O Barrau

C Boher
email: boher@enstimac.fr

R Gras

F Rezai-Aria

Analysis of the friction and wear behaviour of hot work tool steel for forging

Keywords: Friction, Wear, Hot forging, Plastic deformation

A significant part of the energy in forging is used to break the interfacial junctions due to friction between the tool and the workpiece. The life of hot-forging tools is usually limited by complex interactive mechanisms under cyclic loading such as abrasive, adhesive and scaling wear, thermal and mechanical fatigue, and plastic deformation.

This contribution deals with the wear mechanisms of the tempered martensitic X38CrMoV5 steel (AISI H11) under high-temperature and dry-sliding wear. The investigations are carried out with high-temperature pin-on-disc tests. The pin is cut from bars of X38CrMoV5 steel treated at 42 and 47 HRC. The disc is made of common steel (AISI 1018, XC18). Temperature of the disc ranges from 20 to 950 • C. Before the test starts, the disc is first pre-heated for 1 h. The experiments are performed under constant load and velocity. The friction coefficient decreases quasi-linearly with the rising disc temperature up to 800 • C. Over this temperature, it decreases drastically for the 42 HRC steel but remains linear for the 47 HRC steel.

Scanning electron microscopy (SEM) and energy dispersive spectrometry (EDS) investigations have revealed that wear is essentially due to abrasion, plastic deformation and fatigue. Set of cracks due to contact rolling fatigue is observed on the pin and the disc. Those cracks are located on the transferred scale on the pin and on the oxide scale of the disc wear track. The cross-section observations of the pin have revealed a plastically deformed zone beneath the surface. In this sub-surface layer, the tempered martensitic microstructure seems to be more aligned due to friction and the plastic deformation.

Introduction

A specific disadvantage of the hot and warm die-forging process is that the tools are exposed to high thermal and mechanical stresses. These stresses cause failure of the dies because of wear and thermo-mechanical fatigue [START_REF] Andreis | The wear behaviour of hot-work tool steels used in forging processes[END_REF][START_REF] Walter | Material failure mechanisms of forging dies[END_REF][START_REF] Kircher | Analyse des dégradations d'outillages de forge à chaud à l'aide de la simulation numérique[END_REF][START_REF] Jean | Heat-checking of hot work tool steels[END_REF][START_REF] Doege | Aspect of wear prediction in precision forging[END_REF]. The tools then have to be exchanged after a certain time of use. It leads to considerable costs not only for the tools themselves but also for the needed set-up times and thus may cause delays in delivery of the forged parts.

The hot working steels usually used for the die-forging tools are exposed to tempering effects because of high thermal and mechanical loads. These tempering effects on their part cause a greater susceptibility to wear.

Generally, due to the forging temperature being well above 1000 • C, the temperature of the surface of the tool temporarily exceeds 500 • C [START_REF] Andreis | The wear behaviour of hot-work tool steels used in forging processes[END_REF][START_REF] Walter | Material failure mechanisms of forging dies[END_REF][START_REF] Kircher | Analyse des dégradations d'outillages de forge à chaud à l'aide de la simulation numérique[END_REF] and thus the tempering temperatures of conventional hot work tool steel. In such a case, the hardness of the tool is reduced and the mechanical impacts during forging operations can easily cause plastic deformation as well as abrasion of tool material [START_REF] Andreis | The wear behaviour of hot-work tool steels used in forging processes[END_REF] (Fig. 1).

In fact, for each fabrication operation, temperature variations occur more or less quickly on the working tool surface due to the heat exchange between the hot workpiece and the tool. After contact with the hot workpiece, the die surface is quickly cooled. Then, transient thermal gradients are developed inside the tool by thermal conduction. These thermal gradients lead to crack the surface by heat checking [START_REF] Jean | Heat-checking of hot work tool steels[END_REF].

Besides, tools undergo mechanical strains during forging [START_REF] Kircher | Analyse des dégradations d'outillages de forge à chaud à l'aide de la simulation numérique[END_REF]. These strains can enhance diffusion pathways in the die oxidation that plays an important role in the tool wear. The damage caused by friction may be very different according to the nature and the physical properties of the contact surfaces (metal or formed oxide layers).

At last, under thermal and mechanical stresses, the tempered martensitic steels employed in hot-forging tools are inclined to loose their mechanical properties [START_REF] Jean | Heat-checking of hot work tool steels[END_REF][START_REF] Doege | Aspect of wear prediction in precision forging[END_REF][START_REF] Delagnes | Influence of temperature and initial hardness on fatigue behaviour and life of a 5% Cr hot work tool steel[END_REF]. Also, the die surface damage is the result of a complex process connected to fatigue (cracking origin), friction (wear origin) and test ambience (oxidation origin) [START_REF] Kircher | Analyse des dégradations d'outillages de forge à chaud à l'aide de la simulation numérique[END_REF].

The aim of this contribution is to assess some wear mechanisms of a tempered martensitic tool steel at various test temperature and initial hardness. The friction tests were performed on a high-temperature pin-on-disc tribometer developed in our laboratory, in order to control load, speed, temperature, surface conditions and chemical state of the materials.

Experimental equipment, procedure and materials

High-temperature pin-on-disc tribometer

The high-temperature pin-on-disc tribometer developed in our laboratory is reported in [START_REF] Vergne | Analysis of the friction and wear behavior of hot work tool scale: application to the hot rolling process[END_REF]8]. The pin presents a hemispherical contact surface with a radius of curvature of 20 mm. The disc is a cylinder of 30 mm diameter.

After each test, wear surfaces are observed by optical microscopy and/or scanning electron microscopy (SEM) with dispersive energy analysis capability. To complete these investigations, a cross-section observation on each pin is also performed on an environmental SEM (ESEM).

Test procedure

The disc is first heated up to a given temperature and kept it constant for 1 h. During the disc pre-heating, the pin is kept out of the contact at room temperature. After 1 h of heating of the disc, the pin is put on the disc surface and the friction test is started immediately.

To assess the effect of the disc temperature on wear damage, the normal load (20 N) and the linear sliding speed (0.167 m s -1 ) are kept constant. Test conditions are summarised in Table 1.

It is considered that the temperature of the forging tools do not reach the high temperatures applied in the test (800 and 950 • C). The temperature of the forged piece is often over 1000 • C, so temperature of the tool surface may reach these temperatures. Therefore, tests are conducted at these temperatures to assess their influence on the wear behaviour of X38CrMoV5.

Materials

The pin is made of a 5% chromium tempered martensitic steel grade (X38CrMoV5, AISI H11). On the other hand, the disc is a ferritic-pearlitic mild steel (XC18, AISI 1018). The X38CrMoV5 steel is widely used for forging dies [START_REF]Forming and Forging[END_REF][START_REF] Leveque | Techniques de l'Ingénieur[END_REF], whereas AISI 1018 mild steel is used as a forged material in automotive industry. The chemical composition of the two steels is reported in Table 2. The 5% chromium steel was studied in quenched and tempered conditions. The heat treatments are performed to achieve two initial hardnesses, 42 and 47 HRC, with a tempered martensitic microstructure (Table 3). The tempered martensitic structure is in fact ferrite and cementite with a lath shape. The microstructure has a high density of dislocations, which gives a good strength to the material at room temperature [START_REF] Mebarki | Relationship between microstructure and mechanical properties of a 5% Cr hot work tool steel[END_REF]. At high temperature, the interprecipitates distance increases, so the mobility of dislocation is enhanced.

The initial hardness of AISI 1018 steel is about 168 HV at room temperature. The initial arithmetic roughness of the disc and the pin are 0.04 and 0.32 m, respectively.

Friction and pin damage

Friction evolution

First, the average value of the coefficient of friction decreases with an increase of the test temperature (Table 4) regardless the initial hardnesses of the pin. The friction coefficient versus time curves for a given test temperature are quite similar for both initial hardnesses of the pin substrate.

At room temperature and 200 • C, the mean value of the friction coefficient of the couple X38CrMoV5/XC18 is about 0.6 of whatever the initial hardness of the pin is. This friction coefficient is generally found for steels in dry friction. From 500 to 800 • C, the average value of the coefficient of friction decreases slightly to 0.5 and there is still not a significant difference between pins with two levels of hardness.

Over 800 • C, the value of the friction coefficient decreases but its evolution remains quite linear for the 47 HRC initial hardness pin while it decreases drastically for the 42 HRC pin. So, 950 • C seems to be a critical point from which the friction behaviour of the couple X38CrMoV5/XC18 is modified depending on the disc temperature and the pin hardness.

The overall decreases of the friction coefficient may be connected to the loss of the mechanical properties with the increase of the test temperature [START_REF] Jean | Heat-checking of hot work tool steels[END_REF][START_REF] Doege | Aspect of wear prediction in precision forging[END_REF][START_REF] Delagnes | Influence of temperature and initial hardness on fatigue behaviour and life of a 5% Cr hot work tool steel[END_REF] and to the presence of an oxide layer for the high-temperature test. It seems that the 42 HRC initial hardness pin looses its mechanical properties quicker than the one of 47 HRC.

Surface observations

The damaged surfaces of the pin are observed by SEM for each test temperature. The surface damages of the pins up to 800 • C, were already presented in previous works [START_REF] Barrau | Investigations of friction and wear mechanisms of hot forging tool steels[END_REF]. No difference was observed between the 42 and 47 HRC pin at the same test temperature but the pin wear track changes with the temperature.

Under 500 • C, we claim that tribo-oxidation is prevailing. The metallic debris enter into the contact region and are oxidised during the sliding. At 500 • C, a two zones layer constitutes the wear track. The light zone is the matrix of the pin and the dark area is oxides from the disc and oxidised debris. These zones form a metal-oxide mixed zone. Beyond 500 • C, hot tribology prevails: the sliding contact surfaces generate debris already oxidised mainly from the disc surface. At 700 • C, this mixed zone is gradually transformed in a compacted layer of oxide debris which tends to become glazed at higher temperature. At 800 • C, the mixed zone becomes totally glazed surface. These glazed surfaces present cracks.

