O Joos

C Boher

C Vergne

C Gaspard

T Nylen

F Rezaï-Aria

Assessment of oxide scales influence on wear damage of HSM work rolls

Keywords: Wear, Friction, Hot rolling, Oxidation

Improvement of hot rolling process involves the lengthening of rolling campaigns. This can be achieved through the wear resistance improvement of work roll grades. The wear damage observed in service on the hot working rolls is the result of a complex interaction between oxidation, friction and thermal fatigue. An approach is to assess the coupled effect of oxidation and friction on the overall tribological behaviour at high temperature. A first step consists in a good knowledge of the material behaviour against each stress.

Tribological behaviour of roll grades at high temperature is indeed strongly affected by the nature, the thickness and the thermo-mechanical properties of their oxide scales involved into the contact. All these parameters depend on roll grade microstructure.

An experimental methodology has also been performed to assess the influence of the roll grade microstructure on their tribological behaviour at high temperature. It constitutes the subject of the present paper.

Results have focussed on high temperature friction tests and on the analysis of oxide morphologies (through TGA tests and environmental SEM, ESEM, observations). Nevertheless this approach does not aim to reproduce strictly rolling conditions, but only to analyse the chemical and mechanical response of roll grades regarding thermal and mechanical stresses involved in hot rolling.

Material investigations have shown heterogeneous oxidation according to the different microstructural states and the environmental testing conditions. A particular scale roughness, depending on grades and oxidation conditions, and influencing the tribological behaviour, has been brought out.

Introduction

The development of high speed steels (HSS) in the early of 1990s aims at substituting HSS for high chromium cast irons (HiCr) in the finishing stands of hot strip mills [START_REF] Vergne | Contribution of laboratory tribological investigations on the performance appraisal of work rolls for hot strip mill[END_REF]. The roll damage mechanisms usually observed in-service are abrasion, adhesion, thermal fatigue and oxidation [START_REF] Boccalini | Microstructure and wear resistance of high speed steels for rolling mill rolls[END_REF][START_REF] Serantoni Da Silva | Thermal fatigue of high speed steels for rolls[END_REF][START_REF] Milan | Effect of temperature, normal load and pre-oxidation on the sliding wear of multi-component ferrous alloys[END_REF][START_REF] De Mello | Tribological behavior of multi-component ferrous alloys[END_REF].

Typical microstructures of HiCr and HSS are well described in the literature [START_REF] Boccalini | Microstructure and wear resistance of high speed steels for rolling mill rolls[END_REF][START_REF] Serantoni Da Silva | Thermal fatigue of high speed steels for rolls[END_REF][START_REF] Milan | Effect of temperature, normal load and pre-oxidation on the sliding wear of multi-component ferrous alloys[END_REF][START_REF] De Mello | Tribological behavior of multi-component ferrous alloys[END_REF][START_REF] Pellizzari | Tribological behaviour of hot rolling rolls[END_REF][START_REF] Molinari | High speed steels for hot rolls with improved impact and thermal fatigue resistance[END_REF][START_REF] Molinari | Oxidation behaviour of ledeburitic steels for hot rolls[END_REF][START_REF] Molinari | Primary carbides in spin cast HSS for hot rolls and their effect on the oxidation behaviour[END_REF]. It should be noticed that the name of HSS is relative to a grade family with a larger range of chemical composition than HiCr one.

Generally, HSS differ to HiCr by their lower carbon contents and their higher carbide former contents. The differences in chemistry and heat treatment allow to modify the nature and distribution of both eutectic and secondary carbides [START_REF] Vergne | Influence of oxide s on friction in hot rolling: experimental investigations and tribological modelling[END_REF].

From these first developments, it resulted that HSS wear resistance is much higher in comparison with HiCr [START_REF] Collins | Factors affecting the use of HSS rolls in the hot strip mill[END_REF]. MC carbides, more particularly VC carbides, are normally the main carbides in HSS, whereas M 7 C 3 carbides are preponderant in HiCr. MC carbides are harder and their distribution as secondary precipitates in the matrix is relatively fine and homogeneous [START_REF] Boccalini | Microstructure and wear resistance of high speed steels for rolling mill rolls[END_REF][START_REF] Molinari | Primary carbides in spin cast HSS for hot rolls and their effect on the oxidation behaviour[END_REF]. The wear resistance of the HSS matrix at high temperature is also higher than HiCr and performances of hot strip mills are consequently increased (in terms of lengthening of rolling campaigns).

Nevertheless an increase of friction [START_REF] Boccalini | Microstructure and wear resistance of high speed steels for rolling mill rolls[END_REF][START_REF] Vergne | Experimental investigations on the influence of oxidation of hot rolling working roll grades on their tribological behaviour against a strip material-Consequences at the industrial level[END_REF], peeling phenomena, and sometimes a drop of spalling resistance, were industrially observed in the case of HSS grades. All these phenomena tend to increase the mill power consumption and to alter the surface quality of the strip due to rolled-in-scale defects [START_REF] Thonus | Off-line analysis of the HSS roll behaviour in the hot strip mill by the use of a rolling load prediction model[END_REF].

Literature attributes this ambivalent tribological behaviour of HSS to [START_REF] Boccalini | Microstructure and wear resistance of high speed steels for rolling mill rolls[END_REF]:

• A preferential wear of the matrix, which microhardness is too low compared with the hardness of MC eutectic carbides. • A lower adhesion resistance due to a lower carbide volumetric fraction in comparison with HiCr. • The fragility of MC carbides that can be removed during contact and lead to gripping.

Next developments consisted in finding for both grades a compromise in order to:

• Ensure a high wear resistance with hard eutectic carbides and homogeneously distributed small secondary carbides [START_REF] Pellizzari | Wear and friction behaviour of high chromium iron and high speed steels for hot rolls[END_REF]. • Maintain a good roughness retention capacity with a reduced hardness difference between matrix and eutectic carbides [START_REF] Collins | Factors affecting the use of HSS rolls in the hot strip mill[END_REF][START_REF] Pellizzari | Wear and friction behaviour of high chromium iron and high speed steels for hot rolls[END_REF]. • Obtain a high resistance to thermal fatigue with eutectic carbides relevant regarding the crack nucleation and forming discontinuous primary carbide networks to limit crack propagation paths [START_REF] Serantoni Da Silva | Thermal fatigue of high speed steels for rolls[END_REF][START_REF] Molinari | High speed steels for hot rolls with improved impact and thermal fatigue resistance[END_REF][START_REF] Collins | Factors affecting the use of HSS rolls in the hot strip mill[END_REF]. • Have good adhesion and spalling resistances, by the way of high carbide volumetric fraction and without M 7 C 3 /M 2 C carbide network [START_REF] Boccalini | Microstructure and wear resistance of high speed steels for rolling mill rolls[END_REF][START_REF] Thonus | Off-line analysis of the HSS roll behaviour in the hot strip mill by the use of a rolling load prediction model[END_REF].

Researches allow for example to reduce the friction coefficient of HSS without decreasing their wear resistance in a large scale [START_REF] Pellizzari | Wear and friction behaviour of high chromium iron and high speed steels for hot rolls[END_REF].

The grade oxidation behaviour holds an important part in wear and friction behaviour: the oxide scale has to be homogeneous, thin and adherent to be efficient against wear. A high carbide fraction (as M 2 C) favours oxidation because the interfaces with matrix are excellent sites of nucleation for oxidation [START_REF] Boccalini | Microstructure and wear resistance of high speed steels for rolling mill rolls[END_REF][START_REF] Molinari | Oxidation behaviour of ledeburitic steels for hot rolls[END_REF][START_REF] Collins | Factors affecting the use of HSS rolls in the hot strip mill[END_REF][START_REF] Pellizzari | Wear and friction behaviour of high chromium iron and high speed steels for hot rolls[END_REF]. In HSS, M 7 C 3 carbides are very resistant to oxidation, whereas MC carbides and the matrix oxidise heavily. M 2 C carbides have a halfway behaviour [START_REF] Collins | Factors affecting the use of HSS rolls in the hot strip mill[END_REF].

Oxidation rate depends also on the chromium content, the nature and the distribution of carbides [START_REF] Collins | Factors affecting the use of HSS rolls in the hot strip mill[END_REF]. Moreover, the tribological behaviour is strongly affected by the nature, the thickness, the adherence, and the morphology of the oxide scales [START_REF] Molinari | Primary carbides in spin cast HSS for hot rolls and their effect on the oxidation behaviour[END_REF]. On the one hand, thick oxide layers induce a lower friction coefficient and act as a lubricant. On the other hand, thin layers adhere better to the substrate and they are also more difficult to remove [START_REF] Munther | The effect of scaling on interfacial friction in hot rolling of steels[END_REF]. The mechanical properties of scales are important: a soft oxide scale may induce a decrease in wear and friction while a hard layer is abrasive, increasing wear and friction.

Previous experimental works [START_REF] Vergne | Contribution of laboratory tribological investigations on the performance appraisal of work rolls for hot strip mill[END_REF][START_REF] Milan | Effect of temperature, normal load and pre-oxidation on the sliding wear of multi-component ferrous alloys[END_REF][START_REF] De Mello | Tribological behavior of multi-component ferrous alloys[END_REF][START_REF] Pellizzari | Tribological behaviour of hot rolling rolls[END_REF][START_REF] Vergne | Experimental investigations on the influence of oxidation of hot rolling working roll grades on their tribological behaviour against a strip material-Consequences at the industrial level[END_REF] compared some HSS and HiCr grades in studying their tribological behaviour at different temperatures. The large differences between experimental set-ups (wear test device configuration, counter-part body, normal load, sliding speed), and between used grades, prevent from making general comparisons and conclusions and lead to still debated results.

De Mello and co-workers [START_REF] Milan | Effect of temperature, normal load and pre-oxidation on the sliding wear of multi-component ferrous alloys[END_REF][START_REF] De Mello | Tribological behavior of multi-component ferrous alloys[END_REF] brought out a stabilization period of the friction coefficient at the beginning of Plint wear tests for both grades. This period corresponds to the formation of oxidized regions at the interface between the two rubbing surfaces. The higher the temperature is, the shorter the period of stabilization is. Moreover, for both grades, higher the temperature is, lower is the friction. At 20 • C, the wear rate of HiCr is five times higher than HSS. At a higher temperature, friction curves and SEM observations of wear scar show that the tribological behaviour and wear mechanisms of both grades are quite similar.

