Ricardo Sgarbi

Kavita Kumar

Viktoriia A Saveleva

Laetitia Dubau

Raphaël Chattot

Vincent Martin

Michel Mermoux

Pierre Bordet

Pieter Glatzel

Edson A Ticianelli

Frédéric Jaouen

Frédéric Maillard
email: frederic.maillard@lepmi.grenoble-inp.fr

Electrochemical Transformation of Fe-N-C catalysts into Iron Oxides in Alkaline Medium and Its Impact on the Oxygen Reduction Reaction Activity

Keywords: Metal-N-C catalyst, Earth-abundant metal catalyst, Fe oxide formation, Oxygen reduction reaction, Anion-exchange membrane fuel cell

Precious metal-free Fe-N-C catalysts efficiently electrocatalyze the oxygen reduction reaction both in acid and alkaline electrolyte. Their stability is however limited in acidic medium, but generally accepted to be much higher in alkaline electrolyte. Herein, by combining advanced electron and X-ray based techniques, we provide comprehensive evidence of a Fe dissolution/reprecipitation mechanism, which partially transforms single Fe atoms into Fe oxide nanoparticles and Fe carbide nanoparticles into Fe carbide core@Fe oxide shell nanoparticles, and is independent on the gas atmosphere used during the accelerated stress test. Our work shows that Fe-N-C materials based on zero-valent Fe nanoparticles should be designed so that all Fe nanoparticles are protected by a defect-free graphite shell, for improved durability. For single atom Fe-N-C catalysts, the present study raises the question of a possible synergy between minute amount of Fe oxide nanoparticles and FeNxCy single-atom sites, leading to the higher apparent durability of this catalyst.

Introduction

Electrochemical energy conversion devices are promising systems for the world transition from fossil to renewable energies. Among these systems, fuel cells convert efficiently and, in a carbonneutral manner the chemical energy of a fuel (e.g. hydrogen, H2) into electricity, provided the fuel is produced from sustainable resources (e.g. via water electrolysis using renewable energy). Acidic fuel cells (proton-exchange membrane fuel cell; PEMFC) are at a more advanced stage of development than anion-exchange membrane fuel cells (AEMFC), but the widespread commercialization of the former is impeded by the high cost of their constituting materials, in particular by the platinum (Pt) nanoparticles (NPs) supported onto high surface area carbon (Pt/C).

While Pt/C is used at both electrodes, the Pt loading is mainly at the cathode, due to the sluggish oxygen reduction reaction (ORR) in acid. Approaches pursued to decrease the loading of Pt at the cathode are essentially focused on alloying Pt with less expensive transition metal elements (e.g. Co, Ni, Cu) [START_REF] Dubau | Probing the structure, the composition and the ORR activity of Pt3Co/C nanocrystallites during a 3422h PEMFC ageing test[END_REF][START_REF] Lopez-Haro | Atomic-scale structure and composition of Pt3Co/C nanocrystallites during real PEMFC operation: A STEM-EELS study[END_REF][START_REF] Dubau | Nanoscale compositional changes and modification of the surface reactivity of Pt3Co/C nanoparticles during protonexchange membrane fuel cell operation[END_REF][START_REF] Dubau | Tuning the performance and the stability of porous hollow PtNi/C nanostructures for the oxygen reduction reaction[END_REF][START_REF] Henning | Pt-Ni aerogels as unsupported electrocatalysts for the oxygen reduction reaction[END_REF][START_REF] Alia | Exceptional oxygen reduction reaction activity and durability of platinum-nickel nanowires through synthesis and post-treatment optimization[END_REF][START_REF] Asset | A review on recent developments and prospects for the oxygen reduction reaction on hollow Pt-alloy nanoparticles[END_REF] or lanthanides (e.g. Y, Gd, Pr) [START_REF] Escudero-Escribano | Chorkendorff, Pt5Gd as a highly active and stable catalyst for oxygen electroreduction[END_REF][START_REF] Escudero-Escribano | Tuning the activity of Pt alloy electrocatalysts by means of the lanthanide contraction[END_REF][START_REF] Fichtner | Top-down synthesis of nanostructured platinum-lanthanide alloy oxygen reduction reaction catalysts: PtxPr/C as an example[END_REF][START_REF] Roy | Scalable synthesis of carbon-supported platinum-lanthanide and -rare-Earth alloys for oxygen reduction[END_REF] or substituting Pt with platinum group metal (PGM)-free catalysts such as transition metals (Fe, Co, Sn) embedded in a carbon matrix (C) doped with nitrogen (N). [START_REF] Wagner | Electrochemistry and the future of the automobile[END_REF][START_REF] Martinez | Progress in the development of Fe-based PGM-free electrocatalysts for the oxygen reduction reaction[END_REF] Nevertheless, both PGM-containing and PGM-free catalysts suffer from corrosion of the carbon support/carbon matrix, metal NP/single metal atom detachment, and metal dissolution in PEMFC cathode operating conditions, leading to a loss of active sites and to a drop of the ORR activity of the cathode over time. [START_REF] Dubau | Probing the structure, the composition and the ORR activity of Pt3Co/C nanocrystallites during a 3422h PEMFC ageing test[END_REF][START_REF] Lopez-Haro | Atomic-scale structure and composition of Pt3Co/C nanocrystallites during real PEMFC operation: A STEM-EELS study[END_REF][START_REF] Dubau | Nanoscale compositional changes and modification of the surface reactivity of Pt3Co/C nanoparticles during protonexchange membrane fuel cell operation[END_REF][START_REF] Guilminot | Detection of Pt z+ ions and Pt nanoparticles inside the membrane of a used PEMFC[END_REF][START_REF] Guilminot | Membrane and active layer degradation upon PEMFC steady-state operation[END_REF][START_REF] Dubau | Durability of Pt3Co/C 36 cathodes in a 16 cell PEMFC stack: Macro/microstructural changes and degradation mechanisms[END_REF][START_REF] Dubau | An identical-location transmission electron microscopy study on the degradation of Pt/C nanoparticles under oxidizing, reducing and neutral atmosphere[END_REF][START_REF] Asset | Porous hollow PtNi/C electrocatalysts: Carbon support considerations to meet performance and stability requirements[END_REF][START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF][START_REF] Kumar | On the influence of oxygen on the degradation of Fe-N-C catalysts[END_REF] In contrast, in alkaline media, many oxides of abundant metals are thermodynamically stable, [START_REF] Serov | Hot topics in alkaline exchange membrane fuel cells[END_REF] and the formation of carbonates passivates carbon, thus slowing down the CO2 evolution rate. [START_REF] Castanheira | Carbon corrosion in proton-exchange membrane fuel cells: From model experiments to real-life operation in membrane electrode assemblies[END_REF][START_REF] Castanheira | Carbon corrosion in proton-exchange membrane fuel cells: Effect of the carbon structure, the degradation protocol, and the gas atmosphere[END_REF] Electrocatalyzing the ORR is also generally more facile in alkaline than in acid (except for Pt) due to the suggested possibility for both inner and outer-sphere electron transfer mechanisms to take place. [START_REF] Mukerjee | Fundamental mechanistic understanding of electrocatalysis of oxygen reduction on Pt and non-Pt surfaces: Acid versus alkaline media[END_REF] Recently, we reported that, in alkaline electrolyte, catalysts based on metal NPs surrounded by a N-C shell (Metal@N-C, with Metal = Fe or Co) feature slightly higher ORR mass activity (MA) than some Metal-N-C catalysts with atomically-dispersed Metal-NxCy sites (metal = Fe, Co), [START_REF] Sgarbi | Oxygen reduction reaction mechanism and kinetics on M-NxCy and M@N-C active sites present in model M-N-C catalysts under alkaline and acidic conditions[END_REF] and carbon-supported Pt NPs (Pt/C). [START_REF] Chen | Molecular-confinement synthesis of sub-nano Fe/N/C catalysts with high oxygen reduction reaction activity and excellent durability for rechargeable Zn-Air batteries[END_REF][START_REF] Gao | Graphdiyne-supported single-atom-sized Fe catalysts for the oxygen reduction reaction: DFT predictions and experimental validations[END_REF][START_REF] Chen | Atomic Fe dispersed on N-doped carbon hollow nanospheres for high-efficiency electrocatalytic oxygen reduction[END_REF][START_REF] Zhang | Molecular-level design of Fe-N-C catalysts derived from Fe-dual pyridine coordination complexes for highly efficient oxygen reduction[END_REF][START_REF] Ferrero | Fe-N-Doped carbon capsules with outstanding electrochemical performance and stability for the oxygen reduction reaction in both acid and alkaline conditions[END_REF][START_REF] Zhong | Identifying the active sites of a single atom catalyst with pH-universal oxygen reduction reaction activity[END_REF] The Fe-N-C materials are also tolerant to anodic fuels (such as alcohols and borohydride) [START_REF] Chen | Atomic Fe dispersed on N-doped carbon hollow nanospheres for high-efficiency electrocatalytic oxygen reduction[END_REF][START_REF] Zhong | Identifying the active sites of a single atom catalyst with pH-universal oxygen reduction reaction activity[END_REF][START_REF] Chen | Zinc-mediated template synthesis of Fe-N-C electrocatalysts with densely accessible Fe-Nx active sites for efficient oxygen reduction[END_REF][START_REF] Sgarbi | Oxygen reduction reaction on metal and nitrogen -Doped carbon electrocatalysts in the presence of sodium borohydride[END_REF] and to common contaminants and impurities, which are present in reformed H2 or in air. [START_REF] Martinez | Progress in the development of Fe-based PGM-free electrocatalysts for the oxygen reduction reaction[END_REF][START_REF] Reshetenko | Study of degradation and spatial performance of low Pt-loaded proton exchange membrane fuel cells under exposure to sulfur dioxide in an oxidant stream[END_REF] Thus, the interest in Metal-N-C catalysts for application in AEMFCs is rapidly rising, with recently reported high performance. [START_REF] Sgarbi | Oxygen reduction reaction on metal and nitrogen -Doped carbon electrocatalysts in the presence of sodium borohydride[END_REF][START_REF] Setzler | Activity targets for nanostructured platinum-group-metal-free catalysts in hydroxide exchange membrane fuel cells[END_REF][START_REF] Varcoe | Anion-exchange membranes in electrochemical energy systems[END_REF][START_REF] Dekel | Review of cell performance in anion exchange membrane fuel cells[END_REF][START_REF] Adabi | High-performing commercial Fe-N-C cathode electrocatalyst for anionexchange membrane fuel cells[END_REF][START_REF] Santori | High performance FeNC and Mn-oxide/FeNC layers for AEMFC cathodes[END_REF] The advantage of Metal-N-C catalysts over PGM-containing catalysts in alkaline electrolyte is not limited to the first few hours of operation but extends far beyond that. Using the protocols from the Fuel Cell Commercialization Conference of Japan (FCCJ) [START_REF] Ohma | Membrane and catalyst performance targets for automotive fuel cells by FCCJ membrane, catalyst, MEA WG[END_REF], Zadick et al. [START_REF] Zadick | Huge instability of Pt/C catalysts in alkaline medium[END_REF] and Lafforgue et al. [START_REF] Lafforgue | Accelerated stress test of Pt/C nanoparticles in an interface with an anion-exchange membrane -An identical-location transmission electron microscopy study[END_REF] reported severe degradation of PGM NPs supported on high surface area carbon. Identical-location transmission electron microscopy studies (IL-TEM) and in situ Fouriertransform infrared spectroscopy measurements provided evidence of PGM-catalyzed corrosion of the carbon support leading to detachment of the PGM NPs at potentials higher than 0.6 V vs. the reversible hydrogen electrode (RHE). [START_REF] Lafforgue | Degradation of carbonsupported platinum-group-metal electrocatalysts in alkaline media studied by in situ Fourier transform infrared spectroscopy and identical-location transmission electron microscopy[END_REF] It was shown that the ability to corrode carbon depends on the nobleness of the metal NPs and decreases in the order: Pt > PtRu > Pd > Ni. [START_REF] Lafforgue | Degradation of carbonsupported platinum-group-metal electrocatalysts in alkaline media studied by in situ Fourier transform infrared spectroscopy and identical-location transmission electron microscopy[END_REF][START_REF] Zadick | Nickel-based electrocatalysts for ammonia borane oxidation: enabling materials for carbon-free-fuel direct liquid alkaline fuel cell technology[END_REF] In contrast, only a mild decrease of the half-wave potential was reported after accelerated stress tests (ASTs) on Metal-N-C catalysts. [START_REF] Chen | Molecular-confinement synthesis of sub-nano Fe/N/C catalysts with high oxygen reduction reaction activity and excellent durability for rechargeable Zn-Air batteries[END_REF][START_REF] Mufundirwa | Durability of template-free Fe-N-C foams for electrochemical oxygen reduction in alkaline solution[END_REF][START_REF] Santori | Effect of pyrolysis atmosphere and electrolyte pH on the oxygen reduction activity, stability and spectroscopic signature of FeNx moieties in Fe-N-C catalysts[END_REF] Yet, the most resistant site structure within Fe-N-C

