S Mathieu

L Le Pivaingt

O Feny

M Vilasi

A Stuppfler

J-L Guichard

Put C A Vande

D Monceau

A Alloy

B Mass

C Oxidation

C Carburization

Investigation of the metal dusting attack on the temperature range 500-700 °c using X-ray tomography

Keywords:

A test rig consisting of a quartz tube placed in a horizontal fumace made of five independently regulated heating zones allowed the evaluation of the metal dusting attack of a FeNiCr alloy. Fifteen samples were exposed in a temperature gradient from 504 ° to 704 °C, 1.1 bar, to a highly carburizing atmosphere for 1500 h. Below 561 •c the high density of pits led to uniform corrosion whereas localized pits developed at higher ten1peratures. In depth pit growth rate raised to a maxinmm at 632 •c, then decreased showing that it depends both on ten1perature and on the carbon activity gradient.

Introduction

When exposed in carburizing atmosphere in the intem1ediate 400-800 •c temperature range, heat resistant alloys may suffer from severe attack by carbon, like metal dusting. This latter is a prominent cause of corrosion daniage which leads to the local disintegration of the alloy into a dust of carbides, oxides, metallic particles and graphitic carbon [1-9]. Because it is characterized by a pit like degradation which grows with tin1e exposure to the carbon-bearing gas, this catastrophic wastage is a severe problem because it seriously decreases the lifetin1e of the materials [START_REF] Nishiyama | Metal dusting behaviour of Alloy 800H in laboratory carbonaceous environments under high pressure[END_REF]. Meta! dusting occurs under conditions where carbon deposition and oxide formation competed. For this reason, aluminum and/or chromium are generally added either to the alloy composition [START_REF] Nishiyama | Metal dusting behaviour of Cr-Ni steels and Nibase alloys in a simulated syngas mixture[END_REF][START_REF] Young | High Temperature Oxidation and Corrosion of Metals[END_REF] or as coating [START_REF] Rosado | Protective behavior of newly developed coatings against metal dusting[END_REF][START_REF] Chun | Metal dusting resistant alumina forming coatings for syngas production[END_REF][START_REF] Alvarez | Protective coatings against metal dusting[END_REF] because they are able to develop protec tive alumina or chromia scales under very low oxygen potential, that have the potential to prevent the alloy from metal dusting.

The metal dusting phenomenon is characterized by an incubation period which partly depends on the protective nature of the oxide scale.

Meta! dusting phenomenon involves supersaturated gas (ac> 1) with respect to graphite and the presence of e.g. Fe or Ni containing phases, acting as catalysts. Thanks to their partially filled d-orbital by electrons, these metallic phases are able to achieve overlap with CO orbitais and push elecn• on density into the anti-bonding orbital of CO [START_REF] Nishiyama | Improving metal dusting resistance of. transition-metals and Ni-Cu alloys[END_REF][START_REF] Andreoni | Binding and dissociation of CO on transition-metal surfaces[END_REF], facilitating its dissociation according to the push-pull mechanism of Seip et al. [START_REF] Seip | Interaction of CO with an Fe (111) surface[END_REF]. The ability of a metallic phase to catalyze CO dissociation is therefore function of its d-orbital filling by elecn•ons. Once the oxide scale fails to protect the alloy, catalysts are in contact with the super saturated gas. The carbon released by CO dissociation diffuses within the alloy up to its saturation and then leads to the formation of carbides, and/or graphite [START_REF] Young | Recent advances in understanding metal dusting: a review[END_REF]. This results in the alloy degradation and generally in the formation of pits at the locations where the oxide scale failed to protect the alloy. Pits growth rate can be very rapid as recently shown by Fabas et al. [19] who evaluated on a 800HT alloy an in depth pit growth up to 0.1 µm.h-1 at 570 •c and 21 bars in a methane stean1 reforming attnosphere.

Multiple mechanisms were proposed to explain the metal dusting behavior for ferritic and austenitic materials [1-9,20-26]. For iron and low alloyed Fe-based materials, degradation is based on the formation of metastable cementite, and its decomposition into graphite and iron at the graphite/cementite inter f ace [START_REF] Grabke | Thermodynamics, mechanisms and kinetics of metal dusting[END_REF] or its disintegration due to graphite nucleation and grow within cementite [START_REF] Young | Recent advances in understanding metal dusting: a review[END_REF]. Corrosion of nickel and low alloyed Ni-based materials involves the formation of a carbon super saturated matt• ix (small carbon solubility in the austenitic matt• ix [START_REF] Nishiyama | Metal dusting behaviour of Cr-Ni steels and Nibase alloys in a simulated syngas mixture[END_REF][START_REF] Fabas | Mechanism of metal dusting corrosion by pitting of a chromia-forming alloy at atmospheric pressure and low gas velocity[END_REF]) before degradation occurs either due to growth inside the alloy of graphitic sloping planes [START_REF] Schneider | Microprocesses of metal dusting on nickel and Ni-base alloys[END_REF][START_REF] Grabke | Resistance of 9-20%Cr-steels against metal dusting[END_REF] or because of C crystallization within the Ni-matt•ix [START_REF] Zeng | Relationship of carbon crystallization to the metal-dusting mechanism of nickel[END_REF]. As for high alloyed Fe-and Ni-based materials, degra dation mechanisms sinular to those of low alloyed materials were pro posed by some authors while others proposed more complex and diverse https:/ /doi.org/10.1 Ol 6/j.corsci.2021.109863 mechanisms [START_REF] Fabas | Mechanism of metal dusting corrosion by pitting of a chromia-forming alloy at atmospheric pressure and low gas velocity[END_REF][START_REF] Szakálos | Mechanisms and driving forces of metal dusting[END_REF][START_REF] Albertsen | A model for high-temperature pitting corrosion in nickel-based alloys involving internal precipitation of carbides, oxides, and graphite[END_REF].

A multiplicity of parameters, among these the temperature [START_REF] Chun | Metal-dusting corrosion of low-chromium steels[END_REF][START_REF] Müller-Lorenz | Coking by metal dusting of steels[END_REF][START_REF] Chun | Metal dusting corrosion of austenitic 304 stainless steel[END_REF][START_REF] Rouaix-Vande Put | Performance of Chromiaand Alumina-Forming Fe-and Ni-base alloys exposed to metal dusting environments: The effect of water vapor and temperature[END_REF], the gas pressure [START_REF] Nishiyama | Metal dusting behaviour of Alloy 800H in laboratory carbonaceous environments under high pressure[END_REF][START_REF] Natesan | Development of materials resistant to metal dusting degradation[END_REF][START_REF] Rouaix-Vande Put | Performance of Chromiaand Alumina-Forming Fe-and Ni-base alloys exposed to metal dusting environments: The effect of water vapor and temperature[END_REF][START_REF] Maier | Metal dusting of 9-20%Cr steels in increased pressure environments at 560 \u0002C[END_REF][START_REF] Levi | Metal dusting of type 316 stainless steel in high pressure environments between 450 \u0002C and 650[END_REF], the nature of the atmosphere [START_REF] Rouaix-Vande Put | Performance of Chromiaand Alumina-Forming Fe-and Ni-base alloys exposed to metal dusting environments: The effect of water vapor and temperature[END_REF][START_REF] Putrevu | Effect of water vapor on metal dusting behavior of ferrous alloys[END_REF][START_REF] Yin | Effect of gas composition on coking and metal dusting of 2.25Cr-1Mo steel compared with iron[END_REF][START_REF] Nishiyama | Effect of syngas composition on metal dusting of alloy 800H in simulated reforming gas atmospheres[END_REF][START_REF] Zhang | Effect of gas composition on cementite decomposition and coke formation on iron[END_REF][START_REF] Guevara | Statistical lifetime modeling of FeNiCr alloys for high temperature corrosion in waste to energy plants and metal dusting in syngas production plants[END_REF], the gas velocity [START_REF] Walker | Carbon formation from carbon monoxide-hydrogen mixtures over iron catalysts. II -rates of carbon formation[END_REF][START_REF] Rouaix-Vande Put | Relevance of other parameters than carbon activity in defining the severity of a metal dusting environment[END_REF], the alloy composition [START_REF] Nishiyama | Metal dusting behaviour of Cr-Ni steels and Nibase alloys in a simulated syngas mixture[END_REF][START_REF] Grabke | Resistance of 9-20%Cr-steels against metal dusting[END_REF][START_REF] Zhang | Coking and dusting of Fe-Ni alloys in CO-H2-H2O gas mixtures[END_REF][START_REF] Zhang | Alloying with copper to reduce metal dusting of nickel[END_REF][START_REF] Grabke | Metal dusting of nickel-base alloys[END_REF][START_REF] Strauß | Role of alloying elements in steels on metal dusting[END_REF][START_REF] Fabas | Metal dusting corrosion of austenitic alloys at low and high pressure with the effects of Cr, Al, Nb and Cu[END_REF], its microstructure [START_REF] Young | Metal dusting reaction mechanisms[END_REF][START_REF] Speck | Metal dusting of nickel-aluminium alloys[END_REF][START_REF] Grabke | Effects of grain size, cold working, and surface finish on the metal-dusting resistance of steels[END_REF] or still its surface features (cold work or surface finish [START_REF] Chun | Metal-dusting corrosion of low-chromium steels[END_REF][START_REF] Grabke | Metal dusting of nickel-base alloys[END_REF]), are recognized to affect the rate of the degradation by MD [START_REF] Grabke | On the mechanism of catastrophic carburization: metal dusting[END_REF]. In fact, the multiplicity of factors affecting metal dusting made hard the comparison of literature results. Still more complicated is the estimation of the service life of the materials basing on the available data. These are very specific to a set of conditions and generally correspond to a definite temperature that authors assumed to be the more severe for their application. A limited number of studies reports the metal dusting progression on a wide range of temperature [START_REF] Schneider | Microprocesses of metal dusting on nickel and Ni-base alloys[END_REF][START_REF] Chun | Mechanisms of metal dusting corrosion of Iron[END_REF][START_REF] Nishiyama | Metal dusting behaviour of Alloy 800H in laboratory carbonaceous environments under high pressure[END_REF], although it is fully recognized that metal dusting occurrence strongly depends on oxide formation. Considering this difficulty and because of the specificity of the gas atmosphere which has to be tested, a test rig was specially built for the present study.

