts evidenced that La and Fe species are present as La 3+ and Fe 3+ ions, whether the ferrite was modified by Ti or not. Indeed, on the pristine LaFeO3 material, the La 3d core level spectra revealed the presence of a La 3d5/2 -La 3d3/2 orbital doublet contribution at 833.4 eV and 850.1 eV (spin orbit splitting of 16.7 eV [43][44][45] and multiplet splitting of 3.8 eV [46]), characteristic of La 3+ species. Also, the presence of Fe in the formal oxidation state +3 was confirmed by the binding energies of Fe 2p3/2

and Fe 2p 1/2 orbitals at 710.3 eV and 723.7 eV, with a 13.4 eV spin orbit coupling [46,47], together with the low intensity and broad shake-up satellite peak at about 718 eV characteristic of Fe 3+ ions [48,49].

After substitution of La by Ti within the perovskite structure, the XPS Ti 2p orbital profile evidenced a single contribution, with the doublet related to Ti 2p3/2 -Ti 2p1/2 spin-orbit components at 457.3 eV and 463.0 eV, characteristic of Ti species in lower oxidation state, and that might be assigned to Ti 3+ substituting La 3+ in the perovskite network [d]. It was worth nothing that this resulted also in a slight upward (+0.6-7 eV) and downward (-0.5 eV) shift of the La 3+ and Fe 3+ binding energies, respectively.

The upward shift observed for La 3+ is characteristic of an electron deficiency induced by its chemical environment. Here, in La-O-Ti configurations, it might result from the O → Ti electron transfer (Ti being more electronegative than La), that would lead to shift the electronic density of the La-O bond towards the more electronegative oxygen atoms. Similarly, but in a mirrored reversed manner, the downward shift observed for Fe 3+ in Fe-O-Ti configurations might result from the Ti →O electron transfer (Ti being less electronegative than Fe), that would lead to shift the electronic density of the Fe-O bond towards the less electronegative Fe atoms.

Catalytic activity

First, the performances of non-modified LaFeO3 reference catalysts were evaluated for the degradation of 4-Cl-Phenol in water in absence and in presence of H2O2. Without H2O2, a very low photocatalytic activity was observed, and 42% of phenol removal with no TOC reduction was achieved in 240 min in the most efficient case using the LF-800 catalyst (Figure S5). Further, Figure 2 A-L shows the evolution of 4-Cl-Phenol concentration, TOC, H2O2 decomposition and iron leached during the photo-assisted CWPO process performed on the LaFeO3 catalysts and selected Ti-substituted LaFeO3 catalysts. The results obtained with the complete LaxTiyFeO3 catalyst series are reported in Figure S8.

LaFeO3 catalysts in the photo-assisted CWPO

Non-modified LaFeO3 materials were first used as reference catalysts in the combined photoassisted process. Whatever the calcination temperature, the pristine LaFeO3 perovskite showed ability to decompose H2O2 in a typical photo-Fenton reaction (Figure 2 A-B-C). The LF-600 catalyst led to a total depletion of H2O2 in 120 min, with a Cl-phenol complete oxidation in 150 min and a mineralization rate of 85%. Both the LF-700 and LF-800 catalysts decomposed H2O2 slower than their LF-600 counterpart. Indeed, they needed about 300 min of reaction to achieve full H2O2 decomposition, while the complete phenol abatement was delayed to 210 and 150 min, respectively, with a TOC removal of 88% and 75%, respectively. The different behavior observed as a function of the calcination temperature could be related to the perovskite structure. The robustness of the material in terms of iron release to the water was influenced by the calcination temperature and the iron leaching was reduced from 2 mg/L at 600°C down to 0.8 mg/L at 700°C and 0.5 mg/L at 800°C. The lesser robustness and the consequent lesser stability of the LF-600 catalyst was proposed to be responsible for the faster H2O2 decomposition. Nevertheless, the greater H2O2 decomposition rate did not result in a faster TOC disappearance which means small catalyst efficiencies as corroborated by the incomplete effluent mineralization. On the other hand, the limited photocatalytic activity of those materials under UV-A light (Figure S5) did not enhance the mineralization degree vs. the one obtained for photo-Fenton process.

CWPO reaction in the dark

Preliminary CWPO experiments performed on pristine and Ti-substituted LaFeO3 evidenced the low oxidation ability of the catalysts in the dark (Figure S6 A-C for the catalyst series calcined at 800°C). In the best case, the H2O2-assisted oxidation of 4-Cl-phenol only reached 40% after 360 min of reaction while a total H2O2 conversion was obtained, and very low and stable TOC mineralization yields within the 6-24% range were achieved. This typical CWPO behaviour was related to the large generation of short-chain acids (formic, oxalic and acetic) during the process (Figure S6C), known to stop the reaction due to the formation of highly stable iron complexes.

Ti-substituted LaFeO3 catalysts calcined at 600°C in the photo-assisted CWPO

First, the incorporation of Ti inside the LaFeO3 catalysts did not inhibit the catalyst ability to decompose H2O2 into HOX° radicals used to further oxidize the organic compounds. For the LFTi catalysts calcined at 600°C (Figure 2 D-G-J), 100% of H2O2 decomposition was obtained whatever the iron content in the material. However, as expected, the lower the iron content, the slower the H2O2 decomposition. The apparent pseudo first-order kinetic rate constants of H2O2 decomposition evidenced the highest depletion rates for smaller Ti/Fe ratios, at 0.019 min -1 for LFTi10 vs. 0.007 min -1 and 0.008 min -1 for LFTi20 and LFTi50, respectively (Table 3). The evolution of the H2O2 conversion was directly related to the Cl-Phenol removal profile, that showed a faster abatement with catalysts with higher iron contents. Indeed, 120, 150 and 300 min were needed for the total degradation of the phenolic compound using LFTi10, LFTi20 and LFTi50 catalysts, respectively, whereas the apparent kinetic rate constant for Cl-phenol disappearance was decreased from 0.022 min -1 for LFTi10 down to 0.008 min -1 for LFTi50 (Table 3).

By contrast to both the phenolic compound and the H2O2 profiles, the TOC profiles were fitted by a zero-order kinetic model as usually occurs in photocatalytic processes. The mineralization rate obtained with the Ti-substituted catalysts displayed a maximum for the LFTi10 catalyst at r0= 0,13 mg/L min, before to substantially decrease with the increase in the Ti content, down to r0= 0,03 mg/L min for the highly loaded LFTi50 sample (Table 3). Despite the strong differences in terms of rate, all catalysts showed a high activity level with XTOC values between 83% (for LFTi15) to 98% (for LFTi10 and LFTi20). The values of XH2O2 obtained with all the materials calcined at 600°C corroborated that existence of additional reactions to decompose the peroxide (Table 3), total H2O2 conversions were achieved even when working at a high Ti/Fe ratio.

First, the H2O2 conversion profile can be influenced by additional surface as well as homogeneous reactions. Indeed, the adsorbed peroxide can act as charge acceptor and be therefore reduced or oxidized by the photogenerated charges (e-/h+) issued from the perovskite (Eq. 2) for forming HO°X (HO° and HOO°) radicals (Eq. 2-4) [13]:

!" 7 89 : -.% & → ;< . = + ℎ ? [Eq.2]
. = + * + % + → *%°+ %* = [Eq.3]

ℎ ? + * + % + → *%%°+ * ? [Eq.4]
Secondly, the introduction of titanium inside the structure did not improve the stability of the material in terms of iron leaching when calcination is performed at 600°C, with amounts of leached iron released to the solution of about 1.5-2 mg/L. Consequently, the low stability of the materials was responsible for the very probable strong contribution of the homogeneous Fenton process to the peroxide decomposition. These different reactions could provoke a different use of the oxidant, since the systems differed in terms of efficiency of the oxidant use, different mineralization yields being achieved. For instance, the reaction with LFTi5 obtained a ξ=0.87 efficiency when 100% of peroxide was decomposed, while by contrast an efficiency of 0.96 was obtained for the same total peroxide conversion using the LFTi50 catalyst (Table 3).

Whatever the Ti/Fe ratio, no complete mineralization of the effluent was reached on catalysts calcined at 600°C. This typical behavior of CWPO-like processes is associated to the presence of iron in solution, here resulting from the iron leaching. It has been reported that the iron in solution reacts with the latest oxidation intermediates, e.g. short-chain acids as oxalic acid, leading to the formation of iron-oxalate complexes [11,50]. These complexes are slower photodegraded which can confirm the incomplete TOC conversion obtained even in the presence of notable homogeneous Fenton contribution (Eq.5).

