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carbon composite friction
Wear 263 (2007) 1220–1229
Interdependence between wear process, size of detached particles and CO2 production during carbon/carbon composite friction Haytam Kasem a,∗ , Sylvie Bonnamy a , Bernard Rousseau a , Henriette Estrade-Szwarckopf a , Yves Berthier b , Pascale Jacquemard c a
Centre de Recherche sur la Mati`ere Divis´ee, UMR 6619 CNRS-Universit´e d’Orl´eans, 1B, rue de la F´erollerie, 45071 Orl´eans Cedex2, France b Laboratoire de M´ ecanique des Contacts, UMR 5514, CNRS-INSA de Lyon, 20, Avenue Albert Einstein, 69621 Villeurbanne Cedex, France c Messier-Bugatti, 7, Avenue du Bel Air, 69627 Villeurbanne Cedex, France Received 18 September 2006; received in revised form 23 January 2007; accepted 23 January 2007 Available online 23 May 2007
Abstract This work is focused on the study of the wear mechanisms occurring during C/C composite friction. The friction experiments are performed on a pin/disc tribometer coupled to a mass spectrometer. This set-up allows the in situ gas analysis in the contact during friction. Worn surfaces and polished sections done perpendicularly to the rubbing surface are characterized at several scales by optical and scanning electron microscopies to follow the degradations of the material induced by friction. The damages are correlated to the flow source, the size of detached particles and the CO2 production in the contact during friction at different temperatures. © 2007 Elsevier B.V. All rights reserved. Keywords: Tribology; C/C composite; Wear; Mass spectrometry; CO2 ; Flow source
1. Introduction The carbon/carbon (C/C) composites have a low density and preserve their mechanical and thermal properties at very high temperature. Therefore, they have become the best candidate as aeronautical brake disk material, being efficient in the different types of aircraft braking operations. To assure braking effectiveness, comfort and transportation safety, a stable friction coefficient is required, combined with a low wear rate to reduce costs. In the literature, the effects of densification cycles [1], structure [2,3] and fiber orientation [4] of carbon/carbon composite on the tribological properties of C/C composites have been well described. The relations between wear and decisive parameters such as the sliding speed [5,6], the load [7], the temperature [8] and the atmosphere [9] have been demonstrated, however, the wear mechanisms remain unclear. Numerous authors demonstrated that an abrupt transition of friction coefficient from a weak value (∼0.15) to a high value (∼0.4) takes place during
∗
Corresponding author. Tel.: +33 238255815; fax: +33 238255376. E-mail address: [email protected] (H. Kasem).
0043-1648/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2007.01.077
carbon/carbon composite friction, when the friction conditions become more severe, for instance when temperature is increased. This transition phenomenon is associated with a strong particle detachment, this regime was named “dusting regime” [10,11]. Furthermore, C/C composites are known to be chemically very reactive and sensitive to the oxidation, especially at high temperature, depending on their texture [12,13]. The tribological properties were shown to evolve under oxidizing conditions [14,15]. So, to a better knowledge of the tribological behavior of carbon/carbon composite during friction, it became necessary to couple mechanical and physicochemical approaches [16–18]. Recently, Gouider et al. studied the physicochemical reactions occurring in situ in the contact during friction, thanks to a mass spectrometer directly coupled to the tribometer [19]. They evidenced for the first time, that a sudden carbon dioxide (CO2 ) production and an oxygen (O2 ) consumption perfectly coincide with the friction coefficient transition. In order to progress in the understanding of the wear and friction mechanisms, the aim of this paper is to precisely correlate the surface [20] and subsurface [21,22] degradations resulting from friction at different temperatures to the flow source (particle detachment) [23] and to the gas exchanges occurring in the contact during friction. For that, the friction experiments
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are performed at temperature ranging from 150 to 450 ◦ C, on a laboratory pin-on-disc tribometer equipped with a mass spectrometer. 2. Experimental 2.1. Materials The materials used are carbon/carbon PAN-CVI composite, SEPCARBTM . They consist of 3D ex-PAN fiber mats densified with pyrocarbon (rough lamellar texture). One sample is treated at high temperature, i.e. over 2000 ◦ C after densification (“G” material); the other one is untreated (only densified) “NG” material. For each experiment the pin and the disc are machined from the same carbon composite (G or NG). 2.2. Set-up: pin-on-disc tribometer and mass spectrometer The friction experiments are performed on a laboratory pin-on-disc tribometer with vertical axis coupled to a mass spectrometer. This set-up allowing the analysis of the gas exchange in the contact during friction. Two external heating, one for the pin the other for the disc, permit to impose and to maintain the chosen temperatures during friction (Fig. 1). The disc is 160 mm in diameter and 8 mm in thickness and the pin is 30 mm in diameter and 8 mm in thickness, with a hole of 7 mm at its center to introduce the capillary of the mass spectrometer. During friction, the pin center is shifted about 51 mm from the disc center (see Fig. 3). Experiments are carried out in air, under a relative humidity ranging from 45 to 55%. The imposed parameters are the following: • a constant linear sliding speed of 2 m/s at the center of the track friction; it corresponds to about a 375 rpm disc rotation, • a contact pressure equal to 0.5 MPa, • a preliminary running-in of the system pin and disc, performed at 200 ◦ C leading to about 150 m wear. This preliminary step is done to avoid trace machining and to assure conformity and reproductibility of the surfaces. The system is then left 12 h in equilibrium under air without disassembling the parts. The obtained surface is our original surface. The optical microscopy images of these surfaces are similar to the ones given in Fig. 8a and c.