Pellizzari et al. [START_REF] Pellizzari | Tribological behaviour of hot rolling rolls[END_REF] studied the wear behaviour of several HSS grades and a HiCr grade at 700 • C with an Amsler tribometer. They showed that abrasion and oxidation are here the main wear mechanisms occurring for both grade families. High hot hardness of HSS makes the wear rate lower in comparison with HiCr, because of a higher resistance to abrasion and a higher oxide scale load bearing capability. In addition, they explained the tendency of HiCr rolls to decrease in roughness with the increasing rolling distance by a lower oxidation resistance in comparison with HSS. That allows to maintain a low surface roughness, despite the high matrix wear rate.

Finally, Vergne et al. [START_REF] Vergne | Contribution of laboratory tribological investigations on the performance appraisal of work rolls for hot strip mill[END_REF][START_REF] Vergne | Experimental investigations on the influence of oxidation of hot rolling working roll grades on their tribological behaviour against a strip material-Consequences at the industrial level[END_REF] showed that the coefficient of friction, on a pin-on-disc tribometer, is higher for HSS than for HiCr, only if the rubbing counter-face temperature is lower than 650 • C. Above 650 • C, the trend is inverted. Activation energy has been determined by thermogravimetric analysis in the thermal range of 650-950 • C. For a HSS grade, the value is 160 kJ/mol, whereas for HiCr the value reaches 330 kJ/mol. These values are representative respectively of the oxidation of iron alloys and the oxidation of chromium iron alloys. Oxide scales are also thin and adherent on HiCr.

The main objectives of the present study are to identify and assess wear mechanisms involved in the hot tribological behaviour for the two roll grades through coupled analysis methods [START_REF] Vergne | Contribution of laboratory tribological investigations on the performance appraisal of work rolls for hot strip mill[END_REF][START_REF] Vergne | Experimental investigations on the influence of oxidation of hot rolling working roll grades on their tribological behaviour against a strip material-Consequences at the industrial level[END_REF]. The effect of temperature on friction, through the formation of oxide on the pins, is studied. The thermal fatigue behaviour is not taken into account in this approach.

Materials, equipments and experimental set-ups

Materials

The chemical compositions of both roll grades involved in this study are given in Table 1.

The HSS microstructure is made of a matrix of tempered martensitic and a high fraction of primary carbides and secondary hardening precipitation carbides. Primary carbides are essentially: • MC carbides, rich in vanadium, less in iron, chromium, molybdenum and tungsten; • M 2 C carbides, rich in molybdenum, less in chromium, iron and vanadium; • M 7 C 3 carbides, rich in chromium, less in iron, vanadium and molybdenum.

The two last carbides are often mixed.

As HSS, the HiCr microstructure is made of a tempered martensitic matrix with a high fraction of primary carbides and secondary hardening precipitation carbides. Nevertheless, primary carbides are essentially M 7 C 3 carbides, rich in chromium. M 2 C carbides, rich in molybdenum, are present too.

In conclusion, the significant difference between both microstructures lies in two points:

• The volumetric fraction of carbides rich in molybdenum is much higher in HSS than in HiCr.

• The carbides rich in chromium are most widely present in

HiCr whereas carbides rich in vanadium are preponderant in HSS.

Equipments and experimental set-ups

An experimental methodology has been performed to correlate the work roll grade microstructure to oxidation and high temperature tribological behaviours. It consists in confronting experimental results obtained from:

• High temperature tribological tests completed by SEM observations and chemical analyses. • SEM observations on TGA samples (completed by chemical analyses). • In situ growth oxide tests (high temperature environmental SEM (ESEM)).

High temperature tribological tests

They have been performed on high temperature pin-on-disc tribometer [START_REF] Vergne | Contribution of laboratory tribological investigations on the performance appraisal of work rolls for hot strip mill[END_REF][START_REF] Vergne | Experimental investigations on the influence of oxidation of hot rolling working roll grades on their tribological behaviour against a strip material-Consequences at the industrial level[END_REF]. The device is not a hot rolling simulator, but this laboratory apparatus may allow to understand oxidational wear mechanisms involved in hot rolling.

In this configuration, the pin represents the tool and is made of a work roll grade (HSS or HiCr). The disc represents the rolled material and is made of a strip material (AISI 1018). The chemical composition of AISI 1018 is given in Table 2. Its structure is ferrito-pearlitic and the mean hardness is around 170 HV.

The disc, which has a continuous rotating motion, is heated by high frequency induction. The disc surface temperature is monitored by an infrared pyrometer. The spherical-ended pin (curvature radius of 20 mm) is heated during contact by conductive, radiative, convective thermal transfer and friction-released thermal energy.

During a tribological test, the disc is heated up to the test temperature while the pin is kept outside the contact at room temperature. When the setting temperature is reached, the pin is put on the disc, the load is applied and sliding starts.

In a hot strip mill, a scale breaker is often found between the rougher and the finishing stands in order to remove the strip oxide layer. In these conditions, the strip oxide scale is rather thin as its entry in the finishing stands. In our test configuration, at the beginning of friction, the disc oxide scale is thicker than in the industrial conditions but not enough to take in charge all the tribological contact.

Tests conditions are summarised in Table 3.

During each friction test, friction forces are recorded. Energetic power dissipated by friction is calculated in order to compare the tribological behaviour of both grades (Eq. ( 1))

P = F N V t t 0 µ dt ( 1
)
where P is the power dissipated by friction (J/s); F N , the normal load (N); V, the linear sliding speed (m/s); t, the friction test duration (s); and µ, the Coulomb friction coefficient.

SEM observations on TGA samples

Operating conditions for the thermogravimetric tests [START_REF] Vergne | Contribution of laboratory tribological investigations on the performance appraisal of work rolls for hot strip mill[END_REF][START_REF] Vergne | Experimental investigations on the influence of oxidation of hot rolling working roll grades on their tribological behaviour against a strip material-Consequences at the industrial level[END_REF] are given below (Table 4).

Surface as well as cross-section observations on TGA samples are compared with those made on the pins after friction tests to assess the nature and the morphology of oxide scales.

Environmental SEM observations

Isothermal in situ oxidation is carried out in an environmental scanning electron microscope ESEM-FEG. In order to reduce the number of samples, an only thermal cycle with three successive temperature stages is carried out (Fig. 1). The temperature is recorded by thermocouple close to the heating region, and could be slightly higher than the real temperature of the sample. The oxygen partial pressure is always fixed to 0.25 Torr, and is consequently much lower than in TGA or tribological tests. Nevertheless, thermodynamic reactions and phase reactivity occurring during oxidation are not changed in comparison with atmospheric pressure oxidation tests. The test atmosphere is the laboratory air. The heating and cooling rates are in agreement with the TGA tests [START_REF] Vergne | Contribution of laboratory tribological investigations on the performance appraisal of work rolls for hot strip mill[END_REF][START_REF] Vergne | Experimental investigations on the influence of oxidation of hot rolling working roll grades on their tribological behaviour against a strip material-Consequences at the industrial level[END_REF].

This equipment allows to understand the growth mechanisms of oxide scales (correlation between microstructure and oxide morphology, phase reactivity in oxidative ambience) and to give information about oxide involved in friction contact.

Results

Study of tribological behaviour

Macroscopic approach through friction curves

The evolution of the Coulomb friction coefficient versus the disc temperature is displayed in Fig. 2. The variation of the energetic power dissipated by friction is given in Fig. 3.

For both grades, friction coefficient decreases with disc temperature. Values lower than 0.5 are only reached for disc temperatures higher than 650 • C. For a disc temperature of 20 and 650 • C, the coefficient of friction and the power dissipated by friction are higher for HSS than HiCr. For a disc temperature of 950 • C, the trend is inverted: the power dissipated by friction goes on to drop for HSS while it keeps quite constant for HiCr. For HSS, the running-in period (instability of friction coefficient) is short. Then, the friction coefficient remains stable, whatever the temperature.

Contrary to HSS, there is strictly no running-in or stability period for HiCr.

For the same sampling rates, the HiCr friction coefficient is locally and macroscopically less stable compared to HSS friction curves.

Microscopic approach through pin SEM observations

On the following figures, the coarse white arrows indicate the sliding direction.

At 20 • C, strips of abraded and agglomerated debris are observed on the wear track for both grades. These strips are finer and more homogeneously distributed in the case of HSS pins. Between strips, matrix and carbides are not oxidised at all. Moreover, the carbides could be considered as large asperities, which retain oxide debris. Shedding of carbides is observed only for HiCr (Fig. 4).

For a disc temperature of 650 • C, the surface is partially covered by oxide strips, composed of compacted debris. In these iron oxide strips, residues of chromium are found only on HiCr pin, but with a very low percent. In the case of HSS, the light areas correspond to sintered iron oxide, whereas in HiCr they correspond to the matrix slightly oxidised (Fig. 5).

At 950 • C (Fig. 6a andb), the rubbing surface is mainly composed of sintered and glazed oxides that take in charge the contact. The regions close to glazed surfaces are surrounded by porous oxidised areas and rounded oxide debris. The density of re-oxidation cells attests the high level of mechanical stresses achieved during the friction tests. In the case of HiCr, the glazed oxide scale presents cracks.

The surface observations on the pin wear scar have been completed by observations in cross-section. The cross section is taken parallel to the sliding direction. SEM observations out of wear scars are added to show the effect of thermo-mechanical contact stresses.

Out of wear scars (Fig. 7a andb), a duplex, continuous and thick oxide scale with protuberances is observed on HSS. On HiCr, a preferential oxidation of the matrix leads to a thin and discontinuous oxide scale (protuberances).

In the wear scars of HSS pins (Fig. 7c andd), contact pressure and abrasion lead to a very smooth and compacted oxide scale, thick enough to support the contact. On HiCr, the oxide appears essentially above the matrix and oxide debris are issued from matrix oxidation. The scale is still very thin and discontinuous.