At 950 • C, the contact surfaces are oxide on oxide. Even though there is an important difference between the value of the coefficient of friction of the 42 and 47 HRC pin for this test temperature, the morphology of the contact surfaces is quite similar for the both hardnesses (Fig. 2A). We observe a compacted oxide layer on the surface of the pin. The morphology of this layer looks like an iron oxide (Fe 2 O 3 ). This oxide on the pin surface may come from the oxide formed on the disc during the pre-heating treatment. As can be seen in Fig. 2B, the surface oxide morphology is modified on the contact area between the pin and the disc. This deformation looks like an indentation which tends to transform oxide into glazed zone.

In addition, another damage mechanism contributing to the wear in the couple X38CrMoV5 steel on XC18 steel is the surface oxide layers cracking for the temperature ranging 500-950 • C. We do not observe cracks for the lowest temperatures [START_REF] Barrau | Investigations of friction and wear mechanisms of hot forging tool steels[END_REF]. The form of the cracks suggests their physical origin. The fatigue cracks have a horseshoe form. We could attribute the superficial fatigue cracks to friction stress but the thermal stress generated during the cooling can as well cause such cracking.

Cross-section observations

The cross-sections of the pin are observed by ESEM for each test temperature. The cross-sections are cut parallel to the direction of friction. Some energy dispersive spectrometry (EDS) analyses were added to complete the investigations. Results from EDS are mainly qualitative.

Plastic deformation

We observe plastic deformation parallel to the direction of friction for each test except at 950 • C. The maximum thickness of sub-surface layer affected by the plastic deformation versus temperature is summed up in Table 5.

From 20 to 200 • C, the flow stress of the 47 HRC is high and do not allow a large plastic deformation. So, the values measured for these temperatures are a bit lower than for the 42 HRC alloy. Up to 500 • C, the measured deformed thickness is quite similar for the two pin hardnesses. At 700 • C, the behaviour changes between the both hardnesses. The resultant thickness deformed on the 42 HRC is more than five times larger than the deformation observed on the 47 HRC pin.

The maximum thickness affected is often measured near the back of the wear track due to the flow of matter, as we will see later on. When it is observed, the plastic deformation is influenced by the initial orientation of the lathes of the microstructure as we can see in Fig. 3. If the lathes have an angle with the surface beyond π/2, it limits the thickness affected. If this angle is below π/2, the lathes are easier to deform and the deformed zone becomes thicker.

At 20 • C, for the both hardnesses, we observe a plastically deformed zone. But the elongation of the lathes is less important compared to those measured at higher temperatures even if the values of the resultant thickness deformed are very close (Fig. 4A andB).

In localised zones, for the low-temperature test (20 and 200 • C), the shape of the plastic deformation rather looks like of an indentation by a normal force than a plastic deformation under shear force (Fig. 5). This indentation may occur when two metallic asperities enter in contact (Fig. 5A) or it may form due to the hardness of the debris in the contact for these test temperatures (Fig. 5B).

In the back of the wear track, we observe an edge of deformed material created by the movement of matter under shear force (Fig. 6A). It is at the back of the wear track where we measure the maximum thickness affected by plastic deformation. Even if the maximum strain due to the normal load and velocity is localised in front of the wear track. As we can observe in Fig. 6B, some big debris are abraded and plastically deformed. The formation of such debris could explain the low resultant thickness observed at and over 500 • C peculiar for the 47 HRC pin. These big debris could easily be abraded from the edge at the back of the wear track.

The formation of dimples, in the plastically deformed zone, near the external surface of the matrix plays a role in the decohesion of the lathes (Fig. 7B). The lathes reach their maximum deformation and microductile cavities appear when the material can not be more deformed. Cavities have been formed at the interface deformed zone-matrix (Figs. 7A and8A), but they also have been formed by the flow of matter under shear force (Fig. 8B). The formation of these cavities may occur at the prior austenite grain boundary. These cavities also play a role in the debris emission.

From 700 to 800 • C, the difference between the two initial pin hardness becomes greater: there is only little resultant thickness affected by the plastic deformation on the 47 HRC. However, we find some big debris of the pin plastically deformed on the wear track. These big debris contribute to the low deformed thickness that was measured. At 950 • C, the matrix has completely lost its mechanical properties and the plastic deformation consists of movement of matter like a viscous flow (Fig. 9).

Microstructure evolution

It remains the same as initial tempered martensite microstructure for the whole tests except at 950 • C. For this test temperature, we observe a loss of the lath structure going with the carbide coalescence and the formation of new grains on the extreme surface (Fig. 10B). The global aspect is close to the "white layer" observed by Walter et al. [START_REF] Walter | Material failure mechanisms of forging dies[END_REF] (Fig. 10A). These grains have the same composition of the initial X38CrMoV5 (5.33 wt.% Cr; 1.7 wt.% Mo; 0.69 wt.% V; 1 wt.% Si; 0.43 wt.% Mn).

For the 42 HRC pin at 950 • C, these grains are only observed outside of the wear track (2-3 m height). For the 47 HRC pin, these new grains are observed on the whole surface but they are smaller in the wear track (2-3 m height in the wear track; 4-5 m height out of the wear track) (Fig. 10B).

We observe that the carbides are missing on the top of grain. Beneath the surface, carbides have the tendency to take a preferential orientation along the friction direction at the interface new grain-pin matrix.

Influence of oxide and oxidation on friction

From 20 to 200 • C, the oxide debris present in the contact region result from the abrasion of the surface asperities of pin and disc. The debris enter into the contact as metallic debris and are oxidised in the contact under shear force.

At 500 • C, there is a transition: we find metallic debris oxidised but also oxide debris mainly from the disc. The alternation of the metallic and the oxidised zone is characteristic of the mixed zone observed on the surface of the wear track for this test temperature.

At 700 • C, we observe localised oxidation of the X38CrMoV5. These oxides are very rich in chromium and molybdenum (18 wt.% Cr; 9.5 wt.% Mo; 1.17 wt.% Si). However, we do not observe depletion of these elements in the matrix around the oxide. We also remark an internal oxidation at the lath boundary where carbides rich in alloyed elements are located (Fig. 11A).

This inter-lath oxide is rich in chromium peculiar to the oxidation of the X38CrMoV5 [START_REF] Jean | [END_REF] and in molybdenum proper to inter-lath carbides (14 wt.% Cr; 5.8 wt.% Mo; 1.2 wt.% Si). This oxidation may lead to the decohesion of tempered lathes.

We also observe internal oxidation out of the wear track (Fig. 11B). These oxides are always very rich in alloyed elements (16.7 wt.% Cr; 5 wt.% Mo; 4 wt.% Si; 1.62 wt.% V). This oxidation seems to follow a preferential way of diffusion that can be a prior austenitic grain boundary.

At and over 800 • C, we note the presence of a continuous oxide on the whole surface of the pin. This oxide scale (the black interface on the Fig. 12A) locates between the matrix and the disc oxide (1.76 wt.% Cr). This interface may be a pin oxide (6.67 wt.% Cr; 3.1 wt.% Mo; 1.2 wt.% Si; 0.92 wt.% V): the presence of vanadium is proper to the pin. Below 800 • C, there are oxides but they are not continuous on the whole pin surface. Like at 700 • C, we observe an inter-lath oxidation leading to the emission of big debris. The oxides coming from the disc are thicker and very adherent to the pin surface (Fig. 12B).

At 950 • C, we find oxides from both the disc and pin on the surface of the pin. We also find debris of the matrix whose microstructure looks like the one of the pin at the surface (Fig. 13A). As at 800 • C, we remark a thin interface (1-1.5 m) very rich in chromium (13.3 wt.% Cr). This interface is present and constant on the whole surface.

We also find on the surface of the pin multi-layer oxide. All these oxides contain chromium (1.5-12 wt.% Cr) and vanadium proper to the pin (Fig. 13B). The concentration of alloyed elements decrease moving closer the external surface. We observe oxidation in the cavities in the under-layer (Fig. 13C). These oxides are rich in chromium and silicon (9.7 wt.% Cr; 2.3 wt.% Si).

In Fig. 13D, we note the presence of oxides from the disc. These oxides are compacted under normal force. So, these layers of oxides tend to crack due to their fragility, more particularly during the cooling stage after the test, but also under the shear force. We note the smooth and rectilinear shape of the surface in contact with the disc (Figs. 10A and13D).

With the increase of the test temperature, the oxides become thicker on the disc surface and their contribution on friction is not negligible especially the abrasive effect of the hematite which can reduce the affected zone by plastic deformation.

Discussion and conclusion

Whatever the test temperature, we note the presence of a plastic deformation of the lathes of the tempered martensitic steel. With an increase of the pin temperature, the lathes are easier elongated, i.e. the allowed plastic deformation increases. In addition, the initial orientation of the lathes influences the plastically deformed thickness of the sub-surface of the pin.

At 20 • C, the abrasive effect of the metallic debris generated in the contact, justifies the low resultant thickness deformed plastically (mostly by indentation). From 200 to 500 • C, the X38CrMoV5 steel mechanical properties decrease and the deformed zone becomes thicker due to the increase of the ductility. The high density of dislocations in our material allows strong deformation before rupture. The movement of the dislocation is thermally activated. We suppose there is a competition between abrasion and deformation leading to a damage cycle. The duration of this cycle may vary according to the initial hardness of the pin or the test temperature. The existence of a such cycle may justify the differences in the damage observations: at 200 • C, the ductility is predominant. At 500 • C, the abrasion phenomenon gets over the ductility and limits the resultant thickness deformed. The appearance of the oxides contributes to the abrasion, especially hematite.