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• a pin and disc heating ramps equal to 25 ◦ C/min. Once reached, the desired temperature is maintained during all the experiment, • for the two materials (G and NG), the trials were done at different imposed temperatures corresponding to cold taxiing (150 ◦ C), heat taxiing (450 ◦ C) and intermediate ones (250 and 350 ◦ C), • each friction experiment lasts about 30 min. During an experiment the following parameters are measured (Fig. 2): • The tangential force undergone by the rotating disc, measured through a force gauge. Knowing the load, the friction coefficient μ is deduced (Fig. 2a). • The wear, estimated through the distance between the upper pin surface and a fix reference. This distance is measured via a displacement gauge and includes the pin and disc wear (thickness loss), the third body thickness and the thermal dilatation of the mechanical system around the pin and the disc. At the beginning of the experiment, the measured distance decreases due to the thermal sensitivity of the system, this part of the curve is thus meaningless. When a linear positive regime is established and temperature stabilized, wear rate (expressed in m/min) is measured as the slope of the separation curve versus time (Fig. 2b). This “wear rate” only takes into account the thickness decrease, not the weight loss due to oxidation. • The pin and the disc temperatures measured through thermocouples located at about 1.5 mm from the contact. Taking into account this distance, this temperature will be called thereafter “subsurface temperature” (Fig. 2c). • The gas exchanges taking place in the contact, detected by the mass spectrometer (Fig. 2d–f). The main information is brought from the signals coming from carbon dioxide, oxygen and water vapor (respectively masses 44, 32 and 18). The gas volume enclosed in the contact is not tightly isolated from the environment, its pressure is almost equal to atmospheric pressure. A positive (or a negative) variation of a gas signal means an increase (or a decrease) of its partial pressure, i.e. a production (or a consumption). Measurements are only semi-quantitative: a calibration is not possible because the gas conductance between pin and disc really evolves during friction. O2 consumption is almost equal to CO2 production [19] (Fig. 2d and e), and in the results only CO2 concentration is reported. Its average concentration is directly measured
Fig. 1. Experimental device: laboratory tribometer in pin/disc configuration coupled with a mass spectrometer.
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Fig. 2. Example of tribological and gas analysis data for G material tested at 250 ◦ C: (a) friction coefficient, (b) wear, (c) disc subsurface temperature, (d), (e) and (f) variation of respectively O2 , CO2 , H2 O partial pressure in the contact.
through its partial pressure in the contact (expressed as an electric current in A unit) (Fig. 2e). • Transition: when temperature increases, at first, the friction remains weak, then all the mechanical and gaseous measured parameters undergo an abrupt transition. The friction coefficient (μ) suddenly increases then decreases to a stable permanent value (Fig. 2a). The CO2 partial pressure follows the same behavior, it means that an oxidation process takes place as soon as transition occurs (Fig. 2e). After the transition, as long as μ remains high, the oxidation process goes on, it is responsible for dusting conditions [10,11]. During the friction tests and after the transition, the ejected particles from the contact are captured by means of a piece of scotch-tape set parallel to the friction direction (Fig. 3). This procedure, even though selective because the finest ejected particles probably do not reach the scotch-tape, avoids their
agglomeration and allows an easier determination of their size for a comparison of the experiments. The ejected particle sizes are determined from optical microscopy images (magnification 200×) in using image analysis processing.
Fig. 3. Collect of the ejected particles from the contact during friction experiment.
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In order to study the pin-disc interface and the third body remaining in the contact, after the friction experiments, the contact is maintained under pressure and the periphery of the pin is glued with a commercial epoxy resin (Araldite) to the disc. Then the pin and disc set is embedded in an epoxy resin and sections, sawed perpendicularly to the rubbing surface, are polished for their characterization by optical and scanning electron microcopies. For the images interpretation of such polished sections, it is important to notice that, the disc and pin are glued just after the disc rotation stop. The wear particles, which should be ejected, are still present either around the pin or in the contact. It is well admit that, in dynamic, the interface thickness changes permanently from one place to another. In static (which is the context), the amount of third body present in the contact will be more abundant and consequently the interface thickness will be overvalued. Furthermore, we have to be cautious during polishing, in order not to deform the interface or to add debris of polishing. Characterizations of the worn surfaces and pin–disc interface were done by optical microscopy (OM, Leica DM IRM) and by scanning electron microscopy (SEM, Hitachi S4200 equipped with a field emission gun). For SEM imaging, the acceleration voltage used is 1 kV, in order to limit the secondary electron analysis to the outermost surface [20]. OM characterization is performed between crossed polarizers with addition of a retarder plate (λ plate).
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Fig. 4. Analysis of CO2 production during dynamic and static experiments.