catalysts remains an open question. Fe particles (zero-valent Fe, Fe carbide) encapsulated in N-C shells (generically labelled as Fe@N-C) have intuitively regarded as more robust than atomicallydispersed Fe atoms (FeNxCy), due to the protective role of multi-layered graphitized N-C shell. [START_REF] Ferrero | Fe-N-Doped carbon capsules with outstanding electrochemical performance and stability for the oxygen reduction reaction in both acid and alkaline conditions[END_REF][START_REF] Sanetuntikul | High pressure pyrolyzed non-precious metal oxygen reduction catalysts for alkaline polymer electrolyte membrane fuel cells[END_REF][START_REF] Tan | Sub-50 nm iron-nitrogen-doped hollow carbon sphere-encapsulated iron carbide nanoparticles as efficient oxygen reduction catalysts[END_REF][START_REF] Thomas | Morphological ensembles of N-doped porous carbon derived from ZIF-8/Fe-graphene nanocomposites: Processing and electrocatalytic studies[END_REF][START_REF] Yan | Nitrogen doped porous carbon with iron promotion for oxygen reduction reaction in alkaline and acidic media[END_REF][START_REF] Peera | Sustainable synthesis of Co@NC core shell nanostructures from metal organic frameworks via mechanochemical coordination self-assembly: An efficient electrocatalyst for oxygen reduction reaction[END_REF][START_REF] García | Study of the evolution of FeNxCy and Fe3C species in Fe/N/C catalysts during the oxygen reduction reaction in acid and alkaline electrolyte[END_REF] However, a more pronounced drop in ORR activity was recently reported for Fe-N-C catalysts based on Fe@N-C sites vs. those based on FeNxCy sites upon potential cycling in Arsaturated alkaline electrolyte at 25 °C. [START_REF] Mufundirwa | Durability of template-free Fe-N-C foams for electrochemical oxygen reduction in alkaline solution[END_REF] These conflicting results partly arise from the simultaneous presence of FeNxCy moieties and Fe@N-C particles in many Fe-N-C materials prepared by pyrolysis. Depending on the synthesis conditions, the carbon matrix may also feature amorphous, turbostratic or graphitic structure, [START_REF] Domínguez | Repercussion of the carbon matrix for the activity and stability of Fe/N/C electrocatalysts for the oxygen reduction reaction[END_REF] different porosity ranges (presence of macro and mesopores [START_REF] Lee | Design principle of Fe-N-C electrocatalysts: How to optimize multimodal porous structures?[END_REF] or micro and mesopores [START_REF] Gokhale | Novel dual templating approach for preparation of highly active Fe-N-C electrocatalyst for oxygen reduction[END_REF]) and is doped with N at different rates. Such structural, textural and chemical heterogeneities prevent establishing reliable function-ORR activity-stability relationships. Moreover, the various experimental conditions used by different groups (liquid vs. solid electrolyte, potential cycling vs. constant potential, ambient temperature vs. T ≥ 60 °C) can add to results disparities.

In this study, we investigate the stability in alkaline medium with load cycling ASTs of two Fe-N-C catalysts. Both were synthesized via low-energy planetary ball-milling of ZIF-8, Fe acetate and phenanthroline followed by heat treatment at 1050 °C in Ar atmosphere. However, depending on the Fe content before pyrolysis, the final materials mostly comprise Fe either as single Fe atoms or Fe carbide NPs supported onto nitrogen-doped carbon matrix, and are referred to as Fe0.5 and Fe5.0, respectively, with the subscript number referring to the Fe weight content before pyrolysis.

Their ORR activity, elemental content and distribution and carbon structure were assessed using various complementary physical, chemical and electrochemical techniques before and after AST under O2-or Ar -saturated 0.1 mol L -1 NaOH electrolyte at 60 °C or 25 °C. Our result point toward a previously undisclosed degradation mechanism into which Fe atoms dissolve and reprecipitate, and which takes place both for atomically dispersed Fe catalysts and Fe carbide NPs.

Experimental

Electrocatalysts

Three different Fe-N-C electrocatalysts were synthesized using zinc(II) zeolitic imidazolate framework ZIF-8 (purchased from BASF, Basolite Z1200), iron(II) acetate, and 1,10phenanthroline mixed via dry planetary ball milling in the optimized ratio, followed by pyrolysis at 1050 °C, as described in Ref. [START_REF] Zitolo | Identification of catalytic sites in cobaltnitrogen-carbon materials for the oxygen reduction reaction[END_REF]. The catalysts are labelled as Fex, where x is the concentration of the Fe employed in the synthesis before the pyrolysis step (0, 0.5 or 5.0 wt.%).

Preparation of the catalytic suspensions

To evaluate the electrocatalytic properties and the stability of the different materials, catalytic suspensions were prepared by ultrasonically dispersing 10 mg of Fe-N-C powder in a mixture of 5 wt.% Nafion ® solution (50 µL, Sigma-Aldrich), isopropanol (854 µL, Carl Roth) and ultrapure water (372 µL, Millipore, 18.2 MΩ cm, 1-3 ppb total organic compounds). [START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF] After sonication for 15 min, aliquots of 20 µL were deposited onto a glassy carbon disc embedded into KeLF (0.196 cm 2 geometrical surface area), then dried using a heat gun, under controlled rotation speed resulting in a catalyst loading of 0.8 mgcatalyst cm -2 for the rotating disk electrode (RDE) measurements. For the rotating ring disk electrode (RRDE) measurements, a Pt-ring and a glassy carbon disk (Pine Research) separated by a PTFE separator and a catalyst loading of 0.1 mgcatalyst cm -2 were used.

Glassware cleaning and solutions

To avoid organic contamination, all glassware, electrodes, volumetric flasks and polytetrafluoroethylene (PTFE)-based materials were cleaned in 50 % v/v solution of H2SO4 (Merck, Suprapur 96 wt.%) / H2O2 (Carl Roth, 30% w/w) overnight followed by thorough washing and then boiling in ultrapure water (Millipore, 18.2 MΩ cm, 1-3 ppb total organic compounds) before their use. The glassy carbon discs (Sigradur  from Hochtemperatur-Werkstoffe GmbH) were polished with diamond polishing paste (1 micron, Presi). The alkaline electrolyte was prepared from NaOH (Alfa Aesar, 50% w/w aq. solution).

Electrochemical set-up

Electrochemical measurements were performed using an Autolab potentiostat (PGSTAT302N).