Between 20 and 500 • C, with the increase of the test temperature, the oxides become thicker on the disc surface and their contribution on friction is not negligible especially the abrasive effect of the hematite which can reduce the resultant affected zone by plastic deformation.

Over 500 and until 800 • C, for the 42 HRC pin, the resultant plastic deformation induces the formation of cavities at the triple point of the prior austenitic grain boundary. For these temperatures, the macroscopic shearing at the interface generated friction coefficient superior to 0.4 that leads to significant macroscopic shear stress.

At the prior austenitic grain scale (about 15 m of grain radius), the 42 HRC allows an elongation of 160% before breaking (measured on the lath elongation in the deformed zone of the micrography). The emission of debris is governed by this elongation capacity of the lathes.

For the 47 HRC material, at the prior austenitic grain scale, the stress accommodation is not took in charge by the plastic deformation: so we observe abrasion and debris emission.

The difference of abrasion resistance between the two hardnesses seems to be due to the difference of microstructure: size and density of carbides and also the dislocations density.

For the higher test temperature, we observe internal oxidation which contributes to the decohesion of pin debris. At 950 • C, the 42 HRC material has a viscous behaviour due to the loss of mechanical properties.

In brief, at the lath scale, the 47 HRC pin has a brittle behaviour which leads to the emission of big debris, even when the 42 HRC allows a "superplastic" deformation (up to 160% of deformation at the lath scale). So, at 700 and 800 • C, the 42 HRC pin is more ductile than the 47 HRC.

The thickness of the plastic deformation is maximum in the back of the contact but the maximum shear stress is in the front of the wear track. It is the flow of matter from the front to the back of the wear track which creates this edge of plastically deformed zone.

The presence of cavities and dimples are a consequence of the plastic deformation. Their size is about a few micrometers but they can influence the emission of big pin debris.

The oxides present at high temperature play the role of solid lubricant by forming glazed surfaces. They also contribute to the enlargement of the wear track that increases the contact surface and therefore decreases the strain and the friction coefficient. The loss of mechanical properties also tends to reduce the friction coefficient especially for the test at 950 • C where the material has a viscous behaviour. The emission of big debris due to the bad ductility of the 47 HRC pin may explain the higher value of the friction coefficient for the higher test temperatures.

For the high temperature, we could think that the decrease of the friction coefficient could reduce the thickness plastically deformed (via the decrease of the shear force), but the loss of the mechanical properties leads to a strong plastic deformation of the tempered martensitic lathes.

The continuation of this study will assess the relation between the macroscopic test parameters and the microscopic damages observed at the extreme surface of the pin.

Fig. 1 .

 1 Fig. 1. Microstructure of the convex radius of different hot work tool steels after 1000 forging cycles. Tool temperature, 200 • C; forging material, C45; forging temperature, 1100-1150 • C; lubricated contact; cycle time, 13 s; hardness of tools, 47 HRC.

Fig. 2 .

 2 Fig. 2. Wear track of the pin after the test at 950 • C.

Fig. 3 .

 3 Fig. 3. Plastic deformation on the surface of the pin. Influence of the initial orientation of the lathes.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Plastic deformation on the surface of the pin.

Fig. 6 .

 6 Fig. 6. Surface of the pin after the test at 500 • C.

Fig. 7 .

 7 Fig. 7. Surface of the pin after the test at 200 • C (47 HRC).

Fig. 8 .

 8 Fig. 8. Surface of the pin after the test at 700 • C (42 HRC).

Fig. 9 .

 9 Fig. 9. Back of the wear track of the pin after the test at 950 • C (42 HRC).

Fig. 10 .

 10 Fig. 10. Microstructure over-etched on the surface of the pin after the test at 950 • C (47 HRC).

Fig. 11 .

 11 Fig. 11. Oxidation on the surface of the pin after the test at 700 • C (47 HRC).

Fig. 12 .

 12 Fig. 12. Oxide and oxidation on the surface of the pin after the test at 800 • C.

Fig. 13 .

 13 Fig. 13. Oxide and oxidation on the surface of the pin after the test at 950 • C.

Table 1

 1

	Friction test conditions
	Pin initial hardness (HRC)	42 or 47
	Normal load (N)	20
	Sliding speed	100 rpm (rotate); 0.167 m s -1 (linear)
	Test duration (s)	3600
	Disc temperature ( • C)	20, 200, 500, 700, 800, 950

Table 4

 4 Evolution of friction coefficient vs. the disc temperature

	Hardness (HRC)	Average friction coefficient (µ)
		20 a	200	500	700	800	950
	42 47	0.60 ± 0.045 0.59 ± 0.060	0.63 ± 0.050 0.60 ± 0.041	0.53 ± 0.020 0.49 ± 0.020	0.46 ± 0.045 0.52 ± 0.020	0.45 ± 0.044 0.44 ± 0.050	0.19 ± 0.040 0.36 ± 0.049

a Disc temperature ( • C).

Table 5

 5

	Evolution of the maximum thickness affected by the plastic deformation
	vs. the disc temperature
	Hardness (HRC)	Plastic deformation maximum (m)
		20 a	200	500	700	800	950
	42	5	14	5	11	5	-
	47	3	10	5	2	2	-

a Disc temperature ( • C).

Acknowledgements

The authors gratefully acknowledge PSA Peugeot-Citroën for supporting these investigations, especially, Mr. Marc Plateau. Dr. Sylvain Jean, from EMAC, is also thanked for his technical assistance in ESEM observations.


Christine Boher
email: christine.boher@enstimac.fr

Olivier Barrau

R Gras

Farhad Rezai-Aria

A wear

Keywords:

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Introduction

Hot metal forging tools used in processes such as forging, rolling or metal sheet forming, are subjected to transient thermal and mechanical loadings. Under these conditions, the contact surfaces of the tools are damaged by complex interactions between wear and thermal fatigue. In addition, the wear and thermal fatigue that are subjected to is coupled with oxidation. It is well known that the wear mechanisms of two bodies in relative movement depend on various parameters and conditions acting conjointly. The loading conditions (stress and speed) the surface and interface properties (dryness, lubrication, oxidation and asperities), the material behaviour (static and cyclic plastic behaviour) and the mechanical properties (flow stress and/or hardness, fatigue and rupture properties) are among the parameters required to investigate the quantitative evaluation of wear.

One of the characterization difficulties encountered here is that surfaces and sub-surfaces cannot be considered as simple laboratory specimens, where stresses and strains are straightforward, but rather as samples subjected to thermo-mechanical loading gradients and micro-structural modifications (Mechanical Mixed Layers for example), requiring appropriate simulations and thermomechanical analysis.

Knowledge of the local stress and strain distributions in the contact region is a key requirement to gain a better insight into the wear mechanisms and thus achieve an appropriate modelling of the wear. The changes in the contact features (e.g. asperity and sub-surface aspects) during the wear process constitute an additional difficulty since the boundary conditions are continuously evolving. Friction evolves during wear, mainly because of the evolution of the contact geometry and also because of the formation and circulation of debris. These complex and combined parameters make wear prediction difficult, in particular where a microscopic or "local" approach to friction and wear is concerned. The coupling effects of material properties and loadings need to be addressed.

Models may be found in the literature dealing with different tribological fields and wear mechanisms [1]. In many cases these are macroscopic and phenomenological approaches aiming to describe the microscopic wear mechanisms occurring at the contact regions. Archard's wear law is one of these well-known quantitative macroscopic models [2]. This law and its modified versions [3][4][5][6], introduce a parameter K that is experimental conditions dependent and therefore needs to be adjusted or estimated for each application, in particular when the industrial applications, such as forming tools, are of concern.

Other authors have found a considerable amount of microscopic evidence revealing that the surface layer close to the "friction surface", in particular in ductile materials, may be subjected to large plastic shearing under sliding. To develop wear models, several authors have used the plastic deformation concept of the surface and the gradient of plastic deformation inwards from the surface [7][8][9][10][11][12][13][START_REF] Hirth | Dislocations in Solids: Application and Recent Advances[END_REF][START_REF] Rainforth | [END_REF][16][17][18].

In delamination theory, the plastic deformation of the more ductile body is caused by the asperities of the harder body and induces a cyclic plastic shear strain that accumulates with repeated cycles.

A further important characteristic, even in sliding friction, involves non-proportional back and forth loading conditions and hydrostatic pressure [19].

The loading undergone by the counterparts in cyclic stressing is similar to that encountered in fatigue loading, but differs in several ways [START_REF] Hirth | Dislocations in Solids: Application and Recent Advances[END_REF]. Firstly, the major deformation mode in friction corresponds to shear [12]. In friction, the shear strain can be much higher than the uni-axial tension ductility, whereas the deformation in compression (due to normal forces in tribological tests) is much lower, with strains of only 1-2%. Secondly, the loading under friction leads neither to constant deformation amplitude nor to constant stress amplitude. Moreover, an asymmetric loading in fatigue mode favours the ratchetting effect.

Furthermore, high hydrostatic pressure may increase ductility by eliminating or retarding the initiation and growth rate of damage [START_REF] Bridgeman | Studies in Large Plastic Flow and Fracture[END_REF][START_REF] Ll | The Mechanical Behaviour of Materials Under Pressure[END_REF]. The friction shear could be compared to torsion strain. So, it could be considered that the hydrostatic pressure could increase ductility and deformation accumulation before rupture by shearing.

Kapoor et al. have studied and are working on the ratchetting concept through a ratchetting failure-based approach to wear modelling, where ratchetting failure occurs when the accumulated deformation exceeds a critical value [11,[16][17][18].

