C Vergne
email: c.vergne@akers.be

Christine Boher
email: boher@enstimac.fr

R Gras

Christophe Levaillant

Influence of oxides on friction in hot rolling: Experimental investigations and tribological modelling

Keywords: Wear, Friction, Hot rolling, Oxidation, Iron oxide

In a hot strip mill, the contact established between the hot strip and the work rolls in the first times of running has to be oxide on oxide to allow the strip to be pulled in the roll bite. The oxide scale formed on the roll is submitted to thermo-mechanical stresses and grows up. From a critical thickness, the scale spalls and causes some superficial damage to the rolls and to the strip.

For the roll manufacturers as well as for the steel makers, it is essential to understand the influence of the creation and the growth of such a scale on friction in order to control the antagonist superficial damage and consequently to reduce the running cost of the mill.

The present work aims to study the interaction between the oxides formed on a work roll grade and the coefficient of friction established with a strip steel usually rolled by this roll grade. A high temperature tribometer was set up in a pin-on-disc configuration. A previous part of study showed that friction was dependent on the nature of antagonist materials and the thermal transfer. We observed the establishment of a running-in period in the case of a metal-on-oxide initial contact between the pin and the disc which corresponds to the creation of an oxide layer on the pin.

The mechanisms that allowed the formation of this scale were determined. SEM observations in conjunction with EDS analysis, both inside and outside the contact area on both antagonists, led to the development of a phenomenological model explaining the creation and the movement of oxide debris in the contact.

Introduction

The study of the wear behaviour of oxide layers has found a renewed interest with the need to understand their contribution to the damage observed in the hot metal forming processes.

Hot rolling process

In hot rolling, friction is considered as the "driving force" of the process: "without friction no rolling" [1]. The appearance of friction depends mainly on the creation of a sufficient oxide layer at the work roll surface in order to prevent all metal-metal contact or metal-oxide contact between the strip and the work rolls. On the one hand, when a metal-metal contact is established, the strip cannot be pulled between the work rolls owing to slipping. On the other hand, when a metalon-oxide contact is established, friction increases strongly leading to sticking phenomena.

Actually the formation of an oxide layer on the work roll surfaces allows the metal sheet to be driven between the work rolls because of the decrease in the shear forces [START_REF] Adams | 40th MWSP Conference Proceedings[END_REF]. In the process, the work rolls are alternately heated by contact with the hot strip and cooled drastically outside the contact by a water spray. In this way, the work rolls are subjected to thermal and mechanical stresses which favour the increase of the oxide thickness on the rolls. Above a critical thickness, the upper layer of the oxide scale breaks by thermal and mechanical fatigue and spalls under the shearing. The repetition of this damage requires the machining of the roll barrel after a certain running in the mill and contributes to the reduction of the roll lifetime. Moreover, the roll spalling produces the adhesion of oxide debris on the strip surface that leads to the marking of the metal sheet and makes it unusable.

Besides, the coefficient of friction generated between the work rolls and the strip usually tends to decrease with the increase in thickness of the oxide scale on the rolls. This decrease in friction results in a reduction in the rolling force and therefore the torque applied to the rolls, which, in turn, saves energy.

In this way, the creation of an oxide scale on the roll barrel has a direct impact on the operating cost of a hot mill by reducing the damage both on the rolls and on the rolled sheet at the same time as the energy consumption.

Nevertheless the continuous decrease in friction versus the increase in thickness of oxide scale on the work rolls finally may lead to skidding of the strip between the rolls.

Tribological behaviour of oxides

More generally the tribological behaviour of oxides is ambiguous, being able to be both abrasive and therefore detrimental or to be lubricant and consequently protective against wear [START_REF] Hong | Proceeding of the 16th Leeds-Lyon Symposium Tribology[END_REF][START_REF] Stott | [END_REF][START_REF] Stott | Proc. R. Soc. Lond. A[END_REF][START_REF] Jiang | [END_REF][7]. Their ability to be lubricant or abrasive is dependent on the fact that the oxides enter into the contact either as free particles or as compacted particles [START_REF] Hong | Proceeding of the 16th Leeds-Lyon Symposium Tribology[END_REF]. And the aptitude of the oxides to be either free or compacted into the contact is itself usually correlated on the one hand to the microstructural and mechanical properties of the oxides and on the other hand to the friction conditions -more particularly to the sliding speed. In general, the coefficient of friction generated between two oxidised surfaces is considered dependent on the nature, the thickness, the adherence to their substrate and the hardness of the antagonist oxide scales. If the oxide particles are free in the contact and hard, then the predominant mechanism of wear is abrasion and the coefficient of friction is high. If the oxide particles are compacted into the contact until the formation of glazed surfaces, then the predominant mechanism of wear becomes adhesion and the coefficient of friction is low. The sliding speed has a strong influence on the wear mechanisms [START_REF] Stott | New Directions in Tribology[END_REF][START_REF] Stott | [END_REF]. At high speed, the oxides may reach their melting point and favour an adhesive wear. Low sliding speeds make easy the formation of thicker and wear resistant scales. The tribological behaviour of the iron oxides usually formed on the strip surface were more particularly empha-sized [10][11][12]. The rhomboedral hematite ␣-Fe 2 O 3 , which presents a high hardness at room temperature is known to exhibit an abrasive behaviour and to tend to increase friction and wear. On the contrary, the cubic oxides, the magnetite Fe 3 O 4 and the wüstite FeO, are more ductile and resist wear better.

Tribological behaviour of oxides in hot rolling process

At the industrial level, the wear resistance of work rolls is usually estimated from the amount of hot steel rolled per millimetre of machined roll diameter (t mm -1 ) [13,[START_REF] Windhager | MWSP Conference Proceedings[END_REF]. This criterion is too restrictive and does not reveal if the machining of the rolls is decided due to a usual wear or to a rolling incident.

The tribological behaviour of the work rolls can be evaluated from the evolution of the rolling load in relation to the mill stand [START_REF] Thonus | MWSP Conference Proceedings ISS[END_REF]. This criterion allows one to define the evolution of friction in the contact. If the rolling load increases, that means friction between the work rolls and the strip increases and vice versa.

The wear mechanisms start to be well known in hot rolling. Whatever the stand in the mill, the predominant wear phenomena of the work rolls remain thermal fatigue, abrasion, adhesion and oxidation [13,[START_REF] Boccalini | Proceeedings of the 6th International Tooling Conference[END_REF][START_REF] Molinari | Proceedings of the 6th International Tooling Conference[END_REF]. The wear mechanisms in the finishing stands were more particularly emphasised. Thermal fatigue is the result of a mixed effect of the cyclic contact of the roll with the hot strip and the drastic cooling of the roll surface by water spray at the contact exit. This solicitation repeated at the frequency of the roll rotation induces compressive and tensile stresses in the subsurface of the roll and favours crack nucleation when theses stresses exceed the yield stress. The firecrack pattern may be extended by the oxidation of the roll surface which favours the propagation of cracks in the bulk. In the presence of a carbide network in the roll matrix, the cracks follow the matrix-carbide interface. Under shearing, the propagation of the cracks in the bulk may cause the loss and the transfer of roll surface material towards the strip surface [13,[START_REF] Colas | [END_REF].

As for abrasion, this damage is the result of the cutting effect of the superficial asperities during the relative motion of the antagonist surfaces. Temperature affects wear due to its influence on the development of both the nature and the properties of the contact surfaces [19][START_REF] Blazevic | 37th MWSP Conference Proceedings, ISS-AIME[END_REF][START_REF] Fukagawa | [END_REF]. This wear mechanism appears as soon as the wear debris present a high hardness and a low ductility even at high temperature and a sharp shape. Some damage like micro-cutting, grooves or plastic deformation may occur.

Adhesion usually corresponds to a transfer of the rolled strip (oxide debris) to the roll surface, which contributes to increase the roughness of the rolls and leads to an increase in friction [13].

At last, oxidation is a frequent phenomenon on the roll surface. The formation of oxide scale on the roll is known to exhibit a good friction behaviour. Nevertheless, above a "critical" thickness, the scale becomes detrimental for the lifetime of the roll and favours some damage like banding on the sheet.

Aim of the study

However, the interaction of the oxide scale formed on the roll surface with friction and wear is not yet well understood. More generally, the tribological behaviour of the oxides can be analysed through the behaviour of the third body. The third body is usually constituted of oxide debris issued from either the strip or the work rolls and it can be considered as a parameter influencing the development of the friction coefficient.

The formation and the behaviour of the third body remain dependent on the nature, the physical properties and the adherence to the substrate of the oxides. Oxides which are not very adherent to the strip or the rolls could be beneficial against friction [13] as long as they are soft. They enter into the contact area more quickly and therefore contribute to the reduction of the friction coefficient by forming a third body able to accommodate the shear. Other oxides, which adhere strongly to their substrate, irrespective of whether they are soft or hard, contribute to increase shear stresses and friction. In this situation, wear occurs either by abrasion or by oxide spalling.