The present paper aims to present the test rig that has been developed with ICAR'partners with the overall objective to evaluate the metal dusting resistance of an austenitic heat resistant alloy (CT15C) devoted to hydrocarbon processing in a 10%H 2 -17%N 2 -70%CO -3%CO 2 (in vol%) atmosphere. As components in service are rarely employed in isothermal conditions, the metal dusting behavior is assessed in the range of temperature 500-700 • C to determine the temperature domain for which the corrosion rate is the highest. X-ray tomography is systematically used to examine the attack morphology and the pit depth and diameter.

Materials and methods

Table 1 shows the nominal composition of the cast CT15C alloy from which the tested specimens were pulled out. The alloy presented a coarse austenitic structure with chromium and niobium rich carbides forming an eutectic network at metal grain boundaries. Grain size was between 20 and 150 µm.

The test rig consisted of a quartz tube placed in a horizontal furnace (Fig. 1a) made of five independently regulated heating zones. The regulation allowed the control of a reproducible and linear thermal gradient of approximately 3 • C per cm along the furnace length. This was checked thanks to the 27 thermocouples introduced in the tube that allow the precise measurement of the thermal gradient (Fig. 1b). The working zone was as long as 120 cm and the used temperature range for the study extended over 504-704 • C. The employed gas contained 10% H 2 -17%N 2 -70%CO -3% CO 2 (in vol%) with a gas flow rate of 60 NL. h -1 , a gas velocity of 2.3 mm.s -1 and an operating total pressure of 1.1 atm.

The carbon activity (a c ) for this carbonaceous atmosphere was calculated both from CO reduction (Eq.1) and Boudouard (Eq.2) reactions, Table 2. The employed thermodynamic data are reported in Table 2. Because they are reputed to be sluggish [START_REF] Grabke | Thermodynamics, mechanisms and kinetics of metal dusting[END_REF], reactions involving CH 4 were not taken in account in this estimation.

In the present work, the oxygen partial pressure p(O 2 ) was supposed to be set by the CO/CO 2 equilibrium (Eq.3). It evolves from 10 -32 to 10 -24 atm between 500 • C and 700 • C. The partial pressure of water was thus deduced from the dissociation equilibrium of water (Eq.4). By the way, the carbon activity a c can be deduced both from Eq.1 or Eq.2. The calculation showed that the carbon activity values were similar using Eq.1 or Eq.2 for this gas mixture all over the temperature range, i.e. from

Table 2

Thermodynamic data employed to calculate a c and the oxygen partial pressure p (O 2 ) according to temperature (Fig. 2). Fig. 2. Theoretical carbon activity (from Boudouard equilibrium) and oxygen partial pressure (from CO +1/2 O 2 = CO 2 equilibrium) according to the temperature. The investigated range of temperature for the present study is designated by the grey dotted area. The carbon activity and the oxygen partial pressure vary from 4×10 3 up to 18 and from 10 32 up to 10 24 atm respectively.

Table 1

Nominal composition of CT15C alloy, in wt%.

500 • to 700 • C.
The calculated values of a c and p(O 2 ) are reported in Fig. 2 for the investigated range of temperature. The carbon activity decreased with increasing temperature from 4500 to 18. These carbon activity values, greater than 1, are only possible because the carburizing atmosphere is supersaturated, i.e. not in equilibrium [START_REF] Young | Recent advances in understanding metal dusting: a review[END_REF]. A mass spectrometer analyser was placed at the furnace outlet to confirm that the composition of the supersaturated gas did not change during its flow.

This out of equilibrium situation constitutes the driving force to deposit carbon. Carbon activity reaches the value of 1 at 860 • C. Therefore, at temperature higher than 860 • C, carburization could still occurs but metal dusting is not expected with the present gas mixture as the formation of graphite is not favored anymore.

In this equipment the gas enters the furnace from the left in the hottest zone and exits at the right (Fig. 1a). Samples were placed on the alumina made holders (Fig. 1c) and introduced in the inner zones of the furnace (in Z2-Z3-Z4) for experiments. Fifteen parallelepiped specimens (20 ×10 × 2 mm, i.e. a surface area of 5.2 cm 2 ) were introduced along the thermal gradient. Sample surface was prior ground using P800 SiC grit paper. Stops were completed at: 250 h; 500 h; 1000 h; 1250 h; 1500 h (end of run). At each stop, the furnace was cooled down at 3 • C min -1 . Once at room temperature, the CO containing atmosphere was replaced by argon gas. Sample holders were then removed from the furnace to characterize the specimens. The mass spectrometer analyser was used to check that the CO was fully evacuated before opening the furnace.

At in-between and final stops the samples were weighed with their adherent carbon when present at the surface. However the mass change measurement is inaccurate because of substantial carbon loss due to the specimens handling. Thus, the samples were slightly brushed to remove carbon deposit and weighed again with an accuracy of 1 mg. Only the mass variation of brushed specimens are considered in the following. Fig. 3 gives a view of the general aspect after 500 h of exposure of the samples a) still on the sample holder and b) after carbon removing. Photographs of both sides of each sample were taken at every withdrawal to follow the evolution of the corrosion damage; e.g. as shown in Fig. 3b.

As the overall mass change measurement of samples is not adapted to determine corrosion advancement for metal dusting corrosion, as it will be demonstrated hereafter, the morphology of the attack was investigated using X-ray tomography. Indeed, alloys suffering from metal dusting were degraded locally via a pitting-type mechanism. X-ray tomography allowed the full characterization of pit dimensions (diameter and depth) which were highly relevant data to determine the resistance of a given alloy to the metal dusting attack. This technique is appropriate to determine the morphology of the volume affected by corrosion because of different X-ray absorption coefficients between the alloy and the carbon rich corrosion products. Nanotom Phoenix X-ray tomograph (GE) at a spatial resolution of 11 µm/vx (vx voxel) was used to examine the samples after the final removing and cleaning (after 1500 h exposure). Samples were illuminated with a tungsten X-ray beam which allowed, using a X-photon detector, to record the beam that had passed through the sample. Image acquisition was repeated at different rotation angles and the different sections were then reconstructed using algorithms to form the three-dimensional image of the sample. Once reconstructed the evaluation of alloy wastage morphology and wastage rate were deduced from the dimensional investigation of these 3D numerical samples. It should be noticed that because of the spatial resolution of 11 µm, no attempt was performed to estimate mass variation from the X-ray tomography results.

Results

Mass change measurements

Fig. 4 reports the mass change measurements vs time and temperature of cleaned samples. It is chosen here to report the mass loss at each stop rather than the mass loss evolution vs time of each sample for a better emphasis of the temperature effect. Moreover, the plot of mass loss of samples is preferred to the one of mass gain because samples exhibit mass gains only for the first runs (250 h and 500 h). The mass gain testifies for CT15C oxidation during the first period. It is supposed that after sample cleaning the mass associated to residual carbon deposit is negligible. No degradation of the sample surfaces was detected after 250 h of exposure after careful observation of the samples using an optical microscope. After 500 h of exposure, the samples exposed to temperatures lower than 561 • C presented mass gains due to carbon deposit (not shown here) but mass loss after cleaning. Some carbon remained stuck to the surface of these samples after cleaning. At the opposite, at higher temperatures samples still presented mass gains showing that the oxidation of the alloy pursued.

After 1000 h of exposure, all samples placed in the ranges 518-575 • C and 632-674 • C were losing mass. At intermediate temperature and at the highest temperatures of 689 • C and 703 • C the mass gain still predominated.

Finally, at longer exposure time (1250 and 1500 h) mass loss was recorded for all samples but the mass losses at 504 • C, 689 • C and 704 • C were lower than 3 mg.cm -2 .

These observations demonstrate that the range of temperature where the metal dusting phenomenon occurs for this alloy spread over 518-674 • C. In this range, the evolution of mass loss with temperature evidences two critical temperature domains where the degradation occurred faster (around 560 • C and 630 • C) and a domain in between where the degradation appears rather low (from 575 up to 618 • C).

Post exposure characterizations

Fig. 5 shows the photographs of the cleaned surface (only one side is presented here) for all samples after the final removal -1500 h -and the corresponding sample side reconstructed from X-ray tomography measurements according to the exposure temperature.

The surface area blackened by residual carbon increases from 504 • to The attack morphology readily changes beyond 561 • C. The number of pits drastically decreases. The edges and the surface area that were in contact with the alumina holder are especially attacked but isolated pits are also evidenced. The latter will be very useful, particularly to determine pit growth rate as developed in Section 3.3. The location in contact with the sample holder leads to the formation of pit lines due to pit coalescence [START_REF] Young | Understanding metal dusting mechanisms[END_REF]. It can be noticed that this line width increases from 589 • C up to 632 • C then decreases. It is the same for the circular isolated pits for which the surface diameter follows the same trend. Pit amount and morphology can be observed using the reconstructed 3D surfaces. The number of pits per surface area has not been evaluated here because i) the number of samples is too low to have a representative statistic, ii) there is an effect of sample geometry as well as of the sample holder and iii) because this criteria does not appears as the most critical to estimate the material lifetime, as will be presented hereafter. The observation suggests their amount increases with the temperature on the range 575-689 • C but this tendency has to be taken with caution. Supplementary characterizations, of the oxide scale notably, would be necessary to definitively conclude on this trend.

Finally, if one pays attention to the diameter of the pits on the surface of a sample, the most obvious is for the sample exposed to 632 • C, it is clear that the values of the diameter of the pits do not take randomized values. Pits sizes can be classified in batches according to their diameter (Appendices A and B). A given lot corresponds to a defined nucleation date; most likely at the time of an intermediate stop.

Exploitation of X-ray tomography results

Fig. 6 shows the information that can be obtained from X-ray tomography reconstruction. Using these results, pit surface diameter and depth were determined measuring isolated pits at each temperature. This work was systematically done on individual pit, i.e. pit without any coalescence with surrounding pits. Moreover the individual pits were selected far from the sample edges and also far from the areas where the sample was in contact with the sample holder (e.g. pits line in Fig. 5). Pits are then classified by batches according to their dimensions as 6. Measurement procedure of pit dimensions (diameter and depth). This work was systematically done on individual pits at distance of sample edges and borders. An example of this work is reported in Appendix A and B. explained above (an example of this work is reported in Appendix A). The employed tomography setup gives spatial resolution of 11 µm/vx so that the smaller the size of pits, the higher is the possible error. Consequently, the measurement error below 561 • C can be high. However from 575 • C and beyond the pit growth rates are high and the error due to measurement falls down.