[-. &? (B0%% = )] +? → ;D -. +? + 0% + + B [Eq.5]

Influence of the calcination temperature on the photo-assisted CWPO using Ti-substituted LaFeO3 catalysts

Considering the increase in the catalyst robustness observed on the LaFeO3 catalysts with a reduced Fe leaching when increasing the calcination temperature, a similar study was performed in the case of the LaxTiyFeO3 catalysts (Figure 2 and Figure S8). Whatever the Ti content, the LFTi-700 catalysts achieved a total H2O2 decomposition within the first 180 min of reaction (Figure 2 E-K), with smaller kH2O2 than on LFTi-600 (Table 3). The catalyst stability was improved compared to that of LFTi-600, with a reduced iron release to the solution lower than 1 mg/L, and all the more reduced as the Ti content increased. Nevertheless, the amount of leached iron was still high enough to partially contribute with homogeneous photo-Fenton [51]. The evolution of Cl-Phenol concentration showed an induction period which was most pronounced at lower Ti content, especially when using the LFTi10-700 catalyst which showed a lag phase of around 120 min. This induction period has been associated

to the Fe(III) to Fe(II) reduction by H2O2 and also by light effect as several authors has reported (Eq. 6-8) [20,52,53]. After the initial consumption of peroxide producing Fe(II), production of HO° can be achieved following Eq. 8. Over higher Ti content catalysts, the absence of any induction period for the 4-Cl-phenol concentration evolution might be ascribed to an additional photocatalytic contribution to the phenol degradation.

! The increase in the calcination temperature to 800°C further improved the catalyst stability, with a substantial reduction of iron leaching, amounts of iron leached lower than 0.2 mg/L being detected whatever the Ti content. At this temperature, by contrast, 100% of H2O2 conversion was not obtained on the LFTi-800 catalysts, and the time required for achieving the final H2O2 conversion level increased as the Ti/Fe ratio increased (Fig. 2 I-L). The time needed for the total removal of the phenolic compound increased from 120 min to 330 min with the increase in the Ti content from LFTi10 to LFTi50, respectively.

Figure 3 shows the correlation between the activity, expressed in terms of apparent kinetic rate constant of TOC disappearance and mineralization degree, and the stability of the catalysts, expressed in terms of total iron leached from the solids. Whatever the calcination temperature, the kinetic rate constant displayed a volcano-like profile, centered around catalysts containing a 2.1-3.2 at.% content of titanium, while it strongly dropped down when further increasing the incorporation of titanium.

Increasing the temperature allowed to increase the maximum rate constant from 0.13 mg/L/min at 600°C to 0.16 mg/L/min at 700°C and further to 0.18 mg/L/min at 800°C, overcoming in all cases the rate of 0.11-0.12 mg/L/min achieved on the non-modified bare LaFeO3 catalysts.

Although some differences were observed, the TOC conversion was not strongly affected by the at.% content of titanium for materials calcined at 600°C and 700°C, and the TOC conversion remained at a high level, within the 83-98% and 80-98% range, respectively. By contrast, the incorporation of titanium inside the structure calcined at 800°C led to a volcano-like profile for the TOC conversion, similar to that shown by the kinetic rate constant, a 100% mineralization degree being achieved with the Ti-substituted LaFeO3 catalyst with 3.2 at.% of Ti.

Also, the incorporation of titanium inside the structure calcined at 600°C led to reduce the iron leaching to the solution, from 2.0 mg/L for the non-modified LaFeO3 catalyst down to 1.4 mg/L for a Ti at.% of 14.8. However, the iron leaching remained at a very high level of 1.4 mg/L for the Ti-rich perovskite structure, so that a pronounced contribution of homogeneous Fenton is expected. The positive effect related to the incorporation of titanium was more pronounced when increasing the calcination temperature, as evidenced by the Fe leached profile in Figure 3B and 3C. This allowed to strongly reduce the contribution of homogeneous Fenton to the TOC conversion and the TOC removal kinetic rate constant.

Especially, the Ti-substituted LaFeO3 catalyst calcined at 800°C with 3.2 at.% of Ti. displayed a very good stability, with a negligible iron release of 0.05 mg/L to the solution that corresponded to 0.1% of its total iron content. As a result, the homogenous contribution could be considered as negligible and the higher mineralization rate at 0.18 mg/L with a final 100% TOC conversion only resulted from heterogeneous surface reactions. The heterogeneous mechanism was corroborated by comparing the CWPO-photoassisted reaction to the homogeneous photo-Fenton reaction performed with 0.05 mg/L of Fe 3+ (Figure S7). Indeed, despite 0.05 mg/L is the total Fe amount released at the end of the reaction in the case of the heterogeneous system and therefore remains higher than the real Fe amount during the main part of the process, and that the homogeneous system benefited from a maximum irradiation compared to the slurry reactor, the heterogeneous surface reaction contribution was overcoming by two orders of magnitude that of the homogeneous photo-Fenton process, with apparent 1 st order kinetic rate constants of 2.5 10 -2 min -1 and 5.6 10 -4 min -1 for the Cl-phenol degradation, respectively.

Further, considering that a theoretical ξ=1 efficiency of peroxide use in Fenton-like processes means that H2O2 and the formed radicals does not suffer from any detrimental scavenger reactions, this catalyst displayed a ξ=1.11 H2O2 efficiency while achieving 100% TOC removal with a 90% H2O2 conversion. So, we proposed that the LFTi10-800 catalyst was active simultaneously in both photoassisted CWPO and photocatalysis. We cannot rule out that more generally the LFTi-800 catalysts with other Ti contents also showed a photocatalytic contribution to the degradation activity, since 100% H2O2 conversion was never achieved with this catalyst series.

The effect of partial substitution of La and/or Fe on the photocatalytic properties of the ferrite has been poorly described in the recent literature. Based on the recent works of Parrino et al. on Cu-substituted LaFeO3 catalysts, we propose also that the superiority of the LFTi10-800 catalyst with optimal Ti substitution may result from the presence of oxygen vacancies [27]. They related the higher activity of the Cu-containing catalyst with an optimum at 10 at.% substitution rate with the presence of oxygen vacancies and with the electron/hole recombination, evidenced through XPS analysis and transient photocurrent measurements. The cation substitution was reported to give rise to an electronic unbalance compensated by a change in the oxidation state of a part of the Fe(III), being oxygen vacancies formed to preserve the electroneutrality, and to adjust with the distortion of the anionic lattice [54]. An optimum in the substituted heteroatom content was also observed by Phan et al. in the degradation of dyes by heterogeneous photo-Fenton on Cu-substituted LaFeO3 catalysts with 15 at.% Fe substitution by Cu ions [24]. Hou et al. also observed an optimum in the enhancement of the photocatalytic activity of Li-substituted LaFeO3 catalysts, with 3 at.% of La substitution [27].

Stability tests of the LFTi10-800 catalyst in the photo-assisted CWPO

One of the main shortcomings of catalytic water treatments remains the stability of the catalysts, and the determination of the active phase release from the catalyst to the water during the process has to be completed with reusability tests for evidencing the catalyst stability. Figure 4 shows the very good stability of the LFTi10-800 catalyst for five consecutive runs, with catalyst recovery by powder filtration. Apparent kinetic rate constants for the Cl-phenol disappearance of 0.23±2 min -1 were obtained with the maintain after the run #5 of a global mineralization yield of 99%±1% after 120 min of reaction, while a residual loss of Fe of 0.03 mg/L was observed, corresponding to a 0.09% Fe release in respect to the Fe content of the catalyst.

However, the XRD pattern of Ti-substituted LaFeO3 catalysts after test shown in Figures S1D evidenced the formation during the reaction of rutile TiO2 phase in very small amount (3-6%).

However, this has no detrimental effect on the catalyst activity in terms of pollutant degradation and of TOC conversion, as well as on its stability in terms of iron leaching and of reusability. By contrast, we could not rule out that the formed TiO2/LaxTiyFeO3 heterojunction within the catalyst was beneficial for improving the photogenerated charge separation, as recently proposed for LaFeO3-based heterojunction photocatalysts [15,31,32], with possible electron transfer from the perovskite conduction band to that of TiO2 [15].