De facto the tribological behaviour of the oxides is very complex in the hot rolling process because it is influenced by the nature and the physical properties of the oxide scales into the contact. In consequence, the microstructure of the work roll grade and more particularly the carbide content of the matrix are very important [START_REF] Adams | 40th MWSP Conference Proceedings[END_REF]13,[START_REF] Boccalini | Proceeedings of the 6th International Tooling Conference[END_REF][START_REF] Molinari | Proceedings of the 6th International Tooling Conference[END_REF][START_REF] Colas | [END_REF]. These carbides reinforce the mechanical resistance and the wear resistance of the roll matrix. Nevertheless, they can contribute also to the damage of the work rolls according to two mechanisms:

• on the one hand, they oxidise differently from the matrix and the formed oxides may have a different influence on friction and wear than the rest of the matrix; • on the other hand, under thermo-mechanical stresses, superficial cracks may occur on the roll and follow the network of primary carbides. In this way, they create some diffusion paths and facilitate internal oxidation of the roll matrix. As mentioned previously, some loops of internal oxidation appear and propagate until they finally emerge at the roll surface. In this way, they contribute to produce cohesive wear debris through shearing and they are the cause of significant damage at the roll surface.

For the roll manufacturers as well as for the steel manufacturers, it is important to understand the contribution the roll grade makes to the damage occurring in the hot rolling process and to determine the interaction between the development of friction and the oxides taking into account the nature of oxides present in the roll bite. The aim of this study is not to simulate the hot rolling process but to reproduce a part of the contact mechanics established between a grade of hot working roll and a hot strip material used in the finishing stands in the first steps of the process. The mechanical contact of a typical rolling bite is decomposed: only the sliding part of the motion is considered, the rolling part of the motion being neglected. The nature of the sliding antagonist surfaces is a thick oxide layer formed on a strip material at a temperature close to the rolling temperature in the finishing stands and a work roll material presenting only a thin oxide layer as a natural passivization product formed at room temperature. The oxide scale considered on the disc is much thicker than the descaled surface of the strip at its entry in the first finishing stands.

Actually the operating conditions of friction tests are rather different from the industrial rolling conditions. Nevertheless, the tribological configuration of contact -a sliding motion at a high temperature close to the rolling temperature with an initial hertzian pressure close to the contact pressure in a rolling bite -allows to display the impact of the chemical composition of the work roll grade on friction and wear mechanisms.

Through the tribological tests, this work aims to follow the development of the coefficient of friction along with the creation and the growth of the oxide scale on the roll grade with the increase in temperature of the pin by thermal conduction and radiation by contact with the warm disc. The correlation between wear damage and thermal fatigue damage has not been investigated for instance. Only the influence of oxides and the contribution of alloying elements in the roll matrix on the development of friction are emphasized.

A pin-on-disc tribometer has been developed for high temperature use and two kinds of friction tests have been carried out in order to display the influence of the creation of an oxide scale on the pin on the friction evolution. Some interrupted tests have been performed to understand the interaction of the oxides with the running-in period that the friction evolution exhibited. After each tribological test, the SEM observations made on both the pin and disc wear tracks have led to a modelling of the evolution of friction coefficient according to the evolution of the oxide debris in the contact.

Materials and experimental conditions

The materials

As part of this study, a tribometer was set up at high temperature. In a pin-on-disc configuration, the pin consists of a roll material and the disc consists of a strip steel usually rolled with the roll grade. The chemical composition of used materials is given in Table 1.

The pin

The grade of the pin -a work roll material -is a cast iron strongly alloyed with carbide formers, more particularly MC carbide formers like Nb and V. The microstucture made of tempered martensite and cementite presents an initial hardness of 63 HRC (or 772 HV) and a roughness Ra of 0.24 ± 0.04 m. This grade is an indefinite chill which has been used for 50 years, always currently used in the last stands of mill. The improvement of the new grades is the hardening of the matrix due to an increase of MC carbides content, more particularly through the Nb and V contents [START_REF] Windhager | MWSP Conference Proceedings[END_REF][START_REF] Molinari | Proceedings of the 6th International Tooling Conference[END_REF][START_REF] Adams | 40th MWSP Conference Proceedings[END_REF][START_REF] Matsubara | MWSP Conference Proceedings[END_REF][START_REF] Biggi | 40th MWSP Conference Proceedings[END_REF][START_REF]Patent application[END_REF]. The addition of niobium and vanadium in substitution of chromium is known to improve the hardness of the matrix and the eutectic carbide and to reduce the fraction and the size of the eutectic carbides [START_REF] Wilmes | Proceedings of the 6th International Tooling Conference[END_REF].

Niobium as well as vanadium precipitate at high temperature in the molten alloy before the solidification [START_REF] Kheirandish | [END_REF]. Actually, niobium and vanadium carbides are present as a eutectic phase. Niobium unlike vanadium presents a low power of solubility at austenitizing temperature and does not participate in the secondary hardening during tempering. The content and the shape of Nb-carbides is directly linked to the carbon content and the Nb-content.

The Nb-carbide may exhibit a cubic or octaedric shape for a high content and only an eutectic shape for a low content. Vanadium may contribute to the hardening of the matrix either by a solid solution hardening in eutectic carbides for low contents or by direct precipitation of MC carbides above.

The addition of niobium and vanadium to the high alloy steels is known to reinforce wear resistance, firecrack resistance and hardening at room temperature. But vanadium unlike niobium is known to favour a catastrophic oxidation of alloys.

That's why more and more tool steels for cold working tools as well as for hot working tools present some contents in MC carbide formers like Nb or V even if their thermo-mechanical behaviour is not well known at higher temperature. More particularly, the influence of vanadium and niobium on the tribological behaviour of this kind of steels at high temperature is unknown.

The disc

The grade of the disc -a strip material -is a low carbon steel (AISI 1018 steel), a steel usually rolled by the studied grade of work roll. The microstructure is ferritic-pearlitic with an initial hardness of 168 Hv and a roughness Ra of 0.04 ± 0.02 m. The oxidation of this steel at high temperature is parabolic and contributes to form a thick scale (around 200 m after 1 h and 350 m after 2 h at 950 • C) on the disc surface.

The tribometer

The principle of the pin-on-disc tribometer is presented on the Fig. 1.

The disc is heated by high frequency induction up to a maximum temperature of 1200 • C. Its superficial temperature is checked either by a K-type thermocouple welded on the surface or by an infra-red pyrometer.

The pin is instrumented with two K-type thermocouples located radially at a depth of 3 mm and respectively at 1.1 mm and 3.4 mm from the contact surface of the pin. The pin temperature increases by thermal conduction, radiation, convection and friction. Afterwards the recorded temperatures of the pin are treated by an inverse method [27] to determine the average temperature at the pin surface during the friction tests. The results of this work as a whole will be the purpose of a next paper [27].

During each friction test, a Coulomb-type coefficient of friction is recorded from a strain gauge sensor. This coefficient corresponds to the ratio of macroscopic forces which are the resistant force to the motion and the normal force applied on the pin.

In order to obtain a sufficient pressure of contact with a low normal load, the pin shape presents an hemispherical surface of contact. In this way, for a load ranging from 2.5 to 20 N, the hertzian pressures vary from 130 to 280 MPa at the start of the friction test.

The tribological tests

The tribological test has been carried out in two steps:

• The first one corresponds to the static pre-heating of the disc -up to 950 • C by a high frequency induction -while the pin is maintained at room temperature outside the contact. When the temperature is reached, the disc is held at high temperature for 1 h. During all the pre-oxidation time, a K-type thermocouple welded outside the wear track records the superficial temperature of the disc. This temperature is controlled also by an infra-red pyrometer. • In the second step, after 1 h of disc pre-oxidation, the pin is brought into contact with the disc, the thermocouple welded at the disc surface is cut and the rotating motion of the disc is immediately started. The heating of the disc is not interrupted between the end of the disc pre-oxidation and the start of sliding.

The operating conditions applied for each kind of test are:

• a normal load of 2.5, 10 and 20 N,

• a linear sliding speed of 0.04, 0.1 and 0.3 m s -1 .

The test conditions were chosen very soft in order to be able to observe the behaviour of the antagonist oxide scales in the contact zone without destroying them too fast.

For each test condition, three tests have been carried out in order to verify the reproducibility of the results. Only the results with a normal force of 10 N and a linear sliding speed of 0.04 m s -1 are emphasized in the present paper. Nevertheless, the phenomena observed in the present case remain valid for the other test conditions.

Tribological results and SEM observations

A running-in period

In a previous paper [28], the influence of the creation of an oxide scale on the pin surface on the evolution of the coefficient of friction was displayed.