3. Results and discussion
between CO2 emission and O2 consumption (Fig. 2d and e) [24]. To better understand the origin of CO2 , the CO2 curve obtained during dynamic friction experiment in the reactive regime was compared with the one obtained in a static heating test (up to 500 ◦ C). During dynamic experiment, CO2 is produced in a large amount, whereas during static heating, only a very weak CO2 amount is produced (Fig. 4). Obviously, mechanical motion is necessary to produce CO2 , which is also associated with third body production (see next paragraph).
3.1. Friction transition and CO2 production in the contact
3.2. Wear and CO2 production in the contact during friction
As seen in Fig. 2a–f, all friction experiments show, at first, a weak wear regime, called “non reactive”. It is characterized by a weak friction coefficient (from 0.1 to 0.2), with no wear detected by our device. Then, after a brutal transition, a high wear regime called “reactive” occurs. It is characterized by a high friction coefficient (from 0.3 to 0.4) and high wear rate [19]. The gas analyses in the contact bring to light that only the “reactive” regime is systematically accompanied by a CO2 production and an O2 consumption, with always a strong complementarity
For both G and NG materials, the wear rate and the average CO2 concentration in the contact have been measured at four temperatures (T) ranging from 150 to 450 ◦ C. Taking into account our experimental device, neither the third body nor the CO2 production rate could be really calibrated. We assume that the CO2 partial pressure given by the mass spectrometer is proportional to the CO2 production rate. The amount of debris produced per minute in the contact cannot be directly measured, but it is proportional to the wear rate, if we assume
Fig. 5. (a) Decrease of wear rate (m/min) as temperature increases. (b) Decrease of CO2 production as temperature increases.
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Fig. 6. (a) CO2 production as a function of wear rate. (b) Ratio of CO2 production over wear rate as a function of the subsurface temperature.
that oxidation has no effect on the pin + disc thickness decrease measured on the tribometer. Results are reported in Fig. 5a and b. The wear rates decrease as T increases for both materials, the G one being more sensitive to temperature. Similar decreases are observed when CO2 production in the contact is reported as a function of T (for the first time such data are presented) (Fig. 5b). This behavior is more surprising, because in apparent contradiction with the usual thermal activation responsible for oxidation at high temperature. In order to solve this contradiction, the origin of the CO2 production
has to be determined, i.e. the origin of the carbon components able to oxidize in the contact. During friction, both the first bodies and their debris may undergo oxidation. However, the debris, composed of a whole of particles, are probably more sensitive to oxygen than the first bodies. Such affirmation is in agreement with the results of Fig. 5b. Indeed, the G material shows the higher wear rate, consequently it produces a higher amount of debris during friction and has a higher CO2 production. In the following discussion, we will assume that the whole CO2 detected originates only from the third body, neglecting the
Fig. 7. OM images of the ejected particles collected on a scotch tape for the particle size measurement by image processing: (a) during friction at 150 ◦ C, after the transition. G material; (b) during friction at 450 ◦ C, after the transition. G material; (c) during friction at 150 ◦ C, after the transition. NG material; (d) during friction at 450 ◦ C, after the transition. NG material.
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first bodies oxidation. So, in order to better grasp the correlation between CO2 and third body productions, from the data presented in Fig. 5a and b, we plot the CO2 production versus the wear rate, for both materials (Fig. 6a). The first evidence is the great difference between both material behaviors, at least regarding the extent of their thermal evolution. One similarity is worth to notice as T increases from 150 to 450 ◦ C. For G material, the wear rate is divided by a factor 6 whereas its CO2 production is reduced by only a factor 1.3. For the NG material, the decreasing factors are respectively 7 and 3. In both cases, there is, apparently and surprisingly a strong reduction of oxygen reactivity as the experiment T increases. However, if now we plot the ratio CO2 production over wear rate versus temperature (Fig. 6b), we obtain the CO2 production per unit of worn thickness, i.e. as seen above, the CO2 production per unit of third body production. The thermal evolution of G and NG materials can be now compared: (1) the two curves increase with T, as expected for a thermally activated phenomenon; (2) they are not superimposed, the NG curve being over the G one, for all the T range. Obviously, the thermal activation is not the only phenomenon responsible for the thermal evolutions. The other phenomenon has to be found in the wear process acting on those different materials. One reason of this hierarchical order could be that the debris have characteristics similar to the first body from which they
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are detached: the NG material was not heat treated, so its texture is less organized with more aromatic layer edges. Thus, it is more easily oxidable than the G material, heat treated over 2000 ◦ C after densification. Another reason could be the size of the detached particles. In the next sections, confirmation is given that they are much smaller for the NG material, so more sensitive to oxidation. 3.3. Ejected particle size Particles (agglomerates of crushed and compacted particles and identifiable fragments of first body) ejected from the contact after the transition were collected and characterized by optical microscopy. The images were analyzed using an image processing software (Microvision), in order to determine the particle number and surface (expressed in m2 ). The particles are then classified according to their individual surface (from 0 to 50, from 50 to 100 m2 , etc.), then the percentage of the surface of each class over the total surface is calculated. The results show that during friction at 150 ◦ C (high wear rate), ejected particles and agglomerates have a large size. It ranges from 80 to 200 m for G material and from 10 to 30 m for NG material (Fig. 7a and c). On the contrary, during friction at 450 ◦ C (weak wear rate), their size is smaller, ranging from 10 to 50 m for the G material and from 5 to 15 m for NG material (Fig. 7b and d).