SEM observations (Fig. 7) well exhibit two oxide scale morphologies on the pins after the friction tests. These morphologies influence the tribological behaviour of grades. In the next section, the aim consists in understanding the influence of grade microstructures on oxide scale morphologies with static oxidation tests.

Morphology, nature of the oxide scales and the relation to microstructure 3.2.1. Global characterization of oxide scales

Experiments of thermogrvimetric analysis (TGA) give data on global oxidation rates [START_REF] Vergne | Contribution of laboratory tribological investigations on the performance appraisal of work rolls for hot strip mill[END_REF][START_REF] Vergne | Experimental investigations on the influence of oxidation of hot rolling working roll grades on their tribological behaviour against a strip material-Consequences at the industrial level[END_REF]. Morphology and nature of oxide scales can be studied moreover.

For both grades, protuberances grow at the surface at a temperature higher than 800 • C. The duration of oxidation for a given temperature leads to an increase of both oxide scale surface roughness and surface fraction covered by protuberances. (Fig. 8a andb).

These evolutions versus oxidation duration have not been yet quantified by topography measurements. Nevertheless, SEM observations show that, for given sets of parameters, the oxide scale surface roughness is higher for HSS than for HiCr, whereas the protuberance surface fraction covered by protuberances The main difference between the two grades is that oxide scales are composed of protuberances surrounded by a thick and duplex base oxide scale for HSS, whereas the oxide scale is composed only of protuberances for HiCr. In this last case, oxidation-free zones correspond to coarse M 7 C 3 carbides, leading to a very discontinuous oxide scale (Fig. 8c andd).

The chemical composition of oxides versus their morphology is given in Table 5 for both grades.

Comprehension of growth mechanisms of oxide scales

ESEM observations are carried out for both grades. The most interesting steps of oxidation are illustrated in this section.

HSS grade.

For the HSS grade, during the first temperature ramp, a slight oxidation of matrix/mixed carbides (M 2 C and M 7 C 3 ) interfaces occurs near 350 • C. (Fig. 9a-arrows1).

The oxidation of the matrix at the level of dendritic cells begins near 400 • C. Oxide of the matrix presents a granular morphology. The interface between matrix and M 7 C 3 carbides is less oxidised (Fig. 9b-arrow 2).

Between 400 and 650 • C (Fig. 10a), oxidation of M 2 C-M 7 C 3 /matrix interfaces and dendritic cells goes on. The oxidation of interfaces between matrix and MC carbides begins (Fig. 10a-arrow 3). Theses carbides are not oxidised. The oxide growth is higher at the matrix/M 7 C 3 carbides interfaces than at the matrix/M 2 C carbides interfaces. Both morphologies tend to become granular. At 650 • C (Fig. 10b), MC carbides oxidation occurs. They are simultaneously covered by the lateral growth of the matrix/MC carbides interface oxide and by their core oxidation. The slight growth in depth of the matrix oxide scale is also observed (Fig. 10b-arrow 4).

During the stage at 800 • C, lateral and in-depth growth of the matrix oxide takes place rapidly and induces the formation of protuberances. Primary carbides are totally covered, even the chromium-rich carbides.

At 950 • C, the oxide scale, that covers the network of MC carbides grows rapidly and the oxidation products are very porous grains.

At the end of the heating stage, the oxide scale on the HSS ESEM specimens is composed of:

• Protuberances with compact and cuboïdal grains, which correspond to the oxidation of dendritic cells.

• An oxide scale constituted of porous grains (which corresponds to the oxidation of the surrounding matrix oxide covering MC carbides), and with a second morphology resulting from the oxidation of M 2 C/M 7 C 3 carbides and their interfaces with matrix.

HiCr grade.

For HiCr, a very slight oxidation of the dendritic cells begins near 300 • C. A very thin and homogeneous oxide scale grows on M 2 C carbides at this temperature. At 400 • C (Fig. 11a), fine cuboïdal oxide crystallites nucleate on the M 7 C 3 carbides (arrow 1). This oxidation is heterogeneous. A porous scale grows on dendritic cells (arrow 2). The oxidation rate is higher near the M 2 C/matrix interface (arrow 3). From 950 • C, the oxidation rate of M 7 C 3 carbides increases but the scale seems to be very thin (Fig. 11b-arrow 5). Nevertheless, at the end of heating stage, oxide scale morphology is similar to this observed at 650 • C.

Discussion

SEM and ESEM (in ambient air) observations highlight the large influence of grade microstructures on the final morphology of oxide scales.

Interfaces between carbides and matrix are preferential sites for oxide nucleation for both grades. Microstructures of HSS allow to form thick, duplex and continuous oxide scales, whereas the oxide scales are thin and very discontinuous for HiCr. The matrix is very prone to oxidation, in comparison with carbides, especially chromium-rich carbides. Roughness of oxide scales is linked to the presence of protuberances surrounded by a thick base oxide scale for HSS, to oxide protuberances surrounded by oxidation-free areas for HiCr.

The differences in microstructure allow to explain these two oxidation behaviours.

ESEM results confirm that for HSS, the matrix is poor in chromium and, in this way, less resistant to oxidation in comparison with the HiCr matrix. Despite the depletion of chromium due to the precipitation of the M 7 C 3 carbides, the HiCr matrix chromium content is high enough to ensure high oxidation resistance.

In addition, ESEM results show the contribution of the carbide distribution (fraction and size) in the oxidation mechanisms of the two grades.

These two contributions (matrix and carbide distribution), added to low oxidation resistances of matrix and carbides, lead to a continuous oxide scale at the surface of the HSS grade. In HiCr, the coarse carbides are resistant to oxidation. Their high fraction prevents from forming a continuous external oxide layer, which could totally cover the substrate surface.

The differences of oxide scale morphologies between TGA and ESEM specimens for HiCr could be explained by the very low oxygen partial pressure in ESEM tests and the high oxidation resistance highlighted in previous studies [START_REF] Vergne | Contribution of laboratory tribological investigations on the performance appraisal of work rolls for hot strip mill[END_REF][START_REF] Vergne | Experimental investigations on the influence of oxidation of hot rolling working roll grades on their tribological behaviour against a strip material-Consequences at the industrial level[END_REF].

The different tribological behaviours of grades between 650 and 950 • C was previously [START_REF] Vergne | Contribution of laboratory tribological investigations on the performance appraisal of work rolls for hot strip mill[END_REF][START_REF] Vergne | Experimental investigations on the influence of oxidation of hot rolling working roll grades on their tribological behaviour against a strip material-Consequences at the industrial level[END_REF] explained in considering mostly the influence of disc oxide scales. Nevertheless, SEM observations of worn pin surfaces give complementary results and the variations of friction coefficient versus the disc temperature for each grade seem to be well explained by nature of contact. These differences, summed up in Table 6 for HSS and in Table 7 for HiCr, provide complementary results for discussion.

For a disc temperature of 20 • C, the contact is metal against metal for both grades. The wear mechanism is abrasion. Debris attrition phenomena lead to the formation of oxide debris. The friction coefficient is high for both grades.

For a disc temperature of 650 • C, oxidation of the pin surface is low for both grades. The wear mechanism is still abrasion by disc oxide scale. The decrease of the friction coefficient for both grades could be only attributed to disc oxide layer that plays the role of solid lubricant.

For a disc temperature of 950 • C, the low oxidation resistance of HSS leads rapidly to the formation of a continuous oxide scale on the pin surface, thick enough to take in charge the contact. That contributes to the drop of friction in comparison with tests at 650 • C. At 950 • C the pin oxide scale contribution becomes important. In contrary to HSS, for friction tests at 950 • C, the peculiar microstructure and chemical composition of HiCr do not allow to form thick and continuous oxide scales on pin, which could contribute to the friction drop, as disc oxide scales. In this case, the pin contact surface is still quite similar to 650 • C tests and the friction coefficient remains constant.

Structure and roughness of pin oxide scales are quite similar to those observed on TGA samples for both grades. But the role of oxide scale protuberances, exhibited from TGA and ESEM experiments, during sliding is difficult to assess in case of HSS.

The assumption is that, either the protuberances are abraded, or the vertical growth is constrained by contact pressure. Moreover, SEM observations showed that the external oxide layer on HSS TGA samples adhere poorly for the highest temperature tests.

That might have an effect on HSS tribological behaviour during rolling through roll oxide scale removal.

Conclusions

The aim of this study is to link oxidation and high temperature tribological behaviours of two roll grades (HSS and HiCr) that differ strongly from their microstructure. During static oxidation tests, the contribution of matrix, carbides and interfaces between matrix and carbides induces the formation of continuous external oxide layers on HSS, and discontinuous external oxide layers on HiCr.

This difference of growth and morphology of oxide scales is still present on pin surfaces during the pin-on-disc friction tests. For a disc temperature below 650 • C, the decrease of the friction coefficient is essentially taken in charge by the disc oxide scale for both grades. Above 650 • C, the contribution of the pin oxide scale influences the friction evolution. For HSS, friction drops due to a thick and continuous pin oxide scale. In contrary, friction of HiCr remains constant because of thin and discontinuous pin oxide scales.

Fig. 1 .

 1 Fig. 1. Temperature cycle in ESEM tests.

Fig. 3 .

 3 Fig. 3. Energetic power dissipated by friction for both grades.

Fig. 2 .

 2 Fig. 2. Typical friction curves (Coulomb coefficient vs. time) for both grades.

Fig. 4 .

 4 Fig. 4. Wear scar for HSS (left) and HiCr (right) for a disc temperature of 20 • C.

Fig. 5 .

 5 Fig. 5. Wear scar for HSS (left) and HiCr (right) for a disc temperature of 650 • C.

Fig. 6 .

 6 Fig. 6. Surface SEM observations of pin wear scar for disc temperature of 950 • C for HSS (left) and HiCr (right).

Fig. 7 .

 7 Fig. 7. Cross-section SEM observations of pin for disc temperature of 950 • C for HSS (left) and HiCr (right).

Fig. 8 .

 8 Fig. 8. Surface SEM observations of oxide scale for HSS (a) and HiCr (b), cross-section SEM observations of oxide scale for HSS (c) and HiCr (d), After TGA test at 800 • C for 3 h.

Fig. 9 .

 9 Fig. 9. (a) M 2 C/M 7 C 3 surrounding matrix oxidation at 350 • C for HSS grade, (b) dendritic cells oxidation at 400 • C for HSS grade.