Two kinds of contact were tested. On the one hand, the pin was brought into contact with the pre-oxidised disc and the sliding was started immediately. In this case, the initial contact was considered as a metallic pin on an oxidised disc. On the other hand, the pin was put on the pre-oxidised disc and the stabilization of the temperature in the pin -established essentially by thermal conduction and radiation from the warm disc -was waited for before starting the sliding. In this case, the initial contact was considered as an oxidised pin on an oxidised disc.

In the first kind of tests -a metal-on-oxide contact -a running-in period was observed in the first 15 min of sliding before the stabilization of the friction coefficient. In the second case -an oxide-on-oxide contact -the coefficient of friction reached a stabilized value very quickly and the transitory period was considered as insignificant. For both kinds of test, the average value of the friction coefficient, the average value of the temperatures in the pin (Fig. 2) and the superficial features of damage on the antagonist surfaces were found identical in the stabilized period of the coefficient of friction. The running-in period was attributed to the formation of an oxide scale on the pin surface. So the evolution of friction coefficient was estimated dependent on the nature and the thermal transfer initially established between the antagonist surfaces (Fig. 3).

In the present study, we focussed on the tribological tests where the initial contact was a metallic pin on a pre-oxidised disc.

In order to understand the influence of the pin microstructure and more particularly the contribution of its MC carbides (NbC or spinels (Nb, V)C) on the evolution of the coefficient of friction in relation to their nature and their location in the contact zone, some tribological tests were interrupted at different intervals during the running-in period and beyond.

A typical tribological test has been subdivided into four steps (Fig. 3):

• the first one, noted Stage 1, corresponds to the start of the friction curve when the coefficient of friction increases; • the second one, noted Stage 2, is the following part of the curve when the coefficient of friction decreases; • the third one, noted Stage 3, corresponds to the re-increase in the coefficient of friction after the minimum value; • and the last one, noted Stage 4, the stabilization step of friction.

The stages from 1 to 3 constitute the running-in period of the friction curve. The interruption of the friction tests were carried out in three steps:

• the first one at the minimum value of the coefficient of friction at the end of the stage 2, • the second one when the coefficient of friction increases again during the stage 3, • the last one after 1 h of friction in the stage 4.

For a better understanding of the tribological phenomena, the average values of the superficial temperature of the pin determined by inverse method were reported in the Table 2 according to the different interruption time. The thermal model integrates the Beck's resolution method which compares the calculated temperatures and the experimental values in order to determine the density of thermal flux at the pin contact surface [29].

The times given for each interrupted point of friction tests are representative only in the specific conditions of 10 N and 0.04 m s -1 . The length of the running-in period on the friction curves is not constant versus the test conditions. The stabilisation length of friction is observed as being an exponential function of the mechanical power. This stabilisation length increases significantly with the sliding speed and decreases more noticeably with the normal load (Fig. 4).

SEM observations

The antagonist surfaces -the pin and disc surfaces -were observed by SEM in conjunction with EDS analysis after each friction test. The aim of these observations is to estimate the contribution of the oxide scales to the evolution of the Coulomb coefficient in relation with their nature and their location into the contact.

Observations outside the wear track

In order to identify correctly the wear mechanisms, it is advisable to study the surface morphologies of the pin and the disc away from the wear tracks before examining the wear features.

The tribo-elements involved into the contact zone and thus in the development of friction are observed outside the wear track but very close. The oxidation of the pin surface up to 640 • C for 4 min leads to the following oxide morphologies (Fig. 5).

The oxide scale formed on the pin is complex owing to the composition and the microstructure of the white cast iron. A dark scale reveals crimps, which seem to follow partly the machining ridges or to develop perpendicularly to these ones (Fig. 5(1)). The background oxide scale as a whole is essentially made up of iron oxide with some traces of Cr, V and Mn. At the pin's edge far from the wear track, iron oxide needles are observed. According to the literature [START_REF] Benard | L'oxydation des métaux, tome I: Processus fondamentaux[END_REF], they could be made of a kind of rhomboedral hematite (␣-Fe 2 O 3 ), which appears below 400 • C.

Other forms of oxides are observed:

• large excrescences of Fe-Nb oxide (Fig. 5(1) and ( 2)),

• small excrescences of Fe-Nb-V oxide.

These oxides are formed by the oxidation of the MC carbides -NbC and spinels (Nb,V)C) -present in the pin matrix. For example, the large excrescences rich in Fe-Nb present a On the disc, the oxide scale is simpler (Fig. 6). This scale corresponds to an oxidation period of more than 1 h at 950 • C. It reveals a pitted structure (Fig. 6(1)). At higher magnification, these pits appear as craters whose width can reach several hundreds of micrometers. The disc surface, made up of plateau and craters, displays a microstructure of columnar cells of iron oxide (Fig. 6(2)).

For the other stages of the friction tests, the morphologies identified above remain unchanged for both pin and disc. They can however be magnified by increasing the pin temperature or the holding time in contact. Essentially an increase in oxide thickness is observed.

Observations in the wear track

After each interrupted test, the features of both contact surfaces were investigated.

At the maximum value of the coefficient of frictionend of stage 1. This is the only part of the friction-time curve

where no interrupted test has been performed. The physical state of the tribological contact at the end of the stage 1 was extrapolated. At the beginning of the test, the initial contact between the pin and the disc is considered as metal on oxide at high temperature around 950 • C. Before being brought into contact with the disc, the pin presents superficially a natural passivization scale formed at room temperature whose the thickness is so thin that the pin surface is considered as metallic due the predominant mechanical influence of the bulk material.

When the pin is put on the disc, the surface of the disc creeps under loading and the contact surface of the pin becomes circular. When the motion of the disc is started, the contact surface assumes a quite elliptic shape due to a difference of stresses between the entry and the exit side of the contact and the edges of the contact zone. This elliptic shape of the pin wear track is more marked for the low test conditions and tends to become circular and more compact with the friction time increasing (Fig. 7).

The first increase observed on the friction-time curve corresponds to the increase in the shearing force necessary to break the micro-junctions established at the interface of contact between the metallic asperities of the pin and the oxidised asperities of the disc.

At the minimum value of coefficient of friction -end of stage 2.

During the entire sliding period, the disc is continuously heated by induction at 950 • C. The temperature of the pin rises continuously by thermal conduction, radiation, convection and friction until around 684 • C at the maximum value of friction. The free surface of the pin has oxidised continuously, more particularly the MC-carbides like Nb-carbides and (Nb,V)-carbides which start to oxidise at 430 • C.

These oxidised carbides form some excrescences distributed on all the pin surface in particular close to the contact zone. With sliding, the initial hertzian area increases and the excrescences of oxidised carbides rich in Nb come gradually into the contact. Composed of little grains, the excrescences are subjected to an attrition phenomenon which tends to decrease shear and also friction.

At the minimum of the coefficient of friction (end of stage 2), some little grains of Nb-oxide and some white trails rich in Nb-oxide are observed in the wear track of the pin (Fig. 8).

On the antagonist surface of the disc, some grains of Nb-oxides are observed as agglomerated at the top of the columnar cells of Fe-oxide (Fig. 9).

This assumption is confirmed by the EDS analysis (Fig. 9) and the observation of some excrescences of oxidised Nb- carbide partially abraded at the edge of the pin wear track (Fig. 10).

Besides, the average length of white trails observed on the pin wear track corresponds to the average distance between the columnar cells of Fe-oxide observed on the disc surface.

The roughness of the oxidised disc surface due to the columnar cells of Fe-oxides causes a cutting of the excrescences of oxidised Nb-carbides or (Nb, V)-carbides present at the pin surface. In this way, the white grains constituting the excrescences are transferred from the pin surface to the disc surface.

New increase in coefficient of friction -during stage 3.

The wear track on the pin becomes gradually more circular and more compact. The contact area presents always some white trails but to a lesser extent. These tracks are always rich in Nb while the remaining part of the wear track is made up of iron oxide with some traces of Cr, V and Ni (Fig. 11(1)). At high magnification, the pin wear track shows some damage resulting from surface fatigue: cracks and scaling arising from adhesion (Fig. 11(2)). In these damaged zones, apart from iron oxide, traces of Nb, V and Si are found.

The break of the sheared oxide scale occurs at the metal-oxide interface in the Si-oxide scale. All the mechanical phenomena observed on the pin are responsible for the increased friction.

The contact surface of the disc still reveals the craters formed during its pre-oxidation phase. These craters, made of columnar cells of iron oxide, form some anchorage points for the wear debris generated in the contact. These anchorage zones extend as the friction increases.

The layer of oxide debris seems to be more compact and thicker.

The composition of the agglomerated debris (Fig. 12) is iron oxide in association with traces of Nb, V and Si. The scaling of the pin wear track and the attrition of the scaled chips feed the debris layer.

After 1 h of friction -end of stage 4.

After 1 h of sliding, the coefficient of friction is completely stabilised and the wear mechanisms do not change a lot and do not produce more debris inside the contact area. The pin wear track once more tends to become more and more circular and seems to be very compact.