Two different PTFE cells were used, one exclusively for the cyclic voltammograms (CVs) and ORR polarization curves at 25 °C ('characterization cell') and the other for the ASTs at 60 °C and 25 °C ('degradation cell'). A commercial RHE (Hydroflex, Gaskatel GmbH) connected to the cell via a Luggin capillary, and a glassy carbon plate (Sigradur  from Hochtemperatur-Werkstoffe GmbH) were used as reference electrode and counter electrode, respectively. All electrode potentials are referred to the RHE.

Electrochemical characterization and accelerated stress tests (ASTs)

Prior to the RDE and RRDE experiments, the electrolyte was deaerated with argon (Ar > 99.999 %, Messer). Then, 50 CVs between 0.0 and 1.0 V were performed at 100 mV s -1 in Ar-purged 0.1 mol L -1 NaOH ('break-in' cycles). The Ohmic drop was determined at E = 0.10 V using electrochemical impedance spectroscopy, and 85 % of its value was dynamically compensated during the electrochemical measurements. Three CVs between 0.0 and 1.0 V at 10 mV s -1 and one at 5 mV s -1 were recorded in 0.1 mol L -1 NaOH ('initial cycles'). The 5 mV s -1 CV served to correct the ORR polarization curves from the pseudocapacitive current. The ORR activity was assessed using polarization curves at 5 mV s -1 and 1600 rpm in O2-saturated 0.1 mol L -1 NaOH (O2 > 99.99 %, Messer).

The percentage of peroxide species (%HO2 -) and the number of electrons exchanged per O2 molecule during the ORR (ne-) were determined using a RRDE setup (Equation 1 and Equation 2). During the measurement, the Pt-ring was polarized at 1.2 V vs. RHE and the electrode was rotated at 1600 rpm.

𝑛 𝑒-= 4 |𝐼 𝑑 | |𝐼 𝑑 | + ( 𝐼 𝑟 𝑁 ) (1) %HO 2 -= 200 I r N ( I r N )+ |𝐼 𝑑 | (2)
where Id and Ir are the currents at the disk and ring, respectively.

The collection efficiency (N) was determined experimentally using the Fe 3+ /Fe 2+ redox couple from K3Fe(CN)6 salt. The experimental value was found to be N = 0.24.

The thin-film electrode was then transferred into the 'degradation cell', and 10,000 square-wave steps were performed between 0.6 and 1.0 V (3 s at each potential). [START_REF] Ohma | Membrane and catalyst performance targets for automotive fuel cells by FCCJ membrane, catalyst, MEA WG[END_REF]. The 0.1 mol L -1 NaOH electrolytes were purged with Ar or O2 gas and kept in the controlled temperature of 60 °C; for comparison measurements were also performed at 25 °C. After AST, the thin-film electrode was transferred again in the 'characterization cell' and the (break-in + initial cycles + ORR polarization curves) procedure was repeated.

The extent of degradation of the catalysts was tracked using the kinetic current densities for ORR (ik) obtained at 1600 rpm, calculated according to the Koutecky-Levich equation. We used the O2 diffusion-limited current density at 0.2 V and the Faradaic current obtained after pseudocapacitive current subtraction. The ik values were then normalized by the mass (m) of catalyst deposited onto the glassy carbon disk, and expressed as MA.

Transmission electron microscopy (TEM), scanning transmission electron microscopy (STEM) and energy-dispersive X-ray spectroscopy (X-EDS)

A JEOL 2010 TEM instrument operated at 200 kV with a point-to-point resolution of 0.19 nm was used for TEM imaging. X-EDS spectra were obtained in at least 6 different regions of the TEM grid. The quantification analysis was performed on the Fe K lines, using the K-factor provided by the JEOL software. The mean nanoparticle size and nanoparticle density were determined using the software ImageJ.

The STEM/X-EDS elemental maps were acquired using a JEOL 2100F microscope operated at 200 kV equipped with a retractable large angle Centurio Silicon Drift Detector (SDD) detector.

We used the Fe K, C K and O K lines and the K-factors provided by the JEOL software.

X-ray photoelectron spectroscopy (XPS)

XPS data were obtained on a Thermo Scientific Kα spectrometer using a monochromated Al Xray source (hν = 1486.6 eV and spot size 400 μm). They were measured directly onto the thin-film electrodes before/after ageing. The XPS spectra of O 1s, N 1s and C 1s were fitted using CasaXPS software to obtain the surface composition of the catalysts. Binding energies were corrected to the reference of the C-C component of C1s (sp 2 and sp 3 -hybridized carbon atoms) peak at 284.3 eV.

Raman spectroscopy

The Raman spectra were recorded on a Renishaw inVia Raman system, with an excitation wavelength at 532 nm. Measurements were performed in a backscattering configuration, using a 50x microscope objective, and a 2400 grooves mm -1 grating. This configuration ensured a spectra resolution much better than 1 cm -1 . To decrease the incident power at the sample, the line mode of the spectrometer was used. This configuration allowed to record 'averaged' spectra over an area of ca. 50 µm 2 in a single shot, with a power density at the sample much less than 50 µW µm -2 . For visualization purposes, the spectra were simply normalized to the amplitude of the 'G' mode, located at about 1580 cm -1 .

Inductively coupled plasma-mass-spectrometry (ICP-MS)

The amount of Fe dissolved in the electrolyte was determined using a PerkinElmer NexION 2000 ICP-MS. The Fe calibration curve was obtained from standard monometallic solution (Iron ICP Standard Solution, 1000 mg L -1 , Carl Roth GmbH & Co. KG), diluted with a 0.05 mol L -1 NaOH solution to obtain analytical metal concentrations of 2, 5, 10, and 20 µg L -1 . The collected electrolyte was diluted twice to decrease the aliquot's pH, and bring the analyte concentrations into the specified calibration ranges. Rhodium (Rh) was used as internal standard due to its similar first ionization energy compared to Fe (7.5 and 7.9 keV, respectively). Sample and calibration solutions were spiked with a 2.5 µg L -1 of 103 Rh internal standard solution (PerkinElmer). To attenuate polyatomic interferences (e.g. 40 Ar and 16 O), we analysed 56 Fe and used the helium collision mode with kinetic energy discrimination.

X-ray absorption spectroscopy (XAS) and X-ray emission (XES) spectroscopy

High energy-resolution fluorescence-detected X-ray absorption near edge structure (HERFD-XANES) and Kβ XES spectra were recorded at beamline ID26 at the European Synchrotron

Radiation Facility (ESRF), Grenoble, France. Si (111) double-crystal monochromator was used for the measurements. The maximum of Fe Kβ fluorescence line (7.058 keV) was selected with an emission spectrometer in Rowland geometry with five Ge (620) analyser crystals (Bragg angle, 79°). The incident beam absolute energy calibration was performed using a reference metallic Fe foil by setting the first inflection point of the Fe K edge at 7.112 keV. The incident energy was varied from 7.10 to 7.20 keV over Fe K edge. HERFD-XANES spectra were recorded in continuous mode during 5 min with an energy step of 0.1 eV. The XES spectra were collected with a step size of 0.1 eV and an incident energy of 7.80 keV. The measurements were performed on glassy carbon-based electrodes, using a catalyst loading of 0.8 mgcatalyst cm -2 . The analyses were performed before and after ASTs, at room temperature and in the presence of air. HERFD XANES and XES spectra were normalized in area using the ranges 7.10 -7.20 keV and 7.02 -7.07 keV, respectively. Several scans were averaged.

Wide-angle X-ray scattering measurements (WAXS) and pair distribution function (PDF) analysis

The WAXS measurements were performed at ID31 beamline of the ESRF in Grenoble, France.

Radiation from one undulator was monochromatized with a multilayer monochromator (bandwidth 2 %) to the final energy of 70 keV (λ = 0.177 Å). Sample powders were measured in Kapton capillaries of 1 mm in diameter and the scattered signal was collected using a Dectris

Pilatus CdTe 2M detector. The energy, detector distance and tilts were calibrated using a standard CeO2 powder and the 2D diffraction patterns were reduced to 1D curves using the pyFAI software package [START_REF] Ashiotis | The fast azimuthal integration Python library: PyFAI[END_REF].

The PDF patterns were calculated using the PDFGetX2 software. [START_REF] Qiu | PDFgetX2: a GUI-driven program to obtain the pair distribution function from X-ray powder diffraction data[END_REF] After subtraction of the environment contribution using an empty capillary measurement and corrections for absorption and inelastic scattering, the data were normalized and Fourier transformed using Qmax=19.3 Å -1 .

In order to calculate the difference-PDF patterns, the PDFs from the 3 samples were normalized by using the intensity of the first peak at 1.4 Å, to which Fe atoms are not expected to contribute due to the too short distance. The difference-PDF patterns will thus contain the contributions of atomic pair containing at least one Fe atom.

Results

Structural and chemical properties of the fresh and aged Fe-N-C electrocatalysts

The catalysts studied in this work have been extensively characterized by XAS, Raman spectroscopy, 57 Fe Mössbauer spectroscopy, TEM, X-EDS, X-ray diffraction and Brunauer-Emmett-Teller (BET) techniques in our former works. [START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF][START_REF] Sgarbi | Oxygen reduction reaction mechanism and kinetics on M-NxCy and M@N-C active sites present in model M-N-C catalysts under alkaline and acidic conditions[END_REF][START_REF] Zitolo | Identification of catalytic sites in cobaltnitrogen-carbon materials for the oxygen reduction reaction[END_REF][START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF][START_REF] Armel | Effect of ZIF-8 crystal size on the O2 electro-reduction performance of pyrolyzed Fe-N-C catalysts[END_REF] In brief, TEM images showed the absence of Fe particles in the Fe0.5 catalyst and this was confirmed by the absence of a peak at ca 2.1-2.2 Å in the Fourier transform of its EXAFS spectrum and also by the absence of a sextet component in its 57 Fe Mössbauer spectrum [START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF][START_REF] Sgarbi | Oxygen reduction reaction mechanism and kinetics on M-NxCy and M@N-C active sites present in model M-N-C catalysts under alkaline and acidic conditions[END_REF][START_REF] Li | Identification of durable and non-durable FeNx sites in Fe-N-C materials for proton exchange membrane fuel cells[END_REF]. In contrast, the same characterizations performed on Fe5.0 revealed only or mostly Fe carbide NPs [START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF]. These conclusions are supported by Figure 1 showing the PDF analyses of the WAXS patterns for Fe0.5 and Fe5.0 and for a catalyst synthesized in the exact same manner as Fe0.5 and Fe5.0 but in the absence of Fe (Fe0.0). Indeed, after normalization to the intensity of the C-C peak at ca. 1.41

angströms, [START_REF] Petkov | Local structure of nanoporous carbons[END_REF] the 'Normalized Fex-Fe0.0' traces allow to directly visualize the structure of the minority compounds, once the signal of the carbon matrix is cancelled. S3 and Table S1). This experiment suggests that the morphological changes are controlled by the electrode potential, not by the gas atmosphere. Interestingly, not only does the morphology of the Fe-N-C catalyst change after AST, but also its chemical composition.