4-CONCLUSIONS

A series of novel Ti-substituted LaFeO3 materials with varied titanium content have been synthesized via a simple sol-gel method using commercial TiO2 as titanium precursor. The influence of the calcination temperature and of the titanium at.% content was evaluated upon both the activity in photoassisted CWPO under UV-A light and the stability of catalysts. The catalysts calcined at 600°C suffered from the iron leaching resulting in notable homogeneous photo-Fenton contribution, while the activity of the catalysts calcined at 800°C could be ascribed to heterogeneous surface reactions due to the increase in the catalyst stability with strongly reduced Fe leaching. The Ti-substituted LaFeO3 catalyst calcined at 800°C showed an optimum in activity for a 3.2 at.% content of titanium, with a higher mineralization rate than the Ti-free LaFeO3 counterpart, while achieving complete Cl-phenol removal and 100% mineralization at neutral pH over 5 cycles of reuse with stable efficiency and a limited Fe leaching lower than 0.1% of its total content. We proposed that this single-phase catalyst combined both photoassisted CWPO and photocatalytic processes. Works are ongoing for increasing the material crystallinity and for taking advantage of its band gap value for operating the combined CWPO and photocatalysis process under visible light. In addition, further works will deal with the elucidation of the active species formed during the combined process, and with the use of the magnetic properties of the Ti-substituted LaFeO3 materials for improving and simplifying the powder recovery process.

  Figures S1).Only α-Fe2O3 in small amount was observed as extra phase in some samples, while no

Figure 1 .

 1 Figure 1. XRD patterns of the Ti-modified LaFeO3 materials calcined at (a) 600°C, (b) 700°C and (c) 800°C. Dotted black lines corresponded to the main reflexes of the α-Fe2O3 extra phase formed in small amounts in some materials. LaFeO3: JCPDS card 75-0541; α-Fe2O3: JCPDS card 01-089-8104.

Figure 2 .

 2 Figure 2. Evolution of 4-Cl-Phenol (▪), TOC (•), H2O2 decomposition (○) and iron leached (▪) during the photo-assisted CWPO process over (A-C) the pristine LaFeO3 catalysts

Figure 3 .

 3 Figure 3. Mineralization rate, TOC conversion and total iron leached at the end of photoassisted CWPO process as a function of the Ti at. % in the Ti-substituted LaFeO3 catalysts calcined at: 600°C (A), 700°C (B) and 800°C (C). Operating conditions: [4-Cl-Phenol]0=25 mg/L; [H2O2]0=125 mg/L; T=25°C; [cat]=0.5 g/L. Trend curves have been drawn for visually evidencing the evolution profiles as a function of the Ti at.% content.

Figure 4 .

 4 Figure 4. Consecutive runs with reused LFTi10-800 catalyst. Operating conditions: [4-Cl-Phenol]0=25 mg/L; [H2O2]0=125 mg/L; T=25°C; [cat]=0.5 g/L.

Table 1 .

 1 Some physico-chemical properties of the Ti-modified LaFeO3 catalysts.

	Catalyst	Nominal content (% wt TiO2)	Fe (at.%)*	Ti (at.%)*	Ti/Fe molar ratio	S BET (m 2 /g)** 600°C 800°C 600°C 800°C dp*** (nm)
	LFO	0	23.0	0.0	0	17	8	16	23
	LFTi5	5	17.7	2.1	0.12	22	17	16	18
	LFTi10	10	16.0	3.2	0.20	45	28	15	16
	LFTi15	15	14.8	6.4	0.43	44	19	17	15
	LFTi20	20	12.6	8.0	0.63	44	20	20	17
	LFTi30	30	12.3	9.2	0.76	43	25	17	14
	LFTi50	50	9.6	14.8	1.66	56	40	14	17

*The Fe and Ti at. % contents were determined by chemical analysis after a microwave-assisted acidic dissolution in aqua regia at 185°C under autogenic pressure. ICP-OES was carried out on an Optima 7000 DV spectrometer (Perkin Elmer) at the Analysis Platform of IPHC-Strasbourg, France.

**The Brunauer-Emmett-Teller (BET) specific surface area has been calculated from the N2 adsorption isotherm.

*** derived from XRD pattern, as the average size of the coherent diffraction domains, calculated from the Scherrer equation applied on the most intense (1 1 0) plane diffraction peak with the usual assumption of spherical crystallites.

Table 2 .

 2 Refined cationic distribution in the LaxTiyFeO3 perovskite catalysts and weight percentage of extra phases obtained after Rietveld refinement

		La site distribution	Fe site distribution	%a-Fe2O3 (wt. %) %TiO2 (wt.%)
		La	Ti	Fe	Ti
	LFO-600	1	0	1	0	0	0
	LFO-700	1	0	1	0	0	0
	LFO-800	1	0	1	0	11	0
	LFTi10-600	0.98	0.02	1	0	0	0
	LFTi10-700	0.94	0.06	1	0	0	0
	LFTi15-800	0.95	0.05	1	0	15	0
	LFTi50-600	0.96	0.04	1	0	0	0
	LFTi50-800	0.8	0.2	1	0	3	0
	LFTi15-600_used	0.92	0.08	1	0	7	3
	LFTi15-800_used	0.86	0.14	0.62	0.38	12	6

Table 3 .

 3 Kinetic rate constants of H2O2 decomposition and Cl-Phenol oxidation, mineralization rate, Fe leached, H2O2 depletion percentage, TOC conversion and H2O2 efficiency parameters.

		k H2O2	k Cl-Phenol	r 0 TOC	[Fe]leached	XH2O2	XTOC
	T(°C)/ %Ti	(min -1 )	(min -1 )	(mg/L min)	(mg/L)	(%)	(%)	ε H2O2
	600°C/ LFO	0.018	0.021	0.11	2.0	100	85	0.85
	LFTi5	0.015	0.022	0.12	1.7	100	87	0.87
	LFTi10	0.019	0.023	0.13	2.0	100	98	0.98
	LFTi15	0.015	0.022	0.11	1.5	100	83	0.83
	LFTi20	0.007	0.025	0.12	1.6	100	98	0.98
	LFTi30	0.007	0.012	0.05	1.5	100	88	0.88
	LFTi50	0.008	0.008	0.03	1.4	100	96	0.96
	700°C/ LFO	0.012	0.022	0.11	0.8	100	88	0.88
	LFTi5	0.010	0.020	0.16	0.4	100	85	0.85
	LFTi10	0.008	0.013	0.15	0.2	100	80	0.80
	LFTi15	0.007	0.013	0.14	0.1	100	84	0.84
	LFTi20	0.007	0.011	0.15	0.2	100	98	0.98
	LFTi30	0.009	0.012	0.05	0.3	100	85	0.85
	LFTi50	0.009	0.011	0.03	0.2	100	95	0.95
	800°C/ LFO	0.010	0.020	0.12	0.5	100	75	0.75
	LFTi5	0.011	0.022	0.13	0.1	95	81	0.85
	LFTi10	0.017	0.025	0.18	0.05	90	100	1.11
	LFTi15	0.012	0.015	0.08	0.2	92	87	0.95
	LFTi20	0.006	0.008	0.07	0.2	97	85	0.88
	LFTi30	0.005	0.009	0.07	0.1	95	87	0.92
	LFTi50	0.005	0.007	0.05	0.2	98	80	0.82

ACKNOWLEDGMENTS

This Special Issue is dedicated to honor the retirement of Prof. César Pulgarin at the Swiss Federal Institute of Technology (EPFL, Switzerland), a key figure in the area of Catalytic AOPs.

The authors want to thank the European Fund for regional development (EFRE/FEDER) for the financial support of the PHOTOPUR project which is performed within the framework of Interreg V and the Sciences Offensive.


Julien Said
email: julien.said@ec-lyon.fr

Siegfried Fouvry
email: siegfried.fouvry@ec-lyon.fr

Georges Cailletaud

Christine Yang

Fikri Hafid

Shear driven crack arrest investigation under compressive state: prediction of fretting fatigue failure of aluminium strands

Keywords: Fretting fatigue, crack arrest, Stress Intensity Factors, aluminium, mode II mechanisms

Fretting fatigue crack propagation in aluminium strands was investigated through experimental tests and FEM simulations. Fretting fatigue tests revealed that crack nucleation predictions are not sufficient to fully predict the total strand failure, and crack arrest conditions may be reached for nucleated cracks. The geometry of arrested cracks was characterized and used to perform simulations using FEM in order to dedude Stress Intensity Factor (SIF) distributions along the crack front. These results showed that even in a fully compressive state, cracks are still able to propagate to a certain extent, and a mode II SIF threshold has been proposed.