At high magnification (Fig. 13), some crack-like damages are observed in the contact area, which result from the shear stresses in the upper oxide layer. The opening of these defects shows that the thickness of the surface affected by friction is rather thin. Inside the cracks, we find again the morphology of the oxide formed on the pin outside the wear track. The chemical composition of the wear track is only iron oxide with no further traces of Nb, V or Si.

Therefore, at the end of test, when the coefficient of friction is stabilised, only iron oxide is involved in the contact interface.

The wear track on the disc is wide after 1 h of sliding. After the separation of the mating tribological system components and during cooling, two phenomena are apparent: • some large cracks formed at the centre of the wear track due to the thermal stresses during the cooling of the sample; • some small cells observed in the wear track always located at the extreme surface of the columnar cells of iron oxide. These cells correspond to a new or a re-oxidation of the elements constituting the wear track (Fig. 14).

These observations reveal the stress level of the sheared oxide layer on the disc and its behaviour, comparable with that of a ceramics.

Wear model

Outside the wear track, the pin constituted by the indefinite chill presents a quite complex oxidised surface with a background made of iron oxide. Excrescences rich in Nb and Nb-V ensuing from the oxidation of the MC carbides are distributed at the pin surface near the wear track border.

Other morphologies are observed like iron oxide needles supposed to be hematite on the edge of the hemispherical surface of the pin, farther from the pin tip and where the surface temperature is lower. All these structures of oxides emerging from the pin surface constitute preferential sites of contact with the oxidised disc surface.

On the oxidised disc in AISI 1018 steel, the morphology of the oxide is simpler. The superficial oxide scale is only made of iron-oxide with small craters distributed at the surface. Its basic structure is constituted of columnar cells of iron oxide.

The microscopic study of wear features after tribological tests showed the evolution of a part of these morphologies under friction.

A scenario was elaborated which explains the influence of these oxide morphologies on the evolution of friction coefficient.

Figs. 15 and 16 present the modelling of each stage of friction evolution.

Fig. 15 presents the morphology oxide scales formed on the antagonist surfaces after 1 h of disc pre-oxidation and some minutes of contact of the pin with the warm disc. On the pin, two morphologies are observed. On the one hand, a thin and adherent iron oxide scale probably composed by magnetite with a very thin hematite scale as upper layer cover continuously the pin surface. On the other hand, excrescences rich in Nb-oxide and issued from oxidation of matrix carbides (NbC or (Nb, V)C carbides) emerge dispersed everywhere on the pin surface. On the disc, four scales are noted. As outer scale, a thin hematite scale identified as ␣-Fe 2 O 3 rhomboedral hematite formed at high temperature (above 400 • C) is observed. As underlayer, a porous magnetite scale is found with a lot of porosities considered as the result of oxygen diffusion paths and the growth stresses of oxide scales. The inner scale and the thickest one is the wiistite scale in which some aggregates of magnetite formed during cooling of the tribo-system are observable. At the metal-oxide interface, a thin oxide scale rich in silicon is exhibited with a big fracture. The appearance of this fracture has two origins: on the one hand, the stresses generated during cooling of the sample, on the other hand, the presence of Si-oxide which presents a low melting point limiting the adherence of the scale on the disc surface.

For the modelling, only the two first outer iron oxide scales formed on the disc are taken into account while all the oxide scale formed on the pin is considered.

When the pin is put on the disc at 950 • C, its temperature increases very quickly owing to the important radiation from the disc surface and the thermal conduction by contact. In a few minutes, the pin surface temperature exceeds 500 • C, a temperature from which some carbides start to oxidise. In this way, the cementite oxidises from 458 • C and the MC carbides type of NbC and VC, respectively, at 430 and 492 • C. These last one are at the origin of the formation of excrescences on the pin surface around the wear track border.

The excrescences are constituted by agglomerated small grains of oxide with a cauliflower-type macrostructure. Prominent at the pin surface close to the wear track (Fig. 15), these oxidised structures come preferentially into contact with the disc.

Under the action of the applied normal load and the shear, these excrescences are compressed and cut off (Fig. 15).

Formed by agglomerated small grains, the Nb-oxide excrescences are sheared and move in the contact in form of free small grains by attrition. In this way, they contribute to the third body formation.

They are found again in the disc craters which constitute of preferential sites of anchorage in form of agglomerated grains and on the pin, after shearing and rolling, in form of white trails.

The remaining part of wear track is made of iron oxide, abraded and plastically deformed. This phenomenon results from the shearing and loading of the background iron oxide scale formed on the pin as well as on the disc.

It is the first phenomenon of transfer from the pin to the disc which is responsible of the minimum value of friction coefficient (stage 2). The friction attenuation can be explained by a decrease of the tangential force due to attrition and rolling of the Nb-oxide grains in the contact.

These small grains seems in fact to roll in the contact until they anchor at the surface asperities of the disc, and more particularly in the craters observed on Fig. 6(1) and ( 2).

The Nb-oxide grains issued form the oxidation of MC carbides are located in the disc craters and they are going to become preferential sites of contact with the oxidised disc surface.

The iron oxide scale at the pin surface goes on growing during friction and comes in contact with the Nb-oxide grains agglomerated in the disc craters. These grains initiate a new transfer of iron oxide from the pin to the disc.

The tribological contact between the pin and the disc becomes step-by-step iron oxide on iron oxide. The friction Fig. 15. Modelling of the contact between the pin and the disc at the end of the stage 1 from SEM observations. generated between both oxidised surfaces causes a strong interaction of these surfaces and their plastic deformation.

The shearing stresses are so high that phenomena of mechanical fatigue and delamination of the oxide scale appear at the pin contact surface.

The sheared oxide scale of the pin is so thin that its scaling appears at the metal-oxide interface in the Si-oxide scale.

This observation explains the Si traces found at the extreme surface of the pin.

These wear mechanisms clarify the increase of the coefficient of friction (stage 3).

During sliding, the iron oxide scale of the disc grows continuously due to high temperature being maintained. The thickness of iron oxide is so high than the Nb-oxide grains transferred to the disc surface are trapped in the iron oxide scale.

Henceforth, the two contact surfaces of pin and disc are sheared in their superficial iron oxide scale. Then it becomes very difficult to determine the source of iron oxide observed in the wear tracks.

Both contact surfaces of pin and disc become more compact than in the running-in period and are plastically deformed. Furthermore, the compactness of the sheared iron oxide scale on the pin surface constitutes of a barrier to the oxygen diffusion towards the metal-oxide interface and slows down the oxidation of inner MC carbides.

Only the delaminated zones at the pin surface could allow these carbides to come at the surface and to be oxidised once again.

In this stabilised friction regime (stage 4), the temperature recorded by thermocouples in the pin seems to be stabilised. The tribo-system achieved a thermo-mechanical equilibrium where the wear mechanisms have no more notable influence on the friction coefficient evolution.

These assumptions are confirmed by the SEM observations in the cross sections of both pin and disc (Figs. 17 and18). The micrographs present the surface of the pin and the surface of the disc on both sides of the wear track limit. In the pin wear track, a thin layer of compacted oxidised debris is observed while in the disc wear track, the consumption of the superficial iron oxide scale identified as hematite is exhibited.

Discussion

SEM observations and EDS analysis of wear tracks on both antagonists after each tribological tests have led to the phenomenological modelling of wear mechanisms on both antagonists versus the oxidation level of chemical components of sliding materials and friction curves.

Whatever the test conditions, a thermal and mechanical stability was displayed after a running-in period of friction.

First, this stability was related to the establishment and the holding of a permanent contact between two sliding iron oxide scales formed by either wear transfer or oxidation at high temperature. This analysis can be also supported by the approach developed by Felder [1] with the criterion H established in the hot rolling application. The H criterion is defined as the rate between the mean thickness of the oxide scale formed on the strip material and the penetration depth of heat in the oxide scale. The mean thickness of oxide is calculated from the approach of Munther and Lenard [START_REF] Munther | [END_REF] and the constant of oxidation K p and the activation energy Q determined by thermogravimetric tests. Furthermore, at high temperature, the oxide scale formed on the disc is considered as being mainly wiistite FeO.

This criterion H has been applied at the different stages of the friction curve (Table 3). The H values are always found below 0.05. In this way, the superficial contact area of the disc is considered as cooled by contact with the pin and friction corresponds always to a Coulomb-type friction. Shearing is proportional to the normal load and is not very sensitive to the friction duration. The disc oxide scale is harder than Fig. 18. SEM observation: cross-section of the pin at the wear track limit.

the metal and can be assimilated to a rigid solid. The oxide scale of the disc is not very adherent, brittle and responsible for abrasion phenomena. Shearing remains located at the contact interface. Then no modification of wear mechanisms and tribological sites of contact is observed. The friction evolution is only due to a continuous circulation of iron oxide debris into the contact. The analysis of contact pressures versus the test conditions shows that the tribological test conditions have a negligible effect on friction and wear mechanisms.