Fig. 10 .

 10 Fig. 10. (a) M 2 C/matrix and M 7 C 3 /matrix interfaces oxidation between 400 and 650 • C for HSS grade, (b) MC carbides oxidation at 650 • C for HSS grade and growth in-depth of matrix oxide scale.

  From 650 to 950 • C, oxidation of dendritic cells remains low and homogeneous. The scale is quite porous. At 650 • C, the oxidation rate at the interface M 2 C/M 7 C 3 increases (Fig. 11b-arrow 4): only grains and needles compose the morphology. The oxidation of M 7 C 3 and MC carbides is slight. From 800 to 950 • C, growth of oxide needles at M 2 C/M 7 C 3 interface continues. The needles become coarse.

Fig. 11 .

 11 Fig. 11. (a) M 2 C/matrix oxidation at 400 • C for HiCr grade, (b) M 2 C/M 7 C 3 interface oxidation between 650 and 950 • C for HiCr grade.

Table 1

 1 Chemical composition (in weight percent) of the two grades

		C	Mn	Cr	Mo + W + V	Mo + V
	HSS	1-2	0.5-1	4-6	8-9	-
	HiCr	2-3	0.5-1	15-20	-	2-4

Table 2

 2 Mean chemical composition (in weight percent) of AISI 1018

	Fe	Bal.
	C	0.18
	Si	0.26
	Mn	0.62
	Cr	0.15
	Cu	0.18

Table 4

 4

	Operating conditions of TGA tests
	Atmosphere	Temperatures ( • C)	Duration (h)
	Ambient air	650	1-2-3
		800
		950

Table 5

 5 Morphology and chemical composition of oxide scales on TGA samples

	Zones	HSS	HiCr
	Protuberances
	External layer	Pure ferrous oxide	Pure ferrous oxide
	Internal layer	None	Chromium-ferrous oxide
	Duplex base scale
	External layer	Pure ferrous oxide	None
	Internal layer	Alloyed (Cr, V, Mo)	None
		ferrous oxide

Table 6

 6 Contact nature in tribological tests for HSS Thin and discontinuous oxide scale + oxidation-free zones Thin and continuous Fe 2 O 3 /Fe 3 O 4 oxide scale Oxidised debris 950 Thin and discontinuous glazed oxide scale Thick and continuous ferrous Fe 2 O 3 /Fe 3 O 4 /FeO oxide scale

	Disc temperature ( • C)	First bodies


Andréa Oliveira Nunes

Luciano Rodrigues

Pierre-Marie Guineheuc

Virgínia Aparecida Da

Silva Moris

Jane Maria Faulstich De Paiva

Radu Barna

Yannick Soudais

Luciano Rodrigues Viana

Andréa Oliveira Nunes
email: andreaoliveira_n@hotmail.com

Life cycle assessment of a

Keywords: Carbon fiber-reinforced polymer, Composite, Life cycle assessment, Recycling, Steam thermolysis, Thermal process, Waste valorization

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The use of carbon fibers has widely increased in a number of applications such as aerospace, wind energy, automotive, sporting goods, and other industrial fields, due to their excellent characteristics like high mechanical properties, low weight, high corrosion resistance, temperature tolerance, and low thermal expansion [START_REF] Wang | Carbon fibers modified with silicone peroxide containing vinyl groups for silicone rubber reinforcement[END_REF][START_REF] Ma | Effects of surface methods treating methods of high-strength carbon fibers on interfacial properties of epoxy resin matrix composite[END_REF]Industry Experts 2013). Despite the high price of carbon fiber, Responsible editor: Shabbir Gheewala the global demand is expected to grow from 46,000 t in 2011 to 140,000 t in 2020 [START_REF] Roberts | The Carbon Fibre Industry Worldwide 2011-2020: an evaluation of current markets and future supply and demand[END_REF].

More than 97% of carbon fiber produced is processed into composite materials, such as carbon fiber-reinforced polymers (CFRPs) [START_REF] Jahn | Composites Market Report[END_REF]). These composites have acquired great importance in major industrial sectors, mainly in the aerospace and automotive industry. For example, in the aircraft industry, the new Boeing 787 and Airbus A350 have up to 50% of their weight in CFRP. Consequently, an increasing amount of CFRP waste is also generated. The sources of waste include out-of-date pre-pregs, manufacturing cutoffs, testing materials, production tools, and end-of-life (EoL) components [START_REF] Pimenta | Recycling carbon fibre reinforced polymers for structural applications: technology review and market outlook[END_REF]. As composite materials are very difficult to fractionate into elemental components, the waste has been mainly disposed in landfills or incinerated [START_REF] Morin | Near and supercritical solvolysis of carbon fibre reinforced polymers (CFRPs) for recycling carbon fibers as a valuable resource: state of the art[END_REF]). However, these techniques have became strictly regulated by the environmental legislations. In Europe, waste directives have limited landfill disposal and imposed that 95% of average weight of end-of-life vehicles manufactured after January 2015 must be recycled (EU 2000/53/EC).

The economic and environmental factors have motivated the development of recycling technologies, including mechanical recycling (shredding, crushing, milling), chemical process (solvent, catalyst, or supercritical fluids), and thermal process (pyrolysis, oxidation, steam thermolysis) [START_REF] Morin | Near and supercritical solvolysis of carbon fibre reinforced polymers (CFRPs) for recycling carbon fibers as a valuable resource: state of the art[END_REF][START_REF] Oliveux | Current status of recycling of fibre reinforced polymers: review of technologies, reuse and resulting properties[END_REF][START_REF] Sun | Recycling of carbon fibers from fiber reinforced polymer using electrochemical method[END_REF]. The aim is to recover the carbon fibers, as close as possible to their initial state, in order to envisage a reuse in other applications.

Mechanical recycling involves comminution techniques to reduce the size of the composite waste into granulated fractions [START_REF] Pickering | Recycling technologies for thermoset composite materials-current status[END_REF]). This process does not recover individual fibers, and the mechanical properties of the recycled fibers are significantly affected. On the other hand, the chemical process (solvolysis) provides very high retention of fiber length and mechanical properties, as well as a high potential for material recovery from polymer matrix (resin) [START_REF] Pimenta | Recycling carbon fibre reinforced polymers for structural applications: technology review and market outlook[END_REF][START_REF] Morin | Near and supercritical solvolysis of carbon fibre reinforced polymers (CFRPs) for recycling carbon fibers as a valuable resource: state of the art[END_REF]. However, hazardous solvents for the environment are generally used, and under supercritical conditions, high pressures are required [START_REF] Liu | Recycling of carbon/epoxy composites[END_REF][START_REF] Pinero-Hernanz | Chemical recycling of carbon fibre composites in nearcritical and supercritical water[END_REF].

The thermal recycling by pyrolysis is already used industrially. Pyrolysis consists of a thermal degradation of the resin in the absence of oxygen, at atmospheric pressure and temperatures between 450 and 750 °C. The matrix (resin) degradation produces an oil, gas, and a carbonaceous residue (char). The char formation on the carbon fiber surface is a situation that should be avoided, since the fibers must be free of residues to be reused in the formulation of new composites. Thus, the pyrolysis is generally combined with a post-oxidizing treatment in the presence of air (oxygen) to obtain clean fibers (without residual char). Nonetheless, high temperature and highly oxidizing atmosphere lead to a higher degradation of the carbon fibers [START_REF] Yang | Recycling of composites materials[END_REF][START_REF] Oliveux | Current status of recycling of fibre reinforced polymers: review of technologies, reuse and resulting properties[END_REF].

The steam thermolysis process has been developed in the RAPSODEE Laboratory, Albi, France. This process uses superheated steam, as an oxidant medium, under pyrolysis conditions to decompose the polymer matrix of the composite and reclaim the carbon fibers. The matrix degradation produces oil and gases, as well as in the pyrolysis process. The presence of steam as a soft oxidant produces a less oxidizing atmosphere than the thermal processes in the presence of air, leading to greater degradation of the resin and the removal of residual char on the fiber surface without an extensive reduction of mechanical properties of the remaining carbon fibers. The carbon fibers recovered from the optimized steam thermolysis process present a resin-free and uniform surface and retain over 80% of their original tensile strength [START_REF] Ye | Parameter optimization of the steam thermolysis: a process to recover carbon fibers from polymer-matrix composites[END_REF][START_REF] Nunes | Carbon fiber reinforced composites: recovery of carbon fiber by steam-thermolysis, optimization of the process[END_REF].

Another reason for the increase in research and development of recycling technologies is the price of carbon fiber, a high-value-added material (cost over US$30 per kg), which reflects the high energy consumption in their manufacturing [START_REF] Baker | Recent advances in low-cost carbon fiber manufacture from lignin[END_REF]. The recycling of carbon fibers from CFRP waste contributes to the sustainability and sustainable development of industrial processes, as well as leads to resource and energy savings for their production [START_REF] Yang | Recycling of composites materials[END_REF]. However, while the recycling processes allow such benefits, an assessment of their environmental performance is still needed. Recycling is considered environmentally appropriate when the environmental impacts of the process are smaller than the impacts generated by alternative disposal practices (landfills, incineration) and virgin material production [START_REF] Witik | Carbon fibre reinforced composite waste: an environmental assessment of recycling, energy recovery and landfilling[END_REF].

Life cycle assessment (LCA) is an environmental management tool used to assess the environmental impacts associated with a product, process, or service throughout its entire life cycle, from raw material extraction to the final disposal (SETAC 1993;Georgakellos 2002). Several studies have been developed in order to evaluate the environmental impacts from recycling of different types of waste, like e-waste, plastics, wood waste, and composites [START_REF] Menikpura | Assessing the climate cobenefits from waste electrical and electronic equipment (WEEE) recycling in Japan[END_REF][START_REF] Arena | Life cycle assessment of a plastic packaging recycling system[END_REF][START_REF] Kim | Analysis of the global warming potential for wood waste recycling systems[END_REF][START_REF] Witik | Carbon fibre reinforced composite waste: an environmental assessment of recycling, energy recovery and landfilling[END_REF]).