Results are compiled in Fig. 7, where the diameter and the depth of the largest pit identified on each sample after 1500 h of exposure vs the exposure temperature are reported. The mean depth/diameter ratio of the pits identified on each sample vs the exposure temperature (Fig. 7c) is also calculated as previously done by Natesan [START_REF] Fabas | Mechanism of metal dusting corrosion by pitting of a chromia-forming alloy at atmospheric pressure and low gas velocity[END_REF] and Fabas [START_REF] Fabas | Modelling of the kinetics of pitting corrosion by metal dusting[END_REF]. The number of pits that were analyzed strongly depends for each sample. It was hard to define isolated pits below 561 • C. Beneath this temperature, the measurement scattering was high, as illustrated in Fig. 7c by the standard deviation. For samples exposed between 603 and 689 • C, it was possible to estimate the dimension of more than 15 isolated pits by sample.

This treatment evidenced that the maximum pit diameter and depth increase with temperature up to 632 • C and then decrease. This trend is different of the mass measurements evolution (Fig. 4) that indicates two critical temperature ranges at which the degradation occurred faster. Using these data, it can be concluded that the critical temperature range is around 630-660 • C.

Moreover, these two parameters (pit diameter and depth) are fully correlated as demonstrated by the depth/diameter ratio evolution. For temperatures lower than 561 • C, this ratio is not really indicative because of the error made on the measurements However, from 575 • C this ratio takes a constant value of 0.35.

As indicated in Section 3.2, measurements were done on all isolated pits on both surfaces (Appendix A) and then sorted according to their size parameters (Appendix B). Putting the pictures taken at different exposure times and the pit measurements together, it is possible to estimate an initiation period for each batch of pits. According to the results, it can be deduced that pits initiate at the intermediate stops. This supposes that defects were introduced in the oxide scale during thermal cycling or sample handling. This observation is fully in agreement with the fact that the first pits were observed at the 500 h removal: i.e. pits initiated at 250 h and grew during 250 h. In Fig. 8a are reported the mean pit diameter vs the estimated growth time from crosschecking information. The results show that pit diameters evolved linearly with time for all temperatures once pits are initiated. From the latter it is extracted an estimation of the lateral pits growth rate (Fig. 8b). In agreement with mass loss (Fig. 4) and dimensional measurements (Fig. 7), the higher lateral growth rate (2.4 µm/h) was determined for the sample exposed at 632 • C.

Discussion

The mechanisms of metal dusting and the effect of testing conditions have been extensively studied and conversed by the past [START_REF] Grabke | On the mechanism of catastrophic carburization: metal dusting[END_REF][START_REF] Grabke | Metal dusting[END_REF][START_REF] Klower | Metal dusting of Ni-based alloys[END_REF][START_REF] Schneider | Microprocesses of metal dusting on nickel and Ni-base alloys[END_REF][START_REF] Chun | Mechanisms of metal dusting corrosion of Iron[END_REF][START_REF] Grabke | Thermodynamics, mechanisms and kinetics of metal dusting[END_REF][START_REF] Young | Recent advances in understanding metal dusting: a review[END_REF][START_REF] Nishiyama | Metal dusting behaviour of Alloy 800H in laboratory carbonaceous environments under high pressure[END_REF][START_REF] Young | High Temperature Oxidation and Corrosion of Metals[END_REF][START_REF] Fabas | Modelling of the kinetics of pitting corrosion by metal dusting[END_REF][START_REF] Hochman | Metal deterioration in carbon monoxide and hydrocarbons at elevated temperatures[END_REF][START_REF] Hochman | Catastrophic deterioration of high-temperature alloys in carbonaceous atmospheres[END_REF][START_REF] Szakálos | Mechanisms and driving forces of metal dusting[END_REF][START_REF] Zeng | Relationship of carbon crystallization to the metal-dusting mechanism of nickel[END_REF][START_REF] Albertsen | A model for high-temperature pitting corrosion in nickel-based alloys involving internal precipitation of carbides, oxides, and graphite[END_REF][START_REF] Zhang | Coking and dusting of Fe-Ni alloys in CO-H2-H2O gas mixtures[END_REF]. Some of them are still debatable and it is not the purpose of the present paper to discuss these now well-established mechanisms. The overall behavior of the austenitic CT15C alloy which contains 19-23% Cr is in fact not really different than those previously reported for NiFeCr alloys on this range of temperature. The obtained data mainly confirmed the competition that exists between the formation of a protective oxide scale and the attack by carbon as reported by Schneider et al. [START_REF] Schneider | Microprocesses of metal dusting on nickel and Ni-base alloys[END_REF] for the Ni-15Cr alloy.

It should be first recalled that the driving force for metal dusting, i.e. the chemical potential gradient between gas and alloy, decreases as a function of temperature, as displayed by the variation of the carbon activity with temperature in Fig. 2. In opposite, the oxide growth rate as well as the kinetic of the carburization reactions, both governed by solid state diffusion, increases with temperature. As oxides scales provide diffusion barriers against carbon ingress due to their low solubility for carbon [START_REF] Young | Recent advances in understanding metal dusting: a review[END_REF], a severe competition is expected on the temperature range on which protective oxide scale slowly develops and metal dusting occurs; in our case below the temperature of 860 • C for the used atmosphere.

The results evidenced the partial pressure of oxygen at equilibrium within the used carbonaceous gas was high enough to develop oxide scale at all temperatures. Indeed all specimens have gained mass -have oxidized -after the first period (250 h of exposure), Fig. 4, and all have kept at least a few areas of their surface with bright colored shades characteristic of very thin oxide scales (Figs. 3 and5) after 1500 h of exposure, revealing these area are covered by a thin and protective oxide scale. Mass gains in relation with specimen oxidation increased with temperature, confirming the oxidation reaction is a thermally activated process.

Under the very high carbon activity range (4500 < a c < 18) used for this test, all samples suffer from metal dusting on the range 504-704 • C. Nevertheless two domains can be distinguished from Fig. 5 showing the evolution of the attack vs temperature: below 561 • C and from 575 • C to 689 • C.

Metal dusting attack on the temperature range [504-561 • C]

Specimens look more or less uniformly corroded below 561 • C because of the very high number of local attack. It was more difficult to precisely determine pit parameters because of pits overlapping and because maximum pit depth didn't exceed 250 µm. This led to large discrepancy of the depth/diameter ratio over this temperature range. The pit nucleation density at low temperatures should thus be very high in comparison to higher temperatures. This finding should be in relation first with the high driving force for carbon ingress existing at low temperature, increasing nucleation sites like for precipitation reactions, and second with the oxide scale thickness and its eventual defects. In the low -the pit depth evolution vs exposure time follows linear kinetics (Fig. 8a). The linear regression that is obtained passes close to zero (Fig. 8a). -no pits were observed on the samples at the 250 h intermediate stop.

The first pits were observed at the 500 h intermediate stop. As the treatment of data has evidenced that the lateral pit growth rate was as high as 2.4 µm/h, no pits nucleated before the first stop. Thus it is concluded that all pits of a same batch have nucleated simultaneously, at a stop.

Therefore several authors [START_REF] Young | Recent advances in understanding metal dusting: a review[END_REF][START_REF] Young | Metal dusting reaction mechanisms[END_REF][START_REF] Speck | Metal dusting of nickel-aluminium alloys[END_REF][START_REF] Zhang | Effect of copper on metal dusting of austenitic stainless steels[END_REF] have previously used thermal cycling to make the metal dusting test more severe and to reduce the incubation time.

Mass change or pit density measurements vs dimensional analysis

By the past, most of the authors have quantitatively characterized metal dusting either looking at the number of pits per surface area (pit density) at a given time [START_REF] Nishiyama | Metal dusting behaviour of Alloy 800H in laboratory carbonaceous environments under high pressure[END_REF] or measuring the mass change vs time at a given temperature [START_REF] Grabke | On the mechanism of catastrophic carburization: metal dusting[END_REF][START_REF] Nishiyama | Metal dusting behaviour of Alloy 800H in laboratory carbonaceous environments under high pressure[END_REF][START_REF] Young | High Temperature Oxidation and Corrosion of Metals[END_REF]. Nishiyama et al. [START_REF] Nishiyama | Metal dusting behaviour of Alloy 800H in laboratory carbonaceous environments under high pressure[END_REF] used a thermal gradient experiment (454-777 • C) to evaluate the corrosion by metal dusting in 24%CO-47%H 2 -6%CO 2 -23%H 2 O for the 800 H alloy (having a composition close to the one of the CT15C alloy). They determined the number of pits per surface area to define the critical temperature range for this alloy and found 650-660 • C at P T 40 bars and 610-620 • C at P T 25 bars. These values are not so far from the critical temperature range observed in the present study at 1.1 bar (630-660 • C), Fig. 7b. However the authors didn't characterize the pits dimension vs temperature such that the temperature range at which the pit growth was really the fastest and the pit growth rate itself were not determined.

The present study also evidenced that the metal wastage rates in mg/ cm 2 /h or mm/year are valid for general attack of the entire surface; i.e. in the case of uniform degradation as previously proposed by Grabke [START_REF] Grabke | Thermodynamics, mechanisms and kinetics of metal dusting[END_REF]. Thus, in the present study only the corrosion rate below 561 • C, where a rather uniform degradation occurred, can be approached using mass loss. However this situation is not the most problematic for the alloy as evidenced in Fig. 7b that shows that the in depth pit growth can be very high. In fact, none of these methods, the numeration of pits per surface area (pit density) and mass loss measurements, can be used to extrapolate the in depth pit growth rate which appears to be to the present authors' point of view the most critical data to extrapolate service lifetime of materials.