Fig. 8. Characterization of the worn surfaces: OM images between crossed polarizers with addition of a retarder plate; (a) G material and (c) NG material, after friction at 150 ◦ C (degraded surfaces); (1) a lot of third body, (2) torn off fibers and (3) degraded pyrocarbon; (b) G material and (d) NG material, after friction at 450 ◦ C (smooth surface); (4) “polished” pyrocarbon, (5) “smooth” fibers and (6) small amount of third body.
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These results are in agreement with data presented in Section 3.2 and give evidence that the detached particle size decrease with T, contributing to the increase of oxidation reactivity. 3.4. Worn surfaces characterization after friction After friction at 150 ◦ C (high wear rate), OM images show that the first body surfaces are degraded at a large extent. The degradation consists of a lot of third body (1), torn off fibers (2) and degraded pyrocarbon (3) (Fig. 8a and c). Obviously, a high flow source (particles detachment) is dominating, with large size detached particles, as seen previously. After friction at 450 ◦ C (weak wear rate), the surfaces are bright, as if they were “polished”, with occurrence of mainly polished pyrocarbon (4), smooth fibers (5), small quantity of third body (6) and a few torn off fibers (Fig. 8b and d). The “polished” aspect of the surface is the result of small size detached particles. In this case, a low flow source is obviously dominating. 3.5. OM characterization of the pin–disc interface For both materials, sections perpendicular to the worn surfaces were performed in the pin-disc unit glued after friction experiments at 150 and 450 ◦ C. It is important to remind that such data on the interfaces are obtained after friction, so in static. It would be erroneous to interpret the OM images as images of
Fig. 9. OM image of G material: Characterization of the pin–disc interface and of the third body trapped after friction experiment at 150 ◦ C.
the interface during friction. For instance, the interface thickness could not remain constant during friction, i.e. in dynamic. Indeed, taking into account the composite heterogeneity, it is clear that the local pressure is highly non-uniform. The pressure variability induces strong deformations of the wearing surfaces. So, during friction, the interface thickness continually changes from one point to another and at every moment. Consequently, the transverse section of the worn surface is only an instant image of the real interface. In all cases, OM images highlight that the interface thickness fluctuates from one point to another and particles are not evenly
Fig. 10. OM images of the pin/disc interface observed in static. For both materials, the interface is thicker at low temperature (high wear rate): (a) G material after friction at 150 ◦ C, wear rate ≈27 m/min, (b) G material after friction at 450 ◦ C, wear rate ≈4 m/min, (c) NG material after friction at 150 ◦ C, wear rate ≈7 m/min and (d) NG material after friction at 450 ◦ C, wear rate ≈1 m/min.
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Fig. 11. G material after friction at 150 ◦ C. Characterization of the damages at the surface vicinity on polished section (SEM images): (a) fiber–matrix decohesions on a depth of about 40 m and (b) cracks on a depth of about 40 m.
distributed in the interfaces (Fig. 9). Let us recall that both the sawing and the polishing processes used for the sample preparation could be responsible for locally interface separation and for part of the particles observed in the interface. However, undoubtedly, the highest value of the interface thickness is related to the higher wear rate and thus to the local presence of third body particles. After friction at 150 ◦ C (high wear rate), the interface thickness is relatively significant for the G material, where it ranges up to 50 m. It is up to 30 m for the NG material (Fig. 10a and c). When the third body is present in the interface, it consists of small compacted and agglomerated particles and of first body fragments easily identifiable (fibers and matrix). It is important to note the large length of some fragments (up to 100 m) in the case of G material (Fig. 9). The high interface thickness at low temperature probably facilitates and accelerates the ejection of particles, once detached from the first body. In this case, the particles would not remain long enough in the contact to be completely crushed. Hence, source flow (detached particles) could be mainly directly transformed into wear flow (ejected particles). It can explain the existence of large size particles coming from the first body, easily recognizable in the wear flow. Moreover, large interface thickness corroborate large size agglomerates of third body ejected at low temperature. After friction at 450 ◦ C (lowest wear rate), the interface thickness is smaller for both materials. The highest (20 m) is observed for the G material, it is no more than 12 m for the NG material. The size of the particles present within the interface is also smaller (Fig. 10b and d). The weak interface thickness after friction at high temperature can be explained both by the weak flow source and by the smallness of the detached particles. Therefore, the ejection of detached particles is more difficult and would lead to more crushing, thus to smaller ejected particles.
Fig. 12. NG material after friction at 150 ◦ C. Fiber–matrix decohesion at the surface vicinity on a depth of about 40 m (SEM image).
thermo-mechanical stresses, which affect the “skin” of the material and may change the allowable stress (σ a ). It is probable that this mechanism is related to the “Tribological Transformations of Surface (TTS)” well studied and identified in the case of metals [21,22].
3.6. SEM characterization of the damages at the surface vicinity For both materials, SEM images of the surface vicinity were realized on the polished sections done perpendicularly to the worn surface. Various damages are observed, their predominance depends on the experiment temperature. They result from
Fig. 13. NG material after friction at 150 ◦ C. Damages observed at the vicinity of the disc surface: fiber–matrix decohesion: (1) and cracks into the matrix and (2) (SEM image).