Introduction

The lifetime assessment of overhead conductors is becoming a key point for any Transmission System Operator (TSO) in charge of a power grid. In order to adapt their maintenance and repair protocols, they need to be able to predict the mechanical behavior of their power lines with physical comprehension. Among all the damaging loadings that affect the total lifetime of a conductor, the one addressed in this work is fretting fatigue. A typical conductor is a wire rope assembly, constituted of several layers of helical strands (figure 1a) that can be made of steel, aluminium alloys or quasi-pure aluminium. When this complex assembly is subjected to external loadings such as wind vibrations, it may cause a small oscillatory movement within all the contacts between neighboring strands. This specific tribological load is defined as fretting, and the combination of this phenomenon with the fatigue induced by the conductor's motion results in fretting fatigue. In such a configuration, fretting nucleates cracks in the contact zone, and the fatigue bulk stress propagates these cracks until total failure. It has been frequently reported in the literature that this process reduces the total lifetime of overhead conductors [START_REF] Fricke | Importance of Fretting in Vibration Failures of Stranded Conductors[END_REF]- [START_REF] Lalonde | Numerical analysis of ACSR conductor-clamp systems undergoing wind-induced cyclic loads[END_REF] . Moreover, studies are widely focused on the clamping zone, as most of the strand failures observed on the grid were located in this particular area (figure 1c) [START_REF] Ramey | Effects of clamps on fatigue of ACSR conductors[END_REF], [START_REF] Cardou | Fatigue strength characterization of ACSR electrical conductors at suspension clamps[END_REF]. Thus, in a previous work, a numerical and experimental strategy has been proposed to predict the crack nucleation risk within a conductor subjected to both the clamping force and an oscillating bending movement [START_REF] Said | A multi-scale strategy to predict fretting-fatigue endurance of overhead conductors[END_REF]. This work was also specifically focused on the contacts between the two aluminium outer layers. To achieve this prediction, two numerical models have been developed: a macroscopic model, as it has also been proposed in other studies [START_REF] Lalonde | Modeling multilayered wire strands, a strategy based on 3D finite element beam-to-beam contacts -Part I: Model formulation and validation[END_REF]- [START_REF] Belkhabbaz | Méthodologie d'analyse fine des contacts critiques au sein d'un conducteur aérien via un modèle numérique filaire[END_REF], as well as a local model [START_REF] Redford | Modélisation numérique du phénomène de fretting-fatigue intervenant dans le vieillissement des conducteurs de lignes aériennes[END_REF], [START_REF] Redford | Calibration of a numerical prediction methodology for fretting-fatigue crack initiation in overhead power lines[END_REF]. The introduced macroscopic model represents a full portion of a conductor and its interactions with a clamp (figure 1b), using volume hexahedra elements and the ABAQUS Explicit solver. Even if this model has a high computational cost and isn't suitable with implicit calculations, it is easy to handle and is meant to give a first evaluation of the fretting loading conditions between the aluminium strands. On the other hand, the local model stands for a single contact between two individual strands. It also uses volume hexahedra elements with a refined mesh in the contact zone, and is suitable with implicit calculation.

The crack nucleation prediction was achieved using the Crossland multiaxial fatigue criterion associated with a non-local critical distance l opt approach, as previously applied by several authors [START_REF] Fouvry | Identification of the characteristic length scale for fatigue cracking in fretting contacts[END_REF]- [START_REF] Ferré | Stress gradient effect on the crack nucleation process of a Ti-6Al-4V titanium alloy under fretting loading: Comparison between nonlocal fatigue approaches[END_REF]. These numerical predictions were then compared to experimental results obtained using a dedicated fretting fatigue test bench that recreates the exact same conditions. These comparisons revealed that the numerical strategy manages well to predict the occurrence of crack at the contact edges, and the higher the equivalent Crossland stress is, the longer the cracks would be. However, it has also been observed that the presence of such cracks is not enough to conclude whether the strand will display total failure or not.

Finally, further numerical analyses showed a possible strong link between an increase of normal force and the propagation behavior, with high compressive stress around the crack tip. This stands as the starting point of the current analysis. Only considering crack nucleation may not be enough to predict comprehensively the total failure of an aluminium strand under fretting fatigue loading. Thus, the proposed work investigates crack propagation with crack closure effects, induced by compressive hydrostatic pressure. Fretting fatigue tests were carried out to study experimental crack arrests conditions, and numerical simulations were achieved with a fully meshed crack to proceed to Stress Intensity Factors (SIF) calculations. The main purpose of this study is to propose a SIF based criterion in order to predict the crack arrest phenomenon.

Crack nucleation prediction on a single contact

As mentioned in the introduction, a previous research work has been conducted to propose a prediction of the crack nucleation risk within an aluminium-aluminium mono contact. Thus, this section will sum up the main results from these previous predictions and highlight the conclusions that led to investigate further the crack arrest phenomenon. 1a) with aluminium strands (purity >99%) for electricity transportation and steel strands to ensure the mechanical strength of the conductor. These aging lines are the most likely to be replaced by the next decade, which is why the study focuses on this specific type of conductor. Even among ACSR, various designs and geometry exist.

(b) (c) (a)
The current study focuses on one specific conductor geometry, with the following characteristics: 3.6 mm of diameter for all aluminium strands while the steel strands diameter is 2.40 mm. Because of their respective lay angles, the resulting configuration corresponds to a crossed cylinder system with a total relative angle of β = 30°. This choice was motivated by the observation that nearly no failure was observed on steel strands on the French grid during service. All samples used for experimental testing were taken from a dedicated spool of aluminium strands without their helical shape to avoid successive manual handling. This handling would induce additional plastic strain and residual stresses within the strands and may ultimately affect the results.

2.2. Numerical local modeling using Finite Element Analysis (FEA)

FEA model description

The numerical strategy relies on a 3D model represented in figure 2a. The crossed-cylinder configuration is obtained using two half-cylinders to represent the aluminium strands, and are meshed the same way.

This first model used hexahedra volume elements and ran with the ABAQUS/Implicit solver. Both the augmented Lagrangian and Penalty algorithms were tested to describe the contact behavior, and gave systematically extremely similar results. Thus, most of the results presented throughout this study were obtained using the Penalty algorithm. It can also be mentioned that this local modelling considers straight strands, while the actual material has a helical shape, depending on its layer. However, this work focuses on the aluminium layer, which displays the lower local curvature and longer laying period (> 160 mm).

While the upper strand applies the fretting loading (i.e. the tangential and normal loads), the fatigue bulk stress is applied on one end of the lower strand. These boundary conditions are applied through reference points during three distinct time steps (figure 2b) throughout a single simulation:

-Step (1): a very small vertical displacement is applied on the upper strand to initiate the contact and ensure the stability of the next steps (especially when the Augmented Lagrangian algorithm is used) -Step (2): the static normal force P is imposed on the upper strand while the mean value for the fatigue bulk stress is applied on the lower part.

-Step (3): the normal force remains constant while the tangential and fatigue loadings Q(t) and σ(t) describe a sinusoidal cycle. This model considers an isotropic and elastic material, for which the Young's modulus E = 65 GPa and

Poisson ratio ν = 0.34 were experimentally identified. The partial-to-gross slip transition coefficient µ t = 1.1 was measured using the same procedure as described in [START_REF] Said | A multi-scale strategy to predict fretting-fatigue endurance of overhead conductors[END_REF], this time specifically in fretting fatigue.

Because of the aluminium softness, it would be relevant to take into account plasticity in the model.

0 1 2 3 amplitude time (s) (1) (2) (3)
P(t) Q(t) σ f (t) P Q(t) (t) (a) (b)
However, adding more non-linearity to this 3D problem with contact makes the convergence with the implicit solver more difficult. Another key aspect of a fretting contact concerns the gradient effects.

Fretting is characterized by severe stress gradients that imply to consider a non-local fatigue stress analysis. The critical distance approach is currently applied, using a reverse post-processing analysis of plain fretting experiments to find the critical distance l opt = 130 µm [START_REF] Said | A multi-scale strategy to predict fretting-fatigue endurance of overhead conductors[END_REF]. By considering a subsurface stress state (reaching quasi elastic stress conditions) the given critical distance fatigue stress analysis is in fact less affected by plasticity and gradient effects and the proposed 3D elastic investigation remains representative.