In the case of composite waste, specifically the recycling of CFRP, some studies employing LCA methodology were performed. For the mechanical recycling of carbon fiber composite, [START_REF] Howarth | Energy intensity and environmental analysis of mechanical recycling of carbon fibre composite[END_REF] propose a model to estimate the energy demand in mechanical recycling by a milling process and therefore provide new data set for a further LCA. [START_REF] Li | Environmental and financial performance of mechanical recycling of carbon fibre reinforced polymers and comparison with conventional disposal routes[END_REF] conducted a life cycle cost (LCC) and a LCA research in order to evaluate financial and environmental performance of mechanical recycling of carbon fiber-reinforced polymers, comparing with landfill and incineration in a UK context. In that work, the treatment by mechanical recycling produced the lowest global warming impact compared with the other disposal methods. However, mechanical recycling presented high costs and low rate of carbon fiber recovering. [START_REF] Pinçaud | Environmental feasibility of the recycling of carbon fibers from CFRPs by solvolysis using supercritical water[END_REF] evaluated the environmental impacts of the chemical recycling of carbon fiber/epoxy composite by solvolysis under supercritical water. In that case, the recycling process provides an average reduction of approximately 80% for all impact categories compared to disposal via landfill. [START_REF] Witik | Carbon fibre reinforced composite waste: an environmental assessment of recycling, energy recovery and landfilling[END_REF] carried out a study to compare the environmental viability of recycling by pyrolysis against incineration and landfill disposal, including an assessment of how reused materials may change the environmental impacts. The data of the pyrolysis recycling process were based on commercially technical specifications and literature.

In the present work, a LCA was performed to assess the environmental impacts of the recycling of carbon fiber from CFRP waste by steam thermolysis process, identifying the sources of impacts of this process conducted in France. This recycling process was compared with the French classic disposal scenario, 50% landfill and 50% incineration, in order to position the steam thermolysis process from an environmental point of view against a classic disposal scenario.

Methodology

The methodology of LCA is structured by ISO series 14040 standards and consists of four steps: goal and scope definition, inventory analysis, impact assessment, and interpretation (ISO 2006).

Goal and scope definition

The goal of this study is to compare the steam thermolysis recycling process with the French classic disposal scenario by using two life cycles of a CFRP composite in two different scenarios: one of them without recycling with an end of life of 50% disposing in landfill and 50% in incineration and the other one with recycling carbon fibers by steam thermolysis process.

Functional unit

The functional unit set for this study is 2 kg of composite (1 kg of long fiber composite and 1 kg of short fiber composite) to compare the scenario with the steam thermolysis recycling process with the other scenario without recycling. To attend the objective of this LCA (comparison of two different waste management scenarios), a mass-based functional unit is chosen rather than selecting a specific composite product. For this reason, in the two scenarios, it is assumed that the composites have the same application.

It is estimated that the two facilities associated with the recycling process (the steam thermolysis reactor and the cutting machine used to cut the composite waste) has a lifespan of 10 years. It is also considered that the steam thermolysis reactor has a treatment capacity of about 3000 kg of composites over 10 years.

System boundaries

Figure 1 shows the life cycle stages and the system boundaries of CFRP composite for the two scenarios covered in this study. The scenario without recycling is composed of two life cycles in parallel, one in long fiber composite and the other in short fiber composite. Thus, it can be compared with that of recycling. In fact, in the steam thermolysis recycling process, the recovered carbon fibers are necessarily reduced in length. Their use in a new composite formulation requires the implementation of an adapted process to the size of these short fibers (Fig. 1). It is also imperative that both scenarios follow the same functional unit, i.e., 2 kg of composite (1 kg of long fiber composite and 1 kg of short fiber composite).

In the scenario without recycling, both identified parallel cycles take place in the same way (Fig. 1a: cycle 1 and cycle 2). The new carbon fibers (long and short) are combined with the resin polyamide 6 (PA6) to produce 1 kg of composite in each cycle, i.e., 2 kg in total. The only difference between these two parallel cycles is the composite manufacturing process, which is appropriate to each type of starting fiber. The pultrusion manufacturing process is used to produce long fiber composites, and the injection manufacturing process is well adapted for the production of short fiber composites (Fig. 1). Then, once the composite material is produced, it goes on to the distribution and use phase, and after that, it is sent to end of life (50% landfill and 50% incineration).

In the case with recycling by steam thermolysis (Fig. 1b), after the first use phase, the composite waste (1 kg) is transported to the treatment site, where it is cut using a water jet machine, in order to fit in the steam thermolysis reactor. At the end of recycling process, short carbon fibers are recovered to reproduce again 1 kg of composite material. Finally, after the second use phase, the short fiber composite is disposed in landfill and incineration. It is assumed that the recycling of the carbon fibers takes place only once.

It is also considered that the two composites have, respectively, the same use in both scenarios: 1 kg long fiber composite (use 1) and 1 kg short fiber composite (use 2), as shown in Fig. 1.

This methodology of comparing two parallel cycles in the scenario without recycling with the other of the recycling process enables avoiding the allocation issue of the recycling stage.

As mentioned above, the steam thermolysis process has been developed in France. Thus, this LCA study aims to evaluate waste treatment within the geographical boundaries of France.

Inventory analysis

The life cycle inventory (LCI) is the collection and calculation data of material, energy, and emission flows of a product system (ISO 1998). The inventory input and output flow analysis is established on the elementary processes for the different phases of the two systems considered in the study. In this work, it can be identified the manufacturing phase, the distribution and use phase, the recycling phase, and the end-of-life phase. In our case, the distribution and use phase is not included in the inventory analysis. In fact, as previously mentioned, it is assumed that the two composites have, respectively, the same use, and therefore, the impacts of this phase are the same in both scenarios.

The life cycle assessment was performed considering as product a thermoplastic composite of carbon fiber and polyamide 6 resin (carbon fiber/PA6). All inventory data related to the steam thermolysis process were experimentally determined by tests conducted at the pilot scale.

The optimized steam thermolysis process leads to a degradation rate of the resin higher than 99%. The recovered carbon fibers present a resin-free uniform surface and retain over 80% of their original tensile strength. The mechanical tensile properties of the composite made with recycled fibers from the steam thermolysis (breaking strength 136 MPa, elastic modulus 8.4 GPa) are close to those of the composite made with virgin fibers (breaking strength 141 MPa, elastic modulus 8.9 GPa) [START_REF] Boulanghien | Using steam thermolysis to recycle carbon fibres from composite waste[END_REF][START_REF] Nunes | Carbon fiber reinforced composites: recovery of carbon fiber by steam-thermolysis, optimization of the process[END_REF]. In addition, the microstructure of both recovered carbon fibers and virgin ones was subject to analysis in environmental scanning electron microscopy (ESEM). Elemental analysis (CHNS) was also conducted to determine the exact composition of carbon fibers. The ESEN images show that carbon fiber surface recovered by steam thermolysis appeared to be resin-free and virtually undamaged (Fig. 2). The elemental analysis indicates that the composition of the recycled carbon fibers (N 3.23%, C 93.19%, H 0.09%, S 0.01%) is also close to the virgin carbon fibers (N 2.57%, C 95.69%, H 0%, S 0%). As the consequence of an oxidation under superheated steam condition, a minor reduction in the carbon weight fraction of the recycled carbon fibers is observed [START_REF] Ye | Characterisation of carbon fibres reclaimed from steam-thermal treatment[END_REF][START_REF] Ye | Parameter optimization of the steam thermolysis: a process to recover carbon fibers from polymer-matrix composites[END_REF][START_REF] Nunes | Carbon fiber reinforced composites: recovery of carbon fiber by steam-thermolysis, optimization of the process[END_REF].

The carbon fibers recovered by steam thermolysis have a reduced length (50 mm), limited primarily by the reactor size. However, many applications require the use of short cut fibers, i.e., finite length fibers. The stiffness of staple fiber composites is lower than that of the unidirectional composites. Nevertheless, the staple fiber composites can be shaped more easily, mainly using injection molding process, especially where rapid production of complex geometry parts is required, such as in the automobile sector for primary structures and internal parts of vehicle [START_REF] Ogi | Temperature dependence of electrical resistance in carbon fiber and carbon fiber composites[END_REF][START_REF] Boulanghien | Formulations de composites thermoplastiques à partir de fibres de carbone recyclées par vapo-thermolyse[END_REF].

Manufacturing phase

The manufacturing phase takes into account the different manufacturing processes of raw materials (polyacrylonitrile, It is worth to remind that the functional unit is 2 kg of composite divided in 1 kg of long fiber composite and 1 kg of short fiber composite. The chosen composite consists of 55% by weight of carbon fiber and 45% by weight of resin (PA6). It is assumed that the carbon fibers and composites are manufactured on the industry partner site located in Pau, France. The fibers of polyacrylonitrile (PAN) are used as raw material for the manufacture of carbon fibers. According to [START_REF] Griffing | Carbon fibre HS from PAN. Chemical Life Cycle Database[END_REF], 1.82 kg of PAN is required to produce 1 kg of carbon fiber. As reported in literature by [START_REF] Song | Life cycle energy analysis of fiber-reinforced composites[END_REF] and by the industrial partner, the energy employed in the production of carbon fibers is about 286 MJ kg -1 .

Once the manufacture of the carbon fiber is completed, the resin is added to shape the composite. The PA6 resin is furnished by an industry located in Indiana, USA. It is therefore also necessary to consider the transport (ship and lorry) to the site of Pau, France, where the composite is manufactured. Two different composite manufacturing processes are used depending on the size of the fibers. As previously mentioned, the pultrusion is appropriated for long fiber (> 50 mm) composites, and the injection process is well known to be more suited for short and mid-long fiber composites [START_REF] Boulanghien | Formulations de composites thermoplastiques à partir de fibres de carbone recyclées par vapo-thermolyse[END_REF]. Table 1 shows the inventory of fiber production, composite manufacturing, and the assumptions related to the transport stage of this phase.

Recycling phase

The recycling phase is divided into two parts: cutting of composites and the steam thermolysis process. The cutting is necessary to reduce the size of composite waste in order to facilitate the feeding process and the efficacy of the steam thermolysis treatment. In this study, this task is performed by a water jet cutting machine, the Byjet Pro 3015.