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Fig. 14. (a) G material and (b) NG material after friction at 450 ◦ C. Damages at the vicinity of the disc surface: “exfoliation” within the matrix on a depth of about 2 m (SEM images).
After friction at 150 ◦ C, the predominant degradations are fiber–matrix decohesions and cracks, visualized at the fiber–matrix interface and within the matrix. The first body depth damage is about 40 m (Figs. 11a and b, 12 and 13). These degradations lead to detachment of large size particles. After friction at 450 ◦ C, the predominant degradations are “exfoliations” occurring within the pyrocarbon matrix. They damage the materials on about 2 m in depth (Fig. 14a and b). Micro-cracks are also observed close to the rubbing surface, within fibers, on about 1 m in depth (Figs. 15 and 16). Taking into account these relatively low depth damages, they are obviously at the origin of small size particle detachment (micrometric), leading to a “polished” aspect of the first body surfaces. 3.7. Effect of the heat treatment on the wear of carbon/carbon composite Both materials (G and NG) exhibit similar behavior, with regard to the thermal evolution of worn surface aspect, the wear rate, the CO2 production in the contact and the ejected particle size. For similar friction experiments, the G material (heat
Fig. 16. NG material after friction at 450 ◦ C. Image illustrating damages of longitudinal fibers, on a depth of about 1 m (SEM image).
treated over 2000 ◦ C) is characterized by a higher wear rate, a weakness of the fiber–matrix interface, particles of larger size. As a consequence of the thermal treatment, G material is characterized by a higher flow source and therefore higher CO2 concentration than NG material, this latter being densified without further treatment. 4. Conclusion
Fig. 15. G material after friction at 450 ◦ C. Image illustrating damages of transversal fiber and “exfoliation” within the matrix (SEM image).
This investigation allowed, for the first time, a (semi) quantitative study of the CO2 production during carbon/carbon composite friction and its relationships with the detached particle size and the wear mechanisms. The amount of CO2 produced in the contact closely depends on the wear rate (i.e. on the amount of third body formed during friction), on the size of the detached particles formed in the contact and also on the experiment temperature. At low temperature (150 ◦ C), the in situ gas exchange analysis indicates a high CO2 production. Paradoxically, the ratio CO2 concentration over wear unit (i.e. over the wear flow) is the weakest, especially for the G material. These data are explained by the larger size of the particles formed at low temperature,
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which limits their oxidation. Characterizations of the worn surfaces and of the sections perpendicular to the rubbing surface show that, fiber–matrix decohesions and cracks can damage the material up to 40 m in depth, leading to the detachment of large particles (up to 100 m in length in G material), thus to important surface degradations. These phenomena result in a high flow source, dominant during friction at low temperature. At high temperature (450 ◦ C), the in situ gas analysis displays a low CO2 production. However, the ratio CO2 concentration over wear unit (i.e. over wear flow) is the highest, especially for the NG material. The particles formed are smaller, hence more sensitive to oxidation. “Exfoliation” occurring in the matrix and micro-cracks affecting the fibers damage the materials on a depth of 1–2 m. In addition, taking into account the interface analysis after friction, its average thickness decreases together with the wear rate and with the size of detached particles. Furthermore, the interface thickness could influence the particles ejection (wear flow): the thicker the interface is, the easier is the particles ejection. A low flow source appears to be the major phenomenon during friction at high temperature. In fact, the various modes of the source flow could coexist together within a same contact, with fluctuations in space and time. Depending on friction conditions, one is statistically preponderant on the other. As well seen by mass spectrometry, carbon oxidation is governed by the wear processes. In order to better understand the carbon oxidation, our perspectives are, on one hand, to characterize the structure and texture of the third body (MET, DRX and BET). On the other hand, to perform modeling of chemical reactions occurring in the contact, in order to quantify the lost of carbon by oxidation. Acknowledgments The authors greatly thank Caroline No¨el for the OM characterization and the image processing of the ejected particles and Annie Richard (Centre de Microscopie e´ lectronique, Universit´e d’Orl´eans) for her kind help in SEM imaging. References [1] K.-J. Lee, H.-Z. Cheng, J.-S. Chen, Effect of densification cycles on continuous friction behavior of carbon–carbon composites, Wear 260 (2006) 99–108. [2] X. Xiong, B.-Y. Huang, J.-H. Li, H.-J. Xu, Friction behaviors of carbon/carbon composites with different pyrolytic carbon textures, Carbon 44 (2006) 463–467. [3] S. Ozcan, P. Filip, Microstructure and wear mechanisms in C/C composites, Wear 259 (2005) 642–650. [4] T.-J. Hutton, D. Johnson, B. McEnaney, Effects of fiber orientation on the tribology of a model carbon–carbon composite, Wear 249 (2001) 647–655.