In depth pit growth rate

Because the experimental determination of the pit growth rate requires many materials, precise and time consuming operations, the literature about pit growth rate is poor and the work of Fabas et al. [START_REF] Fabas | Modelling of the kinetics of pitting corrosion by metal dusting[END_REF] has, from this point of view, to be emphasized. Indeed these authors have proposed a modelling of the kinetics of pitting corrosion by metal dusting for the 800HT alloy at 570 • C and 21 bars. Based on the lateral pit growth rate and the observed pit depth/diameter ratio of one fifth, authors determined indirectly the pit growth rate in depth.

The highest pit growth rate in depth in their case (800HT, 570 • C, 21 bars) was around 0.09 µm.h -1 [START_REF] Fabas | Modelling of the kinetics of pitting corrosion by metal dusting[END_REF]. Although this rate is already high for the structural materials of a methane reformer plant, it could be significantly larger if 570 • C, the temperature used in [START_REF] Fabas | Modelling of the kinetics of pitting corrosion by metal dusting[END_REF] to evaluate metal dusting resistance, is not the most critical temperature for 800HT alloy exposed to metal dusting under 21 bars. In fact, this temperature is low regarding the temperature at which operate parts of methane reforming equipment. It corresponds to a temperature of the equipment during the gas cooling stage. Performing exposures in a thermal gradient allows the identification of this critical temperatures range. In the present study, the highest pit growth rate in depth is obtained at the temperature of 632 • C and is equal to 0.84 µm.h -1 ; i.e. nine to tenfold the one obtained at 570 • C, 21 bars by Fabas et al. for 800HT, an alloy with a composition not so far from the one of the present study. Of course the direct comparison between Fabas' results and the ones obtained in the present study should be done with more care as is done here because the gas pressure, the carbonaceous atmosphere and the used test rig are different. Nevertheless the comparison gives an idea of what can be missed and what can be deduced from the thermal gradient test.

Contribution of X-ray tomography to metal dusting attack measurements

The 3D X-ray tomography characterization technique used in the present study allows the evaluation of the morphology of the metal dusting attack with a reasonable accuracy. Although the resolution of temperature range, where the oxide scale is very thin (a thickness of 60-80 nm was measured on thin lamella prepared by focused ion beam on the sample exposed at 504 • C after 1500 h), it might be suggested that the diffusion length of carbon through the chromia oxide scale grain boundaries [START_REF] Nguyen | Microstructures of chromia scales grown in CO2[END_REF] can be larger than the oxide scale thickness. The handling of samples (cleaning, hand weighing, positioning on sample holder) also might in itself damage the oxide scale. Carbon ingress can, thus, occur at physical defects in the scale [START_REF] Young | Recent advances in understanding metal dusting: a review[END_REF]. As a consequence the mass loss (Fig. 4) first concerns the entire surface of the sample on this temperature range and second, increases with temperature because of the increase of the diffusion rate of carbon in the alloy substrate. This constitutes the first mass loss peak of the two reported on Fig. 4.

Regardless of the metal dusting initiation mode, the results mainly showed the weakness of the oxide scale to protect the alloy from the corrosion by carbon in this low temperature range from 504 • to 561 • C. Further characterization of the oxide scales nature and composition would be necessary for discussing the initiation mechanism, but this does not fall in the scope of the present paper.

Metal dusting attack on the temperature range [575-689 • C]

At temperatures higher than 561 • C, the oxide layer looks to be a more efficient diffusion barrier to carbon and the attack becomes limited to local areas. The attack is no more generalized to the entire surface and as a consequence the mass loss sharply decreases.

However, one of the conclusions of the present study is also to reveal that the use of mass loss to quantify the attack by metal dusting can lead to erroneous results. Indeed if the mass gain evolution is considered only, Fig. 4, two temperature ranges where the attack is severe are obtained and in between a temperature range where the attack is very low. One could conclude that the degradation rate in the temperature range 532 -561 • C is more or less the same as the one at 646-660 • C while the attack is rather negligible on the range 575 -618 • C. These conclusions fall down when comparing the mass loss results to the pit depth evolution vs temperature (Fig. 7b). This latter figure shows that the pit depth continuously increases from 504 • to 632 • C, then decreases. This tendency is in agreement with diffusion mechanisms being activated by temperature (carbon ingress), and carbon activity evolution, the driving force for metal dusting, that decreases when temperature increases according to the CO reduction and the Boudouard reactions (Eq. 1 and 2, Table 2, Fig. 2). To the author knowledge, this is the first time it is evidenced that the in depth pit growth rate is a function of both temperature and carbon activity.

The results also evidence that on this range of temperature pit initiation has occurred, most probably during one of the intermediate stops required for weighing the samples, as observed at atmospheric pressure by Fabas et al. [START_REF] Fabas | Mechanism of metal dusting corrosion by pitting of a chromia-forming alloy at atmospheric pressure and low gas velocity[END_REF]. Cooling produces stresses in the oxide scale which can create defects such as cracks where metal dusting degradation initiates. This suggestion is sustained by two facts:

Conclusions

Fifteen samples of the Ni-Fe-Cr CT15C alloy have been exposed in a temperature gradient from 500 • to 700 • C in a highly carburizing atmosphere. The main conclusions of this experimental work are as follow:

-All specimens suffer from metal dusting attack by pitting.

-At temperatures lower than 561 • C, the corrosion is rather uniform.

This result comes from the development of a high number of pits (high pit density) causing an extensive overlapping of the pits. Nevertheless the attack is characterized by a "low" alloy recession rate. In such a case of metal dusting, mass loss measurement can be relevant to quantify the degradation. -At higher temperatures (> 561 • C) the density of the pits is reduced and single pits develop with a regular spherical cap shape. In this case, mass loss is not relevant anymore to monitor corrosion by metal dusting and X-ray tomography succeeds in providing quantitative and practical data. -Pits are first observed at the second stop of 500 h showing pit initiation is due to defects introduced during thermal cycling or sample handling. -Pit growth rates are peculiarly high on the 589-689 • C range with a maximum at 632 • C for the alloy CT15C in the present condition. The attack increased up to this maximum, and decreased above, because of the opposite evolution of carbon activity and diffusion /reaction kinetics. -The in depth pit growth rate has been shown to be a non-monotonous function of temperature, with a maximum at intermediate temperature. The in depth pit growth rate is thus considered to be both a function of the temperature and of the carbon activity. -The pit diameter/pit depth ratio is 0.35 for this alloy in this temperature and carbon activity range. Further investigations are required to evaluate the effect of the alloy microstructure.

The metal dusting experiments carried out with a large thermal gradient, as was done in the present study, are relevant for the determination of all the morphologies of carbon attacks. They make it possible to identify the most critical cases and conditions for a given alloy in a given atmosphere. When the spatial resolution of the X-ray tomography is compatible with the size of the degradation, this technique is relevant. It makes it possible to characterize the damage in 3D at each stop. Conventional metallographic techniques do not allow this non-destructive analysis.

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. such a technique is not very high in the used conditions (11 µm/vx), it is sufficient to obtain quantitative data about pit development and metal dusting wastage. In all cases, this accuracy is lower than the errors that could be made by metallography. The 3D pit characterization evidences that pits have a spherical cap shape with a constant pit diameter/pit depth ratio at temperatures higher than 575 • C. For temperatures lower than 561 • C, this ratio is not indicative because of the error made on the measurements and also because of the number of pits; but from 575 • C the ratio takes a constant value of 0.35. This trend was also observed by [START_REF] Fabas | Mechanism of metal dusting corrosion by pitting of a chromia-forming alloy at atmospheric pressure and low gas velocity[END_REF] and [START_REF] Natesan | Development of materials resistant to metal dusting degradation[END_REF]. The former determined a constant ratio of about 0.2 for 800HT, 601, 602CA, 617, 45TM alloys. 800HT is a Fe-based alloy and the latters are Ni-based alloys. It can be suggested that the pit morphology (pit diameter/pit depth) depends on the alloy composition and microstructure, and/or of the gas pressure. However, further experiments would be necessary to evaluate the influence of these factors on this pit depth/diameter ratio. The importance of this ratio is obvious for engineering and maintenance teams since it permits the monitoring of the internal attack of industrial tubes. Indeed if tubes surface inspection can be completed in the critical temperature range after carbon removing, using optic fiber for example, the diameter of the larger individual pits can be used to evaluate pit depth and so the residual tubes thickness.

2 Fig. 1 .

 21 Fig. 1. a) Test rig developed for metal dusting characterization operating at 1.1 atm.; b) actual temperature gradient (in • C) along the furnace (made of five individually regulated zones); c) sample holder scheme. In this equipment, the gas flow (60 NL h 1 ) enters the furnace from the left in the hottest zones and exits at the right. Samples were placed on the sample holders situated in the three inner zones of the furnace (Z2-Z3-Z4).

Fig. 3 .

 3 Fig. 3. Specimens observation at the 500 h intermediate stop: a) still on the sample holder (before handling) and b) both sides of the corresponding sample after cleaning (sample dimension 10 × 20 × 2 mm).

Fig. 4 .

 4 Fig. 4. Mass loss versus temperature according to the exposure time. The negative reported values have to be considered as mass gains: such situation happens when mass gain due to oxidation of alloys is larger than the metal loss due to metal dusting. Accuracy on mass change measurement was of ± 1 mg. Mass losses at 689 and 704 • C at 1250 h and 1500 h were lower than 3 mg.cm 2 .

Fig. 7 .

 7 Fig. 7. a) Diameter and b) depth of the largest pit identified on each sample after 1500 h of exposure vs the exposure temperature, c) the mean depth/ diameter ratio of the pits identified on each sample vs the exposure temperature (with vertical bar corresponding to standard deviation). Fig. 8. a) Mean pit diameter vs pit growth time; b) lateral pit growth rate determined using the mean pit diameter vs temperature (µm.h 1 ).

Fig. A1 .

 A1 Fig. A1. a) Photographs of the sample exposed at 632 • C; b) 3D reconstructed sample after 1500 h of exposure at 632 • C. The arrows indicate the isolated pits taken in account in the data analysis.

Fig. B1 .

 B1 Fig. B1. Example of pit sampling made on the sample exposed at 632 • C for 1500 h.

Funding

  ADEME provided financial support for the conduct of the research. CRediT authorship contribution statement S. Mathieu: Methodology, Conceptualization, Formal Analysis, Validation, Data computation, Writing-original draft. L. Le Pivaingt: Methodology, Investigation, Data computation. O. Ferry: Investigation. M. Vilasi: Data computation, Writing-review & editing. A. Stuppfler: Methodology, Investigation. J-L. Guichard: Conceptualization, Methodology, Investigation. A. Vande-Put: Validation, Writing-review & editing. D. Monceau: Validation, Writing-review & editing.