Contact pressures have been compared between the beginning and the end of friction tests (Fig. 19). The initial hertzian pressures have been determined versus the surface chemistry considered as predominant against the mechanical behaviour of contact, either as wüstite which is the thickest iron oxide scale formed at high temperature on the disc or as the bulk material according to its mechanical properties at high temperature.

At the end of tests, the contact pressures have been determined either as apparent contact pressures or real contact pressures. Apparent contact pressures were calculated from the measure of the global wear track observed on the pin (Fig. 20). Real contact pressures have been estimated by imaging analysis of the pin wear track in order to determine the real contact area at the extreme surface of pins (Fig. 20).

After 1 h of friction, a strong decrease in pressure is observed from 130-400 MPa to 0.6-5.1 MPa according to the test conditions. The difference between the apparent and the real contact pressures is more significant at low test conditions. At high test conditions, the real and apparent contact area are very close which indicates that the contact area are compact, typical of iron oxide-iron oxide sliding surfaces, the cission remaining located at the interface. The complete study of the test condition impact on friction and wear mechanisms is the purpose of an another paper [27].

Besides the running-in period, the contact is stable whatever the test conditions due to a thermal and chemical stabilisation. The influence of the pin chemistry and more particularly the bulk carbides is only significant during the transitory period of the friction curve.

This study suggests all the interest of the judicious choice of the work roll chemistry to adjust the friction value and the wear mechanisms in the rolling bite.

Conclusion

The aim of the study was to define the influence of oxidation on the friction coefficient in the case of a couple of materials involved in the hot rolling process. The influence of the alloying element oxidation of a cast iron was emphasized more particularly on the friction curve and wear mechanisms.

The study was carried through a pin-on-disc tribometer at high temperature. Friction tests stopped in the runningin period of the friction coefficient curve were carried out in order to determine the contribution of oxides formed on the tribo-elements, and more particularly the influence of the oxidised MC carbide rich in Nb and V. The microscopic observations of the wear features of the pin as well as of the disc, led to the development of a wear model explaining the mechanisms of wear debris evolution in the contact, mainly during the running-in period of friction.

This model includes four stages. The first one corresponds to the oxidation of the pin surface by thermal conduction and radiation from the disc, and more particularly the oxidation of the MC carbides rich in Nb and V present in the pin matrix. At the test beginning, a high friction coefficient is recorded due to the shearing forces necessary to break the initial microjunctions between the passivization oxide scale of the pin considered as metallic and the disc surface oxidised at high temperature during more than 1 h.

The second stage corresponds to the initiation of the third body with the attrition of the oxidised carbides and their transfer to the disc surface. In this case, a decrease in friction is observed.

During the entire test, the disc is held at high temperature and its superficial oxide layer goes on growing. Soon the debris coming from the MC carbide oxidation and transferred to the disc surface are included in the iron oxide scale of the disc, so that the contact becomes step-by-step iron oxide on iron oxide. As a consequence, the friction coefficient starts to rise again. When the contact has totally become iron oxide on iron oxide, a stabilization of friction coefficient is observed corresponding to a chemical and thermal stabilization of the contact.

Actually, the contribution of the alloying elements of the work roll grade is sensible only in the running-in part of the friction curve. Nevertheless, this transitory period constitutes the tribological running phase of hot rolling and the effect of the alloying elements on wear mechanisms and friction was brought out.

It has to be noted, finally, the mutual and beneficial effect of the niobium and the vanadium elements which counterbalances the low chromium content. Above a certain content -usually 2% content -chromium is known to present at high temperature a good resistance to oxidation and to prevent the selective oxidation of iron. The oxide scale is thin and adherent and provides a good resistance against wear and a low coefficient of friction. Even alloyed alone to chromium [START_REF] Wilmes | Proceedings of the 6th International Tooling Conference[END_REF], vanadium, usually used in cast iron metallurgy for its contribution to the wear resistance at room temperature, is not enough to obtain such good tribological properties at high temperature due to its catastrophic oxidation.

Fig. 1 .

 1 Fig. 1. The pin-on-disc tribometer at high temperature.

Fig. 2 .

 2 Fig. 2. An example of experimental curves of friction and pin temperature versus sliding length.

Fig. 3 .

 3 Fig. 3. The four tribological stages and the three interrupted points considered in a typical friction test.

Fig. 4 .

 4 Fig. 4. Stabilisation length of friction (length of running-in period) vs. normal load and sliding speed.

Fig. 5 .

 5 Fig. 5. SEM and EDS analysis of the oxidised pin surface outside wear track.

Fig. 6 .

 6 Fig. 6. SEM and EDS analysis of the oxidised disc surface outside wear track.

Fig. 7 .

 7 Fig. 7. Pin wear track at the end of the different interrupted tests (10 N, 0.04 m/s).

Fig. 8 .

 8 Fig. 8. SEM and EDS analysis of pin wear track at the minimum value of friction coefficient (end of stage 2).

Fig. 9 .

 9 Fig. 9. SEM and EDS analysis of disc wear track at the minimum value of friction coefficient (end of stage 2).

Fig. 10 .

 10 Fig. 10. SEM observation: excrescences of oxidised Nb-carbides partially abraded at the edge of the pin wear track.

Fig. 11 .

 11 Fig. 11. SEM and EDS analysis of pin wear track when the coefficient of friction increases again (during stage 3).

Fig. 12 .

 12 Fig. 12. SEM and EDS analysis of disc wear track when the coefficient of friction increases again (during stage 3).

Fig. 13 .

 13 Fig.13. SEM and EDS analysis of pin wear track when the coefficient of friction is stabilised (stage 4).

Fig. 14 .

 14 Fig. 14. SEM and EDS analysis of disc wear track when the coefficient of friction is stabilised (stage 4).

Fig. 16 .

 16 Fig. 16. Wear model on oxide influence on friction evolution in the running-in period.

Fig. 17 .

 17 Fig.17. SEM observation: cross-section of the disc at the wear track limit.

Fig. 19 .

 19 Fig. 19. Evolution of contact pressures at the beginning and the end of friction tests.

Fig. 20 .

 20 Fig. 20. Determination of apparent and real contact area from imaging analysis.

Table 1

 1 Chemical composition of materials (wt.%)

		Cast iron pin
		Cr; 1-2		Mo; 3-5		Nb; 1-2		V; <1
		C	S i	M n	C r	N i	M o	A l	C u
	AISI 1018 steel disc	0.18-0.20	0.24-0.29	0.60-0.65	0.12-0.18	0.07-0.13	0.02	0.02-0.06	0.15-0.20

Table 2

 2 Pin surface temperature at the different interruption times issued from the thermal modelling (950 • C, 10 N, 0.04 m s -1 )

		Friction situation	Average	Time (s)
			temperature of
			pin surface ( • C)
	End of stage 1	Maximum of friction	610	120
	End of stage 2	Minimum of friction	705	290
	Middle of stage 3 Re-increase of friction 742	470
	End of stage 4	Stabilised friction	771	3600

Table 3

 3 Definition of the H criterion in a specific tribological case (950 • C, 10 N, 0.04 m s -1 )[1]

		Time (s)	Mean thickness of oxide scale (m) a	Heat penetration depth (m)	H
	End of stage 1 End of stage 2 Middle of stage 3 End of stage 3 End of stage 4	120 290 470 720 3600	243 248 254 262 338	16.5 × 10 3 24.7 × 10 3 31.4 × 10 3 38.9 × 10 3 86.9 × 10 3	0.015 0.010 0.008 0.007 0.004

Characteristics of the thick oxide scale formed on the disc during the friction tests (950 • C, 10 N, 0.04 m s -1 ).

a Thickness calculated from constants of oxidation K p and Q established by thermogravimetry and the approach of Munther and Lenard

[START_REF] Munther | [END_REF]

.

Acknowledgement

The authors wish to thank ÅKERS Group for its contribution to this study.


C Vergne
email: vergne@enstimac.fr

C Boher
email: boher@enstimac.fr

C Levaillant

R Gras

Analysis of the friction and wear behavior of hot work tool scale: application to the hot rolling process

Keywords: Wear, Friction, Oxidation, Hot forming

In hot forming processes, the interface tool/product is important for the quality of the finished product. In hot rolling, the scale formed on the roll material plays an essential role. As soon as the contact oxide-oxide is established between the roll and the slab, friction allows the process to start. However, the oxide scale will continue to grow under the cyclic action of hot contacts and water cooling and will be subjected to thermo-mechanical stresses. Beyond a certain critical thickness, the oxidized surface layer of the cylinders has not sufficient mechanical strength to withstand the shear stresses.