Indeed, point X-EDS analyses performed at several particles of the aged Fe0.5 catalyst indicated an oxygen:iron (O:Fe) stoichiometry of 3.1 ± 0.3 and 2.5 ± 0.5 after AST at 25 and 60°C, respectively. Similarities but also pronounced differences were observed for the Fe5.0 catalyst (Figure 3). Ferich particles with sizes of 5-30 nm are seen in the fresh sample (Figure 3a-b), while O atoms homogeneously cover the surface of the carbon matrix (adventitious oxygen and oxygen groups on carbon matrix), with no evidence, initially, for increased O signal at the Fe-rich particles (Figure 3c and Figure 3d). However, a distinct core@shell structure composed of a Fe-rich core covered by a Fe-poor and O-rich shell (Figure 3g-h) is observed for some of the NPs after the [0.6-1.0 V -3s/3s -10 k -O2 -60°C] protocol. This core@shell structure is confirmed by the point X-EDS analyses performed in the core or the shell region of the NP (Figure S4a), the colour map composition (Figure S4b) and the line-scan profiles displayed in Figure S4c-d. Combined

with the marked increase of the mean particle size from 17 nm to 36 nm in the particle size distribution histograms (Figure S2) and the drop in the NP density (Table S1), the results suggest that Fe atoms redistributed during the AST, as a result of a Fe dissolution/Fe oxide reprecipitation mechanism. This result is in line with what we have reported previously in acidic electrolyte, [START_REF] Kumar | On the influence of oxygen on the degradation of Fe-N-C catalysts[END_REF][START_REF] Li | Identification of durable and non-durable FeNx sites in Fe-N-C materials for proton exchange membrane fuel cells[END_REF] and with recent IL-TEM images and XAS results from Garcia et al. [START_REF] García | Study of the evolution of FeNxCy and Fe3C species in Fe/N/C catalysts during the oxygen reduction reaction in acid and alkaline electrolyte[END_REF] showing that Fe To investigate changes in the electronic structure of Fe atoms during ageing in 0.1 mol L -1 NaOH, we performed HERFD-XANES and XES on the Fe0.5 catalyst before and after the [0.6-1.0 V -3s/3s -10 k -Ar -60°C] and [0.6-1.0 V -3s/3s -10 k -O2 -60°C] protocols. The Fe K edge spectra (Figure 4a) can be divided into two regions based on the electronic transitions that give rise to the spectral features: the rising absorption edge or the white line (1s → 4p transition) and the pre-edge (1s → 3d transition), the latter being displayed in the inset of Figure 4a. One can clearly observe a shift of the edge position in the aged Fe0.5 sample that can be assigned either to an increase in the average oxidation state of Fe atoms and/or to changes in the local geometry of Fe sites [START_REF] Glatzel | The electronic structure in 3d transition metal complexes: Can we measure oxidation states?[END_REF]. The analysis of the pre-edge features (Figure 4a, inset) also shows significant changes in the peak intensities after the ASTs. The assignment of these peaks to specific structures is not-trivial due to the intrinsic complexity of these materials' composition. However, based on the observed changes, one may assume one or several of the following phenomena took place: (i) distortion of FeNxCy sites; (ii) transformation of certain FeNxCy sites into ferric oxide upon ageing.

We also measured Kβ XES spectra on the fresh and aged Fe0.5 catalysts (Figure 4b). This method is traditionally used for spin-state studies [START_REF] Lafuerza | Chemical sensitivity of Kβ and Kα Xray emission from a systematic investigation of iron compounds[END_REF][START_REF] Saveleva | Potential-induced spin changes in Fe/N/C electrocatalysts assessed by in situ X-ray emission spectroscopy[END_REF] as the shape of the Kβ line is dominated by the 3p -3d exchange interaction. This emission line comprises two features: high-energy Kβ1,3 and low-energy Kβ', where the intensity of the latter and the energy separation between these two peaks are spin sensitive. [START_REF] Lafuerza | Chemical sensitivity of Kβ and Kα Xray emission from a systematic investigation of iron compounds[END_REF] The increase of the Kβ' shoulder observed in the aged samples (inset of Figure 4b) as well as the increased energy split between the features in comparison to a fresh sample evidence higher average spin state of Fe in the aged Fe0.5 catalyst. The increase of the spin state is directly correlated to the local geometry changes, e.g. due to oxidation of Fe atoms or to the formation of other structures, such as Fe oxide NPs. Moreover, the changes in HERFD-XANES and XES spectra discussed above are independent of the gas atmosphere used during the AST, which confirms the STEM/X-EDS analyses (Figure 2, Figure 3 and Figure S4).

Fe redistribution at the electrode  electrolyte interface

At this point, it is however still unclear whether the transformation process of some single Fe atoms or some Fe3C NPs into Fe oxides occurs via (i) de-coordination of Fe 2+ /Fe 3+ ions from N atoms, mobility on the carbon surface and aggregation upon collision (applicable not only for Fe3C

particles, but also to FeNxCy sites, as recently observed in Ref. [START_REF] Kumar | Fe-N-C electrocatalysts' durability: Effects of single atoms' mobility and clustering[END_REF]) or (ii) passage of Fe 2+ /Fe 3+ ions in the electrolyte and then re-precipitation as Fe oxides. To answer this question, the percentage of Fe dissolved in electrolyte was calculated by assessing the increase in Fe concentration in the electrolyte during AST normalized to the maximal Fe concentration achievable based on the Fe content in the fresh thin-film electrode (Figure S5a). The results show that ca. 15 % of the Fe atoms was dissolved in the electrolyte after either [0.6-1.0 V -3s/3s -10 k -Ar -60°C] or [0.6-1.0 V -3s/3s -10 k -O2 -60°C] for the Fe0.5 sample, while only ca 3 % of all Fe atoms was dissolved for Fe5.0 during the same AST protocols. The similar Fe leaching observed in Ar-or O2-saturated NaOH electrolyte (for a given Fe-N-C catalyst) confirms the conclusions derived from HERFD-XANES (Figure 4) and TEM/STEM (Figure 2, Figure 3 and These results are important for the practical application of various Fe-N-C materials with different Fe speciation in AEMFCs and metal-air batteries. For Fe0.5, they are in good qualitative agreement with the reported decrease of the amount of FeNxCy sites and the concomitant increase of Feoxides, as observed by 57 Fe Mössbauer spectroscopy on another Fe-N-C material based on singleatom-sites, before/after a 100 h durability test at 600 mA cm -2 in air/H2 AEMFC. [START_REF] Adabi | Understanding how single-atom site density drives the performance and durability of PGM-free Fe-N-C cathodes in anion exchange membrane fuel cells[END_REF] We also stress that while the reprecipitation of Fe as Fe oxide during AST was quantitatively limited for Fe0.5 in liquid alkaline electrolyte, the outcome in an ionomeric environment free of support liquid electrolyte (stronger increase in local Fe concentration in the ionomer phase) is expected to favour the reprecipitation of leached Fe cations as Fe oxide. [START_REF] Li | Identification of durable and non-durable FeNx sites in Fe-N-C materials for proton exchange membrane fuel cells[END_REF] The question now arises whether the release of Fe cations in the electrolyte was caused or simply accelerated by the corrosion of the carbon matrix. Raman spectroscopy and X-ray photoelectron spectroscopy are ideal tools to provide answers to this question. The Raman spectra of the Fe-N-C catalysts before and after ageing at 60°C are shown in Figure S6. They are dominated by the defect and/or disorder-induced D1-band at υ ∼1350 cm -1 and D2 band at υ ∼1610 cm -1 and the Raman-allowed graphitic G band at υ ∼1580 cm -1 , thus signing the presence of disordered and ordered domains, respectively. [START_REF] Sadezky | Raman microspectroscopy of soot and related carbonaceous materials: Spectral analysis and structural information[END_REF] Second-order Raman bands at υ ∼ 2690, 2950 and 3190 cm -1

were also observed, mostly due to the combination and overtones of D1 and G bands. Again, the second-order regions of the spectra were ill-defined, translating structural disorder within the materials. [START_REF] Park | G′ band Raman spectra of single, double and triple layer graphene[END_REF] In more details, a slight decrease in the intensity of the D1and D2-bands relatively to the G-band intensity was observed on the Fe0.5 catalyst after all ASTs, suggesting preferential corrosion of the most defective regions of the carbon matrix. As such domains may correspond to the microporous carbon regions, hosting some of the Fe-NxCy sites in MOF-derived catalysts, the results are in line with the drop of the Fe content monitored by X-EDS analyses (performed on NP-free areas of the Fe0.5 catalyst, Figure S5a). In contrast, for the more graphitic Fe5.0 catalyst, the intensity of the D1and D2-bands slightly increased, suggesting the formation of point inplane defects or a small decrease of the mean in-plane coherent domain size. Note that similar experimental trends were observed on Pt/high-surface-area carbon (Ketjenblack type) and Pt/reinforced graphite NPs by Castanheira et al. [START_REF] Castanheira | Carbon corrosion in proton-exchange membrane fuel cells: From model experiments to real-life operation in membrane electrode assemblies[END_REF][START_REF] Castanheira | Carbon corrosion in proton-exchange membrane fuel cells: Effect of the carbon structure, the degradation protocol, and the gas atmosphere[END_REF].