Acknowledgments

We are pleased to acknowledge Mr. C. Morlot for his assistance with the X-ray tomography experiments. Authors would like to thank the French Environment Agency ADEME for their financial support.

Data Availability

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. Data of the present study will be made available on demand.

Availability of data and material

The raw/processed data required to reproduce these findings cannot be easily shared at this time due to the amount of data generated by each analysis by tomography.

APPENDIX A

See Appendix Figs. A1,B1.


D E Embvani

C Corpet

Petit

D Tardieu

J P Jaeg

J Cadet

E Embvani

D E Corpet

C Petit

Dextran sulfate enhances the level of an oxidative DNA damage biomarker, 8-oxo-7,8-dihydro-2 0-deoxyguanosine, in rat colonic mucosa

Keywords: Oxidative DNA damage, 8-OxodGuo, Ulcerative colitis, Free radicals, Colonic inflammation

Dextran sulfate enhances the level of an oxidative DNA damage biomarker, 8-oxo-7,8-dihydro-2'-deoxyguanosine, in rat colonic mucosa.

Introduction

Dextran sodium sulfate (DSS), a mixture of polysaccharides of different molecular weights differing in their degree of sulfate substitution [START_REF] Nilsson | Clinical dextrans. Specifications and quality of preparations on the market[END_REF], given per os to rodents induces an Inflammation of the colonic mucosa. These rodents are relevant experimental models for ulcerative colitis [START_REF] Okayasu | A novel method in the induction of reliable experimental acute and chronic ulcerative colitis in mice[END_REF]. In humans, long standing ulcerative colitis and Crohn's disease are generally described as important risk factors for colorectal cancer development [START_REF] Hinton | Risk of malignant change in ulcerative colitis[END_REF], which is the second leading cause of death from cancer in Western countries including North America [24]. In rodents, DSS induces colonic tumors but the carcinogenic mechanisms are not known because DSS is not directly mutagenic [START_REF] Ishioka | Induction of colorectal tumors in rats by sulfated polysaccharides[END_REF][START_REF] Therkelsen | Polysaccharides and Their Derivatives[END_REF]. Inflammation via repeated epithelial necrosis and regeneration and/or via DNA alterations might explain the initiation of the carcinogenic process [START_REF] Shacter | Activated neutrophyls induce prolonged DNA damage in neighboring cells[END_REF].

8-Oxo-7,8-dihydro-2 0-deoxyguanosine (8-oxod-Guo), as a result of hydroxylation of the guanine base residues in DNA, is considered as an important biomarker of oxidative DNA damage. 8-OxodGuo has been implicated in mutagenic and carcinogenic processes [START_REF] Cheng | 8-Hydroxyguanine, an abundant form of oxydative DNA damage, causes G-T and A-C substitutions[END_REF][START_REF] Moriya | Single-stranded shuttle phasemid for mutagenesis studies in mammalian cells. 8-Oxoguanine in DNA induces targeted G.C-T.A transversions in simian kidney cells[END_REF][START_REF] Moriya | Site-specific mutagenesis using a gapped duplex vector: a study of translesion synthesis past 8-oxodeoxyguanosine in E. coli[END_REF]. Other investigations have provided strong indirect evidence supporting the role of oxidative stress in carcinogenesis [START_REF] Ames | The causes and prevention of cancer: gaining perspective[END_REF]. We make the hypothesis that DSS can produce free radicals, likely via Inflammation, and induce oxidative DNA damage in colonic mucosa that may explain the carcinogenic activity of a non-genotoxic compound.

By measuring 8-oxodGuo with HPLC and electrochemical detection, the present study investigated DNA damage in the colonic mucosa of rats given DSS for only 2 days and shows for the first time that oxidative DNA damage may be a consequence of colonic Inflammation.

Materials and methods

Animal treatments and analytical procedures

Thirty 4-week-old female Fisher 344 rats (Iffa credo, Lyon, France) were acclimatized for 5 days to the animal colony, fed a low fat rodent chow (UAR, Villemoisson, France) ad libitum and randomized to three groups of 10 rats. A control group was given distilled drinking water ad libitum. Two experimental groups received 3% or 6% DSS in distilled drinking water for 2 days.

Body weight and water intake were recorded daily. Diarrhea was estimated by the ratio of fecal wet weight/dry weight. Fecal occult blood was assayed with the Hemoccult II test (SKD, Gagny, France); the intensity of the color showing occult blood was graded on a scale between 0 and 3. Animals were sacrificed 2 days after the start of DSS administration by cervical dislocation. The colon was dissected between the ileocecal junction and the proximal rectum. The colon was placed on a non-absorbent surface, measured and flushed with cold 0.9% NaCl (4°C). The colon was opened longitudinally and the mucosa was removed by scratching the distal surface with a lancet blade (5 cm at the rectal end). The samples were rinsed with 0.9% NaCl and centrifuged at 3000 £ g for 10 min. The pellets were immediately frozen at -80°C until 8-oxodGuo was assayed within the next 2 days.

DNA extraction and 8-oxodGuo assay

The Quiagen genomic DNA kit was used to extract DNA at an ambient temperature from cellular pellets. After homogenization with a Potter homogenizer, the samples were lysed with proteinase K (1 mg/ml) at 50°C for 2 h in buffer G2 (800 mM GuHCl, 30 mM EDTA, 30 mM Tris±HCl, 5% Tween-20 and 0.5% Triton X-100 (pH 8.0)). The lysates (10 ml) were then applied on the equilibrated (750 mM NaCl, 50 mM MOPS and 0.15% Triton X-100 (pH 7.0)) Quiagen genomic tips. After washing the tips with QC buffer (1.0 M NaCl, 50 mM MOPS and 15% ethanol (pH 7.0)), the purified genomic DNA was eluted with QF buffer (1.25 M NaCl, 50 mM Tris±HCl and 15% ethanol (pH 8.5)). The DNA was precipitated with 2-propanol, washed with 70% ethanol at -20°C, airdried and diluted in 100 ml of sterile water before analysis. DNA in aqueous solution was hydrolyzed to nucleotides by 10 units of nuclease P1 for 2 h at 37°C in acetate buffer (pH 5.3) according to the method of Floyd [START_REF] Floyd | The role of 8-hydroxyguanine in carcinogenesis[END_REF]. Dephosphorylation was achieved by incubation with 2 units of alkaline phosphatase in Tris±HCl buffer (pH 8.0) for 1 h at 37°C. Proteins were precipitated with chloroform and the aqueous layer was analyzed by HPLC with electrochemical (EC) detection.

The HPLC system consisted of a pump M 2200 (Bischoff, Leonberg, Germany) and an autosampler 738 (ICS, Toulouse, France) equipped with a 12:5 £ 4:6 mm Spherisorb ODS 2 column (Bischoff). A detector focus (Spectra-Physics, Les Ulis, France) set at 280 nm and an EC detector coulochem II (ESA, Chelmsford, MA) set at 1200 and 1400 mV for electrodes 1 and 2, respectively, monitored unmodified and modified nucleosides. An isocratic eluent, 50 mM phosphate buffer (pH 5.5) containing 10% methanol, was used at a flow rate of 1.0 ml/min. The PIC 3 software (ICS) permitted quantification 2 D. Tardieu et al. / Cancer Letters 134 (1998) 1±5 of DNA oxidative damage using calibration curves obtained with authentic standards.

Statistics

Data were first analyzed by one-way analysis of variance and then Student's t-test was used to compare experimental and control group means. Scores for fecal occult blood were analyzed by the non parametric Kruskal±Wallis test.

Results

As shown in Table 1, rats given 6%DSS in drinking water for 2 days gained less weight (P < 0.05) and drank significantly more water than controls (P < 0.001).

Colonic Inflammation manifestations

According to Axelsson et al. [START_REF] Axelsson | Dextran sulfate sodium (DSS) induced experimental colitis in immunodeficient mice. Effects in CD41[END_REF], colonic Inflammation could be simply assessed by diarrhea, colon length and rectal bleeding. Visual inspection of feces revealed obvious diarrhea in rats given 6% DSS in drinking water. A 55% increase in the fecal wet/dry ratio was observed in rats given 6% DSS compared to control rats given pure water (P < 0.05). This increase was not seen in rats given 3% DSS (Table 1). No significant difference in colon length was found between the three groups of rats (data not shown). No blood could be detected by visual inspection of feces. Fecal occult blood was induced by DSS in a dose-dependant manner and significant differences were found between groups (Table 1).

Table 1. Effects of the administration of dextran sulfate sodium (DSS) via drinking water for 2 days in F344 rats a P-values were calculated by parametric ANOVA, except for fecal occult blood scores. b Data are the mean ± standard deviation. *P < 0.05, **P < 0.001 when compared with controls given 0% DSS.

8-Oxo-7,8-dihydro-2 0-deoxyguanosine levels

In a pilot study, three Wistar rats were given 5% DSS in drinking water for 2 days. The ratio 8-oxod-Guo/dGuo was doubled compared to controls given pure water (data not shown).

Fig. 1 shows the effect of DSS on the 8-oxodGuo level in Fisher 344 rats. This level in the control group ranged from 1.2 to 4.6 mol of 8-oxodGuo per 105 mol of dGuo. The levels of 8-oxodGuo in the mucosa of rats given 3% and 6% DSS ranged from 2.5 to 7.1 mol per 105 mol of dGuo and from 2.5 to 8.0 mol per 105 mol of dGuo, respectively (Fig. 1).

The means of 8-oxodGuo levels in rats treated by DSS were higher than those of the control and the differences were statistically significant (P < 0.014 for 3% DSS and P < 0.001 for 6% DSS). The difference between rats given 3% and 6% DSS was not significant (P = 0.21) Fig. 1. 8-OxodGuo levels in colonic DNA after administration of dextran sulfate sodium (DSS) via drinking water for 2 days in F344 rats. Data are the mean ± standard deviation of 10 independent measures from 10 rats. Treated groups are compared to 0% DSS controls by t-test and two-way P-values.