The wear and friction behavior of the oxides appearing on the surface of the hot working rolls is not well known. The influence of these oxides on the friction and, consequently, the quality of the products of finishing mills, seems very significant. So, in this study, we investigate the evolution of the friction coefficient and the wear, according to the growth, the nature and the thickness of the formed scale. We use a high temperature pin on disc tribometer. The pin consists of material "rolls" while the disc consists of the slab. The pin is instrumented with thermocouples in order to couple the friction coefficient measurements with the thermal gradient in the pin and the surface temperature and the formed oxides. Then, the characterization of the surfaces is done by scanning electronic microscopy (SEM) and EDS analyses. We use the method of sin 2 Ψ to evaluate residual stresses of oxide and correlate these data with shear stress behavior.

Introduction

The thermal cyclic working of tools in hot metal forming causes a superficial oxide scale. In thermo-mechanical working this scale grows to a critical thickness and then deteriorates and causes damage by inlaying and breakdown on the surfaces of rolled product and tools.

In hot rolling this oxide scale plays a major role because it allows the starting and the driving of the metal sheet between the rolls [1]. Without the generation of an oxide-oxide contact, much scuffing appears which is characteristic of a metal-oxide contact [START_REF] Bocquet | 37èmes Journées du Cercle d'Etude des Métaux[END_REF]. If a metal-metal contact is established at the start of mounting, the sheet is not pulled between the rolls what gives rise to sliding. For these reasons it is very interesting for the manufacturers to understand the birth and the growth of this oxide scale formed on the hot working rolls in or-der to optimize the parameters of the process (pressure, speed, torque, etc.) and the quality of finished products.

The superficial damage of the tribological antagonists will depend on the nature and mechanical properties of oxides in the contact [START_REF] Vergne | 38èmes Journées du Cercle d'Etude des Métaux[END_REF][START_REF] Magnée | [END_REF]. Thus, a hard oxide may give abrasive behavior whereas a ductile oxide may decrease the friction coefficient as well as the wear. The second factor often considered is the thickness of the oxide scale which is associated with adherence. Many studies have assessed the mechanical and tribological characteristics of the oxide scale formed on the rolled product, but the oxidation of rolls and its interaction with the strip are less reported. Nevertheless, one fact seems established: the coefficient of friction increases when the scale thickness decreases. The explanation of this remains controversial [5,[START_REF] Blazevic | Proceedings of the 37th MWSP Conference[END_REF].

The aim of this contribution is to correlate the evolution of the coefficient of friction with the appearance, the nature and the mechanical properties of the scales formed on hot metal working tools and their products.

Experimental equipment, materials, procedure and analysis

High temperature pin on disc tribometer

A high temperature pin on disc tribometer was developed in our laboratory. The disc (Fig. 1-(3)) has a continuous rotating movement and the rotating speed can vary from 30 to 3000 rpm. Linear velocity depends upon radius of the wear track and ranges from 0.05 to 50 m/s (Fig. 1). The disc can be heated to 1000 • C by a high frequency induction heating system before rotation (Fig. 12). The homogeneity of the surface temperature of the disc is checked by spot-welded thermocouples. While in rotation, the disc temperature is controlled by an IR-pyrometer (350-1400 • C). A thermal screen protects the engine shaft (Fig. 1-(1)). The loading is carried out using dead weights (maximum capacity 100 N -Fig. 1-( 5)). The tangential force is measured using a strain gauge placed parallel to the friction plane (Fig. 1-( 6)). The friction coefficient is recorded with a software developed on LABVIEW. After test, wear surfaces are observed by optical microscopy and/or scanning electronic microscopy (SEM) with dispersive energy analysis.

The radius of curvature of the hemispherical pin was 20 mm. The pins (Fig. 1234)) have been instrumented with two thermocouples located at 1 and 3 mm depths from the center of the pin contact. The temperatures in the pin have Test conditions are summarized in Table 1.

Materials

A white cast iron rich in carbides, called cast iron "A", and a ferritic-pearlitic mild steel XC18 (AISI 1018) (Fig. 2a and b, Table 2) were examined. The cast iron had a high hardness of 63 HRC (772 HV) and was brittle whereas the steel XC18 (AISI 1018) had a lower hardness of 168 HV.

The pin was always made of cast iron "A" and the disc was always made of AISI 1018 mild steel. The pin represented the tool (roll material) and the disc represented the sheet (rolled product).

Oxidation

The oxidation of these alloys was studied. The purpose of these tests was to define a reference in thickness and to determine the nature of the oxide scales formed on the antagonists during the tribological tests. We performed phase analysis on the samples in order to identify the nature of surface oxides. Thermo-gravimetric analysis was done to study the oxidation kinetics. We used an electronic SETSYS thermobalance. The temperature was chosen to represent the friction test temperature and the various rolling temperatures. Different holding times were selected. The heating and cooling rates were 20 and 50 • C/min, respectively.

Oxide scale phase analysis

The X-rays were used to determine the different nature of the oxide scale on the pin and on the disc after oxidation. Measurements were made with a diffractometer in the configuration θ-2θ. The sample turned with a speed ω and the detector turned with a speed 2ω. The rotation of the sample and the detector unit was continuous or step-by-step. A linear detector with Cr K␣ rays was used. The collimator beam diameter was about 800 m. The acquisition time was 3 h and the range of the scanning angle was 15-160 • (Fig. 3a).

Residual stress calculation

In crystalline structures, {h k l} planes are characterized by interplanar spacing d(h k l). A residual stress introduces a variation of the lattice parameter and of the interplanar spacing d(h k l). This variation produces modifications of θ, the diffraction angle. If λ, the wavelength of the X-ray, is constant, the microscopic deformation of the crystal lattice is given by

d d + sin θ sin θ = 0 (1)
and

ε micro = d d (2)
A well-known classical X-ray residual stress measurements using the sin 2 ψ technique was used [START_REF] Liu | [END_REF]. Details of this method can be found in [8]. It can be summarized by the following expression for an isotropic material:

[2θ φ,ψ (h k l)] = - 1 2 S 2(h k l) σ φ 2 cot gθ sin 2 ψ +S 1(h k l) (σ 1 + σ 2 ) 2 cot gθ (3)
where (φ, ψ) is the measurement directions, {h k l} the diffraction planes, [2θ φ,ψ (h k l)] the Bragg angle stress induced variation, σ 1 and σ 2 the principal stresses, σ φ the stress in the direction φ and 12(S 2 (h k l)) and S 1 (h k l) the X-ray elastic constants. Changes in the Bragg angle correlate with residual stresses.

The apparatus is the Set-X equipped with a linear detector having an angular accuracy of 0.09 • . The goniometer can make an angular movement of ±180 • for the φ angle and an angular movement of ±44 • for the ψ angle (Fig. 3b). To measure deformation in the oxide scale, a supply voltage of 20 kV and an intensity of 4.5 mA were used. Vanadium K␣ radiation was used. The acquisition duration, for each peak (value of ψ angle) took 15 or 30 min. The penetration depth of the beam in the oxide is about 5-10 m.

Results

Nature and thickness of oxide scales

For the mild steel, the analysis of oxidized samples was given in Fig. 4a. Oxide scale basically consisted of hematite. The intensity of peaks in the diffraction spectrum of hematite was not in agreement with JCPDS cards. In addition, some peaks could not be detected. The difference in intensity is assumed to be caused by the fact that the hematite is not statistically isotropic, i.e. that it was not composed of fine grains distributed in a random way. So, we can conclude that hematite with a preferential direction has been formed on the surface of our samples.

On the surface of cast iron "A" samples oxidized at 900 • C for 24 h, we observed peaks for hematite and peaks for chromite FeCr 2 O 4 or to a compound (FeO 6 , CrO 4 ) 2 O 3 (Fig. 4b). The chromite peaks are observed at the base of hematite peaks. So, the hematite on the cast iron "A" samples is much less textured than that observed on the surface of XC18 samples.

According to [5], the AISI 1018 steel has parabolic oxidation kinetics with regard to the time and an exponential dependence on temperature. In the range of temperature studied, between 900 and 1000 • C, the thickness of the scale formed on the AISI 1018 samples increases linearly. So we can suppose that the oxide scale which is formed at 900 • C has a thickness of about 50 m after 1 h and about 70 m after 2 h.

Residual stresses in an oxide scale

Residual stresses in different oxide scales were measured for AISI 1018 samples oxidized at 900 • C for different oxidation times [START_REF] Trimbitasu | Internal Report of EMAC[END_REF]. Whatever the testing time, two peaks were detected versus ψ angle. The hematite texture phenomenon is responsible for the presence of two peaks. These two diffraction peaks correspond to the (1 1 9) and (1 0 1 0) planes. The internal stresses have, thus, been calculated for each family of planes. We made measurements with a small ψ angle to characterize the residual stresses in (1 0 1 0) planes and with a large ψ angle to identify stresses for (1 1 9) plane. Fig. 5 shows the results of the calculated internal stresses for (1 1 9) planes. So we have observed.