Figure 3 shows a typical crack nucleation risk distribution [START_REF] Papadopoulos | Invariant formulation of a gradient dependent multiaxial high-cycle fatigue criterion[END_REF], [START_REF] Amargier | Stress gradient effect on crack initiation in fretting using a multiaxial fatigue framework[END_REF], which shows the location of the hotspots where cracks are more likely to initiate. This crack nucleation risk is evaluated by comparing the equivalent Crossland stress σ C with the torsion fatigue limit noted τ d . Moreover, σ C also depends on the tension/compression fatigue limit noted σ d , and is expressed as follows:

√

With √ √ J 2,a represents the second invariant of the deviatoric stress amplitude during a loading cycle, and σ H,max is the maximum hydrostatic stress σ H during the same cycle. The two fatigue limits were identified using plain fatigue tests as described in [START_REF] Said | A multi-scale strategy to predict fretting-fatigue endurance of overhead conductors[END_REF]. According to the Crossland criterion, there is crack nucleation thus risk of failure when σ C ≥ τ d.

Besides the crack nucleation prediction, figure 3b focuses on the multiaxiality aspect usually inherent in a fretting contact. The triaxiality ratio η, defined as the ratio between the hydrostatic stress σ H and the Von Mises equivalent stress σ VM , was computed in the contact zone at Q = +Q* and Q = -Q*. As a reference, it can be noted that η = 0.33, η = 0 and η = -0.33 correspond to plain tension, plain shear and plain 1. All these cases are considered as realistic conditions, which is why they are relevant to investigate. Based on these conditions, the local model described in the previous section has been used to simulate the same configurations. Then, the equivalent Crossland stress σ C was computed below the hotspot at the critical distance l opt and compared to the torsion fatigue limit τ d . The corresponding results are displayed figure 4, and highlight the fact that 4 configurations among 6 are likely to nucleate thus to ultimately fail according to the current numerical methodology.

The final step of the initial strategy was to test these conditions experimentally using a dedicated fretting fatigue test bench that will be presented in detail in the next section. This bench is meant to recreate the single contact configuration between two aluminium strands and is illustrated in figure 5. The associated tests that were conducted to recreate the same loading cases revealed two key points:

-No total failure was observed on all 5 cases after 10 7 cycles of fretting fatigue This presence of cracks associated with the absence of total failure even after 10 7 cycles strongly suggests that there may be a crack arrest phenomenon involved. This new hypothesis implies that the sole consideration of the crack nucleation risk is not sufficient to fully predict the fretting fatigue response of the considered material, and the crack propagation behavior needs to be addressed. The following details will focus on the investigations achieved on this topic, with a special attention given to the influence of the fretting normal load. The goal of the present work is to complete the initial crack nucleation strategy by identifying a Stress Intensity Factor (SIF) threshold to account for possible crack arrest phenomena. The hydraulic fretting fatigue rig used for this work was initially designed to recreate the same conditions as those predicted by the numerical strategy described in the previous section. However, thanks to its double actuator configuration, it is perfectly suited to investigate various behaviors by controlling fretting and fatigue separately. The lower actuator (figure 5a) is force controlled and imposes the fatigue loading σ f (t), while the upper actuator is displacement controlled to ensure the test stability. The tangential force is measured using two force sensors: one placed at each end of the fatigue sample. Then, the tangential force Q diff (t) corresponds to the difference between the two forces. If there is no contact, both sensors will measure the same value (the fatigue loading) and their difference will be null. For each test, the frequency was fixed at 20 Hz for a limit lifetime of 10 7 cycles.

Figure 5c represents how the vertical fatigue sample is loaded. The fretting contact is obtained using a separate and shorter aluminium strand with the relative angle β = 30°. To avoid any bending, a counter body is placed on the opposite side of the fatigue sample. This counter body consists in a PTFE polymer, which displays a very low partial-to-gross slip transition coefficient against aluminium. Prior to the fretting fatigue tests that will be discussed in the following section, tests with two PTFE-aluminium contacts were conducted to characterize the fretting response for this kind of contact. From these preliminary tests, it was deduced that one PTFE-aluminium contact has a friction coefficient µ PTFE/al =0.04.

It means that for P = 200 N, the PTFE-aluminium contact induces less than 10 N whatever the slipping regime. This value was kept in mind for all following fretting fatigue tests, and the actual Q* corresponding to the aluminium/aluminium contact would be deduced as follows:

(2)

13

While the lower actuator applies the fatigue loading, the fretting displacement amplitude δ(t) is manually increased until the tangential force Q* reaches the targeted value.

Results and influence of normal force

Four series of tests were performed, and all the corresponding conditions are listed in table 2. For all tests, the fatigue loading ratio R = σ f,min /σ f,max was fixed at R = 0.5. Figure 7 plots the results obtained and shows how the fretting fatigue life of a strand is affected by an increase of normal force P. The two fatigue loadings tested were chosen to get the most significant results. Lower fatigue stresses, for example σ f,max < 50 MPa, would not ensure strand failure within 10 7 cycles even with high tangential forces. On the contrary, it has been witnessed that σ f,max > 80 MPa may induce plain fatigue failures around the upper fatigue jaw. For the fatigue stresses listed in table 1, failures were systematically located in the contact area. These plots illustrate the concrete influence of the normal force and hydrostatic pressure on the actual fretting fatigue life of aluminium strands. It shows how an increase of the normal force, while keeping all other parameters constant, can delay or prevent the strand failure. It may also be noticed that there seem to be a threshold effect: while P remains below a threshold normal force noted P CA , the lifetime evolution doesn't seem deeply affected. Then, when P gets near this threshold P CA , the lifetime before failure exhibits a sharp increase, as it can be seen especially for tests with σ f,max = 60 MPa (figure 7a). Eventually, for P ≥ P CA the strand lifetime is higher than 10 7 cycles. This specific behavior suggests once again that an increase of normal force and compressive hydrostatic pressure may be related to crack arrest and closure effects. Another interesting observation coming from these data concerns the experimental lifetimes for P < P CA . Whatever the fatigue and tangential loadings, the fretting fatigue life to failure is stable with most occurrences between 2 and 4 millions of cycles. The most significant results extracted from these plots are the threshold values P CA for the normal force, and are displayed in table 3. According to all four series of tests, the tangential force amplitude Q* has a way greater influence on this threshold than the fatigue stress σ f . For Q* = 200 N, it remains the same at P CA,200 = 450 N for both fatigue loads. For Q* = 150 N, fatigue has a slight influence with P CA,150 ranging from 250 N for σ f,max = 60 MPa to P CA,150 = 300 N for σ f,max = 70 MPa. Still, fatigue doesn't stand out as a key parameter for this threshold value. On the contrary, a raise of about 30% of tangential force Q induces an increase of 60 % for the crack arrest threshold P CA . It suggests that the shear stress generated in the fretting contact has much more influence than the fatigue bulk stress. Further post-processing analyses of non-failed samples also revealed that the associated crack depths were systematically between 170 and 250 µm (figure 8). This tends to confirm that the crack arrest phenomenon is quickly reached in the contact zone, where fretting induced stresses are predominant compared to the fatigue stress. In addition to With these data and especially the P CA values, the next step is to proceed to Stress Intensity Factor calculations using finite element analysis and 3D modeling.

mm

In order to evaluate the Stress Intensity Factors along a crack tip in a fretting configuration, a crack geometry has to be considered in the previous 3D model. The chosen method to achieve that was to include a fully meshed crack inserted into the initial mesh, using the Z-cracks tool. Z-cracks is a part of the Z-set suite that allows to study the cracking behavior in various 3D configurations, and is suitable with FEA solvers like the ABAQUS/Implicit solver used in this work. In the following section, two tools from Z-cracks have been used:

-The remeshing utility. It can insert a user-defined crack geometry, insert a crack into a sane mesh and remesh the model only using tetrahedral elements. The newly created mesh is refined around the crack front to account for its inherent discontinuity. For this study, this tool takes as input both a crack geometry (figure 9a) and an ABAQUS templated input file. The output is then a new ABAQUS templated input file corresponding to the cracked model.