The Byjet Pro 3015 is a robust machine (9850 kg), used mainly for machining materials in large scale. However, this work is based on a pilot scale, where the steam thermolysis reactor has a treatment capacity of only 1 kg per day. Therefore, it is assumed that only part of the machine working time is dedicated to cutting the composite wastes under investigation in this study.

It was assumed that the machine, which has a dimension of 300 × 150 × 23 cm and a maximum cutting capacity of 50 m min -1 , operates 300 days per year and 8 h per day, i.e., a total working time of 24,000 h for the whole lifespan. It should be remembered that the cutting machine and the steam thermolysis reactor have a lifespan of 10 years, and it is envisaged to treat 3000 kg of composite waste by steam thermolysis over 10 years. The use percentage of the machine is calculated based on the desired size of composite parts (5 × 5 × 0.028 cm). Thus, a cutting rate of 20 m min -1 was estimated and considered to be suitable for cutting 1 kg of c o m p o s i t e w a s t e , i . e . , a b o u t 6 6 6 . 6 7 c m 3 (ρ composite = 1.5 g cm -3 ). The machine working time dedicated only to cutting the composite wastes is calculated about 231 h. Therefore, the use percentage of the cutting machine is about 0.96%.

The raw materials needed for the construction of the cutting machine (steel, aluminum, copper), as well as the water and energy used to cut the composites, are amortized over a period of 10 years, also considering the percentage of use. The inventory of this step is shown in Table 2. In collaboration with the industrial partner, the transport distance between the composite waste disposal site and the recycling facility, where the cutting machine and the steam thermolysis reactor are placed, is estimated at about 600 km. It is planned to collect the composite waste in a collection center in the city of Marseille and to transport them to the recycling site located in Brevans, France.

Thereafter, the steam thermolysis process takes place. The sized composite wastes are introduced into the reactor under an inert atmosphere (nitrogen) and in the presence of steam, where they are kept at the ideal temperature needed to achieve the resin degradation. The amounts of nitrogen and water are determined on the optimal conditions established by pilotscale tests. During the steam thermolysis, the following outputs are produced: a solid phase, which consists of the recovered carbon fibers, and a gas phase, consisting of a condensable fraction (oil) and a non-condensable fraction. The amount of each output flow is calculated based on the material balance performed for the process from experiments conducted in the steam thermolysis pilot reactor. Table 3 shows the inventory of steam thermolysis process. The materials used for the construction of the steam thermolysis reactor, such as steel, aluminum, and rock wool, are also considered in this inventory.

According to the characterization of the gases by gas chromatography, the non-condensable gases, produced by the resin degradation, consist primarily of hydrocarbons, carbon dioxide (CO 2 ), and carbon monoxide (CO). It is considered that these gases then pass through a combustion gas boiler and are released into the atmosphere as carbon dioxide. The energy released by the combustion of these gases can be used to produce heat energy [START_REF] Gustafsson | Pyrolysis for heat production-biochar the primary byproduct[END_REF][START_REF] Honus | Replacing conventional fuels in USA, Europe, and UK with plastic pyrolysis gasespart I: experiments and graphical interchangeability methods[END_REF]). The amount of CO 2 produced from the combustion reaction and the heat of reaction generated for each gas are shown in Table 4. The treatment of 1 kg of composite by steam thermolysis generates about 0.76 kWh of energy (Table 4). In addition, for the condensable fraction, the oil obtained can be used as fuel [START_REF] Devaraj | Experimental investigation of performance, emission and combustion characteristics of waste plastic pyrolysis oil blended with diethyl ether used as fuel for diesel engine[END_REF][START_REF] Krutof | Blends of pyrolysis oil, petroleum, and other bio-based fuels: a review[END_REF]. Therefore, in this LCA, this oil is considered as avoided impacts.

End-of-life phase

It should be recalled that the scenario without recycling consists of two parallel cycles: one in long fiber composite (1 kg) and another (1 kg) in short fiber composite. The composite wastes (2 kg) are directly sent to end of life after used, as shown in Fig. 1a. On the other hand, in the recycling scenario, the first step of end of life is avoided by the introduction of the recycling stage. Finally, only the composite made with the recovered carbon fibers are sent to end of life, that means, 1 kg (Fig. 1b).

As mentioned above, the geographical boundaries of this LCA study were defined within France, since the steam thermolysis process has been developed in this country.

According to ORDIMIP (The Regional Observatory of Industrial Waste of Midi-Pyrénées, France), until now, there are no specific regulations for waste composites in France and general waste regulations have been applied. Recycling of composite materials is not yet an industrial reality. Nevertheless, the recovery routes are known and have been researched and developed (ORDIMIP 2017).

In addition, the overall composition of household waste has not changed fundamentally in 15 years. In 2007, the distribution among the different materials is quite close to that of 1993. The main categories are putrescible waste (32.2%), paper/cardboard (21.5%), glass (12.7%), plastics (11.2%), textiles (10.6%, including sanitary textiles), metals (3%), and different composite materials or unclassified (8.9%) (ADEME 2014).

Therefore, the end-of-life scenario assumed is representative of the current average end-of-life household waste in France, which is about 50% landfill and 50% incineration (ADEME 2012). It is also assumed an average distance of 100 km to final disposal site [START_REF] Witik | Carbon fibre reinforced composite waste: an environmental assessment of recycling, energy recovery and landfilling[END_REF]).

Impact assessment

The LCIA is carried out using the SimaPro software and the Ecoinvent 3 database with the implementation, in a first moment, of the CML-IA baseline method. This LCIA method is a result of the work undertaken by different scientists in the Center of Environmental Science of Leiden University [START_REF] Guinee | Handbook on life cycle assessment operational guide to the ISO standards[END_REF]. The CML-IA baseline LCIA method is a midpoint approach, linking all stages of life cycle inventory via 11 impact categories: depletion of abiotic resources (mineralskg Sb eq and fossil fuels-MJ), global warming (kg CO 2 eq), ozone layer depletion (kg CFC-11 eq), human toxicity (kg 1,4-DB eq), freshwater aquatic ecotoxicity (kg 1,4-DB eq), marine ecotoxicity (kg 1,4-DB eq), terrestrial ecotoxicity (kg 1,4-DB eq), photochemical oxidation (kg C 2 H 4 eq), acidification (kg SO 2 eq), and eutrophication (kg PO 4 eq).

In order to verify the robustness of results obtained using the baseline CML-IA method, another life cycle impact assessment method, the ILCD 2011 midpoint, was used. The ILCD 2011 midpoint LCIA method, which proposes 16 midpoint impact categories, was developed by the European Commission (EC-JRC-IES 2011). After analyzing different impact assessment methods and from a first pre-selection of existing methods and criteria definition, the European Commission established a new list of recommended methods for each impact category [START_REF] Pré | PRé Consultants. SimaPro Database Manual -Methods Library[END_REF]. The impact categories of this method are climate change (kg CO 2 eq), ozone depletion (kg CFC-11 eq), human toxicity cancer and non-cancer effects (CTUh), particulate matter (kg PM 2.5 eq), ionizing radiation HH (kBq U235 eq), ionizing radiation E (CTUe), photochemical ozone formation (kg NMVOC eq), acidification (molc H + eq), terrestrial eutrophication (molc N eq), freshwater b Glass jacketed reactor used to condense the outgoing gas eutrophication (kg P eq), marine eutrophication (kg N eq), freshwater ecotoxicity (CTUe), land use (kg C deficit), water resource depletion (m 3 water eq), and mineral, fossil, and renewable resource depletion (kg SB eq).

3 Results and discussion

3.1 Environmental impact assessment using CML-IA baseline LCIA method

The life cycle assessment for 2 kg of composite is evaluated for both scenarios. Figure 3 shows the comparison between the scenario without recycling and with recycling, considering all life cycle phases, using the CML-IA baseline LCIA method.

The impact assessment shows that the scenario with recycling is less impactful on the environment in eight impact categories (Fig. 3). In fact, for the other three categories (depletion of abiotic resources, human toxicity, and marine ecotoxicity), the difference of impacts between the scenarios with and without recycling is not significant enough to conclude (less than 20%). In a LCA, the differences below 20% are not sufficient to conclude with certainty because it is always necessary to consider the uncertainties of the input data and impact assessment methods. However, overall, the scenario with recycling is less harmful to the environment, decreasing on average about 25% of impacts (Fig. 3). It reduces the inputs and outputs of virgin carbon fiber manufacturing process.

In order to explore the impact sources for each scenario, a series of analyses are performed on the manufacturing and recycling life cycle phases. Figure 4 shows that during the manufacture of the new composite, it is the production of carbon fibers that most contributes to all environmental impact categories, except to abiotic depletion. The impacts of carbon fiber manufacturing are primarily related to energy consumption, followed by the impacts of the raw materials (Fig. 4). The carbon fiber manufacturing takes place twice for the scenario without recycling, which can explain the higher impacts in 8 out of 11 categories (Fig. 3) compared to the scenario with recycling where carbon fiber manufacturing takes place just one time.

Considering now the scenario with recycling, as described previously, there is also the recycling phase (Fig. 1b), which includes the transport of the composite waste to the recycling site, the cutting of these composites, and the steam thermolysis process with the outgoing gas and oil produced during the treatment. As it is observed in Fig. 5, the cutting of composite and the steam thermolysis are the steps responsible for the majority of environmental impacts in all categories. These two elementary processes were then analyzed separately (Figs. 6 and7) to better understand the origin of these impacts.

According to Figs. 6 and 7, the impact assessment shows that the energy required to the recycle phase is a major source of potential impacts on the environment. However, this energy represents only 45% of that used in the manufacturing of virgin carbon fibers, as shown in Fig. 11 by an energy balance for electricity throughout the life cycle phases for both scenarios under study. It also observed in Figs. 6 and 7 that for all categories, water has no significant potential impacts compared with the nitrogen and energy used. In the steam thermolysis process, the outgoing gas, which is converted into CO 2 by combustion, causes little impacts to global warming, only about 10% of the total of kg CO 2 eq, as seen in Fig. 7.

However, the cutting machine and the steam thermolysis reactor are an important source of impacts, mainly for the and7). These impacts are due to the materials used in their construction (cooper, steel, aluminum, etc.). Copper and steel are the most impactful materials for the abiotic depletion, human toxicity, and eutrophication, whereas aluminum is the main responsible for the impacts in marine ecotoxicity. In fact, these impacts occur during the production of these materials.