Discussion

This work shows for the first time that in rats fed with DSS, the level of 8-oxodGuo in DNA of colonic mucosa increased two-fold after 2 days. 8-OxodGuo is considered as a major class of oxidative DNA damage, which is involved in mutagenic and carcinogenic processes. Furthermore, high levels of 8-oxodGuo have been detected in target organs of various carcinogens [START_REF] Floyd | The role of 8-hydroxyguanine in carcinogenesis[END_REF][START_REF] Kasai | Oral administration of the renal potassium bromate, specifically produces 8-hydroxydeoxyguanosine in rat target organ DNA[END_REF][START_REF] Nagashima | Formation of an oxidative DNA damage, 8-hydroxydeoxyguanosine, in mouse lung DNA after intratracheal instillation of diesel exhaust particles and effects of high dietary fat beta-carotene on this process[END_REF][START_REF] Shen | Aflatoxin B1-induced 8-hydroxydeoxyguanosine formation in rat hepatic DNA[END_REF]. Relationships between oxidative DNA damage and Inflammation have previously been convincingly demonstrated in chronic diseases like hepatitis [START_REF] Hagen | Extensive oxidative DNA damage in hepatocytes of transgenic mice with chronic active hepatitis destined to develop hepatocellular carcinoma[END_REF] or atrophic gastritis caused by Helicobacter pylori [START_REF] Baik | Increased oxidative DNA in Helicobacter pylori-infected human gastric mucosa[END_REF].

The amount of 8-oxodGuo tended to increase with the concentration of DSS but there was no significant difference between rats given 3% and 6% DSS. Thus, it is conceivable that the 3% regimen might have saturated the oxidation process, while the 6% DSS dose might have been too toxic to the mucosa, leaving few living cells. Indeed DNA can be extracted and measured for oxidation only from living cells. DSS (3% and 6%) in drinking water induced a slowing down of the body weight gains after 2 days and also induced diarrhea. The subsequent loss of water may explain both why rats given DSS did not grow as rapidly as controls and the increased water consumption. Also rectal bleeding was induced by 3% and 6% DSS. This would confirm that Inflammation was effective in a short time. This is consistent with the experiments of Axelsson et al. [START_REF] Axelsson | Dextran sulfate sodium (DSS) induced experimental colitis in immunodeficient mice. Effects in CD41[END_REF] which induced moderate Inflammation (demonstrated by histological analysis) in mice with 1.25% DSS within 1 week. Reactive oxygen species (ROS) such as superoxide anion and other oxygenated radicals are implicated in the Inflammatory reaction [START_REF] Babior | Biological defense mechanisms. The production by leukocytes of superoxide, a potential bactericidal agent[END_REF][START_REF] Curnutte | Chronic granulomatous disease[END_REF][START_REF] Grisham | Oxidants and free radicals in Inflammatory bowel disease[END_REF]. We speculate that DSS provokes an Inflammation of the colon with the generation of ROS. Indeed, ROS have been demonstrated to induce DNA damage [START_REF] Halliwell | Free Radicals in Biology and Medicine[END_REF] and it has been speculated that this DNA damage could lead to carcinogenesis [START_REF] Cerrutti | Prooxidant states and tumor promotion[END_REF][START_REF] Troll | The role of oxygen radicals as a possible mechanism of tumor promotion[END_REF]. Thus, it is conceivable that chronic subclinical colon Inflammation is involved in the high frequency of colon cancer observed in Western countries. Interestingly, most of the protective effects of the so-called Mediterranean diet against cancer might be related to antioxidants and free radical scavengers [START_REF] Ferro-Luzzi | Mediterranean diet, Italian style: prototype of healthy diet[END_REF][START_REF] Jang | Cancer chemopreventive activity of resveratrol, a natural product derived from grapes[END_REF]. This study has permitted the rapid (2 recording of early oxidative damage in vivo which may eventually lead to colon carcinogenesis. Moreover, this protocol may be used to test the effect of xenobiotics or of diets on the oxidative DNA damage process and to determine their antioxidant properties. Further investigations on this point are in progress in our laboratory.

Acknowledgements

We thank S. Boiteux, T. Douki and J.L. Ravanat for their help and advice in 8-oxodGuo measurements, S. Taché and G. Peiffer for the rat treatments and sacrifice and R. Gazel and A.M. Debrusse for taking care of the rats.

study was supported by the Direction Générale de l'Enseignement et de la Recherche, du Ministère de l'Agriculture (France).


A Van Der Laan

R Epherre

C Estournès
email: estournes@chimie.ups-tlse.fr

Numerical approach for the determination of multi-mechanisms of the densification of TiAl by spark plasma sintering

Keywords: Spark plasma sintering, Numerical modelling, Creep parameters, multi-mechanisms

One of the main benefits of numerical modeling is that it can be used to have access to some features, which are not accessible experimentally. For example, it is quite complicated to determine experimentally the sintering mechanisms that occur during spark plasma sintering (SPS). The obtention of a mechanical model of the SPS is usually done with only one mechanism. However, it has been shown that sometimes more than one mechanism is involved in the densification process as it is the case for TiAl. Thus, an innovative multimechanisms approach was developed, which considers the simultaneous effect of two mechanisms on the densification of TiAl. First the two sintering mechanisms of the material were identified numerically. Then, with the method developed in this work, the influence of each mechanism can be decorrelated and interpreted to determine their role during spark

Introduction

Spark plasma sintering (SPS) is an electric current assisted sintering (ECAS) technique that is used to consolidate a wide range of materials with lower processing time and costs compared to conventional techniques like hot pressing (HP) or hot isostatic pressing (HIP) [START_REF] Grasso | Electric current activated/assisted sintering (ECAS): A review of patents 1906-2008[END_REF]. The application of a uniaxial pressure combined with Joule heating allows to sinter materials with high heating rates, and at a temperature lower than their melting points or decomposition temperature [START_REF] Guillon | Field-assisted sintering technology/spark plasma sintering: Mechanisms, materials, and technology developments[END_REF]. SPS is a versatile process, since it has been used to sinter materials like ceramics, metals, alloys, or composites [START_REF] Orrù | Consolidation/synthesis of materials by electric current activated/assisted sintering[END_REF][START_REF] Hu | A review of multi-physical fields induced phenomena and effects in spark plasma sintering: Fundamentals and applications[END_REF]. Besides its low processing time, the SPS process also tends to improve the mechanical properties of the materials [START_REF] Chaim | Sintering and densification of nanocrystalline ceramic oxide powders: A review[END_REF][START_REF] Chaim | Densification and preservation of ceramic nanocrystalline character by spark plasma sintering[END_REF][START_REF] Olevsky | Fundamental aspects of spark plasma sintering: I. Experimental analysis of scalability[END_REF]. This is obtained thanks to a controlled microstructure throughout the process. All these benefits make the SPS a competitive process because it offers the opportunity to produce high added value materials with reduced production costs [START_REF] Kelly | Spark Plasma Sintering as an Approach to Manufacture Bulk Materials: Feasibility and Cost Savings[END_REF].

A large number of publications focus on the study of the influence of processing parameters on the densified material properties and its densification mechanisms [START_REF] Chaim | Sintering and densification of nanocrystalline ceramic oxide powders: A review[END_REF][START_REF] Calderón-Moreno | Microstructure and creep properties of alumina/zirconia ceramics[END_REF][START_REF] Olevsky | Constitutive modeling of spark-plasma sintering of conductive materials[END_REF]. This shows the increasing interest of the scientific community for the understanding and control of the mechanisms occurring during spark plasma sintering. Numerical simulation appears to be an appropriate solution to tackle these new challenges, since it can be used to better understand, predict, or optimize the process. Understanding the process allows to establish a relationship between the operating conditions and the electric, thermal, mechanical, and/or microstructural features of the sintered material during sintering. Once this is achieved, the numerical model can be used as a predictive tool to identify for example thermal gradients [START_REF] Molénat | Temperature Control in Spark Plasma Sintering: An FEM Approach[END_REF][START_REF] Achenani | Finite element modeling of spark plasma sintering: Application to the reduction of temperature inhomogeneities, case of alumina[END_REF], stress concentrations [START_REF] Antou | Spark plasma sintering of zirconium carbide and oxycarbide: Finite element modeling of current density, temperature, and stress distributions[END_REF] or microstructure inhomogeneities [START_REF] Manière | Spark-plasma-sintering and finite element method: From the identification of the sintering parameters of a submicronic α-alumina powder to the development of complex shapes[END_REF]. This allows to anticipate the effects of several parameters on the densification of the material, and thus, to significantly reduce the number of experiments to reach the desired product. Finally, numerical simulation can be used to optimize the sintering parameters or apparatus in order to reduce the production time and costs, while enhancing material properties and the SPS capabilities. For example, this has been used in the literature to produce multi-samples by SPS [START_REF] Manière | How to overcome the main challenges of SPS technology: Reproducibility, multi-samples and elaboration of complex shapes[END_REF]. However, to use the numerical simulation to its full potential, it has first to be thoroughly calibrated. The developed model has to accurately correspond to the mechanisms involved, but such a precise simulation could be difficult to implement. Obtaining a fully coupled simulation of the SPS process requires first an accurate electro-thermal model. SPS uses indeed Joule effect to heat up the apparatus, and most of the sintering mechanisms are temperature dependent [START_REF] Chen | Fundamental investigations on the spark plasma sintering/synthesis process: I. Effect of dc pulsing on reactivity[END_REF][START_REF] Anselmi-Tamburini | Fundamental investigations on the spark plasma sintering/synthesis process: II. Modeling of current and temperature distributions[END_REF][START_REF] Anselmi-Tamburini | Fundamental investigations on the spark plasma sintering/synthesis process: III. Current effect on reactivity[END_REF]. A numerical approach to develop an accurate electro-thermal model of the spark plasma sintering of any material has been developed in a previous study [START_REF] Van Der Laan | Simple method for the identification of electrical and thermal contact resistances in spark plasma sintering[END_REF]. Then, creep and sintering considerations needs to be added to the model to predict the densification of the material. To implement these aspects into the model, the most commonly used method in the literature is based on a Norton-Green model [START_REF] Green | A plasticity theory for porous solids[END_REF] involving creep parameters combined with porosity functions [START_REF] Abouaf | Finite element simulation of hot isostatic pressing of metal powders[END_REF][START_REF] Olevsky | Theory of sintering: From discrete to continuum[END_REF][START_REF] Olevsky | Fundamental aspects of spark plasma sintering: II. Finite element analysis of scalability[END_REF]. The values of the creep parameters correspond to a specific sintering mechanism and they can be determined empirically [START_REF] Ratzker | Creep of polycrystalline magnesium aluminate spinel studied by an SPS apparatus[END_REF][START_REF] Ratzker | Using a spark plasma sintering apparatus as a tool in a compressive creep study of fine-grained alumina[END_REF].