This contribution deals with a wear model based on sub-surface cyclic ratchetting plastic strain accumulations as the basic process of debris formation and rupture. It is considered that the debris is formed when the cumulative plastic deformation in sub-surface layers achieves a critical limit that is governed by the "ductile rupture property" of the material.

Based on experimental observations and detailed microscopic examinations, a material-dependent parameter is introduced to describe the physical wear mechanism that is observed. The model is assessed on a tempered martensitic tool steel, X38CrMoV5-AISI H11, examined on a high-temperature pin-on-disc tribological facility, used in hot metal forming.

In this investigation, attention is only focused on the role of the cyclic plastic strain of the hard material (X38CrMoV5, AISI H11) used as a pin. The role of the cyclic plastic strain behaviour of the more ductile steel (XC18-AISI 1018), used as a disc, is not addressed in this paper. In addition, in order to better disconnect the complex effects and interactions of a high-temperature friction test, it was decided to assess the friction and wear in the specific conditions of a steady-state temperature.

Experiments and materials

High-temperature pin-on-disc tribometer

The investigations were carried out on a high-temperature pin-on-disc tribometer under dry friction conditions. A detailed description of this tribometer is given in [START_REF] Vergne | [END_REF]23]. The disc is a cylinder of 30 mm diameter and the pin has a cylindrical shape (diameter 10 mm) with a truncated conic end with a flat circular surface of 2 mm diameter (surface contact) (Fig. 1).

The disc was heated by a high-frequency induction CELES facility (3 kW). The disc surface temperature was controlled by a bi-chromatic infrared pyrometer. First the disc was heated to a prescribed temperature while the pin was kept out of contact at room temperature. After stabilisation of the disc temperature, the pin was put in contact with the hot disc and the friction test started immediately. The initial contact between the pin and the disc was thus a contact between metal (pin) and iron oxide (disc). The pin temperature increased in several heat exchanges: thermal conduction, radiation, convection, and also generated friction heat (a weak influence). Tribological tests were performed under a normal load of 20 N with a disc rotation speed of 100 rpm (0.13 m/s). The effect of temperature from RT to 950 • C on the friction coefficient evolution and pin wear has been reported elsewhere [24,[START_REF] Barrau | Proceedings of the 6th International Conference on Tooling[END_REF]. The attention of this paper is focused on the results of the experiments performed at 700 • C with different test durations (120, 300, 600, 900 and 3600 s of friction) to measure the wear-loss of the pin. It is interesting to note, however, that the surface temperature of the pin increased from RT to 700 • C after about 5 min. Each test was carried out at least twice to assess the reproducibility of the experiments.

Pin surface and cross-section examinations (parallel to the friction direction) were performed with SEM and ESEM to get a better insight into the micro-structural changes in the sub-surface.

Materials

The pins are machined in 5% chromium double-tempered martensitic steel grade bars (X38CrMoV5, AISI H11) with an initial hardness of 47 HRC, delivered free of charge by Aubert&Duval. Discs are ferrito-pearlitic mild steels (XC18, AISI 1018). The X38CrMoV5 steel is widely used for forging dies, whereas AISI 1018 mild steel is used in forged condition in the automotive industry. The initial hardness of AISI 1018 is about 168HV. The chemical compositions of the two steels are reported in Table 1.

The X38CrMoV5 (AISI H11) steel micro-structure is constituted by randomly oriented lathes. The lath dimensions are about 2 m in thickness and 15 m in length (Fig. 2). This micro-structure has a very high density of tangled dislocations and also a large amount of small carbides, which provide a good strength to the steel at room and high temperatures [START_REF] Mebarki | Proceedings of the 6th International Conference on Tooling[END_REF].

Mechanical cyclic behaviour of X38CrMoV5 (AISI H11)

X38CrMoV5 (AISI H11) is prone to thermal [START_REF] Jean | Proceedings of the 5th International Tooling Conference: Tool steels in the Next Century[END_REF] and mechanical softening [START_REF] Delagnes | Proceedings of the 5th International Tooling Conference: Tool Steels in the Next Century[END_REF][START_REF] Daffos | Proceedings of the High-temperature Fatigue CAMP 2002[END_REF]. Jean et al. [START_REF] Jean | Proceedings of the 5th International Tooling Conference: Tool steels in the Next Century[END_REF] have reported the softening of this steel under several isothermal [START_REF] Delagnes | Proceedings of the 5th International Tooling Conference: Tool Steels in the Next Century[END_REF][START_REF] Daffos | Proceedings of the High-temperature Fatigue CAMP 2002[END_REF] and thermal fatigue conditions. The thermo-mechanical fatigue softening is reported in [START_REF] Oudin | Proceedings of theTemperature-Fatigue Interaction of 9th International Spring Meeting of SF2M, ESIS Publication 29[END_REF]. Detailed Low Cycle Fatigue (LCF) investigations under isothermal and non-isothermal conditions have revealed that X38CrMoV5 tool steel invariably presents a high degree of continuous softening from the early cycles, even at room temperature. The softening is due to the carbides coarsening and dislocation annihilations

Fig. 2.

Tempered martensitic micro-structure of the X38CrMoV5-AISI H11 steel grade. [START_REF] Mebarki | Proceedings of the 6th International Conference on Tooling[END_REF]. In general, the first softening stage is followed by a second linear softening stage, before a rapid decrease of stress due to final crack propagation and rupture of the specimens [START_REF] Delagnes | Proceedings of the 5th International Tooling Conference: Tool Steels in the Next Century[END_REF][START_REF] Daffos | Proceedings of the High-temperature Fatigue CAMP 2002[END_REF][START_REF] Jean | Proceedings of the 5th International Tooling Conference: Tool steels in the Next Century[END_REF][START_REF] Oudin | Proceedings of theTemperature-Fatigue Interaction of 9th International Spring Meeting of SF2M, ESIS Publication 29[END_REF]. Up to 550 • C the fatigue softening rate is "slow" but then increases greatly beyond this temperature [START_REF] Delagnes | Proceedings of the 5th International Tooling Conference: Tool Steels in the Next Century[END_REF]. Daffos et al. [START_REF] Daffos | Proceedings of the High-temperature Fatigue CAMP 2002[END_REF] have shown that fatigue softening is also strain rate dependent and that by lowering the strain rate, the softening increases and its effect becomes very significant when the temperature is higher than 550 • C. Under stress-controlled cyclic experiments, an important progressive and cumulative plastic strain (ratchetting) is observed [START_REF] Velay | [END_REF]. The accommodation rate depends on the test temperature and the stress range amplitude. Fig. 3 shows an example of such behaviour at 300 and 500 • C. At each temperature, the load is increased [START_REF] Velay | [END_REF].

Tensile and torsion ductilities of X38CrMoV5 (AISI H11)

High-temperature rupture ductility under tension (ε c ) and torsion ( c ) of X38CrMoV5 steel (47 HRC) were determined respectively at the "Ecole des Mines d'Albi" and the Aubert&Duval laboratory (Table 2). While the wear experiments were performed at 700 • C, because of technical difficulties, the torsion ductility was measured at a slightly lower temperature (640 • C). As was expected, the high-temperature rupture ductility in tension was very much lower than in torsion (Table 2).

Results and discussion

Friction experiments

Fig. 4 presents the evolution of the measured friction coefficients for different test durations (120, 300, 600, 900 and 3600 s) versus time. A good reproducibility of the friction tests is shown and the coefficients of friction are very close (Table 3) with a constant mean standard deviation of about ±0.02. A steady-state regime of the friction coefficient is reached rapidly (120 s) .

Pin surface damage mechanism

The surface and cross-section of pins were examined postmortem by SEM or ESEM. The surfaces of the flat pins show noor very minor-transferred-wear particles. Wear debris agglomeration in the entrance of the contact zone is not observed; this indicates that the amount of debris particles is not sufficient to cover the contact surface and to form a protective layer. In addition, the transferred oxidized particles (iron oxides) do not develop glazed protective layers. Surface scratches (or grooves) are also observed in the contact zone (Fig. 5a). Parallel, juxtaposed "stripes" with alternately oxide-dominant and metallic-dominant scars are observed (Fig. 5b). Whatever the test duration, the contact surfaces of the flat pins present similar features, presumably indicating the same wear mechanism in steady-state wear regimes (the constant friction coefficient regime). Based on detailed surface and crosssection examinations of flat pins [32], it was concluded that the cumulative plastic deformation is the main mechanism for abrasion wear in the steady-state regimes of X38CrMoV5 AISI H11 steel.

Sub-surface wear damage mechanism

The SEM and ESEM examinations were carried out on crosssections parallel to the friction direction to gain a better insight into the micro-structural evolutions.

In all tests conditions, very drastically elongated tempered martensitic laths were always formed along the sliding direction on the whole sub-surface of the wear contact zone of the pins. Detailed observations revealed that a highly compact laminar "multilayer"-type elongated lath is formed (Fig. 6). This microstructural evolution transforms a randomly orientated lath into a well-paralleled (textured structure), regular and uniform microstructure beneath the pin surface along the contact zone. Such micro-structural feature evolutions (e.g. lath elongation, orientation,) are also observed in industrials tools (Fig. 7). They could be attributed to the lack of necking, that changes stress state from plane stress to plane strain in tensile test, providing the tempered martensitic laths the capability to undergo very highly plastic shear straining, resembling a "super-plastic" capability. The diminution of the elongated lath density observed in depth indicates that inward plastic deformation decreases. These examinations are in good agreement with Kapoor's cyclic plastic deformation statements [18].