On the other hand, all data collected in the inventory for the virgin carbon fibers and composites do not consider any materials for the construction of the machines used in their manufacturing process. Therefore, a new comparison between the scenarios with and without recycling was performed, as shown in Fig. 8. This time, the materials for the construction of the cutting machine and the steam thermolysis reactor are not considered. Subtracting the materials used for the construction of cutting machine and the steam thermolysis reactor (cooper, steel, aluminum), the environmental impacts of the recycling scenario decrease, mainly those related to human toxicity and marine ecotoxicity. Human toxicity category, for example, shows a significant reduction of 30%. The scenario with recycling is now less impactful to environment than the scenario without recycling, in 10 out of 11 categories (Fig. 8). It is also observed in Fig. 8 that the reduction of the impacts increases, on average, from 25 to 30% when the materials of construction are not taking into account in the LCA.

Although the impacts related to the abiotic depletion have decreased, and now for the scenario with recycling is lower than in that without recycling, they are still very close in both scenarios (Fig. 8). The difference is still not sufficient (less than 20%) to conclude for this impact category. In fact, looking at the stages of composite manufacturing, shown in

Environmental impact assessment using ILCD 2011 midpoint LCIA method

In order to verify the reliability of the impact assessment results with the CML-IA baseline LCIA method, the ILCD 2011 midpoint LCIA method was also used to make a comparison between these two methods. The impact assessment results with the ILCD 2011 midpoint method for the comparison between the scenario without and with recycling are shown in Figs. 9 and 10.

The ILCD 2011 midpoint LCIA method presents more impact categories than the CML-IA baseline. For example, human toxicity is divided into two subcategories (cancer effects and non-cancer effects) and eutrophication is divided into three subcategories (terrestrial, freshwater, and marine).

However, the results obtained with this method are equivalent and very close to those found with the CML-IA baseline LCIA method (see Figs. 3 and9). The results for some impact categories (climate change, ozone depletion, acidification, freshwater ecotoxicity, photochemical ozone formation) are similar with the two LCIA methods. The results with the ILCD 2011 midpoint LCIA method show that the scenario with recycling causes less environmental impacts than the scenario without recycling in 12 out of 16 impact categories (Fig. 9).

Regarding the other four categories, only for the human toxicity cancer effect category, the scenario without recycling has less impacts (Fig. 9); for the other three categories (human toxicity non-cancer effects, freshwater eutrophication, and mineral, fossil, and renewable resource depletion), the differences between the two scenarios are not significant enough to conclude (less than 20%), as shown in Fig. 9.

Nevertheless, similar to the precedent LCIA method, the ILCD 2011 midpoint shows that, overall, the scenario with recycling is less impactful to the environment, also decreasing on average about 25% of impacts (Figs. 3 and9).

Moreover, as previously demonstrated with the CML-IA baseline LCIA method, the materials used for the construction of the cutting machine and the steam thermolysis reactor, present in the scenario with recycling, are an important source of impacts, mainly for the categories human toxicity, marine ecotoxicity, eutrophication, and abiotic depletion. Thus, in a similar way as was done with the precedent LCIA method, if these materials are not considered in the study perimeter, the impact assessment with the ILCD 2011 midpoint method shows that the environmental impacts of the recycling scenario also decrease, mainly those related to human toxicity (cancer and non-cancer effects), freshwater eutrophication, and mineral, fossil, and renewable resource depletion (Fig. 10). Therefore, the scenario with recycling becomes less impactful to environment than the scenario without recycling, in all 16 categories (Fig. 10). The reduction of the impacts increases, on average, from 25 to 30% when the materials of construction are excluded (Figs. 9 and 10). This same increase of the reduction of impacts was also observed when the CML-IA baseline LCIA method was used (Figs. 3 and8).

The two LCIA methods used, CML-IA baseline and ILCD 2011 midpoint, lead to similar results even though these two LCIA methods have different factors. The application of these two different LCIA methods made possible to test the robustness of the results and to verify their reliability, validating the LCA study conducted.

Energy balance for electricity

In addition to the environmental impact assessment, an energy balance for electricity was conducted for both scenarios considering every stage of the life cycle (Fig. 11). In the manufacturing stage, the scenario with recycling consumes less energy because it avoids the production of new carbon fibers. However, the steam thermolysis process and the cutting of the composites require a new demand of electricity. Despite this additional demand, the scenario with recycling consumes globally less energy. Overall, the total energy consumption can be reduced by 25%. The scenario with recycling also produces heat by the combustion of gaseous effluents from the steam thermolysis process (0.76 kWh per kg of composite).

Conclusions

The LCA presented in this study enabled a comparison of the environmental impacts in the life cycle of carbon fiberreinforced plastic composite, considering two different scenarios: a scenario without recycling and another with recycling of carbon fibers by steam thermolysis.

The recycling of composite materials with recovery of carbon fibers brings evident advantages from an environmental viewpoint. The scenario without recycling generates between 25 and 30% more impact and requires about 25% more energy than that with recycling. The recovery of carbon fibers saves raw materials and energy consumption in their manufacturing process. In addition, the recycling reduces the impacts associated with the terrestrial and freshwater ecotoxicity, the fossil fuel depletion, as well as the contribution to global warming and ozone layer depletion.

However, the additional recycling phase causes nonnegligible environmental effects. On the one hand, this phase requires a certain amount of energy for cutting composites and steam thermolysis process. This energy is the main source of impacts compared to other process inputs, such as water and nitrogen. On the other hand, the materials used for the construction of the cutting machine and the steam thermolysis reactor cause significant impacts. Nonetheless, the potential impacts of the scenario with recycling by steam thermolysis are globally lower than those of the scenario without recycling, where the composites are sent to landfill and incineration.

The application of two different LCIA methods (CML-IA baseline and ILCD 2011 midpoint) allows the verification of the robustness and reliability of the LCIA results. The two LCIA methods lead to similar results, validating the LCA study conducted.

The majority of inventory data collected is from experimental tests in pilot scale and technical data provided by the industrial partners. However, some data should be used with caution, because they are based on assumptions that may vary. The cutting machine inputs and the transport stages considered have been estimated based in technical data and some hypothesis. In fact, the inaccuracies of these data come from the fact that the study is currently still at the pilot scale.

Despite these limitations, this life cycle assessment study allows the evaluation of potential environmental impacts of steam thermolysis recycling process, comparing it with a scenario where the composites are directly sent to final disposal, incineration, and landfill. The proposed approach can be used in further life cycle assessments on a larger and industrial scale, and furthermore to compare the steam thermolysis to other recycling processes, such as pyrolysis, solvolysis, and/or mechanical recycling.

Fig. 1

 1 Fig. 1 System boundaries. a Scenario without recycling. b Scenario with recycling

Fig. 2

 2 Fig. 2 ESEN images of virgin carbon fibers (left) and recovered carbon fibers by steam thermolysis (right)

  Photochemical oxidaƟonAcidificaƟon EutrophicaƟon

Fig. 3

 3 Fig. 3 Comparison between both scenarios (without and with recycling)-CML-IA baseline

  Photochemical oxidaƟonAcidificaƟon EutrophicaƟon

Fig. 4

 4 Fig.4Impacts associated with the composite manufacturing phase using virgin carbon fiber-CML-IA baseline

Fig. 6 Fig. 7

 67 Photochemical oxidaƟonAcidificaƟon EutrophicaƟon

  Photochemical oxidaƟonAcidificaƟon EutrophicaƟon

Fig. 8

 8 Fig. 8 Comparison between both scenarios without the materials of construction for the cutting machine and the steam thermolysis reactor-CML-IA baseline

Fig.

  Fig. Comparison between both scenarios (without and with recycling)-ILCD 2011 midpoint

Fig. 10

 10 Fig. 10 Comparison between both scenarios without the materials of construction for the cutting machine and the steam thermolysis reactor-ILCD 2011 midpoint

Fig. 11

 11 Fig. 11 Energy balance for electricity for both scenarios

Table 2

 2

	Inventory of cutting of composite waste	Cutting machine
		Inputs

Table 4

 4 Inventory of the non-

	condensable gas	Gas	Percent	Mass (kg)	Combustion reaction	CO 2 (kg)	(kJ/mol) ΔH	Energy (kWh)
		H 2	0.6	0.0019	H 2 + 1/2O 2 ➔ H 2 O	0	285.9	0.08
		CH 4	0.1	0.0002	CH 4 + 2O 2 ➔ CO 2 + 2H 2 O	0.0005	890.4	0.003
		CO	26.8	0.0894	CO + 1/2O 2 ➔ CO 2	0.1404	283.0	0.25
		CO 2	63.3	0.2107	-	0.2107	-	-
		C 2 H 4	2.4	0.0079	C 2 H 4 + 3O 2 ➔ 2CO 2 + 2H 2 O	0.0247	141 1. 0	0.1 1
		C 2 H 6	1.5	0.0049	C 2 H 6 + 7/2O 2 ➔ 2CO 2 + 3H 2 O	0.0143	1560.0	0.07
		C 3 H 6	5.4	0.0181	C 3 H 6 + 9/2O 2 ➔ 3CO 2 + 3H 2 O	0.0568	2058.0	0.25
		Total	100	0.333		0.4474		0.76

a Percentage by weight

Table 3

 3 Inventory of steam thermolysis process

	Steam thermolysis process
	Inputs	Mass (kg)
	Sized composites	1
	Nitrogen	1.4
	Tap water	1.6
	Stainless steel (95%) a	0.1267
	Aluminum (4%) a	0.0053
	Rock wool (1%) a	0.0013
	Glass b	0.0033
	Electricity in France	Energy (MJ)
	Energy consumed by the steam thermolysis process	54
	Outputs	Mass (kg)
	Recovered carbon fibers	0.55
	Total of gas (condensable and non-condensable)	0.45
	Condensable fraction (oil)	0.117
	Non-condensable fraction	0.333

a Estimated by the weight of the steam thermolysis reactor

Funding information

The authors of this paper would like to thank the French Agency for Environment and Energy Management (ADEME) and Alpha Recyclage Composites for their financial support.