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Interdependence between wear process, size of detached particles and CO2 production during carbon/carbon composite friction Haytam Kasem a,∗ , Sylvie Bonnamy a , Bernard Rousseau a , Henriette Estrade-Szwarckopf a , Yves Berthier b , Pascale Jacquemard c a
Centre de Recherche sur la Mati`ere Divis´ee, UMR 6619 CNRS-Universit´e d’Orl´eans, 1B, rue de la F´erollerie, 45071 Orl´eans Cedex2, France b Laboratoire de M´ ecanique des Contacts, UMR 5514, CNRS-INSA de Lyon, 20, Avenue Albert Einstein, 69621 Villeurbanne Cedex, France c Messier-Bugatti, 7, Avenue du Bel Air, 69627 Villeurbanne Cedex, France Received 18 September 2006; received in revised form 23 January 2007; accepted 23 January 2007 Available online 23 May 2007
Abstract This work is focused on the study of the wear mechanisms occurring during C/C composite friction. The friction experiments are performed on a pin/disc tribometer coupled to a mass spectrometer. This set-up allows the in situ gas analysis in the contact during friction. Worn surfaces and polished sections done perpendicularly to the rubbing surface are characterized at several scales by optical and scanning electron microscopies to follow the degradations of the material induced by friction. The damages are correlated to the flow source, the size of detached particles and the CO2 production in the contact during friction at different temperatures. © 2007 Elsevier B.V. All rights reserved. Keywords: Tribology; C/C composite; Wear; Mass spectrometry; CO2 ; Flow source
1. Introduction The carbon/carbon (C/C) composites have a low density and preserve their mechanical and thermal properties at very high temperature. Therefore, they have become the best candidate as aeronautical brake disk material, being efficient in the different types of aircraft braking operations. To assure braking effectiveness, comfort and transportation safety, a stable friction coefficient is required, combined with a low wear rate to reduce costs. In the literature, the effects of densification cycles [1], structure [2,3] and fiber orientation [4] of carbon/carbon composite on the tribological properties of C/C composites have been well described. The relations between wear and decisive parameters such as the sliding speed [5,6], the load [7], the temperature [8] and the atmosphere [9] have been demonstrated, however, the wear mechanisms remain unclear. Numerous authors demonstrated that an abrupt transition of friction coefficient from a weak value (∼0.15) to a high value (∼0.4) takes place during
∗
Corresponding author. Tel.: +33 238255815; fax: +33 238255376. E-mail address: [email protected] (H. Kasem).
0043-1648/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2007.01.077
carbon/carbon composite friction, when the friction conditions become more severe, for instance when temperature is increased. This transition phenomenon is associated with a strong particle detachment, this regime was named “dusting regime” [10,11]. Furthermore, C/C composites are known to be chemically very reactive and sensitive to the oxidation, especially at high temperature, depending on their texture [12,13]. The tribological properties were shown to evolve under oxidizing conditions [14,15]. So, to a better knowledge of the tribological behavior of carbon/carbon composite during friction, it became necessary to couple mechanical and physicochemical approaches [16–18]. Recently, Gouider et al. studied the physicochemical reactions occurring in situ in the contact during friction, thanks to a mass spectrometer directly coupled to the tribometer [19]. They evidenced for the first time, that a sudden carbon dioxide (CO2 ) production and an oxygen (O2 ) consumption perfectly coincide with the friction coefficient transition. In order to progress in the understanding of the wear and friction mechanisms, the aim of this paper is to precisely correlate the surface [20] and subsurface [21,22] degradations resulting from friction at different temperatures to the flow source (particle detachment) [23] and to the gas exchanges occurring in the contact during friction. For that, the friction experiments
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are performed at temperature ranging from 150 to 450 ◦ C, on a laboratory pin-on-disc tribometer equipped with a mass spectrometer. 2. Experimental 2.1. Materials The materials used are carbon/carbon PAN-CVI composite, SEPCARBTM . They consist of 3D ex-PAN fiber mats densified with pyrocarbon (rough lamellar texture). One sample is treated at high temperature, i.e. over 2000 ◦ C after densification (“G” material); the other one is untreated (only densified) “NG” material. For each experiment the pin and the disc are machined from the same carbon composite (G or NG). 2.2. Set-up: pin-on-disc tribometer and mass spectrometer The friction experiments are performed on a laboratory pin-on-disc tribometer with vertical axis coupled to a mass spectrometer. This set-up allowing the analysis of the gas exchange in the contact during friction. Two external heating, one for the pin the other for the disc, permit to impose and to maintain the chosen temperatures during friction (Fig. 1). The disc is 160 mm in diameter and 8 mm in thickness and the pin is 30 mm in diameter and 8 mm in thickness, with a hole of 7 mm at its center to introduce the capillary of the mass spectrometer. During friction, the pin center is shifted about 51 mm from the disc center (see Fig. 3). Experiments are carried out in air, under a relative humidity ranging from 45 to 55%. The imposed parameters are the following: • a constant linear sliding speed of 2 m/s at the center of the track friction; it corresponds to about a 375 rpm disc rotation, • a contact pressure equal to 0.5 MPa, • a preliminary running-in of the system pin and disc, performed at 200 ◦ C leading to about 150 m wear. This preliminary step is done to avoid trace machining and to assure conformity and reproductibility of the surfaces. The system is then left 12 h in equilibrium under air without disassembling the parts. The obtained surface is our original surface. The optical microscopy images of these surfaces are similar to the ones given in Fig. 8a and c.