Examinations of the pin after different friction durations showed that, regardless of the friction duration, this drastic plastic deformation invariably exists in pin sub-surfaces (Fig. 8), indicating that the wear mechanism is unchanged with the friction time. As reported in Table 4, the thickness of the region affected by the plastic deformation is constant for short friction periods and increases for longer periods (from 900 s to 1 h). It is proposed that the micro-plastic strain accumulates close to the pin sub-surface and attains the ultimate shear rupture strain (critical shear ductility).

In addition, micro-cracks were observed at the extremity of the sub-surface in contact with the disc (Fig. 9a). Detailed observations revealed that individual or few-layer "multilayered" lamellar laths are locally ruptured, forming the inter-lamellar micro-cavities. Theses micro-cavities coalesce and form sharp micro-cracks propagating under shear stresses in an inter-lamellar mode along the sliding direction (Fig. 9). It is generally asserted that when such micro-cracks initiating in the sub-surface attain the free surface, debris are formed. Fig. 9b shows a thin debris worn out from the pin surface similar to the debris that are emitted by wear delamination mechanism [19].

As mentioned previously, friction experiments are conducted under constant normal loading. Nevertheless, it is admitted that the normal loading is not truly constant, and neither are the local stresses. The asperities, for example, contribute to these variations of "local" stresses. It can also be considered that the tangential forces are asymmetric. The local micro-strain accumulations therefore take place under non-equivalent back and forth amplitudes.

These local stress and micro-plastic strain variations are highly conceivable under the continuous rotational sliding of a pin on a disc, giving the local loading and cyclic nature of the Low Cycle Fatigue type [18]. This allows micro-cracks to initiate and propagate. As mentioned earlier, under asymmetric cyclic loadings, the tool steels investigated here present symptoms of cyclic "ratchetting". The accumulation of shear strains ultimately achieves the shear rupture ductility strain along the shear bands and forms the micro-cavities. The complex micro-cavities and micro-cracking interactions and their combined effects lead to the formation and emission of debris.

Wear model

Definition of equivalent damage cycle

The micro-structure evolution of the pin sub-surface confirms that the plastic deformation decreases in an inward direction. The location of micro-cavities or micro-cracking very close to the contact sub-surface indicates that only this region -a few micrometers in depth -reaches the critical shear rupture ductility limit. This heavily sheared sub-surface region is a material-dependent characteristic and acts as the major damage process zone in the steady-state wear regime and also in the emission of debris. An "equivalent damage cycle" (EDC) process consisting of plastic deformation and subsequent abrasion with debris emission is proposed here.

The pin surface and sub-surface are highly deformed under local cyclic shearing stresses. The variation of local loadings induces the accumulation of the deformation cycle by cycle with a "mean" plastic strain increment. This deformation achieves an ultimate shear rupture ductile strain (critical shear ductility). It is supposed that beyond this limit, the sub-layer is ruptured and releases wear debris.

The zone where material is plastically affected is called the "Subsurface Deformed Zone" (SDZ). In all friction tests, the SDZ thickness never exceeded 10 m. The ultimate layer of the sub-surface where material flows is identified as the "Debris Process Zone" (DPZ) and has a constant "mean thickness", "b", along the whole sliding track (Fig. 10 and [10]). It is considered that debris is emitted since the DPZ achieves the critical shear rupture strain (or critical shear ductility). Following debris emission, the SDZ moves only inwards and its extent remains unchanged. The wear process starts again in the newly formed DPZ.

To estimate the value "b", the plastic shear strain versus the subsurface deformed zone needs to be measured. The wear height of the pin (␦h in m), which increases with the duration of the test, will be dependent on this value "b".

Sub-surface strain estimation

The estimation of the plastic strain of the tempered martensitic lathes within SDZ was carried out by using the lath orientations [7] (although this method is more appropriate when the deformed layers are thicker than 10 m). In this approach, two angles ( ) and (Â) are measured along curled laths, in fact depicting the plastic shear flow lines (Fig. 10). By slope-change measurement method it is possible to estimate an equivalent shear plastic strain " p " within SDZ (Eq. ( 1)).

p = tan  -tan √ 3 (1)
The estimated equivalent shear plastic strains are presented in Table 5. As can be observed, the estimated shear stain is always greater than 100% and, as is the case on the extreme surface of the DPZ, it can become greater than 1000%.

Authors [8,9] have reported for the estimated plastic shear strain distribution inwards from the contact surface has an exponential trend. Therefore, we have used the same trend to fit our experimental measurements of equivalent shear plastic strain " p " versus depth (Fig. 11).

The strain decrease in depth is rather abrupt in the first few micrometers. Assuming that DPZ achieves the shear ductility " c = 724%" measured by torsion test at 640 • C (Table 2), this means that the thickness "b" is estimated as 0.3 m of the SDZ (Fig. 11). This is only about 5% of the total affected SDZ depth. It is important to mention that the estimated "b" may in fact underestimate the actual SDZ thickness, since only the residual part of the already plastic-shear-worn surface is visible during post-mortem measurements.

Critical shear ductility

The equivalent damage concept "EDC" is consisting of 4 steps. (i) Plastic deformation of the sub-surface, (ii) plastic deformation accumulation, (iii) rupture of the deformed layer and (iv) debris emission.

The EDC is based on the concept of incremental plastic strain accumulation. When the accumulated plastic strain attains the shear ductility ( c ), local rupture occurs. The shear plastic accumulation (cyclic ratchetting) is a relevant process to represent the EDC that results in the height loss of the pin (␦h in m). Therefore, a constant strain increment ε r (per cycle) is introduced.

The strain increment was evaluated by finite element simulations (FEM) [32] of a pin on a rotating disc using ABAQUS TM 6.2. A mean strain of all surface elements was calculated to estimate a mean increment strain of ( ε r ) about 1.14% per cycle. It should be emphasized that even if the ratchetting-type strain increment ε r can change upon the friction and the wear loading conditions, it is considered as constant per cycle and per number of cycles to failure (N f ). Therefore, the number of cycles to failure of DPZ "N f " is estimated from the ratio between the shear ductility and the strain increment (Eq. ( 2)).

N f = c ε r (2)
The total duration of the friction test is converted into a number of cycles "N" corresponding to the total sliding length "d", for the given friction test, divided by the diameter of the circular pin contact surface (2a) (Eq. ( 3)).

N = v × t (2a) (3)
With d = v × t (m) where "v" is the disc rotating speed (m/s), "t" is the friction duration (s) and "a" is the initial pin contact radius (10 -3 m).

It is assumed that under steady-state wear regime, the pin height loss (␦h in m), can be modelled as a linear function of the DPZ thickness "b" by considering the number of cycles to failure (N f ) and the total number of cycles specific to the test duration (N) (Eq. ( 4)).

␦h = b N f × N (4)
Following the determination of the above mentioned parameters (v, b, N, N f , ε r , c ) for the X38CrMoV5 (AISI H11) pin, the wear height ␦h was predicted by Eq. (5).

␦h = b N f × N = b × ε r c × N = v × t × ε r (2a) × c × b (5)
The experimental and predicted wear results (wear height ␦h) for all friction experiments at different durations are compared in Table 6 and Fig. 12.

Fig. 12 shows the good correlation between calculated (predicted) and experimental wear height for all friction tests performed between 900 and 3600 s. As reported in Table 6 and seen in Fig. 2, predicted wear height is underestimated for short period experiments. As pins are initially at RT, for short-time experiments, the periods of the wear under transient temperature and steadystate temperature regimes become very comparable. It is assumed that the critical strain to fracture (rupture ductility) is constant for the steady-state regime but it is known that the rupture ductility decreases with lowering the temperature. The use of a lower rupture ductility value, for short-time tests, could thus be expected to lead to greater wearing heights.

In addition, the strain increment is also temperature-dependent and it can increase with temperature. This could explain the higher experimental and estimated wear height for short-time tests. The next step in the development of the model would be an expression of the different parameters as a function of time and temperature. Another point to take into account is that the model considers that an "equivalent" height is removed (expressed as a mean thickness b) over the whole pin contact surface. The entire wear surface of the pin does not break with a value of "b" strictly at the same time. At this stage of development of the model, X38CrMoV5 AISI-H11 thermoplastic softening and the sliding speed effects are not taken into consideration in FEM simulations. In fact, the sliding speed is assumed to be sufficiently slow (isothermal condition) for frictionally generated energy not to have a drastic influence on the temperature (700 • C) nor thus on the material behaviour. As mentioned, the thickness of the sub-surface zone affected by the plastic deformation must be larger than the visible experimentally observed and measured thicknesses.

Finally, it is agreed that the measured height loss (␦h) can correspond to Archard's law, because Archard's law is also a wear law based on dissipated energy. The main difference between Archard's law and the wear model presented in this paper is found in a scale level aspect. Archard's law can be considered as macroscopic and this new model gives a physical view of the description of the wear mechanism (in the case of this steel grade and more precisely in the case of this typical micro-structure).

Conclusions

These investigations examine the friction and wear behaviour and the wear mechanism of a double-tempered martensitic tool steel X38CrMoV5 AISI-H11 (47 HRC, as pin). A hightemperature pin-on-disc tribometer was used with a flat surface pin, X38CrMoV5 AISI-H11-47 HRC and a mild XC18 disc.

It was observed that the whole sub-surface of the pin contact area suffered significant plastic deformation. Post-mortem SEM observations showed that parallel-juxtaposed "strip-like bands" or a lamellar "multilayered" micro-structure, are formed on the sub-surface along the sliding direction. The lamellar "multilayered" micro-structures revealed that lathes are heavily elongated, as much as 300% or more. Identical plastic deformation and wear mechanisms are invariably observed in a "steady state friction versus time" regime.