-

G is then computed using the Gtheta method [START_REF] Geniaut | Evaluation of stress intensity factors with G-theta method and level sets in Code-Aster[END_REF], [START_REF] Destuynder | Sur une interpretation mathematique de l'integrale de Rice en theorie de la rupture fragile[END_REF]. To deduce the values of K I , K II and K III from this energy release rate, any pure mode I, II or III Westergaard displacement solution v I, II, III can be introduced. These solutions are associated with the corresponding virtual energy release rates G v, I, II, III , which gives the following relations: The last key aspect of this modeling is the crack itself. The crack geometry described here is based on all experimental observations made on failed and unfailed strands after testing and described in section 3.2.

Furthermore, these cracks do not seem to bifurcate even in fretting fatigue and on failed strands (figure 6), as it is often observed when propagation becomes only driven by the fatigue bulk stress. The explanation for this specific behavior may be related to microstructural and residual stress effects induced by the manufacturing process, and especially wire drawing. However, the purpose of the present work is not to propose a physical explanation for these orientations but rather investigate on the consequences of this geometry in a fretting configuration. No outplane propagation criterion was used to try to predict the crack path: the fully-elastic and isotropic behavior used to describe the material would not be able to account for any effect of the microstructure or residual stress. Thus, the crack geometry used was directly based on experimental cracks observed on unfailed samples after 10 7 cycles (i.e. above the crack arrest threshold P > P CA illustrated in figure 7). Three distinct angles are used to describe the crack orientation, which are illustrated figure 9:

-The diving angle α already defined earlier based on optical observations. It was set to α = 30°.

-To quantify the angle between the strand axis and the actual direction of propagation, δ was defined. Cracks propagate below the contact along the median plane M (figure 3) rather than along the strand axis. As it is a direct consequence of the relative angle β between the strands, δ = β/2 = 15°.

-The crack front angular position θ is used to define any point along the crack front. When θ = 0°, the considered point is located at the crack tip, on the median plane M. On the other hand, when θ = -90° or θ = 90°, the point is at the strand surface (figure 9b).

Figure 10 shows how a crack geometry is inserted into the given mesh. In this case, the crack was chosen with a "penny shape", corresponding to a disk surface. The center of this disk was placed on the hot spot location, whose coordinates were also extracted from previous simulations (figure 3). Thus, all the following section will focus on a penny shaped crack with a 400 µm radius. This geometry implies a maximum projected crack depth b CA = 200 µm to match with the experimental crack arrest depth. It is also worth mentioning that in this configuration, b CA > l opt = 130 µm (introduced section 2.2.1.). This gives a first guarantee that gradient effects may not affect too deeply the following SIF calculations.

Finally, this model has to consider two distinct friction coefficient: the friction coefficient µ between the two aluminium strands, same as in the sane model described in the previous section, and a new friction coefficient µ CL corresponding to the contact between the two crack lips. In this new configuration, both contacts were simulated using the ABAQUS Penalty algorithm. This new coefficient μ CL cannot be easily identified through experimental tests, so the first following simulations using Z-cracks will focus on the µ CL influence.

For most of the next simulations, a complete fretting fatigue cycle was considered. Then, all SIF amplitudes were directly defined using the following expression: [START_REF] Said | A multi-scale strategy to predict fretting-fatigue endurance of overhead conductors[END_REF] When these values are mentioned to be located at the crack tip, it means that it corresponds to a crack front angular position θ = 0°.

Influence of friction coefficient between the crack lips µ CL

As it was earlier intuited, the crack arrest phenomena observed with fretting fatigue tests may be related to crack closure effects due to compressive hydrostatic pressure. In that context, it appears crucial to properly address the friction behavior of the crack lips themselves, as they might be in contact during a cycle and try to slide onto each other. Thus, the first SIF results presented will focus on this topic. Furthermore, shear contributions are likely to have a key role in the driving mechanisms of such cracks, which is why ΔK II were specifically investigated. This will be also confirmed in the next sections.

Figure 14 shows the ΔK II evolutions at the crap tip for various friction coefficients between the crack lips from µ CL = 0 (no friction at all) to µ CL = 2. For both tangential force amplitudes Q*, ΔK II describes similar evolutions for a given friction coefficient µ CL . In the case of no friction (µ CL = 0), ΔK II is much higher than for any other µ CL . This result can be expected as in this configuration, both lips are sliding onto each other and all the shear energy is accumulated at the front of the crack. This induces such high values for ΔK II .

However, this cannot be considered as a realistic hypothesis. For such a ductile and adhesive material as the studied aluminium, the crack lips cannot be assimilated as purely smooth surfaces without interaction under closure. This is why non-zero coefficients have to be considered in the modelling. On the other hand, it is interesting to note that for µ CL ≥ 0.75, the ΔK II plots describe an asymptotic decrease, and also quickly converge to the same asymptote as P increases. It means that for P ≥ P CA , ΔK II is not influenced by the friction coefficient µ CL , as long as it is higher than 0.75. This last statement legitimates the arbitrary choice of µ CL = 1.1 which is the same as the friction coefficient used to describe the macroscopic contact between the two strands.

It is interesting to note that at Q = + Q*, the K I evolution along the crack front systematically describes a M-shaped curve, reaching its minimum in the median plane of the crack (i.e. the crack tip). This strong decrease of mode I Stress Intensity Factor is directly related to the compressive hydrostatic pressure induced by the contact. As the crack has a low diving angle α = 30° and its tip is right under the contact, the normal force applied by the upper counter-body directly induces high compressive stress and tends to close up the crack lips. This phenomenon is amplified at Q = -Q*, as K I follows a sharp V-shaped evolution and the crack tip is in a fully compressive state. This first numerical results stands as a first qualitative illustration of the phenomenon observed with the fretting fatigue tests in section 3.2. It was proposed that the normal force may stop the crack propagation, and these K I evolutions illustrates that this normal force promotes crack closure at the crack tip due to high compressive stresses. The difference of behaviors between mode I and II also illustrates the multiaxial aspect of the stress state around the crack tip, confirming the observation made in section 2.2.1.

In addition to this first statement, both plots show that K I,max < 0 at the crack tip. It must be noted that such values do not have a physical sense and must be considered as theoretical figures based on the calculation method used. However, the choice was made to show the associated results as it gives a first estimation of the compressive state around the crack tip. Indeed, it implies that during the entire fretting cycle, the crack tip is in a compressive state. This compressive state is also confirmed by the plots of the normal stress σ n along the crack tip. It highlights that even in such a state, K I seems to follow similar tendencies as σ n , with both behaviors being consistent.

Still, these observations do not mean that the crack has reached its crack arrest state: these SIF results correspond to Q = 200 N, P = 300 N, which displayed failure in fretting fatigue according to the experimental tests presented section 2.3.2. The failure can then be explained regarding the values of K II , which displays a bell-shaped curve at Q = + Q* (figure 12a), reaching its maximum in the crack tip area. This highlights one of the key points of the current study: even in a fully compressive state, a crack can 29 propagate only driven by shear mechanisms and mode II contribution to a certain extent. It can also be observed that the crack propagates below the contact, thus its tip is located in the volume with the stronger multiaxiality (figure 3b). This highlights the fact that with these multiaxial stress conditions, with compressive mode I and strong mode II, the crack still manage to propagate while it would be impossible in any uniaxial configuration.

The following steps of the present work will then try to propose a quantification of this statement. Before that, it can be noted that K Imax > 0 when the position is getting closer to the surface. It may suggest that the corresponding crack may propagate in mode I in these areas, unlike the crack tip. However, this hypothesis does not correspond to experimental observations, where the highest lengths are found in the median plane. This can also be explained by the fact that when closer to the surface, numerical results are more affected by fretting induced gradient effects discussed before. This is the reason why most of the presented results focus on the crack tip. In that sense and regarding K III and the mode III contribution, as it displays rather low values compared to K II around the crack tip, the mode III shear will be considered negligible.