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• a pin and disc heating ramps equal to 25 ◦ C/min. Once reached, the desired temperature is maintained during all the experiment, • for the two materials (G and NG), the trials were done at different imposed temperatures corresponding to cold taxiing (150 ◦ C), heat taxiing (450 ◦ C) and intermediate ones (250 and 350 ◦ C), • each friction experiment lasts about 30 min. During an experiment the following parameters are measured (Fig. 2): • The tangential force undergone by the rotating disc, measured through a force gauge. Knowing the load, the friction coefficient μ is deduced (Fig. 2a). • The wear, estimated through the distance between the upper pin surface and a fix reference. This distance is measured via a displacement gauge and includes the pin and disc wear (thickness loss), the third body thickness and the thermal dilatation of the mechanical system around the pin and the disc. At the beginning of the experiment, the measured distance decreases due to the thermal sensitivity of the system, this part of the curve is thus meaningless. When a linear positive regime is established and temperature stabilized, wear rate (expressed in m/min) is measured as the slope of the separation curve versus time (Fig. 2b). This “wear rate” only takes into account the thickness decrease, not the weight loss due to oxidation. • The pin and the disc temperatures measured through thermocouples located at about 1.5 mm from the contact. Taking into account this distance, this temperature will be called thereafter “subsurface temperature” (Fig. 2c). • The gas exchanges taking place in the contact, detected by the mass spectrometer (Fig. 2d–f). The main information is brought from the signals coming from carbon dioxide, oxygen and water vapor (respectively masses 44, 32 and 18). The gas volume enclosed in the contact is not tightly isolated from the environment, its pressure is almost equal to atmospheric pressure. A positive (or a negative) variation of a gas signal means an increase (or a decrease) of its partial pressure, i.e. a production (or a consumption). Measurements are only semi-quantitative: a calibration is not possible because the gas conductance between pin and disc really evolves during friction. O2 consumption is almost equal to CO2 production [19] (Fig. 2d and e), and in the results only CO2 concentration is reported. Its average concentration is directly measured
Fig. 1. Experimental device: laboratory tribometer in pin/disc configuration coupled with a mass spectrometer.
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Fig. 2. Example of tribological and gas analysis data for G material tested at 250 ◦ C: (a) friction coefficient, (b) wear, (c) disc subsurface temperature, (d), (e) and (f) variation of respectively O2 , CO2 , H2 O partial pressure in the contact.
through its partial pressure in the contact (expressed as an electric current in A unit) (Fig. 2e). • Transition: when temperature increases, at first, the friction remains weak, then all the mechanical and gaseous measured parameters undergo an abrupt transition. The friction coefficient (μ) suddenly increases then decreases to a stable permanent value (Fig. 2a). The CO2 partial pressure follows the same behavior, it means that an oxidation process takes place as soon as transition occurs (Fig. 2e). After the transition, as long as μ remains high, the oxidation process goes on, it is responsible for dusting conditions [10,11]. During the friction tests and after the transition, the ejected particles from the contact are captured by means of a piece of scotch-tape set parallel to the friction direction (Fig. 3). This procedure, even though selective because the finest ejected particles probably do not reach the scotch-tape, avoids their
agglomeration and allows an easier determination of their size for a comparison of the experiments. The ejected particle sizes are determined from optical microscopy images (magnification 200×) in using image analysis processing.
Fig. 3. Collect of the ejected particles from the contact during friction experiment.
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In order to study the pin-disc interface and the third body remaining in the contact, after the friction experiments, the contact is maintained under pressure and the periphery of the pin is glued with a commercial epoxy resin (Araldite) to the disc. Then the pin and disc set is embedded in an epoxy resin and sections, sawed perpendicularly to the rubbing surface, are polished for their characterization by optical and scanning electron microcopies. For the images interpretation of such polished sections, it is important to notice that, the disc and pin are glued just after the disc rotation stop. The wear particles, which should be ejected, are still present either around the pin or in the contact. It is well admit that, in dynamic, the interface thickness changes permanently from one place to another. In static (which is the context), the amount of third body present in the contact will be more abundant and consequently the interface thickness will be overvalued. Furthermore, we have to be cautious during polishing, in order not to deform the interface or to add debris of polishing. Characterizations of the worn surfaces and pin–disc interface were done by optical microscopy (OM, Leica DM IRM) and by scanning electron microscopy (SEM, Hitachi S4200 equipped with a field emission gun). For SEM imaging, the acceleration voltage used is 1 kV, in order to limit the secondary electron analysis to the outermost surface [20]. OM characterization is performed between crossed polarizers with addition of a retarder plate (λ plate).
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Fig. 4. Analysis of CO2 production during dynamic and static experiments.
3. Results and discussion
between CO2 emission and O2 consumption (Fig. 2d and e) [24]. To better understand the origin of CO2 , the CO2 curve obtained during dynamic friction experiment in the reactive regime was compared with the one obtained in a static heating test (up to 500 ◦ C). During dynamic experiment, CO2 is produced in a large amount, whereas during static heating, only a very weak CO2 amount is produced (Fig. 4). Obviously, mechanical motion is necessary to produce CO2 , which is also associated with third body production (see next paragraph).