A new wear model is proposed based on cyclic plastic strain accumulations (the cyclic ratchetting concept) and the shear ductility criterion as a local failure process mechanism. It is considered that when the cumulative shear plastic strain at the sub-surface attains a critical strain limit (shear rupture ductility), the individual lamellar layers -or a small number of them -are locally ruptured, forming the inter-lamellar micro-cavities. These microcavities coalesce and form sharp micro-cracks that propagate under shear stresses. This propagation is along the sliding direction and mostly takes place in an inter-lamellar manner which eventually leads to debris emission. Interrupted tests show that the pin geometry (flat surface) enhances the ejection of wear debris out of the contact surfaces and thus the debris flow does not significantly participate in the wear mechanism.

The model takes into account the mean strain increment ( ε r ), the number cycles (N, related to disc rotation speed), a characteristic material-dependent sub-layer wear thickness (b) and the critical strain to fracture (shear rupture ductility, c ). The average plastic strain increment is estimated by FEM numerical simulation of the friction of pin-on-disc.

A very good correlation between the experimental and predicted wear heights versus number of cycles or time is obtained. The deviation is less than 20% for high test durations. The model underestimates the wear heights for the short-time tests due to the transient effects prevailing in the initial regimes of friction versus time experiments.

Fig. 1 .

 1 Fig. 1. Schema of the pin geometry (the conic angle is 45 • ).

Fig. 3 .

 3 Fig. 3. Stress-controlled experiments performed at 300 • C (left), 500 • C (right) (initial total strain ε = ±0.8%) [31].

Table 2 Fig. 4 .

 24 Fig. 4. Variation of the friction coefficient as a function of friction durations at 700 • C under 20 N normal load.

Fig. 5 .

 5 Fig. 5. SEM flat pin wear surface observations (20 N-700 • C-3600 s) (sliding direction right to left).

Fig. 6 .

 6 Fig. 6. Tempered martensitic laths, elongated and highly deformed by plastic shear staining on the pin sub-surface after 1 h of friction (700 • C-20 N-3600 s).

Fig. 7 .

 7 Fig. 7. A typical hot forging die after 1000 shots of billet at 1100 • C (Tool in X32CrMoV12-28 47 HRC): note drastic plastic elongation of tempered martensitic laths and short cracks filled with oxides.

Fig. 8 . 4 Friction

 84 Fig. 8. SEM micrographs of the pin sub-surfaces versus different durations of friction (700 • C, 20 N). Note: sliding direction is from right to left. Table 4 Maximum and mean thicknesses of the plastically sheared pin's sub-surface region for various friction durations. Friction test durations (s) 120 300 600 900 3600 Thickness (m) affected by plastic deformation (m) or "Sub-surface Deformed Zone" (SDZ) Max value 5 5 5 6 9 Min value 4 4 4 5 6

Fig. 9 .

 9 Fig. 9. MEB micrographs of pin sub-surfaces. Tests performed at 700 • C-20 N-3600 s. Note: sliding direction is from left to right.

Fig. 10 .

 10 Fig. 10. A schematic representation of debris emission from the highly sheared layers on the pin surface according to the "equivalent damage cycle (EDC)".

Fig. 11 .

 11 Fig. 11. Strain as a function of the depth for a total deformed thickness of 6 m.

Fig. 12 .

 12 Fig. 12. Comparison between experimental and calculated wear heights of X38CrMoV5 at 700 • C.

Table 1

 1 Chemical composition of two steels (wt.%).

	Element		C	Cr	Mn	V	Ni	Mo	Si	Fe
	Pin	AISI H11	0.4	5.05	0.49	0.47	0.2	1.25	0.92	Bal.
	Disc	AISI 1018	0.18	<0.4	0.4-0.7	-	<0.4	<0.1	0.15-0.35	Bal.

Table 3

 3 Friction coefficient as a function of test duration.

	Test duration (s)	Friction coefficient
	120	0.45
	300	0.46
	600	0.44
	900	0.48
	3600	0.47

Table 5

 5 Estimated shear plastic strain on top of DPZ for different friction durations.

	Test duration (s)	Estimated mean shear strain " p " (%)
	120	268
	300	371
	600	254
	900	287
	3600	∞

Table 6

 6 Comparison of experimental and predicted wear heights.

	Friction duration (s)
	120	300	600	900	3600

Acknowledgements

The authors would like to acknowledge Aubert&Duval for torsion experiments and delivery of steels free of charge and PSA for financial support during different stages of this work.


C Scandian

Christine Boher
email: christine.boher@enstimac.fr

J D B De Mello

Farhad Rezai-Aria

F Rézaï-Aria

Effect of molybdenum and chromium contents in sliding wear of high-chromium white cast iron: The relationship between microstructure and wear

Keywords:

come

Effect of molybdenum and chromium contents in sliding wear of high-chromium white cast iron: The relationship between microstructure and wear

Introduction

Tabrett et al. [1] gave a range of chromium and carbon contents to define high-chromium white cast iron alloys. The respective content of these elements is between 11 to 30 wt.% for chromium and 1.8 to 3.6 wt.% for carbon. The microstructure of these alloys has been studied by several authors [1][START_REF] Maratray | Facteur Affectant la Structure des Fontes Blanches au Chrome et au Molybdène[END_REF][START_REF] Powell | Proceedings of the 34th Conference Australian Institute of Metal[END_REF][START_REF] De Mello | [END_REF][5]. It is composed of hard primary carbides and/or eutectic carbides (M 7 C 3 type) in a softer iron matrix (i.e. austenitic, martensitic, ferritic, pearlitic or bainitic). By adding the alloying elements such as molybdenum, vanadium, niobium, etc., additional carbides such as M 6 C or M 2 C and MC are formed. These alloys are widely used in the mining, cement, steel making and ceramic industries (crushers, pumps, sieves, etc.) that require materials with excellent abrasion resistance.

Most of the tribological research on white cast iron deals with two-or three-body abrasion resistance with a large range of chemical composition of alloying elements, under various processing conditions and heat treatments.

Generally, wear resistance is dependant on matrix microstructure, carbide types and characteristics (size, morphology, distribution, orientation [6]) as well as the volume fraction, fracture toughness and the hardness of the alloys [7][8][9][10]. It also depends on loading conditions, the features of the tribological environments, the relative movement of the contact surface and the type and size of the abrasive bodies. However, there have been only a, limited number of investigations dealing with sliding wear [11,12]. Milan et al. [12] studied HSS steel and high-chromium cast iron (HCCI) at room and high temperature, showing that, at room temperature, HSS presents a better wear resistance than HCCI.

The addition of molybdenum to a high-chromium cast iron leads to the formation of M 2 C or M 6 C carbides depending on the Cr/C ratio [START_REF] Carvalho | Materials Characterization[END_REF]. Furthermore, the molybdenum content (0.5-3 wt.%) pre-vents the perlitic transformation of the austenite and increases the hardenability [1,[START_REF] Maratray | Facteur Affectant la Structure des Fontes Blanches au Chrome et au Molybdène[END_REF] of alloyed cast irons. A molybdenum content greater than 3 wt.% could improve high-temperature wear resistance. Ikeda et al. [11] have performed sliding wear experiments on a cast iron with a ratio Cr/C of 5. It is shown that by adding molybdenum, M 2 C carbides are formed which contribute to enhancing high temperature abrasion resistances.

The general purpose of this study is to investigate the roomand high-temperature wear resistances of experimental white cast irons with high-chromium and high-molybdenum contents and a Cr/C ratio of 10 [START_REF] Carvalho | Materials Characterization[END_REF]. However, this contribution deals exclusively with the room-temperature results.

The Cr/C ratio of 10 leads to the formation of M 6 C carbides instead of M 2 C carbides [START_REF] Carvalho | Materials Characterization[END_REF]. To study the contribution of M 6 C carbides on the high-temperature wear resistance of these alloys, tribological tests were carried out by using a high temperature pinon-disc tribometer in sliding wear conditions. More precisely, as an initial approach, the aim of this paper is to study and compare the tribological behaviour, in sliding wear, of these different experimental white cast irons at room temperature.

Experimental procedure and materials

Experimental procedure

Friction tests are carried out on a pin on disc tribometer in dry conditions (Fig. 1) [START_REF] Vergne | [END_REF]15]. The discs are 35 mm in diameter and 40 mm thick. They have a continuous rotating movement and the rotating speed can vary from 30 to 3000 rpm (Fig. 2a). The pin has a cylindrical shape (10 mm in diameter, 16 mm in length) with a truncated conic end with a flat circular surface of 2 mm in diameter (contact surface) (Fig. 2b). Before any test, the pin and the disc are first polished down to 1200 grades and then cleaned by acetone and ethanol using ultrasound. Normal loading is carried out by dead weights. The tangential forces (friction) are measured using a strain gauge located in the friction plane. A Kaman inductive sensor (±500 m), located at the extremity of the pin arm, could measure the total wear-loss values (a combination of the pin height loss and depth of the disc wear track).

The friction forces and the total wear loss values are directly recorded during the friction test using software developed on LAB-VIEW. The data sampling rate is 10 Hz. The pin height loss (h) is calculated from the variation between the initial diameter of the contact surface (Di) and its final diameter (Df) (Eq. ( 1)). All diameters are measured by optical microscopy.

h = Di -Df 2 (1)

Set-up conditions

All friction experiments are carried out under the same testing conditions (Table 1). Each friction test is carried out twice for repeatability considerations.

The worn surfaces are examined by optical microscopy, and the cross-sections (along the friction direction) by scanning electronic microscopy and dispersive energy analysis. Topographies of the worn surface of pins and discs are carried out with a quasi-confocal ALTISURF ® microscope with extended zaxis field using Halogen as a light source. Field extension is obtained by spectral coding of the z-axis. The surface topology is reconstructed by contact-less 3D (x-y-z) probe scanning. The resolution of the probe depends on the depth of the field in a range between 1 nm and 300 nm. The measurements are performed with a 350 m probe providing z-axis resolution of 11 nm. The scanning advance step (x, y) is 5 m. The (x, y) area of the 3D surfaces of the disc tracks is 5 mm × 5 mm. The size of the topography area of the pin surface is optimised in order to obtain the image of the whole 3D-surface of the pin. All the 3D disc surfaces and 3D pin surfaces are processed by the roughness analysis software ALTIMAP ® . This method is widely used to measure the depth of the disc wear track.