A numerical method has also been developed in a previous study [START_REF] Van Der Laan | Fully coupled electrothermal and mechanical simulation of the production of complex shapes by spark plasma sintering[END_REF], which allows to obtain these parameters through only one experiment. However, to the best of our knowledge, only one mechanism is considered responsible for the densification. Realistically, it is likely that more than one mechanism is involved in the sintering as it has been showed experimentally for several materials [START_REF] Locci | Modeling of Electric Current Assisted Sintering: An extended fluid-like approach for the description of powders rheological behavior[END_REF][START_REF] Manière | Modeling zirconia sintering trajectory for obtaining translucent submicronic ceramics for dental implant applications[END_REF][START_REF] Martins | Spark plasma sintering of a commercial TiAl 48-2-2 powder: Densification and creep analysis[END_REF]. To perfect the model an innovative numerical multimechanisms approach of the sintering is developed in this work. This method will be applied to a titanium aluminide (TiAl), but it is developed to be used on any other material.

Experimental and computational methodology

Materials and methods

The material used in this work is a titanium aluminide (TiAl) powder TiAl-4822, composed of 48%-at aluminum, 2%-at niobium et 2%-at chromium. The powder is produced by Praxair and has a grain size between 45 and 105µm (with an average of 75.4µm).

All the spark plasma sintering experiments were performed at the Plateforme Nationale CNRS de Frittage Flash located at the Université Toulouse 3, Paul Sabatier (Toulouse, France) with a Dr.Sinter 2080 unit, SPS Syntex Inc., (Japan). The TiAl powder was placed in a graphite mold with an inner diameter of 36mm and an outer diameter of 70mm. A graphite foil (PERMA-FOIL®Toyo Tanso) was placed on the inside wall of the die and at the interface between the punches and the powder. To minimize the heat loss at the surface of the die, a graphite felt was placed on its outside wall. The SPS column, composed of the electrodes, spacers, punches, mold, and sample, is presented in Figure 1. The electric current sent in the system is regulated through a PID regulation that controls the difference between a set control temperature and the one measured in a 3mm hole (with a diameter of 1.8mm) located in the outside wall of the die. This temperature is measured using a lateral pyrometer (IR-AH series Chino).

To sinter the TiAl powder, the setpoint temperature is first set at 600°C for five minutes, because the lower limit of the temperature range measured by the pyrometer is 570°C. Then the temperature is increased at a rate of 100°C/min up to full densification of the powder, which is reached at 1150°C. Once this temperature is reached, the power is switched off and the pressure released.

During the SPS trial, the machine records the electric current and voltage, the control temperature, and the displacement of the electrodes. This displacement is induced by the densification of the powder and the dilation of the whole apparatus. Thus, to extract only the displacement due to the sintering of the material, another SPS cycle is launched on the densified sample [START_REF] Van Der Laan | Fully coupled electrothermal and mechanical simulation of the production of complex shapes by spark plasma sintering[END_REF]. When the system has cooled down, the same SPS cycle is applied to measure the displacement of the column without the influence of the densification. By subtracting the two displacement curves from the two experiments, it is possible to calculate the evolution of the relative density during the sintering as illustrated Figure 2. After the SPS experiments, the density of the sample was measured at 100% using the Archimedes technique.

Figure 2: Evolution of the relative density of a 36mm TiAl sample

All the numerical calculation was realized with Comsol Multiphysics©. The SPS apparatus was modeled in 2D-axisymetric and treated as a union. All the limit conditions were detailed in previous works [START_REF] Van Der Laan | Simple method for the identification of electrical and thermal contact resistances in spark plasma sintering[END_REF][START_REF] Van Der Laan | Fully coupled electrothermal and mechanical simulation of the production of complex shapes by spark plasma sintering[END_REF]. The electrical, thermal, and mechanical properties used in the model are presented in Table 1. The porosity dependence of the properties of the TiAl were implemented using the work of Orrù et al. [START_REF] Orrù | Consolidation/synthesis of materials by electric current activated/assisted sintering[END_REF].

Electro-thermal and mechanical simulation

The development of an accurate simulation of the sintering of the TiAl powder was described in a previous study [START_REF] Van Der Laan | Simple method for the identification of electrical and thermal contact resistances in spark plasma sintering[END_REF]. This study shows a method that allows to numerically determine the electrical and thermal contact resistances at the internal surface of the graphite mold. With this method it is possible to obtain an accurate description of both the electrical and thermal behavior of the entire SPS column (electrodes, spacers, punches, mold and sample). This is illustrated Figure 3 with the comparison between the experimental and simulated evolution of the current and the temperature at several position of a TiAl sample with a diameter of 36mm. These are described in the sample using a Norton-Green creep power law equation [START_REF] Manière | Identification of the Norton-Green Compaction Model for the Prediction of the Ti-6Al-4V Densification During the Spark Plasma Sintering Process[END_REF]:

= (1)
Where ε et σ are the equivalent strain rate and the equivalent stress, the parameter n is the power law creep exponent and A is a temperature dependent parameter defined as such:

= - ( 2
)
Where A0 is a pre-exponential factor, Q the creep activation energy, R the universal gas constant and t the temperature. The simulation of the creep mechanism of the TiAl sample requires the identification of the creep parameters n, Q and A0.

With the Norton-Green creep power law, the sample is considered as a dense visco-plastic material [START_REF] Manière | Identification of the Norton-Green Compaction Model for the Prediction of the Ti-6Al-4V Densification During the Spark Plasma Sintering Process[END_REF]. However, during the SPS trial, the TiAl starts as a powder with an initial relative density of 65%, and then reaches full density. Thus, to take into account the densification of the sample, porosity functions are added in the model with the approach of Abouaf [START_REF] Abouaf | Finite element simulation of hot isostatic pressing of metal powders[END_REF]. This approach consists in the introduction of a dissipative potential in the expression of the strain rate tensor. This dissipative potential can be expressed using to porosity functions as follow:

= 3 2 σ - 1 2 (3)
Where I1 is the invariant of the stress tensor, and c and f are the porosity functions defined as such:

= 1 ! = " # 1 -$ $ -$ %& ' (4)
Where !, ( and Kf are parameters that needs to be determined for each material. However, in a previous work, D. Martins et al. [START_REF] Martins | In-situ creep law determination for modeling Spark Plasma Sintering of TiAl 48-2-2 powder[END_REF] have determined experimentally those parameters.

Those parameters were identified on a TiAl powder using two sets of quite complex experiments: a uniaxial free compaction and a confined compression on porous samples. In this work, the same powder, the same SPS apparatus and similar sintering conditions were used. Thus To consider the modification of the density in the numerical model, the expression of conservation of mass is implemented as follow [START_REF] Abouaf | Finite element simulation of hot isostatic pressing of metal powders[END_REF]:

$ $ = -789: ; = - 3 (7)
To be able to use the model and describe the evolution of the density of the TiAl during spark plasma sintering, the creep parameters n, Q and A0 of the equations ( 1) and ( 2) need to be determined.

Numerical identification of the creep parameters

In the literature, the identification of the creep parameters is usually done using an experimental method [START_REF] Ratzker | Using a spark plasma sintering apparatus as a tool in a compressive creep study of fine-grained alumina[END_REF][START_REF] Martins | In-situ creep law determination for modeling Spark Plasma Sintering of TiAl 48-2-2 powder[END_REF]. In a previous work, a numerical method has been developed that allows to obtain similar results but with only one SPS trial [START_REF] Van Der Laan | Fully coupled electrothermal and mechanical simulation of the production of complex shapes by spark plasma sintering[END_REF]. With this approach the creep parameters are optimized numerically using a curve fitting algorithm. The experimental evolution of the relative density is fed into the curve fitting algorithm to find the set of parameters (n, Q and A0) that will best fit the experimental data. This technique gave good results on two different materials (alumina and TiAl) and for different sample sizes.

In their work, D. Martins et al. [START_REF] Martins | In-situ creep law determination for modeling Spark Plasma Sintering of TiAl 48-2-2 powder[END_REF] not only identified the porosity functions c and f, but they also determined experimentally the creep parameters n, Q and A0. Those parameters were determined using SPS trials, which is more accurate to describe the behavior of the powder spark plasma sintering. However, with this set of parameters, the model was only able to fit the sintering occurring at high temperatures, i.e. for a relative density higher than 80%. The conclusion of this study was that not only one mechanism is responsible of the sintering of the TiAl but at least two: one at low temperatures and another at high temperatures. It is stated that the low temperature mechanism creates bonds between the grains (without affecting the relative density), which leads to a porous 3D-object. For high temperature, the second mechanism, which nature was not specified by the author, is responsible of the material densification. This multi-mechanism hypothesis was also confirmed numerically in our previous work [START_REF] Van Der Laan | Fully coupled electrothermal and mechanical simulation of the production of complex shapes by spark plasma sintering[END_REF]. The curve fitting algorithm was not able to find a set of creep parameters that fit the whole densification curve. Since the algorithm explores a wide range of combination of parameters, this indicates that probably not only one but at least two mechanisms occur during the sintering of TiAl.