Because surface defects of carbon materials are quickly populated by oxygen-containing groups in aqueous electrolyte, [START_REF] Kinoshita | Carbon: Electrochemical and physicochemical properties[END_REF] structural changes in the carbon matrix should also lead to chemical changes. Figure S1a shows the deconvoluted O1s, N1s and C1s regions of the XPS spectra of the However, the balance between the different groups changes upon ageing, C-O-H groups being progressively converted/oxidized into C=O groups (Equation 3):

R-[C-O-H] + 2 OH -→ R-[C=O] + 2 H2O + 2 e - (3)
These findings are in line with the N1s region of the XPS spectra. Indeed, the distribution of N species was mostly unchanged upon ageing (see Table S2); however, the fraction of oxidized N raised at the expense of pyrrolic N for the more graphitized Fe-N-C catalyst (Fe5.0). This is in line with former literature reports pointing towards the instability of pyrrolic N [START_REF] García | Study of the evolution of FeNxCy and Fe3C species in Fe/N/C catalysts during the oxygen reduction reaction in acid and alkaline electrolyte[END_REF] and the stability of graphitic N in alkaline electrolyte. [START_REF] Perazzolo | Chemical and electrochemical stability of nitrogen and sulphur doped mesoporous carbons[END_REF] Finally, as evidenced by the bar chart in Figure S1c, the C-C functional group was predominant for the fresh and aged Fe0.5 and Fe5.0 catalysts, and its intensity mildly varied, corroborating the conclusions derived from Raman spectroscopy (Figure S6).

Summing up, Raman spectroscopy and XPS results suggest that corrosion of the N-C matrix was mild in alkaline electrolyte, and mostly proceeded on the surface and near-surface region of the Fe-N-C catalysts.

Electrocatalytic properties of fresh and aged Metal-N-C electrocatalysts

V -3s/3s -10 k -O2 -60°C], [0.6-1.0 V -3s/3s -10 k -Ar -60°C] or [0.6-1.0 V -3s/3s -10 k -O2 -25°C].
The CVs indicated that the N-C matrix of both catalysts did not suffer severe physical and chemical degradations during the ASTs, in agreement with the conclusions derived from XPS and Raman spectroscopies. Indeed, similar pseudocapacitive currents were observed in the CV of the Fe0.5 and the Fe5.0 catalysts before and after ageing in Ar-or O2-saturated 0.1 mol L -1 NaOH at 60°C, as expected from mild functionalization with oxygen-containing surface groups. [START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF][START_REF] Sgarbi | Oxygen reduction reaction mechanism and kinetics on M-NxCy and M@N-C active sites present in model M-N-C catalysts under alkaline and acidic conditions[END_REF] The ORR polarization curves recorded on the fresh and aged Fe-N-C catalysts are shown in Figure 5f-j.

They display regions where the ORR kinetics is under pure activation control (E > 0.85 V), under mixed activation-O2 diffusion control (0.6 < E < 0.85 V) and under control by O2 diffusion in solution (E < 0.6 V). We note that the MA towards the ORR of Fe0.5 decreased by only ca. 10-20

% at E = 0.85 V during ageing (Figure 5k), but by a higher amount of ca. 45 % at E = 0.80 V (Table S3). A detailed analysis shows that the Tafel slope of Fe0.5 was significantly increased after AST (Figure S7), explaining the dependence of the % loss of MA with the potential chosen to report the MA. These numbers can be compared to the relative amount of FeNxCy moieties lost during AST, which were estimated by X-EDS and ICP-MS results to be in the range of 50-68 %.

The results are similar in the O2 diffusion-limited region of the ORR polarization curve, where the initial current density dropped by less than 10 % upon ageing at 60°C (Fig. 5 g-h), which suggests unmodified selectivity upon AST. The RRDE results displayed in Figure S8, Figure S9 and Table S4 quantitatively confirm this trend. For Fe5.0, the ORR activity at E = 0.85 V decreased more markedly by ca. 30-40 % after the different ASTs (Fig. 5k), while the Tafel slope was unmodified in this case (Table S3). In contrast, there was no significant change of the current density in the O2 diffusion-limited region (Fig. 5 i-j). the ORR measured at E = 0.85 V for the pristine/aged catalysts. Cyclic voltammograms were performed in Ar-purged 0.1 mol L -1 NaOH at a scan rate of 10 mV s -1 using a catalyst loading of 0.8 mgpowder cm -2 and a temperature of 25 °C. The ORR polarization curves were recorded using a catalyst loading of 0.8 mgpowder cm -2 (potential scan rate 5 mV s -1 , T = 25 °C and w =1600 rpm).

Discussion

We now discuss all the results of physico-chemical and electrochemical characterizations to draw conclusions on the transformation process of different Fe-N-C catalysts into Fe oxides in alkaline electrolyte, and its impact on the final ORR activity.

Our findings firstly point towards the absence of massive ORR-assisted carbon corrosion in alkaline compared to acidic electrolyte. Indeed, in acidic electrolyte, Fenton reactions between Fe atoms and H2O2 molecules formed as ORR intermediates catalyse the formation of radical species ( • OH, • OOH). These radical species then irreversibly oxidize the carbon matrix, ultimately leading to the demetallation of the FeNxCy moieties. [START_REF] Kumar | On the influence of oxygen on the degradation of Fe-N-C catalysts[END_REF] The results reported in this work illustrate similar, although much less pronounced, changes in morphology and chemistry during ORR in alkaline electrolyte. They suggest that the superoxide anion O 2-radical species formed at pH > 12 is less reactive than • OH and • OOH species, in line with the former report of Bae et al. [START_REF] Bae | pH effect on the H2O2-induced deactivation of Fe-N-C catalysts[END_REF] The Fe-N-C catalysts based on zero-valent Fe NPs are also prone to dissolution and transformation into Fe oxide, if they are initially accessible by the electrolyte, or as a result of their exposure to the electrolyte due to mild carbon corrosion during the AST.

The dissolved Fe 2+ and Fe 3+ cations are then prone to reprecipitate as Fe(OH)2 and Fe(OH)3, in agreement to what was observed in 0.1 M H2SO4 and in PEMFC in our former studies: [START_REF] Kumar | On the influence of oxygen on the degradation of Fe-N-C catalysts[END_REF][START_REF] Li | Identification of durable and non-durable FeNx sites in Fe-N-C materials for proton exchange membrane fuel cells[END_REF] Fe 2+ + 2 OH -→ Fe(OH)2 (4)

Fe 3+ + 3 OH -→ Fe(OH)3 (5)
Note that any deposited Fe(OH)2 species will spontaneously transform into Fe(OH)3, due to the presence of O2 and/or due to the one order of magnitude lower solubility constant of Fe(OH)3 over Fe(OH)2: [START_REF] Gayer | The solubility of ferrous hydroxide and ferric hydroxide in acidic and basic media at 25°[END_REF] 4 Fe(OH)2 + O2 + 2 H2O → 4 Fe(OH)3

The local STEM/X-EDS analyses support this assertion, as the average ratio between O and Fe atoms (calculated from at least 3 different STEM images) was 3.1 ± 0.3 and 2.5 ± 0.5 for Fe0.5

after AST at 25 °C or 60 °C, respectively.

Importantly, the ORR proceeding at single Fe atoms or Fe3C NPs leads to the formation of OH - ions, and to a more basic environment in the Helmholtz plane that facilitates the rapid complexation of the free Fe 2+ /Fe 3+ ions (see the larger size and higher density of NPs after ageing in O2-vs. Ar-saturated electrolyte in Table S1, respectively). Once formed, Fe(OH)2 and Fe(OH)3 species are in equilibrium with HFeO2 -/Fe2O -and FeO2 -/HFeO3 2-/FeO3 3-species in alkaline solution. [START_REF] Pourbaix | Atlas of electrochemical equilibria in aqueous solutions[END_REF] However, the small solubility constants of Fe hydroxides in high pH electrolyte (close to 10 -6 and 10 -7 for Fe(OH)2 and Fe(OH)3, [START_REF] Gayer | The solubility of ferrous hydroxide and ferric hydroxide in acidic and basic media at 25°[END_REF] respectively) thermodynamically favour the solid products.

The effect of temperature is also worth being discussed. Firstly, the carbon matrix corrodes faster when the temperature increases. [START_REF] Goellner | Degradation of Fe/N/C catalysts upon high polarization in acid medium[END_REF] Besides, in the frame of Le Chatelier principle, the equilibrium between the solid metal oxides and the dissolved Fe 2+ /Fe 3+ species will be displaced to counteract any change in temperature. Since the enthalpy of formation of Fe oxides is exothermic, [START_REF] Pourbaix | Atlas of electrochemical equilibria in aqueous solutions[END_REF] the equilibrium will be displaced to favour their dissolution when the temperature of the AST increases. More pronounced losses of Fe, larger variations of the mean NP size and of the NP density for the Fe0.5 sample aged at 60 °C vs. 25 °C quantitatively indicate that temperature determines the extent of Fe being redeposited in the form of Fe oxides.

For the Fe0.5 catalyst, both its low bulk Fe content and the initial Fe atomic dispersion explain that some leached Fe atoms do no reprecipitate but remain dissolved and diffuse outside the thin-film electrode in the bulk electrolyte. For Fe5.0 in contrast, both its ten-time higher Fe bulk content and the initial presence of Fe3C NPs favour high local Fe cation concentration near the interface during AST, leading to fast reprecipitation of Fe cations as ferric oxides on top of Fe3C particles.