Materials

The disc material is a low-carbon perlito-ferritic steel, AISI 1018. Pins are composed of white cast irons with different highchromium and high-molybdenum contents. The chromium/carbon ratio is always 10. Samples are first sand cast and natural air-cooled. Prismatic samples (40 mm × 40 mm × 70 mm) are removed from the as-cast samples. Then tribological pins are machined from these samples. Four white cast iron groups have been studied:

• Two groups are hypoeutectic alloys (16 and 24 wt.% chromium).

• One group is an eutectic alloy (28 wt.%Cr).

• One group is a hypereutectic alloy (32 wt.%Cr).

For each group, four alloys with different Mo content (0, 3, 6 and 9 wt.%) are investigated. Fifteen specimens have been prepared and tested (Table 2) (the 28 wt.%Cr-6 wt.%Mo sample was not studied).

The microstructure of the Mo-free hypoeutectic alloys with 16 wt.%Cr, consists of a dendritic ferritic matrix (Fe␣) with interdendritic Maratray pearlite (␣ + M 7 C 3 carbides) [START_REF] Maratray | Facteur Affectant la Structure des Fontes Blanches au Chrome et au Molybdène[END_REF][START_REF] Carvalho | Materials Characterization[END_REF] surrounded by small interdendritic as well as eutectic M 7 C 3 carbides (Fig. 3a). According to the equilibrium phase diagram, the matrix should be austenitic and not ferritic. This phase modification is relevant to the die-casting cooling process.

With Mo-free and 24 wt.%Cr, the microstructure looks the same as that described above because it is still dendritic but composed of ␣/␣ ′ (ferritic and martensitic).

For Mo-free and 28 wt.%Cr (eutectic alloys group) the microstructure consists of more or less mixed strips of ␣ and M 7 C 3 carbides. The carbide size is about 10-20 m (Fig. 3b).

For Mo-free and 32 wt.%Cr (hypereutectic alloy group), the large primary carbides capture a considerable amount of carbon content. The matrix is ferritic due to the slow cooling rate of the cast (Fig. 3c).

The Mo-addition in hypoeutectic alloys impedes the austenitic transformation into pearlite, and facilitates the formation of a martensite microstructure, thus increasing hardenability of the alloy (Table 2). For hypoeutectic alloys, three different phases are present in the matrix dendrites (ferrite ␣/martensite ␣ ′ /austenite ␥). The amount of inter-dendritic M 7 C 3 carbides increases with dendrite size enhancements. New eutectic carbides (M 6 C carbides) coarsened because molybdenum is a carburising element.

The Mo alters the Cr-C equilibrium and modifies the phase diagram domains in eutectic and hypereutectic alloys, which strongly influences the alloy microstructure:

• The as-known eutectic alloy (28 wt.%Cr) becomes a hypereutectic type alloy with primary M 7 C 3 carbides, M 6 C carbides and a ferritic matrix. • The as-known hypereutectic alloy (32 wt.%Cr) keeps the primary M 7 C 3 carbides with a ferritic matrix microstructure and develops M 6 C carbides.

The bulk Vickers hardness of pins (HV10) as a function of chromium and molybdenum contents is given in Fig. 4. For an equivalent chromium weight percentage, when the molybdenum content increases, the hardness is enhanced. The bulk hardness of hypoeutectic alloys can reach 700 (HV10). By addition of Mo, new M 6 C carbides are formed and the matrix is transformed from a single-phase (␣) to a multiphase (␣/␣ ′ /␥). Such a modification is not observed in 24 wt.%Cr with 9 wt.%Mo because the addition of Mo changes the phase equilibrium diagram to a ferritic matrix and therefore the hardness decreases.

The eutectic M 6 C carbides, rich in Mo with a "fishbone" microstructure, are closely linked (embedded) in a matrix phase. Even if hard and large M 7 C 3 carbides (eutectic and primary) are formed, the hardness of eutectic or hypereutectic alloys is slightly lower than the previous ones, for a same amount of Mo content, because the matrix remains in the ferritic phase.

The volume fraction of the matrix is determined by image analysis [START_REF] Carvalho | Materials Characterization[END_REF]. The volume fraction of the matrix decreases with an increase in the content of the alloying elements chromium and molybdenum, since M 7 C 3 and M 6 C eutectic carbides are formed, as well as M 7 C 3 primary carbides. The matrix fraction is always greater than 40% for hypoeutectic alloys regardless of the wt.%Mo (Fig. 5).

Results and discussion

Role of the microstructure on wear results

The evolution of the pin height loss by wear as a function of chromium and molybdenum contents is reported in Fig. 6. Regardless of the chromium and molybdenum contents (wt.%), when the matrix microstructure is fully ferritic, the values of pin height loss are the highest (Fig. 6). When the matrix microstructure is multiphased (␣/␣ ′ or ␣/␣ ′ /␥), the values of pin height loss decrease considerably and could be close to zero, whatever the Cr or Mo content (wt.%) may be. For a given Cr content, the pin height loss is dependent on the bulk hardness and on the Mo content (wt.%) and when the bulk hardness increases, the pin height loss decreases. However, for the same level of bulk hardness (e.g. 24 wt.%Cr-3 wt.%Mo-Fig. 6b and 32 wt.%Cr-9 wt.%Mo-Fig. 6d), the pin height losses are not equivalent. The pin height loss is always higher when the matrix is ferritic (32 wt.%Cr-9 wt.%Mo-Fig. 6d). These observations lead to the conclusion that the matrix microstructure is a more pertinent parameter to control wear loss than bulk hardness.

When Mo content increases, the matrix of hypoeutectic alloys (16 wt.%Cr, 24 wt.%Cr) is multiphased, Mo-rich carbides (M 6 C type) appear and the pin height loss is low (16 wt.%Cr-3 wt.%Mo-24 wt.%Cr-3 wt.%Mo) (Fig. 6b) and could be close to zero (16 wt.%Cr-6 wt.%Mo-24 wt.%Cr-6 wt.%Mo-Fig. 16 wt.%Cr-9 wt.%Mo-Fig. 6d). As the volume fraction of the matrix falls, the carbides fraction rises, and thus the pin height loss decreases because the global hardness increases due partly to the contribution of M 6 C carbides but mainly to the strengthening of the matrix by solid solution alloying. In addition, the involvement of M 6 C carbides also favours the wear resistance.

The special behaviour of the 24 wt.%Cr-9 wt.%Mo alloy (Fig. 6d) is significant. Initially the 24 wt.%Cr has a hypoeutectic chemical composition with a multiphased (␣/␣ ′ ) matrix. For low Mo contents (3 wt.% and 6 wt.%Mo), the matrix microstructure is always multiphased (␣/␣ ′ /␥), and the volume fraction of carbides increases and the quantity of M 6 C carbides grows. In this case, the pin height loss is very low (close to zero). For high content Mo alloys (9 wt.%), the phase equilibrium is shifted towards the ferritic-dominant domain [START_REF] Carvalho | Materials Characterization[END_REF]. The bulk hardness falls and the pin height loss increases. The volume fraction of carbides does not prevent wear.

The eutectics alloys (28 wt.%Cr), as well as the hypereutectic alloys (32 wt.%Cr), keep a ferritic matrix regardless of the Mo content. The large M 7 C 3 carbides and the enhancement of M 6 C carbides favour the wear resistance but the pin height loss is not close to 0 (Fig. 6c andd).

These wear results assume that the matrix microstructure plays an important role in wear loss. A ferritic matrix with a dendritic microstructure and eutectic M 7 C 3 carbides (e.g. 16 wt.%Cr-Mo-free) seems to be more resistant to shear stresses than a ferritic matrix with a more "lamellar" microstructure and eutectic or primary M 7 C 3 carbides (Mo-free and 24 wt.%Cr or 32 wt.%Cr). The same result is observed with a ferritic matrix with a dendritic microstructure and eutectic M 7 C 3 and M 6 C carbides (24 wt.%Cr-9 wt.%Mo) in comparison with a ferritic matrix with primary M 7 C 3 carbides and eutectic M 6 C carbides (32 wt.%Cr-9 wt.%Mo) (Fig. 6d).

The topography measurements of the pins clearly reveal the different pin wear morphologies. Considering the scale of roughness measurements, for pins with a single-phased ferritic matrix and eutectic or primary M 7 C 3 carbides, the diameter of the wear sur-face of the pin is greater than the initial diameter and the pin surface loses its flat feature to take on a bowed shape (Fig. 7a). Thus, the shape of the wear track of the disc self-adjusts to be in good conformity with its counter-face (Fig. 7a ′ ). The edges of the pin friction surface sliding "parallel" to the rotation direction are more easily worn because they are the regions of high stresses (friction between the walls of the disc wear track and the pin edges). For the flat pins, the Hertz maximum pressure is located on the pin perimeter. The Hertz pressure could also explain the bowed shape of the pin. The depth of the disc wear track is also high (>400 m). The friction contact is established between two ferritic materials. Examinations of cross-sections of the pin (28 wt.%Cr-Mo-free) (Fig. 8) show that pin debris is constituted of matrix particles and, in a lesser proportion, fragments of the large M 7 C 3 carbides broken under shear stresses. Large M 7 C 3 eutectic carbides are brittle and very sensitive to friction forces, showing a lot of micro-cracks. In addition, the plastic deformation of the matrix, at pin subsurface, contributes to the carbide debris formation (Fig. 8).