For the remaining of the study, it is assumed that two mechanisms are responsible for the sintering of TiAl: one at low temperatures and one at high temperatures. To decorrelate the influence of the two mechanisms on the densification curve, the experimental data was arbitrarily divided in two parts: one at low temperatures (for a relative density below 80%) and one at high temperatures (for a relative density higher than 80%). Then the two parts were fed into the curve fitting algorithm, which was able to identify two distinct mechanisms as illustrated Figure 4. A sensitivity study has been performed on the chosen threshold value of 80% with an offset of +/-5%. This has not affected significantly the results. In the range of temperature considered for each mechanism, the gap between the experimental and numerical data is less than 1%. The values of the creep parameters are reported in Table 2. 13

The parameters identified numerically for the high temperatures are in a very good agreement with the ones identified experimentally by D. Martins et al. [START_REF] Martins | In-situ creep law determination for modeling Spark Plasma Sintering of TiAl 48-2-2 powder[END_REF] with in situ SPS trials. In their work, U. Hofmann et al. [START_REF] Hofmann | Kinetics of high temperature deformation of lamellar Ti48Al-2Nb-2Cr[END_REF] also identified at high temperature under air, the creep parameters of dense TiAl ingots exhibiting full lamellar microstructure, but the values were obtained with a compressive test for pressures from 50 to 390MPa. Although their conditions slightly differ from the SPS ones used in this work (starting from a powder with bi-phased microstructure to full lamellar dense specimen at the end of the sintering cycle), they determined a value of n=3 and Q=350kJ/mol which are quite comparable to the ones found numerically. This confirms the effectiveness of the numerical method as well as the probability the more than one mechanism occurs during the spark plasma sintering of TiAl since it was showed by two different methods.

According to the literature [START_REF] Ratzker | Creep of polycrystalline magnesium aluminate spinel studied by an SPS apparatus[END_REF][START_REF] Manière | Porosity dependence of powder compaction constitutive[END_REF], a stress exponent value close to 1, 2 and 3 are associated respectively with a diffusion, grain boundary sliding (GBS) and plastic deformation mechanisms. The values of n identified in Table 2 suggest that at low temperature, the diffusion and GBS mechanisms are involved in the densification of TiAl, whereas at high temperature it is a combination of GBS and plastic deformation.

Now that the set of creep parameters of the two mechanisms were determined, the objective is to find a way to combine them to obtain a single curve of the relative density.

Results and discussion

Sequential approach

Considering the two curves in Figure 4, a first naive approach would be to combine the two mechanisms sequentially. The first mechanism was obtain using the experimental data of the relative density below 80%, and the second one for values higher than 80%. Thus, the first values. The obtained curve is presented Figure 5. The overall gap between the experimental and numerical data is below 1%, which constitutes a very good results for the simulation of the sintering. However, by looking at the evolution of the ratio < < from the equation [START_REF] Olevsky | Fundamental aspects of spark plasma sintering: I. Experimental analysis of scalability[END_REF] in Figure 6, it appears that there is a discontinuity in the curve when the model switches from one mechanism to another. Since the equation ( 7) corresponds to the conservation of mass, its evolution has to be continuous. Thus, the sequential approach gives a good approximation of the relative density, but it does not relate what really happens mechanistically. The fact that the two mechanisms were considered to happen sequentially cannot be validated. It seems that considering a range of temperatures were both mechanisms occur simultaneously constitutes a more realistic assumption.

Simultaneous approach

The two distinct mechanisms identified, with their respective set of creep parameters reported in Table 2, will be now considered to occur simultaneously over a range of temperature. To do so, two weight functions ! and ! 6 , corresponding to the weight of each mechanism during the sintering, need to be introduced. These functions must be comprised between 0 and 1. Several types of functions were tested (linear functions for example), but it is a sigmoidal form, described in equation [START_REF] Kelly | Spark Plasma Sintering as an Approach to Manufacture Bulk Materials: Feasibility and Cost Savings[END_REF], that showed the most accurate results:

! = > = 1 - 1 1 exp=-B C = -C >> ! 6 = > = 1 -! = > (8)
Where am and Tm are two parameters that need to be determined. This type of function was chosen due to its use in several scientific fields to describe phase transitions for example [START_REF] Zhou | An insight into the sequential order in 2D correlation spectroscopy using polymer transitions: Boltzmann Sigmoid, Gaussian Cumulative, Lorentz Cumulative, and Asymmetric Sigmoid. Findings in experiments and simulations[END_REF].

These two weight functions were implemented in the model by modifying the conservation of mass equation as such:

789 ; = -! = > $ $ C %EF GHC -! 6 = > $ $ C %EF GHC 6 (9)
16

Where the ratio < < of each mechanism is expressed using the creep parameters reported in Table 2. To identify the two parameters am and Tm from equation ( 8), the same curve fitting algorithm used to find the creep parameters was used. Thus, the parameters am and Tm are optimized numerically to find the best fit with the evolution of the relative density. The values obtained for am is 0.038K -1 and Tm is 1214°C. The comparison between the experimental and the numerical relative density is presented in Figure 7. The obtained curve is in a very good agreement with the experimental data with a maximal gap between the two of less than 1%. Moreover, looking at the conservation of mass curve in Figure 8, there are no discontinuity unlike the sequential method. This shows that this method can accurately predicts the evolution of the relative density of a multi-mechanism sintering, which was, to the best of our knowledge, never been done before. Another benefit of this method is that the influence of each mechanism can be extracted from the experimental curve as presented Figure 9, where the two weight functions are plotted. It shows that the first mechanism is alone responsible for the sintering of the TiAl up to a relative density of 73% (which corresponds to a temperature of 880°C). Then, the two mechanisms occur simultaneously up to a density of 96% (or a temperature of 1075°C).

Lastly, the second mechanism is the only one remaining for the end of the densification. Also, the parameter Tm identified from equation ( 8) has a physical meaning since it corresponds to a transition temperature. The value found for this parameter is 1214°C, which is in the range of the transition between the duplex and lamellar phase [START_REF] Martins | Spark plasma sintering of a commercial TiAl 48-2-2 powder: Densification and creep analysis[END_REF]. This phase change could explain the change in the creep mechanism seen between low and high temperatures. This study was dedicated to the development of an innovative simultaneous multi-mechanism consideration of the sintering. In most works, the sintering of the studied material is considered as induced by only one mechanism. However, it has been proven experimentally that in some case, more than one mechanism can occur during the sintering, as it is the case for the spark plasma sintering of TiAl.

Thanks to a numerical method, two different mechanisms were identified as responsible for the sintering of TiAl at low and high temperatures respectively. The mechanism identified for the high temperatures is in an agreement with the one determined with an experimental in situ SPS method. This shows the effectiveness of this numerical approach to easily extrapolate the creep parameters from the experimental densification curve, and without any complex tooling or experimental campaigns. However, the mechanism identified for low temperatures still needs to be validate experimentally.

With two (or more) mechanisms responsible for the sintering of a material, the goal is to find a way to combine the influence of the two mechanisms to obtain a single simulated densification curve. If a sequential method (i.e. considering the mechanisms one after the other) gave a good approximation of the relative density, it failed to describe how those mechanisms really governs the sintering. Thus, an innovative simultaneous multi-mechanism method was developed. This method is based on the introduction of weight functions, which describe the influence of each identified mechanisms during the densification. With this method, the model was able to give an accurate prediction of the evolution of the relative density, as well as extrapolate from the experimental curve the influence of each mechanisms at each temperature.

The main benefit of the multi-mechanisms approach developed here, is that it can be used on any material provided that several mechanisms are responsible of the sintering. Indeed, this approach was developed here on TiAl, but it is totally independent of the material considered.

Moreover, the approach of Abouaf was chosen to describe the sintering of the TiAl but another approach (like the one of Olevsky et al. for example) could be used without affecting the effectiveness of the method.

The main difficulty of the multi-mechanisms approach relies on the identification of the different mechanisms. If the identification of the sintering mechanisms could have been done experimentally, here this was done numerically, since of the goal of this work is to implement a method that can be efficiently and easily used with a wide range of materials or configurations.

In this study, it was assumed that only two mechanisms occurred: one at low temperatures and another at high temperatures. The end results seem to accurately correspond to the experimental data, which tends to validate the two mechanisms hypothesis. However, the multi-mechanism approach could have been used on three mechanisms, but the more mechanisms are considered, the harder it is to extrapolate the weight of each of them.

Figure 1 :

 1 Figure 1 : SPS configuration used to sinter the 36mm TiAl sample

Figure 3 :

 3 Figure 3: Evolution of the temperature at the center (a) and 3mm away from the border of the TiAl sample (b). Evolution of the current through the SPS column (c)

  , the decision was made to use the porosity function determined by D. Martins et al. using the Norton-Green creep law equation(1) and the following relation developed byAbouaf et al. [21] between the equivalent stress and the porosity function and the invariants of the stress tensors I1 and J2:

Figure 4 :

 4 Figure 4: Results of the curve fitting of the densification for low (a) and high temperatures (b)

Figure 5 :

 5 Figure 5: Relative density of a TiAl sample obtained with the sequential approach

Figure 6 :

 6 Figure 6: Evolution of the conservation of mass obtained with the sequential approach

Figure 7 :

 7 Figure 7: Relative density of a TiAl sample obtained with a simultaneous approach

Figure 8 :

 8 Figure 8: Evolution of the conservation of mass obtained with the simultaneous approach

Figure 9 :

 9 Figure 9: Evolution of the weight function of each mechanism during the sintering of a TiAl sample

Table 1 :

 1 Physical properties of Inconel, graphite and TiAl[START_REF] Molénat | Temperature Control in Spark Plasma Sintering: An FEM Approach[END_REF][START_REF] Manière | Finiteelement modeling of the electro-thermal contacts in the spark plasma sintering process[END_REF]

		Inconel	Graphite	TiAl
			34.27 + 2.72 T -9.60 x
	Heat capacity (J.kg -1 .K -1 )	344 + 2.50 x 10 -1 T		583 + 9.40 x 10 -2 T
			10 -4 T 2

Table 2 :

 2 Calculated creep parameters compared to the ones determined experimentally by D. Martins et al.[START_REF] Martins | In-situ creep law determination for modeling Spark Plasma Sintering of TiAl 48-2-2 powder[END_REF]

	n	Q (kJ/mol)	A0 (s -1 .Pa -n )

Acknowledgements

We thank Norimat for the technical and financial support. The SPS experiments were performed at the Plateforme Nationale CNRS de Frittage-Flash (PNF2/CNRS Toulouse). This work was supported by the Association Nationale Recherche Technologie (ANRT) as part of the CIFRE (Industrial Agreement of Formation by Research) contract n°2017/1026; and the Programme Opérationnel FEDER-FSE Midi-Pyrénées et Garonne 2014-2020 as part of the CERAPRINT project n°17014462.