While the results are unambiguous when it comes to the mild carbon corrosion in alkaline medium for these two Fe-N-C catalysts and on the fate of Fe during the AST, the possible catalytic role of the formed Fe oxides on the ORR is more complex to assess, due to their coexistence with a significant amount of (i) non-oxidized Fe3C NPs remaining after AST for Fe5.0, and of (ii) FeNxCy sites for Fe0.5. The challenge to quantitatively assess how much Fe is present as FeNxCy sites / unoxidized Fe3C NPs in aged Fe0.5 / Fe5.0 and how much is present as Fe oxide also contributes to the complexity of analysing the possible catalytic contribution of the operando formed Fe oxides with respect to the initially present ORR-active Fe sites. For Fe5.0, the significant presence of Fe3C

NPs free of oxide shell and the concomitant decrease of 30-40 % ORR activity (without any significant change in the Tafel slope) suggests that most of the activity loss results from two effects: a lowering of the turnover frequency for ORR via the formation of an iron oxide shell over some initially electrolyte-exposed Fe3C NPs, and a decreasing ORR-active surface area through the dissolution of other Fe3C NPs that were initially surrounded by a defective porous graphite shell.

For Fe0.5, the small decrease in ORR activity at 0.85 V after AST despite 68 % of all the Fe-N4 sites situated on the surface initially has been leached in the electrolyte is intriguing, and suggests that a second active site may have formed. Combining ICP-MS analyses of the electrolyte and X-EDS analyses on particle-free regions of the thin-film, we conclude that roughly one half of FeNxCy sites survived the AST, one sixth was leached into the electrolyte, and one third reprecipitated in the thin film as Fe oxide (0.45 wt %, corresponding to 3.6 µgFe (of Fe oxide) cm - 2 geo). While Fe oxides are known to have some ORR activity in alkaline medium, [START_REF] He | Review-Recent progress in electrocatalysts for oxygen reduction suitable for alkaline anion exchange membrane fuel cells[END_REF] previous works on Fe oxide supported on carbon do not suggest that such a low amount of Fe oxide could by itself account for a significant fraction of the ORR activity of Fe0.5 after the AST. However, the significant change in Tafel slope from 79  1 mV decade -1 to 107  40 mV decade -1 for Fe0.5 before/after [0.6-1.0 V -3s/3s -10 k -O2 -60 C] and the resulting more pronounced loss of ORR activity at high overpotential (Table S3) identify a change in mechanism. The low amount of Fe oxide NP formed in situ in this case may work in synergy with the remaining FeNxCy sites. Such a synergy was evoked for a model surface made of FeOx NPs deposited on Fe-phthalocyanine (Fe-Pc) crystals supported on graphene. [START_REF] Cheng | Iron oxide nanoclusters incorporated into iron phthalocyanine as highly active electrocatalysts for the oxygen reduction reaction[END_REF] The authors reported that the FeOx/Fe-Pc/G composite surfaces (with 10 wt. % or more of FeOx) were significantly more active than the Fe-Pc/G surface, and far more active than the FeOx/G surface. The synergy between FeOx NPs and Fe-Pc was proposed to be related to the improved reversibility of the Fe(III)/Fe(II) redox peak of Fe-Pc in the presence of FeOx NPs. While the estimated maximum amount of FeOx NP on Fe0.5 (0.45 wt. %) is far lower than in the above-mentioned work on model FeOx/Fe-Pc surfaces, the surface chemistries are otherwise similar, supporting that an analogous synergetic effect between FeOx and FeNxCy sites takes place in our case. Similar synergy was proposed by Feng et al. [START_REF] Feng | Well-defined Fe, Fe3C, and Fe2O3 heterostructures on carbon black: a synergistic catalyst for oxygen reduction reaction[END_REF] who prepared Fe2O3

NPs supported on high surface area carbon. Those Fe2O3 NPs were then thermally treated, leading to Fe NPs, Fe2O3 NPs or a mix of Fe, Fe2O3 and Fe3C NPs supported on carbon. The composite material performed better than the individual Fe phases. This result was accounted for by considering change in the electronic structure of Fe3C NPs by the formed Fe2O3 NPs (electron withdrawing effect of Fe2O3). It was also suggested that multiple valence states and polymorphism of Fe2O3 facilitate O2 cliving and further dissociation. In addition to a possible synergy between different Fe phases, the small but discernible ORR activity of N-doped carbon supports in alkaline is also worth pointing out. Gan et al. [START_REF] Gan | Fe2O3encapsulated and Fe-Nx-containing hierarchical porous carbon spheres as efficient electrocatalyst for oxygen reduction reaction[END_REF] recently synthesized a composite catalyst simultaneously containing Fe2O3-NPs/FeNxCy moieties encapsulated/embedded into multi-cage carbon spheres (Fe2O3/MCCS) or N-doped multi-cage carbon spheres (Fe2O3/N-MCCS). A decrease in the ORR activity (both half-wave potential and O2 diffusion-limited current) was observed after acidleaching or poisoning the Fe2O3/N-MCCS catalysts with cyanide ions (these treatments are supposed to dissolve/poison the Fe atoms, respectively), yet the residual ORR activity remained higher than that of Fe2O3/MCCS catalyst, pointing towards possible synergetic interactions between the N-doped support and the different Fe phases.

Conclusion

In summary, our results shed fundamental light into the mild carbon corrosion in alkaline medium for Fe-N-C catalysts, but also revealed electrochemical transformations occurring on single Fe

Intense bands at 2 .

 2 60, 3.77, 4.23, 4.57 and 5.19 angströms are observed in the 'Normalized Fe5.0-Fe0.0' difference signal, in close agreement with the PDF calculated using the Fe3C structure. This result is in line with former XAS, XRD and 57 Fe Mössbauer spectroscopy results, which evidenced the presence of Fe3C NPs in Fe5.0.[START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF] The Fe content after the pyrolysis step is close to 15 wt.%, and the structure of the carbon matrix is highly graphitic leading to a BET specific surface area ca. 450.0 m 2 g -1 .

Figure 1 .

 1 Figure 1. Structural characterisation of the fresh (a) Fe5.0 and (b) Fe0.5 catalysts. The graphs

Figure 2

 2 Figure 2 displays TEM, STEM images and STEM/X-EDS elemental maps of the Fe0.5 catalyst

Figure 2 .

 2 Figure 2. Morphological and chemical characterisation of the fresh and aged Fe0.5 catalysts.

oxide

  NPs form during ageing in alkaline electrolyte of a Fe-N-C catalyst initially comprising a mix of Fe3C particles and FeNxCy sites. Some other Fe-based NPs are however free of an O-rich shell after AST, and this may be explained by the perfect encapsulation of these Fe3C NPs by a graphite shell in the fresh Fe5.0 catalyst (Fig.3g, particle on top).

Figure 3 .

 3 Figure 3. Morphological and chemical characterisation of the fresh and aged Fe5.0

Figure 4 .

 4 Figure 4. (a) Kβ -detected Fe K edge HERFD XANES and (b) Fe Kβ XES spectra of fresh

Figure S4 )

 S4 Figure S4) that the gas atmosphere plays a minor role in the degradation mechanism/kinetics of

Fe0. 5

 5 and Fe5.0 electrocatalysts before/after [0.6-1.0 V -3s/3s -10 k -Ar -60°C], and the atomic percentages of the different chemical groups are displayed in Table S2. It can be observed that O atoms contained in the pristine Fe-N-C catalysts mostly participate in C-O-H/C-O-C bonds.

Figure 5a -

 5a Figure 5a-e displays Ohmic-drop corrected CVs obtained before and after [0.6-1.0 V -3s/3s -10

Figure 5 .

 5 Figure 5. Cyclic voltammograms of (a, b, c) Fe0.5 and (d, e) Fe5.0 electrocatalysts and ORR

  atom catalysts and Fe carbide nanoparticles in alkaline ORR conditions. By combining advanced physical, chemical and electrochemical techniques, we provided comprehensive evidence of a previously undisclosed Fe dissolution/Fe oxide reprecipitation mechanism. The results suggest that the redeposited Fe oxide particles possibly act in synergy with the untransformed FeNxCy moieties, translating into a mild change of the apparent activity of the electrode after AST. In contrast, Fe oxide shells on Fe carbide core seem less active than the native Fe carbide particles.We thus propose the following guidelines to maximize the ORR activity/stability of Fe-N-C materials in alkaline electrolyte: for Fe-N-C catalysts based on core-shell particles, further improved stability can be reached if all the Fe carbide particles are surrounded by a defect-free graphite shell. For Fe-N-C catalysts based on single atom sites, even higher initial ORR activity and higher stability can be reached by tailoring the synthesis and optimising the content of FeOx NPs on a N-C matrix comprising single Fe atom sites. Beside their practical interest, these findings also illustrate that operando characterization of atomic/nanometre-scale Fe-N-C catalysts is of prime importance to establish reliable structure-chemistry-performance relationships.CRediT authorship contribution statementRicardo Sgarbi: Sample collection and analysis; Investigation; Formal analysis; Drawing; Data curation; Writing -original draft. Kavita Kumar: Sample collection and analysis; Investigation; Formal analysis; Drawing; Data curation. Viktoriia A. Saveleva: X-ray absorption spectroscopy and X-ray emission spectroscopy measurements; Formal analysis; Data curation. Laetitia Dubau: STEM/X-EDS measurements; Formal analysis; Data curation. Raphaël Chattot: WAXS measurements; Formal analysis. Vincent Martin: Methodology; ICP-MS measurements; Formal analysis; Data curation. Michel Mermoux: Raman spectroscopy measurements; Formal analysis. Pierre Bordet: Methodology; PDF analysis. Pieter Glatzel: X-ray absorption spectroscopy and X-ray emission spectroscopy measurements; Formal analysis; Data curation. Edson A. Ticianelli:

Acknowledgements

This work was performed within the framework of the Centre of Excellence of Multifunctional Architectured Materials "CEMAM" n• ANR-10-LABX-44-01. The authors thank the European Synchrotron Radiation facility for provision of synchrotron radiation facilities at beamline ID06, and gratefully acknowledge financial support from the French National Research Agency through the ANIMA (grant number ANR-19-CE05-0039) and DEEP (grant number ANR-21-CE05-0021) projects. R.S. acknowledges Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil (grant number 1614344) and CAPES/COFECUB program (grant numbers: 88887-187755/2018-00 and Ph-C 914/18). R.S. and E.A.T are thankful to the São Paulo State Research Foundation (FAPESP -grant number: 2019/22183-6). Dr. R. Sgarbi and Dr. K. Kumar contributed equally to this work.