For higher Cr and Mo contents (32 wt.%Cr-3 wt.%Mo), the eutectic M 6 C carbides are tightly embedded in a matrix phase (Fig. 9). Contrary to the M 7 C 3 carbides, these M 6 C carbides do not present micro-cracks, but considering that they are mixed in a ductile phase, a very low plastic deformation is observed. Therefore, it is supposed that they contribute to improving the wear resistance and are not removed from the contact zone as debris. They act as a network to strengthen the shear resistance of the alloy.

The disc and pin debris are significantly involved in the friction contact and contributes to the wear of the two counter-faces.

For alloys with a multiphased matrix, the pin surface keeps its initial flat feature since its wear is very low (Fig. 7b). The shape of the disc wear track is also in good conformity with the pin shape (Fig. 7b ′ ). Examinations of cross-sections of the pin (24 wt.%Cr-6 wt.%Mo) (Fig. 10) show some micro-cracks of the M 7 C 3 carbides and no plastic deformation of the multiphased matrix.

For alloys with a single-phased matrix and large primary M 7 C 3 carbides, the final shape is slightly bowed (Fig. 7c-c ′ ) because there is an intermediate level of wear. The pin cross-section (32 wt.%Cr-6 wt.%Mo) (Fig. 11) always shows micro-cracks of M 7 C 3 The pin surface evolution is also studied through the evolution of the Sa value (m), which is the arithmetic mean deviation of the surface directly measured from worn surface without any filtering operations (without cut-off). The higher the Sa value, the more the pin loses its initial shape. The initial value of Sa (mean value measured from all the pins) is 8 ± 2 m. The values of "Sa" greatly superior to 8 are assigned to ferritic matrix alloys (Fig. 12). The values of "Sa" close to 8 are obtained for multiphased matrix alloys or when the wear loss is very low. The values of Sa are in good agreement with pin height loss tendencies.

Friction results

Fig. 13 illustrates the general aspect of the evolution of friction coefficient versus test duration and it is representative of all tests. Two significant trends are observed:

For alloys with a single-phased matrix and a high matrix volume fraction (>60%), the mean friction coefficient " " is higher than 0.7. The evolution of the friction coefficient versus test duration is mainly constant but displays two stages (Fig. 13). At the beginning of the friction test, the amplitudes of the fluctuations of the friction coefficient values are large (0.6 < < 1.1). The high values and large fluctuations of the friction coefficient confirm that the matrix is a rather ductile or soft type material. Following this stage, the amplitude of the friction fluctuations decreases significantly in the second stage.

For the same chromium content (hypereutectic alloys: 32 wt.%Cr), the duration of the first stage is dependent on the volume fraction of carbides (Fig. 14). When the Mo content increases, the M 6 C carbides volume fraction increases as does the bulk hardness; the volume fraction of M 7 C 3 carbides stays unchanged but their size increases enormously [START_REF] Carvalho | Materials Characterization[END_REF].

As of today, the two main hypothesis, we can develop for the break in the friction evolution for a single-phased matrix alloy is a modification of the ferritic matrix and a third layer made up of debris which could occurs in the contact. The plastic deformation of the matrix could increase its local hardness and lead to this behaviour. In addition, the lower the volume fraction of the matrix (or the higher the volume fraction of the carbides) the shorter is the time in which the modification of the evolution of the friction coefficient happens. A third body layer could made up of debris could accommodate the friction evolution. In the two cases, more investigations are to be carried out.

For alloys with a multiphased matrix, the friction curves versus test duration are different (Fig. 15). They are no longer regular but display large variations during the test. The mean value of the friction coefficient is a little lower than 0.7 (24 wt.%Cr-Mo-free; 24 wt.%Cr-3 wt.%Mo; 24 wt.%Cr-6 wt.%Mo). In this case, it should be noted that even if the friction coefficient is high, the wear loss of the pin is very low.

Conclusions

Room temperature and sliding wear behaviour of experimental white cast irons with various contents of chromium (16 wt.%, 24 wt.%, 28 wt.% and 32 wt.%) and molybdenum (0 wt.%, 3 wt.%, 6 wt.% and 9 wt.%) were investigated.

The wear results highlight that the microstructure of the matrix displays a strong influence on sliding wear resistance: when the matrix is ferritic single-phased, regardless of the Mo content, pin wear loss is significant. When the matrix is multiphased (␣/␣ ′ /␥), the wear loss tends towards zero. Another point is that matrix microstructure is more significant in dictating wear loss than bulk hardness. In fact, bulk hardness is less relevant as a wear control parameter. For the same Cr content and a single-phased matrix, the hardness increases with Mo content and the wear loss decreases. But for an equivalent level of hardness, the wear loss is always higher when the matrix is strictly ferritic. In addition, the ferritic matrix can be more easily plastically deformed under frictional tangential forces and the plastic deformation of the matrix contributes to the carbide micro-cracks and debris formation.

Micro-cracks are always clearly observed with eutectic or primary M 7 C 3 carbides but never with M 6 C (at the level of measurement resolutions used). These last carbides seem to contribute much better to enhancing the wear resistance of the alloy.

The friction results are also very interesting. For a single-phased matrix, the friction curves display two stages. First, there is a stage with high amplitudes of fluctuations in the friction coefficient and a high average friction and, after this stage, a second stage with low fluctuation amplitudes. This result is very significant with 32 wt.%Cr, where the duration of the first stage decreases with the Mo content. For a multiphased matrix, the friction curves do not display the same behaviour.

Fig. 1 .

 1 Fig. 1. General view of the pin-on-disc tribometer.

Fig. 2 .

 2 Fig. 2. Schemata of the tribological pin and disc.

Fig. 3 .

 3 Fig. 3. Typical microstructures of the different groups of alloys: (a) hypoeutectic alloys; (b) eutectic alloys; (c) hypereutectic alloys [13].

Fig. 4 .

 4 Fig. 4. Macro Vickers hardness (HV10) of the different alloys as a function of chromium and molybdenum contents (wt.%).

Fig. 5 .

 5 Fig. 5. Volume fraction of matrix (%) in the different alloys as a function of chromium and molybdenum contents (wt.%).

  6c

Fig. 6 .

 6 Fig. 6. Pin height loss "h" (hachured rectangles) and bulk hardness of the alloys (full lines) as a function of Cr and Mo (wt.%) in relative matrix microstructures (a: 0 wt.%Mo; b: 3 wt.%Mo; c: 6 wt.%Mo; d: 9 wt.%Mo).

Fig. 7 .

 7 Fig. 7. Topographies of the 3D surfaces of the pin (above: a; b; c) and a portion of the counter-face disc wear track (below: a ′ ; b ′ ; c ′ ). The black arrows indicate the sliding directions.

Fig. 8 .

 8 Fig. 8. Examination of the pin cross-section (28 wt.%Cr-0 wt.%Mo). Ferritic matrix with eutectic M7C3 carbides. The white arrow indicates the sliding direction.

Fig. 9 .

 9 Fig. 9. Examination of the pin cross-section (32 wt.%Cr-3 wt.%Mo). Ferritic matrix with primary M7C3 carbides and eutectic M6C carbides. The white arrow indicates the sliding direction.

Fig. 10 .

 10 Fig. 10. Examination of the pin cross-section (24 wt.%Cr-6 wt.%Mo). Multiphased matrix with eutectic M7C3 carbides and eutectic M6C carbides. The white arrow indicates the sliding direction.

Fig. 11 .

 11 Fig. 11. Examination of the pin cross-section (32 wt.%Cr-6 wt.%Mo). Single-phased matrix with primary M7C3 carbides and eutectic M6C carbides. The white arrow indicates the sliding direction.

Fig. 12 .

 12 Fig. 12. Value of the arithmetic mean deviation of the surface "Sa" (m), from the 3D surface, versus Cr and Mo contents.

Fig. 13 .

 13 Fig. 13. Evolution of friction coefficient with test time (28 wt.%Cr-Mo-free).

Fig. 15 .

 15 Fig. 15. Friction coefficient versus test duration (24 wt.%Cr-3 wt.%Mo).

Fig. 14 .

 14 Fig. 14. Friction coefficient versus test duration (32 wt.%Cr): diminution of the first stage of the friction (a: 32 wt.%Cr; b: 32 wt.%Cr-6 wt.%Mo; c: 32 wt.%Cr-6 wt.%Mo; d: 32 wt.%Cr-9 wt.%Mo).

Table 1

 1 Friction experimental conditions.

	Sliding speed	Normal load	Test duration	Ambient
	0.3 m/s	20 N	1800 s	Room temperature

Table 2

 2 Microstructure of different white cast irons as a function of chromium and molybdenum contents (wt.%).

	Mo (wt.%) Cr (wt.%)
		16	24	28	32
	0	Hypoeutectic alloy, matrix: ␣;	Hypoeutectic alloy, matrix: ␣/␣ ′ ;	Eutectic alloy, matrix: ␣; carbides:	Hypoeutectic alloy, matrix: ␣;
		carbides: M7C3	carbides: M7C3	M7C3	carbides: M7C3
	3 6	Hypoeutectic alloy, matrix: ␣/␣ ′ /␥; carbides: M7C3 + M6C	Hypoeutectic alloy, matrix: ␣/␣ ′ /␥; carbides: M7C3 + M6C	Eutectic alloy ⇒ As-hypereutectic alloy, matrix: ␣; carbides: M7C3 + M6C	Hypereutectic alloy, matrix: ␣; carbides: M7C3 + M6C
	9		Hypoeutectic alloy, matrix: ␣;
			carbides: M7C3 + M6C

Acknowledgements

The authors would like to acknowledge the technical assistance and contributions of S. Leroux and S. Tovar from the Ecole des Mines, Albi.