• There are residual stresses in the hematite layer. The initial compressive residual stresses due to the preparation of samples were not considered because such stresses are relaxed when the samples are heated beyond the austenitic temperature. • The measured residual stresses are compressive as described by the following analytical model (Eq. ( 4)). • The stress relaxation by cracking or buckling of oxide scale does not completely release the residual stresses even if some residual stresses approach zero. The same observation was made for the (1 0 1 0) planes.

The internal stresses within the oxide scales were calculated by an analytical model [START_REF] Bull | [END_REF]11]. The effect of stresses related to the growth of the oxide scale and stress relaxation in the substrate were not taken into consideration. The thermal stresses seem to play the major role. We can write them as

σ th = E ox /(1 -υ ox )[α ox (T ) -α s (T )] T 1 + (h ox /h s )(E ox (T )(1 -ϑ ox )/E s (T )(1 -υ s )) (4)
where E i , ν i , α i and h i are the Young's modulus, Poisson's ratio, the thermal-expansion coefficient and the thickness of the substrate (s) or the oxide scale (ox).

We can use this model because the value h ox /h s is not negligible. Considering the fact that the oxide scale mainly consists of hematite, the calculated residual thermal stress value (Eq. ( 4)) is about 550 MPa, which is close to the stress measured by X-rays at room temperature (σ ≈ 400 MPa).

Tribological results

Three types of tribological tests were carried out according to the experimental conditions described in Table 1. At room temperature (series A), the mean value of the friction coefficient "µ" of the couple cast iron "A"/XC18 is 0.60 ± 0.02. Literature [START_REF] Bowden | The Friction and Lubrication of Solids[END_REF] gives a friction coefficient about 0.3 for cast iron on cast iron. In our case, the friction coefficient is close to the value generally found for steel on steel friction without lubrication. The presence of carbides in our cast iron could explain this elevated value. The friction evolution versus test duration includes a non-stationary period (Fig. 6a). This evolution could be characteristic of the mechanical accommodation of the couple cast iron "A"/XC18

In high temperature experiments (950 • C), the friction coefficient versus test duration evolution was different depending on the temperature stabilization time in the pin before sliding. The main difference between these two types of tests was in the non-stationary period. When the temperature in the pin was stabilized before sliding (series B), the pin thermocouples gave a temperature equal to 700 • C at a depth of 1 mm from the contact surface, and equal to 670 • C at a depth of 3 mm (Fig. 6b). In this case, the friction coefficient measured at the start of the test was in the same order of magnitude as the established one. The duration of the non-stationary period of the friction was not significant. So, the average value of the coefficient of friction was 0.46 ± 0.01. In the second case (series C), where we did not wait for the temperature stabilization in the pin before sliding, we observed that the coefficient of friction had two periods, the first one ranging between the test beginning and around 900 s, the second one beyond 900 s (Fig. 6c). The first period is considered as a non-stationary period and the other one is a quasi-stationary period. We note that the non-stationary period corresponds to the duration of stabi- lization of the temperature in the pin and in this case, there is a large variation of the friction coefficient. In the stationary part, the average value of the coefficient of friction is 0.44 ± 0.02, so it is equal to the average value during the first tests (series B).

The same friction evolution is noted when we increase the load (series D), but in the stationary part, the average value of the coefficient of friction is lower 0.37.

When the temperature in the pin was stabilized before sliding, we could consider that the contact in the beginning of the sliding was oxide on oxide. In the second case, without stabilization, the contact was cast iron on oxide. In fact, the thickness of the natural oxide layer formed on the cast iron at room temperature is negligible.

SEM micrographs and EDX spectra

For all friction tests carried out at 950 • C -with or without stabilization of the temperature in the pin -the AISI 1018 discs as the cast iron "A" pins have identical macroscopic wear surface features after 1 h test duration.

On the AISI 1018 discs, out of the friction surface, the oxide scale presents a columnar like micro-structure (Fig. 7a andb). The boundaries between columns are more or less broad and deep, and some could indicate cracks. EDX spectra of these columns reveals that it is iron oxide (Fig. 7c). SEM micrographs of the disc wear surface reveal that the real surface of contact is much lower than the apparent one. In addition, two types of contact can be observed depending on their localization in the friction zone. Outside of the wear scar, plastic deformation of the column is visible (Fig. 8a). The EDX spectrum shows that this bearing pressure area is made only of iron oxide. With a higher magnification, Fig. 8b shows that this plastically deformed area shows "under-cells" whose boundaries are also oxidized. For instance, the metallurgical reason of this microstructure is not well understood. Lastly, we can also observe an area on which plastically deformed material is transferred (Fig. 9) and identified by EDX spectra as being only iron oxide. In the center of the wear scar, there are zones made of aggregates at the top of which plastically deformed oxide layers are found (Fig. 10a). EDX analysis reveals that these layers are always made only of iron oxide, whereas the aggregates present iron, oxygen as well as traces of Mn and Ni (Fig. 10b).

A test of the series C was stopped after 500 s sliding. Surface observations have revealed in the disc wear track small agglomerated crystals zones (Fig. 11a andb), not plastically deformed. EDX analysis shows that these crystals consist primarily of oxygen and iron, but also of Nb, Mn, V and Cr. These crystals could be Nb, V, Cr and Fe carbides which would be oxidized.

With regard to the cast iron pins, three zones are observed. The first one, out of the wear track, has an acicular micro-structure (Fig. 12), made up only of iron oxide, which looks like needles of hematite Fe 2 O 3 . During the high temperature tribological test, this part is the coldest zone of the pin. The pin is hemispherical and this zone is not affected by friction. Near the wear track, SEM micrographs reveal a microstructure like a sponge or nodules made up of agglomerated particles (Fig. 13). The first microstructure is a form of iron oxide, while the second one exhibits iron, oxygen, Cr, V and Mn. We can also see some excrescences of the scale (Fig. 14a), rich in Nb (Fig. 14b). There could be oxidized niobium carbide from the cast iron "A".

Macroscopically, the shape of the pin friction surface is ellipsoidal and the large diameter is perpendicular to the direction of sliding. In the center of this surface, the wear track is not uniform, with an alternation of zones of contact and zones without contact (Fig. 15a). Furthermore, the real contact surface is lower than the macroscopic apparent contact surface. Moreover, plastic deformation of the zone of contact is also observed. This area is made of a layer of iron oxide, plastically deformed and sustained by nodules (Fig. 15b).

These plastically deformed layers seem to be superficial and they do not affect the oxide scale thickness (Fig. 15c). In the limits of the pin wear zone, SEM examinations show that the initial excrescences of oxide coatings, rich in Nb, take place during friction phenomena (Fig. 14a before friction and Fig. 16 after friction).

Finally, if the test duration was longer, perhaps more zones of debris cracking and debris formation could appear in these plastically deformed zones (Fig. 17).

Discussion

Nature and mechanical properties of oxide scales

The thermodynamic calculation of the oxide scale thickness gives a value of 10 m after a testing time of 900 s.

As mentioned earlier (Section 3.2), the calculated residual stresses in the hematite layers are compressive at room temperature. This result may be related to the following three observations.

• The surface oxide layer is hematite.

• The hematite scale is about 6 m.

• The hematite scale is in compression at room temperature. So the internal stresses may explain the macroscopic circular crack of the disc scale in the center of the wear track.

So we can suppose that at high temperature the initial friction contact of the disc is established on the hematite scale which is very textured.

Tribological behavior of oxide scales

For both tests (series B and series C), the calculated heat flow between the pin and the disc surface is about 0.02 W/mm 2 . Friction does not affect the duration of temperature stabilization in the pin (approximately 900 s) nor the pin temperature level (approximately 700 • C) at 1 mm from the wear surface. It does not drastically increase the contact temperature.

The mean friction coefficient is less important when the test is performed under high temperature in comparison to room temperature. So, the oxide scale decreases the coefficient of friction and it can be considered as a solid lubricant.

Furthermore, under high load (10 N), the friction coefficient decreases, for the same conditions of temperature. In this case (Fig. 18), the plastically deformed layer at the pin surface is thicker than in the case of 2.5 N (Fig. 15c). It seems that the bulk behavior of oxide would be more important in friction phenomenon than the surface oxide.

At the end of series B like series C, the wear tracks present the same features. The contact, therefore, friction, is sustained by the nodules and the plastic deformation of the wear tracks. The real contact surface presents a glazed aspect. It is very different (lower) from the apparent surface of contact. EDS spectra show only iron oxides on the pin wear track, whereas this cast iron, outside the friction zones, always presents oxides rich in Cr, Mn, V and Nb. This analysis would indicate a transfer from the disc oxide scale to the pin surface.

EDS spectra show also that the plastically deformed areas consist exclusively of iron oxides. We never observed plastic deformation of presumed oxidized carbides.

No mechanically shear ruptured oxide layer is observed. Nevertheless, a plastic flow of oxide is observed on the contact surface of the disc and the pin. This plastic deformation is not observed in the bulk oxide layer. In fact, the superficial plastic deformation of the oxide layer, formed on the pin and disc surfaces, reinforces the idea that the coefficient of friction, in our case, is a Coulomb type.