Funding acquisition; Supervision. Frédéric Jaouen: Funding acquisition; Project administration; Resources; Validation, Writing -review & editing. Frédéric Maillard: Conceptualization; Data curation; Drawing; Formal analysis; Funding acquisition; Methodology; Project administration; Resources; Supervision; Validation; Visualization; Writing -review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at DOI.


Nguyễn Thế

Denys Gamby

Marie Christine Lafarie-Frenot

LOADING RATE EFFECT ON MATRIX TRANSVERSE CRACKING IN AERONAUTICAL CFRP COMPOSITE LAMINATES

In this research, we address the evolution of matrix cracking in viscoelastic cross-ply laminates made of long Carbon Fibre Reinforced Polymer (CFRP). Monotonic tensile tests performed on [0 3 ,90 3 ] s laminates at 120°C have shown a significant influence of loading rate on cracking development. Several numerical simulations meant to display the effect of possible factors are proposed in turn. First, linear viscoelastic shear-lag approaches using failure criteria are developed to describe cracking evolution as a function of load level, assuming a constant loading rate. Then, a simplified Schapery 1-D model is used to characterize the nonlinear viscoelastic ply behaviour. The Correspondence Principle is applied to compute the time-dependent cracking development. This work shows that the viscoelastic behaviour of undamaged material cannot explain alone the loading rate effect on cracking. On the other hand, the loading rate dependence of critical strength gives good predicted cracking curves, which means that the important rate effect pertains to the damaged viscoelastic material in the process zone close to crack tips.

INTRODUCTION

Weight saving and high lifetime demands in aeronautic applications require using CFRP composite laminates in several aircraft structural parts. During a supersonic flight of Concorde's successor travelling at a speed of Mach 2, the surface temperature will range between 100°C and 130°C, depending on the considered area. Under such an environment with high temperatures and mechanical loads, the composites display several failure modes, such as matrix cracking, fibre breakage and delamination. In order to guarantee the structural integrity, transverse matrix cracking must be assessed and monitored as it often precedes other damage events.

The recent literature contains some experimental and analytical studies of the influence of viscoelastic behaviour on matrix cracking. Time dependent matrix cracking in transverse plies of cross-ply carbon/epoxy laminates was experimentally investigated by K.Ogi and Y.Takao [START_REF] Ogi | Modeling of timedependent behaviour of deformation and transverse cracking in cross-ply laminates[END_REF] and Raghavan and Meshii [START_REF] Raghavan | Timedependent damage in carbon fibrereinforced polymer composites[END_REF]. Under quasi static loading, it is observed that the matrix transverse cracking growth rate depends upon the loading rate at a high temperature of 110°C [START_REF] Ogi | Modeling of timedependent behaviour of deformation and transverse cracking in cross-ply laminates[END_REF], or even at room temperature [START_REF] Raghavan | Timedependent damage in carbon fibrereinforced polymer composites[END_REF]. To the knowledge of the authors, up to now there are very few analytical (linear or nonlinear) viscoelastic models using the fracture mechanics approach to predict crack density as a function of time and applied stress level. A probabilistic failure model has been proposed in [START_REF] Ogi | Modeling of timedependent behaviour of deformation and transverse cracking in cross-ply laminates[END_REF] giving a good agreement between experimental results and predictions under monotonic loading. However, it provides little physical understanding, though the cracking behaviour can be phenomenologically described.

The matrix cracking evolution under monotonic loading in viscoelastic cross-ply laminates is addressed in this research. The objectives are to model the crack development and to assess the respective contributions of different potential causes that might explain the effect of loading rate on damage process. First, several failure criteria are used in a 1-D linear viscoelastic shear-lag approach to predict cracking evolution. Next, a 2-D linear viscoelastic damage analysis is developed. Then, a simplified 1-D non linear analysis is proposed. The numerical simulation results obtained from the above approaches are finally compared with experimental data concerning crack density observed during uniaxial tensile tests on oo nm S 09 0 ⎡ ⎣ ⎤ ⎦ laminates. 1. Monotonic uniaxial tensile tests were conducted on the cross-ply laminates at a temperature of 120°C to measure transverse matrix crack density as a function of applied load [START_REF] Lafarie-Frenot | Experimental and numerical analysis of loading rate and temperature effects on matrix cracking in CFRP laminates[END_REF]. Three different loading rates, producing three respective crosshead velocities (0.01 mm/min; 1 mm/min and 10 mm/min), were imposed. The experimental results are presented in Fig. 1. At this temperature, loading rate has a significant influence on cracking. First, it can be seen that the occurrence of the first cracks is delayed when the loading rate increases. Namely, the higher the stress rate, the higher is the first ply failure stress. It is also observed that the higher the loading rate the greater the tensile strength. Moreover, the crack density increases more rapidly as a function of applied stress level if the loading rate decreases.

EXPERIMENTAL RESULTS

A

Fig. 1. Effect of loading rate on matrix cracking evolution during monotonic tensile tests at 120°C

NUMERICAL

One dimensional linear analysis

In this section, the one dimensional viscoelastic response of the laminate will be considered. We also take into account residual thermal stresses (at 120°C) in this analysis. First, we find the stress and strain responses of the undamaged laminate in the case when there is no transverse matrix crack. The outer 0° layers and the inner 90° layer are supposed to display elastic and viscoelastic behaviours in the x-direction, respectively. Let ( )

(2) x0 1 11 x0 tT J ε-α ∆ = σ % % ( ) t (1)
( )

1 x0 2 22 x0 (t) T J (t) (t) ε-α ∆ = ⊗ σ % % (2) ( ) ( ) (
)

12 12 x0 x0 12 h (t) (t) 1 h (t) σ +σ = + σ %% (3)
where 11 11 J1 / E = and ; a superimposed tilde denotes the through thickness average of a particular variable;

12 1 2 hh / h = ( ) x0 t ε %
is the average x-direction laminate strain; is the average stress in layer i (i=1,2);

(i) x0 (t) σ % a TT T 0 ∆ =-
is the difference between specimen temperature, T a (120°C), and the stress-free temperature, T 0 (180°C);

( )

22 J t is the creep function of the material such that 22 22 E (t) J (t) H(t) ⊗ =
, H(t) being the Heaviside step function. The equation system can be solved by using the Laplace transform. For this

( n 3 t 22 20 2n n1 J( t ) J J 1e -τ = =+ - ∑ )
, where is a constant and is the retardation time related to the amplitude . The identification of these material constants obtained from creep/recovery tests on [90°] specimens is presented in Table 2.

20 J n τ 2n J Table 2.

Parameters of transverse direction compliance at 120°C

If the tensile applied stress becomes high enough, the 90° plies can crack. The experimental observations show that the matrix crack distribution in the central 90° layer tends to become periodic when the applied load increases. As a result, the damaged laminate is divided into several unit-cells comprised between two existing adjacent cracks assuming a 2L uniform spacing. Due to the symmetry of the cracked laminate, only a half of the unit-cell is considered (Fig. 2). The appropriate boundary conditions are given by ( ) ( )

12
Ux 0 U x 0 0 = == = and ( ) ( )

1 x xL 0 σ == %
, where U 1 and U 2 are respectively the x-direction displacements of the 90° and 0° layers. Taking into account the viscoelastic behaviour of the central layer in the x-direction and the residual thermal strains, the constitutive equations of the layers and the interface can be written in the form: ( )

1 (1) x2 2 x2 (x,t) E (t) (x,t) T ⎡ ⎤ σ =⊗ ε -α ∆ ⎣ ⎦ % % (4) ( ) ( ) (2) (2) x1 1 x1 x,t E x,t T ⎡ ⎤ σ =ε -α ∆ ⎣ ⎦ % % (5)
where ( ) ( ) ( ) x,z h ,t * τ= τ = . Now, using the equilibrium equations of the layers and of the entire laminate, taking into account the boundary conditions at x=0 and x=L, results in the time evolutions of the maximum average normal stress and the maximum average strain between two adjacent cracks in the following form: . The predicted curves are obtained by using the above failure criteria for three values of the loading rate at 120°C. It can be seen that the above criteria give practically the same numerical results and that they allow the experimental data to be well represented only if the critical values depend on the loading rate, which amounts to involve the viscoelastic character of the failing material in the process zone around crack tips.