Vincent Laperriere

Dominique Badariotti

Arnaud Banos

SENSITIVITY OF PLAGUE LOCAL EPIDEMICS TO THE POPULATION SIZE AND SPATIAL DISTRIBUTION Contribution of an individual based model, SIMPEST

Keywords: Epidemic model, Individual-based, Sensitivity analysis, Replacement number, Contact network

This document presents some simulation results obtained on an epidemic model, SIMPEST, designed to simulate the dynamics of local bubonic plague epidemics. The individual-based approach allows to consider discrete individuals, their spatial behaviour, and the contingency of interactions among them. This approach allows to perform investigations about how various factors, such as sociological or geographical ones, may influence the development of a local epidemic. We performed some sensitivity analysis on two initial conditions: population density and habitat distribution. The influence of these input variables on the epidemic dynamics is investigated using some key output variables. Our simulation results can then be compared with some well-established elements of the theory of epidemics, more specifically the existence of an epidemic threshold on the population size and the influence of the contact network structure on the epidemic force.

INTRODUCTION

In the study of infectious diseases, the investigation of the causal factors which command the deployment of an epidemic is a crucial step to forecast, control and anticipate the outbreak. With the development of mathematical modelling, the last century has witnessed the emergence of a real theory of epidemics [START_REF] Anderson | Infectious diseases of humans: dynamics and control[END_REF] which led to the development of so-called "compartmental models". The main contribution of classical compartmental models in this field was the definition of the threshold theorem, stating that the population which is susceptible to get infected must exceed a critical size for an epidemic to occur. However, classical compartmental models often ignore the geographical context of the disease transmission, assuming that susceptible and infected individuals are homogeneously mixed. An individual-based approach, which considers discrete individuals and the contingency of interactions among them, provides an adequate framework to design more realistic epidemiological models and to enlarge investigations about how various factors, such as sociological or geographical ones, may influence the development of an epidemic [START_REF] Bian | A conceptual framework for an individual-based spatially explicit epidemiological model[END_REF][START_REF] Dunham | An agent-based spatially explicit epidemiological model in MASON[END_REF].

MODELLING OBJECTIVES

In this paper, we present SIMPEST, a model developed to simulate plague epidemics at a local scale in the context of the rural malagasy bubonic plague. Our task is to integrate in the model the spatial behaviour of the agents -namely fleas and rats -which are implied in the epidemiological cycle. This may help us to investigate the global dynamics of the disease arising at a populational level, taking into account the contingency of the disease transmission that results from the contacts between fleas and rats at an individual level. We consider some key output variables like: [START_REF] Anderson | Infectious diseases of humans: dynamics and control[END_REF] The "global force of the infection", given by the total number of rats and fleas infection cases over the simulation.

[2] The "potential force of infection to human", as an indicator of the disease potential to generate human cases, given by the total number of free-living infectious fleas over the simulation and thus susceptible to fix on and bite a human.

[3] The "replacement number of the infection" R, traditionally considered in compartmental models, defined as the average number of secondary infections caused by a typical infectious individual during its entire period of infectiousness.

[4] Some key properties of the emerging contact network between rats, as the mean degree and the clustering coefficient. In this network, nodes represent rats and edges represent rats that have shared some common fleas during the simulation, hence having been indirectly in contact.

Our modelling objective, here, is to perform some sensitivity analysis and compare our results with some elements of the theory of epidemics [START_REF] Anderson | Infectious diseases of humans: dynamics and control[END_REF][START_REF] Keeling | The effect of local spatial structure on epidemiological invasions[END_REF], or even previous experiences of plague modelling, mainly based on a mathematical formalism [START_REF] Keeling | Bubonic plague: a metapopulation model of a zoonosis[END_REF]. This is a way to validate our model in a first step, and to gain knowledge about factors influencing the epidemic dynamics in a second one, especially those related to the geographical context.

MODEL STRUCTURE

SIMPEST is implemented on the Netlogo platform, that enables us to define a schematical environment representing a malagasy village and its surroundings. Rats and fleas evolve in this environment. Humans, to which the disease can propagate, have not been explicitly represented since they cannot transmit the disease and thus don't influence the disease dynamics that we investigate. Instead, we consider the variable "potential force of infection to human" (defined in [START_REF] Bian | A conceptual framework for an individual-based spatially explicit epidemiological model[END_REF], see below).

The individuals' behaviour is determined by three kinds of rules. 1) Some demographic rules are introduced: rats and fleas are characterized by a life expectancy and a reproductive rate. 2) Specific mobility rules are implemented: rats move by night, leaving their nest and looking for some food. Free fleas wait for a host to fix on and stay fixed until the host dies. 3) Transmission rules between fleas and rats are stochastic and the epidemiological cycle follows a SEIR scheme (Susceptible-Exposed-Infectious-Removed): one susceptible flea may get exposed by biting an infectious rat. After the latent period has expired, the flea gets infectious and thus may transmit the disease to another susceptible host. At the end of the infectious period, a rat might recover and become immunized, whereas a flea automatically dies.

SIMULATION RESULTS

To assess the influence of the local geographical context on a bubonic plague epidemic, we stayed in a theoretical frame and performed some sensitivity analysis on two initial conditions, susceptible to vary from a local area to another: population density and habitat distribution.

Sensitivity analysis to the population density

We first paid attention on the initial population size of fleas and rats. The main reason is that it is the most studied input variable in epidemiological modelling [START_REF] Keeling | Bubonic plague: a metapopulation model of a zoonosis[END_REF]. The threshold theorem state that an epidemic can develop only if the susceptible population size exceeds some critical value, for which the replacement number R is one, otherwise it dies out.

Thus, to verify if such an epidemic threshold exist in our individual-based model, we defined the replacement number R as the product between the replacement number from flea to rat (Rflea) and the replacement number from rat to flea (Rrat). R is reported at the end of the simulation so that it traduces the average replacement number over the simulation, as defined in [START_REF] Dunham | An agent-based spatially explicit epidemiological model in MASON[END_REF].

Varying the initial population size of both fleas has a positive and a more or less linear effect on the global force of the epidemic as defined in [START_REF] Anderson | Infectious diseases of humans: dynamics and control[END_REF]. Now, to go beyond this expected result, we can study the correlation between the global force of the infection and the mean replacement number.

Figure 1: OAT sensitivity analysis results to the initial flea index (1a) and to the rat initial population size (1b). For each simulation realized, we plotted the "mean replacement number of the infection R" [START_REF] Dunham | An agent-based spatially explicit epidemiological model in MASON[END_REF] against the "global force of the infection" [START_REF] Anderson | Infectious diseases of humans: dynamics and control[END_REF]. To take into account stochasticity, 20 simulations are run for each value of the tested parameter.

This way, we can compare our simulation results with the theoretical threshold of unity for a disease to develop. Figure 1 suggests that the threshold effect is more pronounced for the flea population size (Figure 1a) than for the rat one (Figure 1b). Our results show that the initial flea index must exceed a critical value (around 2) for the replacement number R to reach unity, and for an epidemic to develop. This is a slightly upper value than the empirically-observed threshold of one for the flea index [START_REF] Pollitzer | La peste[END_REF]. A same value for the replacement number corresponds to various sizes of the epidemic, especially when it is high. This is due to the contact structure that is different from a simulation to another, because of their stochasticity.

Sensitivity analysis to the rat habitat distribution and mobility

In a second series of simulations, we studied the effect of varying both the rat initial habitat distribution and mobility. We tested four theoretical scenarios, presented in figure 2. As output variables, we considered the mean replacement number R [START_REF] Dunham | An agent-based spatially explicit epidemiological model in MASON[END_REF] and an intermediary one which is the contact network between rats, resulting from a simulation, as defined in [START_REF] Keeling | The effect of local spatial structure on epidemiological invasions[END_REF].

Scenario A: Totally grouped, never moving Rats never move and stay fixed in one nest. This is close to the unrealistic assumption of the simplest compartmental model that the population is constantly mixed in an homogeneous way.

Scenario B: Totally gouped during night, randomly moving during day

Rats stay grouped in one nest during the night and move randomly during the day.

Scenario C: Multi-gouped during night, randomly moving during day

Rats are grouped in several dispersed nests during the night and move randomly during the day. This is the closest scenario to the reality, where the rat population is structured in family groups. Scenario D: Never grouped, always randomly moving Rats constantly move randomly. No distinction is done between night and day. Simulation results, presented below, show that the more grouped the population is, the highest the potential for the disease to develop is (Figure 3a). Hence, the social structure of the rat population, more or less distributed in spatially dispersed family groups, plays an important role in the epidemic development.

To better understand this result, we can study the effect of the different scenarios on the contact network structure traduced by two essential properties: the mean degree, that is the average number of neighbour nodes per node (Figure 3b) and the average clustering coefficient (Figure 3c), measuring the interconnectedness of the network. Defined for one node, it is the number of edges existing among the neighbourhood of this node, divided by the total number of possible nodes. When the dispersal of individuals increases, rats enter in contact (via sharing common fleas) with less other rats and thus the mean degree decreases. Moreover, spatial correlations between rats explain that the interconnectedness of the contact network increases. It means that there are more local connections and less long-range connections than in the totally grouped scenario, where individuals have the same probability to encounter everyone else. We verify Keeling's statements obtained on a network model [START_REF] Keeling | The effect of local spatial structure on epidemiological invasions[END_REF], that is to say: the potential of the disease to develop is reduced by having few neighbours (the mean degree is small) or a highly interconnected network structure (the clustering coefficient is large). These results show that besides the total population size of both fleas and rats, the rat social structure and mobility are factors of huge importance when understanding conditions for plague epidemics to develop. Such investigations on the population composition and spatial distribution are difficult to be led with traditional mathematical models and the individual based approach may be the most appropriate one.

Figure 2 :

 2 Figure 2: Scenarios tested for the sensitivity analysis to the rat habitat distribution and mobility.

Figure 3 :

 3 Figure3: Sensitivity analysis to four scenarios of rat habitat distribution and mobility for three output variables: the mean replacement number of the infection R (3a), the mean degree (3b) and the clustering coefficient (3c) of the rat contact network. Results are averaged over 20 simulations.

AUTHORS INFORMATION