Interpretation of the friction coefficient evolution for initial metal-oxide contact

In experiments without stabilization of the temperature in the pin (series C), we can assume that the non-stationary period of the coefficient of friction, observed in the beginning of the test, is due to the formation of iron oxide layers at the pin surface. This non-stationary period was also observed by other authors [START_REF] Stott | [END_REF]. The average steady friction value is equal to one of the series B.

In the case of tests in non stabilized temperature (Fig. 19a), the general evolution of the friction coefficient can be associated with the change of the pin surface temperature, calculated from a numerical inverse method of integration (Fig. 19b). We can identify four significant stages.

Stage (1) concerns the increase of the friction coefficient at the start of the tribological test. Here, sliding is assumed by the cast iron "A" on AISI 1018 950 • C oxidized steel. So, initially, contact is metal on oxide.

While the friction coefficient increases, the surface pin temperature rises to 500 • C. At this temperature, pin surface oxidation occurs. The pin material is an alloyed cast iron containing Nb carbides. Indeed, these carbides are very numerous at the surface of the cast iron, and they oxidize at 430 • C. In the same way, the carbides of V, Fe and Mo can also be oxidized at temperatures lower than 500 • C. In addition, the Nb carbides, during oxidation, form excrescences perforating the surface oxide scale.

In stage (2), the coefficient of friction decreases. So, the oxide scales play a lubricant role. We can verify, with interruption of the test, transfer of the oxidized Nb carbides on the disc and the onset of debris compaction without plastic deformation. Debris formation is a consequence of the attrition phenomenon which precedes adhesion. It is facilitated by shearing and abrasion. Transfer of oxidized Nb carbides was made possible by the porous columnar-like microstructure of iron oxides on the disc surface (Fig. 9b). This microstructure could contribute to mechanical adhesion. The debris compaction seems to result in the diminution of contact pressures and, thus, a reduction of the coefficient of friction. The calculated pin temperature then reaches 700 • C.

In stage (3), the friction coefficient increases. The tribosystem initiates transfer to the pin, more precisely the transfer of iron oxides formed on the surface of the disc. This transfer may occur on the top of the agglomerated particles, on the top of sponge microstructure iron oxides and on the top of Nb-rich excrescences. Reciprocally on the disc surface, there are zones of compaction of oxidized Nb carbide debris coming from the pin. These zones also constitute an area of mechanical adhesion of iron oxides. The increase of the coefficient of friction is consecutive with the mechanical adhesion, plastic deformation and abrasion of iron oxides, from the pin toward the disc and from the disc toward the pin. When the contact is mechanically and chemically established, the pin surface temperature is steady, and estimated by calculation to be 950 • C.

In stage (4), the stationary regime of the friction coefficient begins as in series B tests. During these experiments, the phases of pin oxidation during sliding are not revealed and the transfer phenomena are much faster. For these reasons, in the series B tests, the stationary state of the friction coefficient occurs more quickly.

At the end of this part, whatever the type of test, a new microstructure is carried out in the contact zones, initially plastically deformed. This new microstructure that we call "under-cells" seems to result from strain-hardening by shearing of the friction surface. The mechanisms of the growth of these "under-cells" are not well known yet.

Conclusion

The high temperature pin on disc tribometer allows study of friction coefficient variations during the oxidation of the samples.

Oxide scale plays a lubricant role in friction. During high temperature experiments (950 • C), the friction coefficient evolution depends on the temperature stabilization time in the pin before sliding. Following two friction regimes are observed.

• Low friction variation when the oxide scale is already formed on the pin before sliding. • Large friction variation when the pin oxide scale grows during friction.

In both cases, wear track features, after friction coefficient stabilization, are the same. We observe plastically deformed zones exclusively made of iron oxides (even on the pin) and oxidized carbide agglomerates (even on the disc). So, we can conclude, there is transfer between the two specimens. The contact is established at the interface of the pin and disc and not in the bulk oxide scale.

The aim of this study is to understand the first step of friction between the roll and the slab in hot rolling. We try to understand the influence of roll oxidation on wear mechanisms and friction values. This work will go on with the tribological study of different cast irons used as "roll" material.

Fig. 1 .

 1 Fig. 1. High temperature pin on disc tribometer.

  been continuously measured using a "Multireg C1732" SIEMENS recorder. The acquisition frequency is 3 Hz. The initial arithmetic roughness of the discs was about 0.04 m R a . The disc was first heated up in rest to achieve the test temperature of 950 • C. The pin, which was initially at room-temperature was put on the disc. The rotation of the disc began (a) as soon as the pin was put on the disc, or (b) after stabilization of the temperature in the pin.

Fig. 2 .

 2 Fig. 2. Optical micrographs of AISI 1018 (a) and cast iron "A" (b).

Fig. 3 .

 3 Fig. 3. (a) Principle of a X-ray diffractometer; (b) rotation of the reference frame in terms of ψ and φ angles, with (X1, Y1, Z1) sample references.

Fig. 4 .

 4 Fig. 4. XRD traces obtained from AISI 1018 samples (a) and cast iron "A" samples (b).

Fig. 5 .

 5 Fig. 5. Calculated compressive stresses of scale formed on AISI 1018 samples at 900 • C for the (1 1 9) plane.

Fig. 6 .

 6 Fig. 6. Evolution of friction coefficient vs. testing time -F n = 2.5 N, v = 0.05 m/s: (a) at room temperature, (b) 950 • C, with stabilized temperature in the pin, (c) 950 • C, without stabilized temperature in the pin.

Fig. 7 .

 7 Fig. 7. (a) Disc micrograph -oxide scale feature out of the sliding contact surface; (b) disc micrograph -columnar-like microstructure of oxide scale; (c) disc analysis -EDX spectrum of the oxide scale columnar-like microstructure.

Fig. 8 .

 8 Fig. 8. (a) Disc micrograph -plastic deformation of the oxide scale columnar-like microstructure; (b) disc micrograph -"under-cells" with oxidized boundaries.

Fig. 9 .

 9 Fig. 9. Disc micrograph -material transfer on the disc wear track.

Fig. 10 .

 10 Fig. 10. (a) Disc micrograph -observation of the wear feature in the friction surface center; (b) disc analysis -EDX spectrum of the aggregates around the plastically deformed layer.

Fig. 11 .

 11 Fig. 11. (a) Disc micrograph -observation of small agglomerated crystals zones not plastically deformed; (b) disc micrograph -magnification of the agglomerated crystals zones.

Fig. 12 .

 12 Fig. 12. Pin micrograph -acicular microstructure of the oxide scale out of the wear track.

Fig. 13 .

 13 Fig. 13. Pin micrograph -observation of the two oxide microstructures (sponge and nodule).

Fig. 14 .

 14 Fig. 14. (a)Pin micrograph -excrescences of the scale rich in Nb; (b) pin analysis -EDX spectrum of the excrescences of the scale.

Fig. 15

 15 Fig. 15. (a) Pin micrograph -pin wear track with contact and no contact zones; (b) pin micrograph -plastically deformed layer of iron oxide, and sustained by nodules; (c) pin micrograph -superficial plastic deformation of the wear track.

Fig. 16 .

 16 Fig. 16. Pin micrograph -participation of an excrescency in the friction.

Fig. 17 .

 17 Fig. 17. Pin micrograph -observation of wear debris.

Fig. 18 .

 18 Fig. 18. Pin micrograph -plastically deformed layer of iron oxide (F n = 10 N).

Fig. 19 .

 19 Fig. 19. Evolution of friction coefficient in the case of the non stabilized temperature in the pin (a) and evolution of the superficial temperature of the pin calculated by a numerical model (b).

Table 1

 1

	Experimental conditions of tribological tests
		Load (N)	Sliding speed (m/s)	Test duration (s)	Temperature of	Stabilizataion of the
					the disc ( • C)	temperature in the pin
	Series A	2.5	0.05	3600	20	-
	Series B	2.5	0.05	3600	950	Yes
	Series C	2.5	0.05	3600	950	No
	Series D	10	0.05	3600	950	No

Table 2

 2 Chemical elements of materials.

		Elements (wt.%)	C	Mn	Si	P	S	Cr	Ni	Mo	Nb	V
	Pin	Cast iron "A" a	3.2-3.5	-	0.9-1.1	0.109	0.077	-	-	-	-	-
	Disc	XC18/AISI1018	0.16-0.22	0.4-0.70	0.15-0.35	<0.035	<0.035	<0.40	<0.40	<0.1	-	-
	a Cast iron "A": the total chemical composition of the case iron is confidential.

Acknowledgements

The authors would like to thank FORCAST Society for their contribution to the study and Mr Beguin of Ecole Nationale d'Ingénieurs de Tarbes for the X-ray analysis.