22 23 Gt E t 21 ⎡ ⎤ =-ν ⎣ ⎦ is
( ) () () ( ) 1 (1) xx 0 1D 1 0, t t 1 cosh L ⎡ ⎤ σ= σ × - ⎢ ⎥ α× ⎢ ⎥ ⎣ ⎦ %% (7) () ( ) ( ) () () ( ) (1

Two dimensional linear analysis

The one dimensional analysis does not take into account the viscoelastic character of the outer layers in the y-direction. We now study the impact of this simplification. Using an approach similar to that developed in the unidirectional analysis, we first find the response of the undamaged laminate, then that of the cracked central layer. Using the two dimensional viscoelastic constitutive equations of the layers, and taking into account the laminate symmetry and the boundary conditions, the x-direction maximum stress and strain between two existing adjacent cracks are obtained in the form: are, respectively, the stress in the 90° layer and the strain of the undamaged laminate subjected to the same loading. They can be found by solving the system of layer constitutive equations, taking into account the "viscoelastic Poisson effect", given in matrix form as [START_REF] Ogi | Modeling of timedependent behaviour of deformation and transverse cracking in cross-ply laminates[END_REF]:

( ) () () ( ) 1 (1) x x0 2D 1 0, t t 1 cosh L ⎡ ⎤ σ= σ × - ⎢ ⎥ α× ⎢ ⎥ ⎣ ⎦ %% ( 10
) () ( ) ( ) () () () ( ) 2 (1) (1
() () () () () () () 1 x0 x0 2 22 12 1 y0 1 12 11 y0 t t JtJ t JJ t ⎧⎫ σ ⎧⎫ ε-α ∆ Τ ⎡⎤ ⎪⎪ ⎪ =⊗ ⎨⎬ ⎨ ⎢⎥ ε-α ∆ Τ σ ⎪⎪ ⎣⎦ ⎪⎪ ⎩⎭ ⎩⎭ % % % % () () () () () () () 2 x0 11 12 x0 1 2 12 22 y0 2 y0 t JJ t JJ t t t ⎧⎫ σ ⎧⎫ ε-α ∆ Τ ⎡⎤ ⎪⎪ ⎪ =⊗ ⎨⎬ ⎨ ⎢⎥ ε-α ∆ Τ σ ⎪⎪ ⎣⎦ ⎪⎪ ⎩⎭ ⎩⎭ % % % % ⎪ ⎬ ⎪ ⎬
where 12 12 11 J =-ν E ; the stresses in the layers must satisfy the averaged equilibrium equations of the laminate in the x-direction and ydirection, namely . Now the same failure criteria can still be used to predict crack multiplication. Fig. 4 represents the zoomed-in simulation results obtained from a maximum strain failure criterion whose critical value is independent of the loading rate, namely

( ) ( ) 1 x 0, t c ε =ε %
, where c ε is a constant. In this case, for the three considered loading rates, the numerically predicted crack curves are very close from each other. This proves that, as was the case in the one-dimensional study, a criterion insensitive to the loading rate does not sufficiently convey the influence of the loading rate on cracking, even when taking into account the two-dimensional stress state.

Fig. 4.

Predicted cracking evolution at 120°C for three loading rates using a rate-independent critical strain criterion (ε c = 0.0058)

One dimensional non linear analysis

The creep tests revealed that the material at hand displays a very marked non linear behaviour, which raises the question whether the non linearity can increase the influence of the loading rate on cracking. A simplified 1-D Schapery model will be used to characterize the non linear viscoelastic behaviour of the 90° layer [START_REF] Kennedy | Threedimensional, nonlinear viscoelastic analysis of laminated composites[END_REF][START_REF] Schapery | On the characterization of nonlinear viscoelastic materials[END_REF].

Supposing that the non linear behaviour of material in the central layer is described by only one stress-dependent function [START_REF] Schapery | On the characterization of nonlinear viscoelastic materials[END_REF] , w e 2 g Fig. 5. Crack density (cm -1 ) versus applied stress (MPa) at 120°C for three loading rates.

Comparison between experiment and 1-D linear and nonlinear simulations using a rate-dependent critical strain criterion obtain:

( ) ( )

1 x x,t ε % = () ( ) () ( ) 1 1 22 2 ef x 2h
Jt g x , z , t ⊗σ σ

, where the symbol 1 2h

denotes the average of a particular function over the thickness of the central layer, and the effective stress [START_REF] Schapery | Nonlinear Viscoelastic and Viscoelastic Constitutive Equations Based on Thermodynamics[END_REF] is defined by: , specimens at several stress levels. A possible identification procedure is described in [START_REF] Gamby | On The Characterization by Schapery's Model of Non-linear Viscoelastic Materials[END_REF]. In order to apply the nonlinear correspondence principle [START_REF] Schapery | Correspondence principle and a generalized J integral for large deformation and fracture analysis of viscoelastic media[END_REF], the constitutive equations of the layers must be written in the form: Dt J t J = and the superscript "R" denotes the solution of a reference nonlinear elastic problem corresponding to the nonlinear viscoelastic problem with the same traction boundary conditions. The viscoelastic and elastic stresses are the same, namely

() ( )( ) ( ) () ( ) () () ( ) 1 1 x2 0 2 e f x 2h 1R x x,t D t J g x,t Dt x , t ε= ⊗ σ σ =⊗ ε % % 1 (12) () ( ) () ( )( ) () ( ) () () ( ) 22
( ) ( ) ( ) ( ii R xx x,
( ) ( ) () ( ) R RR 1 23 2 ef R 1R (2)R (1)R 11 xx 2 x 20 1 2h x 1g k 3 J g J * * * * ∂τ - ∂∂ ⎡ +ν τ τ ⎢ ∂τ ⎣ ⎧⎫ ⎪⎪ ×σ -σ σ= ⎨ ⎪ ⎩ %% % 0 ⎤ ⎥ ⎦ ⎬ ⎪ ⎭ (14)
Combining this with the two following equilibrium equations of the 0° and 90° layers:

(1) R R x 1 0 xh * ∂σ τ += ∂ % ( 15
) (2)R R x 2 0 xh * ∂σ τ -= ∂ % ( 16
)
one now obtains a system of nonlinear differential Eqs. ( 14), ( 15) and ( 16), with boundary conditions:

( ) ( ) 1R x xL 0 σ= = % ( ) ( ) ( ) () 2R x1 xL 1h t σ= = + σ % 2 ( ) R x0 0 * τ= = (17)
The unknowns in the above system are the "R" elastic stresses. A numerical program using the shooting method [START_REF] Press | Numerical recipes in Fortran[END_REF] was developed to solve it.

Then the maximum viscoelastic strain between two adjacent cracks in the central lamina is found by using Eq. ( 12). Finally, a critical strain failure criterion is used to model the transverse cracking evolution. A good agreement between the simulated curves and experiments could only be achieved by again introducing the loading rate into the critical values. In Fig. 5, the simulation of crack density curves predicted from 1-D linear and nonlinear analyses, using a rate-dependent critical strain criterion in the central 90° layer, is represented.

DISCUSSION AND CONCLUSIONS

The monotonic tensile tests performed on the carbon/epoxy oo nm S 09 0 ⎡ ⎣ ⎤ ⎦ at 120°C, with the three respective crosshead velocities (0.01 mm/min, 1 mm/min and 10 mm/min), have displayed a marked loading rate dependence for the transverse matrix cracking evolution.

Several phenomena might explain this effect: the viscoelastic behaviour of the undamaged material in the 90° plies and that of the damaged material surrounding the crack tip vicinities. The aim of this paper is to assess the respective contributions of the different potential causes. For such a purpose, several numerical viscoelastic simulations were proposed in turn.

First, a 1-D linear viscoelastic shear-lag approach, which takes into account thermal stresses, was analyzed. Several failure criteria (critical stress, critical strain and Reiner-Weissenberg free energy density), used to describe cracking evolution as a function of load level assuming a constant loading rate, give very close numerical results. The failure criteria can properly display the loading rate effect only if the stress rate is incorporated.

Next, a 2-D linear viscoelastic analysis was developed. The numerically predicted crack density curves show that, even if the 2-D stress state is taken into account, the viscoelastic character of the undamaged material is not marked enough to explain alone the influence of the loading rate on cracking curves. The improvement brought about by the incorporation of thermal stresses is not significant at the considered temperature.

The simplified 1-D Schapery model was proposed to characterize the nonlinear viscoelastic ply behaviour by using data obtained from creep-recovery tests. A maximum strain failure criterion is used to numerically model the time-dependent cracking evolution. The comparison of 1-D linear and nonlinear numerical results shows that, though important, the material nonlinearity does not significantly enhance the stress rate sensitivity of the damaging process.

This work shows that the viscoelastic behaviour of the undamaged material cannot alone explain the marked effect of the loading rate on transverse cracking. On the other hand, if the loading rate dependence of critical strength is taken into account, good predicted cracking curves are obtained, which means that the observed important rate effect is attributable to the damaged viscoelastic material in the process zone close to crack tips. The precise causes of this loading rate influence remain to be cleared up; cracking tests conducted in a neutral environment will be the next logical step of this research in order to evaluate a possible oxidative effect.

The time-dependent crack density evolution in a viscoelastic laminate subjected to monotonic tensile loading was also modelled. As shown in Fig. 3 and Fig. 5, the predicted cracking curves, for each loading rate, are in good agreement with experiment except for the very early phase of the phenomenon. A probabilistic failure criterion can be attempted in order to better reproduce the S-form of the cracking curves by properly describing the very low crack density range.

  constitutive and equilibrium equations of the undamaged laminate can be written in the form:

Fig. 2 .

 2 Fig. 2. Laminate and crack g eometries

Fig. 3 .

 3 Fig. 3. Measured and predicted cracking evolution at 120°C for three loading rates. Comparison between simulated curves obtained from critical strain criterion (ε c = 0.0058; k ε = 0.001; n = 0.23), critical stress criterion (σ c = 50 MPa; k σ = 11MPa; m = 0.2), and free energy criterion (ϕ c = 0.1975 MNm/m 3 ; k ϕ = 0.065 MNm/m 3 ; p = 0.25)

  g =0.14 and b g =2, obtained from creep-recovery tests on [90°]

Table 1 .

 1 Elastic

	properties and coefficients of
	thermal expansion (CTE) of the unidirectional
	ply at 120°C
	Property		Value
	Longitudinal modulus E 11	148 (GPa)
	Transverse modulus	E 22	7.12 (GPa)
	In-plane Poisson's ratio ν 12	0.326
	In-plane shear modulus G 12	3.3 (GPa)
	Longitudinal CTE	α 1	0.23 (10 -6 °C)
	Transverse CTE	α 2	30 (10 -6 °C)