As a complement of figure 12, figure 13 emphasizes on the effect of the fatigue force on the fretting induced shear behavior, as well as the normal load. It shows the ΔK II evolution along the crack front for the same Q* = 200 N and two distinct normal loads: P = 250 N and P = 500 N. Both plain fretting (σ f,max = 0 MPa) and fretting-fatigue (σ f,max = 60 MPa) are compared, where the fretting-fatigue case corresponds to σ f,max = 60 MPa and R = 0.5 to remain consistent with the previous experimental results. For the lower normal load (figure 13a), the addition of fretting slightly increases ΔK II especially around the crack tip at the top of the bell-shaped curve. On the other hand, for the higher P (figure 13b), fatigue doesn't seem to affect ΔK II at the crack tip anymore. It is consistent with the fact that for P = 500 N, the fretting contact is far more stressing, while the fatigue bulk stress remains constant. Thus, fatigue is hardly impacting the section 3.2., where changing the fatigue loading didn't seem to affect the crack arrest threshold.

The other key observation arising from these plots concerns the influence of the normal load itself. It highlights how an increase of normal load flattens the ΔK II distribution around the crack tip, and sharply reduces its peak value. This tendency was also visible in figure 11, with the asymptotic decrease of ΔK II at the crack tip when P increases. These new plots give another insight on the pressure induced crack closure. The final step is then to try to formalize the crack arrest condition based on experimental tests associated with these FEA simulations. model the kinetics of long cracks in a material. Whenever the equivalent ΔK eff gets lower than ΔK 0 , the crack is expected to stop. This methodology was also developed to account for short crack behavior, for which it was observed that even for ΔK eff < ΔK 0 , some propagation would still take place. A more specific SIF threshold ΔK th was thus introduced. It was defined so as ΔK th = ΔK 0 for long cracks and ΔK th < ΔK 0 for short cracks [START_REF] Miller | the Short Crack Problem[END_REF]- [START_REF] De Pannemaecker | Introduction of a reverse simulation approach to identify the fatigue stress intensity factor crack arrest threshold from fretting cracking experiments[END_REF]. In the latter case, ΔK th would display a non-linear evolution, while it is assimilated as a material constant in the former case. However, these methods usually define their equivalent SIF ΔK eff based on mode I propagation, with possible adjustments to account for shear and friction effects. In some other cases, mode II and III are further investigated, when the shear is high enough to prevent bifurcation due to the mode I contribution [START_REF] Doquet | 3D shear-mode fatigue crack growth in maraging steel and Ti-6Al-4V[END_REF], [START_REF] Otsuka | Mode II fatigue crack growth in aluminium alloys and mild steel[END_REF]. This approach cannot be directly used in the current work: as stated in section 4.3., the studied cracks are always in compressive state. That means that the mode I equivalent SIF amplitude ΔK eff would be systematically equal to zero, thus mode I cannot drive any propagation.

Before focusing specifically on the mode II mechanism when K I,max < 0, Figure 14 illustrates how the tangential force amplitude Q* affects the conditions leading to the crack arrest. Figure 14a sums up the experimental results obtained in fretting fatigue by stressing the link between Q* and the normal force threshold P CA , showing that an increase of Q* sharply raises P CA . On the other hand, figure 14b puts in relevance that when P = P CA , the ΔK II value at the crack tip is not influenced by Q*. This gives a first argument to consider this specific shear SIF value ΔK II,th as the threshold value to characterize the crack arrest under compressive conditions. To deepen this last statement, figure 15 insists on the ΔK II behavior versus the normal force ratio P/P CA for both Q*. It also introduces the normal stress σ n,CL based on the contact pressure existing between both crack lips. For every loading condition at Q = +Q*, this normal stress was averaged on the total crack lips surface, and the resulting scalar ̅ (+Q*) is plotted figure 15c. These values were obtained using a post-processing routine gathering all nodal pressures specifically between the crack lips. This way of plotting ΔK II reveals that for both Q*, the shear state seen at the crack tip is very similar before and after the experimental crack arrest condition. This also gives another way of determining ΔK II,th , as both curves meet at ΔK II = 1.35 MPa.m 1/2 approximately when P = P CA (same threshold as shown in figure 14b) This can be used to propose a first empirical threshold based on this ΔK II value.

Furthermore, the K I,max evolutions in the lower part of figure 15 underline that the cracking behavior is more consistent when considering only the mode II contribution. Indeed, there is no visible condition to characterize the crack arrest by adding into consideration mode I mechanisms, and may even add more discrepancy. This may also be explained by the fact that ΔK II already takes into account (indirectly) the mode I contribution through friction effects and µ CL . As the crack is under closure, the contact pressure between the crack lips associated with friction affects the amount of resulting shear energy at the crack lips. Finally, the comparison between figure 15b and 15c reveals that even though K I negative values have no physical sense, it displays very similar tendencies of evolution when compared to the evolution of the averaged pressure between the crack lips. This stands as a confirmation of the link between K I and σ n observed in figure 12.

The relevance of the proposed quantification can also be addressed. As seen on figure 15, the slope of the ΔK II evolutions are rather low for P = P CA , which can alter the accuracy of the corresponding ΔK II,th value.

On this regard and in order to be conservative, it appears more reliable to choose a lower value to predict the crack arrest phenomenon. These considerations help to propose a first mode II SIF threshold ΔK II,th = 1.3 MPa.m 1/2 identified for this configuration. Still, the existence of the threshold itself can also give valuable hints for anyone working with materials that have been processed with coil rolling or wire drawing. It is likely that the threshold value is dependent of the aluminium strand geometry and surely the material itself, but it highlights the fact that for an equivalent sphere/plane configuration, some materials may display specific propagating mechanisms associated with the multiaxiality of loadings. These crack would only be driven by shear stresses while the sole study of the crack closure would predict no propagation at all. Nonetheless, the previous results give an interesting insight on the propagating behavior of crack suffering lip closure, and how consistent this behavior can be.

Conclusion

The present study proposes to extend a former methodology to account for crack propagation in addition to nucleation prediction. It was based on the initial observation that the presence of nucleated cracks in an aluminium-aluminium strand contact loaded in fretting fatigue does not guarantee the total failure in some multiaxial stress states. Thus, potential crack arrest phenomena have to be considered. Figure 16 sums up the whole methodology and emphasizes the main steps. The following aspects were exposed: -The Z-cracks tool was introduced to add into consideration a fully meshed crack into the numerical local model. The previously defined crack was modeled and inserted into the sane mesh, before proceeding to fretting fatigue simulations.

-The influence of the friction coefficient between the crack lips µ CL has been addressed to justify the choice µ CL = µ = 1.1 corresponding to an aluminium-aluminium contact previously identified.

Finally, the conclusions of the present work rely on the two following points:

-SIF distributions along the crack front reveals that this crack geometry systematically implies that the crack tip is in compressive state with K I,max < 0. However, this does not mean that they cannot propagate further as experiments showed that for some conditions the strand total failure was still observed. This SIF analysis also highlighted the predominance of mode II shear mechanisms to explain how cracks could propagate under closure.

-Finally, a mode II SIF threshold ΔK II,th = 1.3 MPa.m 1/2 was proposed to predict the crack arrest state in the given configuration. This threshold relies on experimental results and numerical simulations and helps to understand the damage mechanisms within overhead conductors. However, the phenomenon exposed in the present study does not only apply on this specific case: such behaviors could be observed in any wire rope structure or more generally in any material having suffered coil rolling or wire drawing. Furthermore, it is also relevant for any application that involves multiaxial stress states with compression. Knowing that, it could be relevant to apply a similar strategy on any of those applications in an effort to update design decisions.

Figure 1 (

 1 Figure 1 (a) 3D rendered view of an Aluminium Conductor Steel Reinforced (ACSR) structure, with inner steel layers and outer aluminium layers; (b) close-up view of potential fretting scar observed in a clamping zone; (c) fully meshed conductor-clamp assembly used for the global FEM model;

Figure 2 :

 2 Figure 2: Local model mesh grid modelling a single contact between two aluminium strands; (b): timeframe used for all fretting fatigue simulations

Figure 3 ( 2 . 2 . 2 .

 3222 Figure 3(a): Typical Von Mises stress distribution in the contact with a close-up view of the Crossland stress distribution (Q = 150 N, P = 200 N) on the contact surface. Hotspots are located at the edges of the contact; (b): overview of a cross-section of the triaxiality ratio η distribution at Q = +Q* and Q = -Q*

Figure 4

 4 Figure 4 comparisons between FEM critical distance Crossland stress analyis (l opt = 130 µm) and experiments

3 .

 3 Experimental crack arrest investigation and normal force effects 3.1. Experimental setup

Figure 5 (

 5 Figure 5 (a): double actuator fretting fatigue rig used; (b): close up view of the contact area; (c) schematic view of the contact zone

Figure 6 :

 6 Figure 6: failed aluminium strand tested in fretting fatigue (Q= 150 N, P=200 N, σ fmax = 60 MPa, R = 0.5)

Figure 7

 7 Figure 7 (a): fretting fatigue lifetime evolution versus the normal force P for σ f,max = 60 MPa; fretting fatigue lifetime evolution versus the normal force P for σ f,max = 70 MPa

  σ f,max = 60 M Pa σ f,max = 70 M pa Q* = 150 N P CA = 300 N P CA = 250 N Q* = 200 N P CA = 450 N P CA = 450 N these lengths, figure 8 also highlights the diving angle α that displays a rather low discrepancy among all observed nucleated cracks, with values close to α = 30°. This consistency among all post-processed cracks helps to establish a typical crack geometry corresponding to the crack arrest state. This will be used in the next section with proper crack modeling. It is also interesting to note that the projected crack depths (b CA = 200 -250 µm) related to the crack arrest condition is nearly twice the critical distance l opt = 130 µm. This experimental correlation seems to confirm the Taylor assumption and former l optb opt stratey developed by Gandiolle et al [15]: l opt = b CA /2

Figure 8 (

 8 Figure 8 (a): cross-sectionnal observation along the contact median plane for Q = 200 N, P = 450 N, σ f,max = 70 MPa; (b) crosssectionnal observation along the contact median plane for Q = 150 N, P = 300 N, σ f,max = 60 MPa

  The SIF post-processing utility: It computes the SIF distribution from Linear Elastic Fracture Mechanics (LEFM) along the crack tip. Fracture modes I, II and III are accounted by K I , K II and K III respectively. This utility takes as input an FEA output database and returns SIF values along the crack front for every time frame available. The relations used for these calculations are expressed in the equations below. The LEFM-based SIF processing is based on the energy release G. It is related to the SIFs following the IRWIN relation: , where

Figure 9 (

 9 Figure 9(a): illustration of the geometric angles used to define the inserted crack; (b) close-up schematic view of the crack front and how the angular position θ is defined

Figure 10 :

 10 Figure 10: penny shaped crack mesh before insertion; (b) sane mesh before insertion; (c) cracked mesh and hotspot location; (d): close up view of the hotspot area with the highlighted crack front; (e) cross-sectionnal view at the crack location

Figure 11 : 3 .

 113 Figure 11: ΔK II at the crack tip as a function of the normal force, for various friction coefficients µ CL between the crack lips; (a) for Q*=150 N and σ f,max = 60 MPa ; (b) for Q*=200 N and σ f,max = 60 MPa

Figure 12 (

 12 Figure 12 (a): Mode I, II and III SIF as well as normal stress σ n distributions along the crack front at Q = +Q* = 200 N and P = 300 N, σ f,max = 60 MPa; (b) distributions at Q = -Q* = -200 N and P = 300 N, σ f,max = 60 MPa

Figure 13 ( 4 . 4 .

 1344 Figure 13 (a): ΔK II distributions along the crack front for plain fretting (Q*=200 N) and fretting fatigue (Q*=200N and σ f,max = 60 MPa) for a normal load P = 200 N; (b) same ΔK II evolutions for P = 500 N

Figure 14 (Figure 15

 1415 Figure 14 (a): Normal force threshold P CA versus the tangential force amplitude Q*; (b) ΔK II evolution versus the tangential force ampliude Q* for P = P CA

Figure 16 :

 16 Figure 16 : recapitulative framework of the proposed approach, from experiments and simulations to the proposition of a shear SIF threshold

  threshold crack arrest normal force (for a given Q* and s fat ) simulation of P CA condition Zcrack simulations crack arrest (no failure) if ΔK II < ΔK II,th =1.3 MPa. √m 37 -A former multi-scale strategy to predict the fretting fatigue life of aluminium strands in an overhead conductor was described. It relies on two FEA numerical models: one to account for the global scale while the other simulate a single 3D contact. This local model was also used in the current work for Stress Intensity Factor calculations. -Several series of experimental fretting fatigue tests were conducted to study the crack arrest occurrence only by modifying the normal force. Normal force Crack Arrest thresholds P CA were deduced from these tests. -A typical crack geometry based on optical observations on unfailed samples was defined to characterize the crack arrest state. It gave a projected crack depth b CA = 200 µm and a diving angle α = 30°.

Table 1 :

 1 Description of five realistic fretting fatigue loading conditions

	LOADING	P	Q*
	CASE	(N)	(N)	(MPA)
	1	71	17	99
	2	117	41	35
	3	320	70	60
	4	777	199	3
	5	64	18	98

Table 2 :

 2 list of all fretting fatigue conditions tested, with associated lifetimes

				Lifetime
	(MPa) R = 0.5	Q (N)	P (N)	( cycles)
	60	150	150	3
	60	150	200	3.2
	60	150	250	6
	60	150	275	9.5
	60	150	300	>10
	60	150	320	>10
	60	200	300	3.3
	60	200	350	2.8
	60	200	400	2.4
	60	200	410	3.1
	60	200	420	7.8
	60	200	450	>10
	60	200	470	>10
	70	150	150	4.4
	70	150	200	2.3
	70	150	210	2.4
	70	150	230	9.2

Table 3 :

 3 normal force thresholds P CA values for various fretting fatigue loadings


Dominique Rauly
email: dominique.rauly@ujf-grenoble.fr

Eric Chamberod
email: eric.chamberod@ujf-grenoble.fr

Pascal Xavier
email: pascal.xavier@ujf-grenoble.fr

Jean M F Martins
email: jean.martins@ujf-grenoble.fr

Jean Angelidis

Interactions between electromagnetic (EM) fields or currents and living cells constitute a recurrent subject of interest for several decades, and their effects have been profusely discussed [1], especially for the frequency bands currently encountered in everyday life of humans. In a more restrictive domain, large number of studies have been done, focused on EM modelling of a bacteria medium, in order to predict the EM field penetration and inner induced currents in living microorganisms. Relevant information to be collected deal with level and frequency of the EM signal that may affect the development of the considered cells. The former because non-thermal effects are nowadays suspected to exist, altering cell's metabolism, the latter because it is well known that the spectral response of the living cell impedance exhibits some dispersion in relation with cell membrane behaviour and shield effects.

It appears that these parameters may be strongly sensitive to shape, dimensions and orientation of bacterial cells with regard to the applied electric field orientation. The present paper aims to examine this problem and brings a streamlined lighting. This is done through the elaboration of a simplified equivalent electric circuit, supported by a prior COMSOL TM Multiphysics analysis and a stochastic approach.

II ANALYSIS

The bacterium selected to test our approach is Escherichia coli DH5α. A first model, suitable for the required level of resolution, may be a 2 µm long and 1 µm wide cylinder filled with physiological fluid and surrounded by a dielectric membrane of thickness 50 nm. The medium is considered also as a physiological fluid. Figure 1 shows the COMSOL TM model, with possible orientations for the external applied electric field, assuming that the field is provided through the application of an AC voltage between two plane parallel electrodes. A simplified equivalent circuit, similar to those explicited in the literature, can then be extracted from COMSOL TM computation, where capacitance and resistor values depend on size and orientation (Fig. 2). Next, the equivalent circuit for the overall bacterial cell is deduced, taking into account the concentration and the orientation of bacteria, as well as the electrodes/medium interface. As an example of interesting result, Figure 3 shows the admittance of a bacterium longitudinally oriented with the electric field. It reveals the well-known shield effect at lower frequencies. The final paper will relate other relevant parameters as inner current in the microorganism. Variations according to the size and orientation of bacteria will be detailed for both uniform and non-uniform media, supported by a stochastic analysis.

[1] M. Cifra, J.Z. Fields, A.

Stochastic

  Approach for EM Modelling of suspended Bacterial cells with Non-Uniform Geometry & Orientation Distribution Dominique Rauly*, Eric Chamberod**, Pascal Xavier*, Jean M.F. Martins*** and Jean Angelidis**** I. INTRODUCTION

Fig. 1 -

 1 Fig.1 -COMSOL TM model of E. Coli Fig.2 -Equivalent circuit for one bacterium, to be inserted in the overall circuit representing the bacterial medium. C and R values are orientation-dependent

FarhadiFig. 3 -

 3 Fig. 3 -Frequency behaviour of the admittance of E. Coli