3.1. Friction transition and CO2 production in the contact
3.2. Wear and CO2 production in the contact during friction
As seen in Fig. 2a–f, all friction experiments show, at first, a weak wear regime, called “non reactive”. It is characterized by a weak friction coefficient (from 0.1 to 0.2), with no wear detected by our device. Then, after a brutal transition, a high wear regime called “reactive” occurs. It is characterized by a high friction coefficient (from 0.3 to 0.4) and high wear rate [19]. The gas analyses in the contact bring to light that only the “reactive” regime is systematically accompanied by a CO2 production and an O2 consumption, with always a strong complementarity
For both G and NG materials, the wear rate and the average CO2 concentration in the contact have been measured at four temperatures (T) ranging from 150 to 450 ◦ C. Taking into account our experimental device, neither the third body nor the CO2 production rate could be really calibrated. We assume that the CO2 partial pressure given by the mass spectrometer is proportional to the CO2 production rate. The amount of debris produced per minute in the contact cannot be directly measured, but it is proportional to the wear rate, if we assume
Fig. 5. (a) Decrease of wear rate (m/min) as temperature increases. (b) Decrease of CO2 production as temperature increases.
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Fig. 6. (a) CO2 production as a function of wear rate. (b) Ratio of CO2 production over wear rate as a function of the subsurface temperature.
that oxidation has no effect on the pin + disc thickness decrease measured on the tribometer. Results are reported in Fig. 5a and b. The wear rates decrease as T increases for both materials, the G one being more sensitive to temperature. Similar decreases are observed when CO2 production in the contact is reported as a function of T (for the first time such data are presented) (Fig. 5b). This behavior is more surprising, because in apparent contradiction with the usual thermal activation responsible for oxidation at high temperature. In order to solve this contradiction, the origin of the CO2 production
has to be determined, i.e. the origin of the carbon components able to oxidize in the contact. During friction, both the first bodies and their debris may undergo oxidation. However, the debris, composed of a whole of particles, are probably more sensitive to oxygen than the first bodies. Such affirmation is in agreement with the results of Fig. 5b. Indeed, the G material shows the higher wear rate, consequently it produces a higher amount of debris during friction and has a higher CO2 production. In the following discussion, we will assume that the whole CO2 detected originates only from the third body, neglecting the
Fig. 7. OM images of the ejected particles collected on a scotch tape for the particle size measurement by image processing: (a) during friction at 150 ◦ C, after the transition. G material; (b) during friction at 450 ◦ C, after the transition. G material; (c) during friction at 150 ◦ C, after the transition. NG material; (d) during friction at 450 ◦ C, after the transition. NG material.
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first bodies oxidation. So, in order to better grasp the correlation between CO2 and third body productions, from the data presented in Fig. 5a and b, we plot the CO2 production versus the wear rate, for both materials (Fig. 6a). The first evidence is the great difference between both material behaviors, at least regarding the extent of their thermal evolution. One similarity is worth to notice as T increases from 150 to 450 ◦ C. For G material, the wear rate is divided by a factor 6 whereas its CO2 production is reduced by only a factor 1.3. For the NG material, the decreasing factors are respectively 7 and 3. In both cases, there is, apparently and surprisingly a strong reduction of oxygen reactivity as the experiment T increases. However, if now we plot the ratio CO2 production over wear rate versus temperature (Fig. 6b), we obtain the CO2 production per unit of worn thickness, i.e. as seen above, the CO2 production per unit of third body production. The thermal evolution of G and NG materials can be now compared: (1) the two curves increase with T, as expected for a thermally activated phenomenon; (2) they are not superimposed, the NG curve being over the G one, for all the T range. Obviously, the thermal activation is not the only phenomenon responsible for the thermal evolutions. The other phenomenon has to be found in the wear process acting on those different materials. One reason of this hierarchical order could be that the debris have characteristics similar to the first body from which they
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are detached: the NG material was not heat treated, so its texture is less organized with more aromatic layer edges. Thus, it is more easily oxidable than the G material, heat treated over 2000 ◦ C after densification. Another reason could be the size of the detached particles. In the next sections, confirmation is given that they are much smaller for the NG material, so more sensitive to oxidation. 3.3. Ejected particle size Particles (agglomerates of crushed and compacted particles and identifiable fragments of first body) ejected from the contact after the transition were collected and characterized by optical microscopy. The images were analyzed using an image processing software (Microvision), in order to determine the particle number and surface (expressed in m2 ). The particles are then classified according to their individual surface (from 0 to 50, from 50 to 100 m2 , etc.), then the percentage of the surface of each class over the total surface is calculated. The results show that during friction at 150 ◦ C (high wear rate), ejected particles and agglomerates have a large size. It ranges from 80 to 200 m for G material and from 10 to 30 m for NG material (Fig. 7a and c). On the contrary, during friction at 450 ◦ C (weak wear rate), their size is smaller, ranging from 10 to 50 m for the G material and from 5 to 15 m for NG material (Fig. 7b and d).
Fig. 8. Characterization of the worn surfaces: OM images between crossed polarizers with addition of a retarder plate; (a) G material and (c) NG material, after friction at 150 ◦ C (degraded surfaces); (1) a lot of third body, (2) torn off fibers and (3) degraded pyrocarbon; (b) G material and (d) NG material, after friction at 450 ◦ C (smooth surface); (4) “polished” pyrocarbon, (5) “smooth” fibers and (6) small amount of third body.
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These results are in agreement with data presented in Section 3.2 and give evidence that the detached particle size decrease with T, contributing to the increase of oxidation reactivity. 3.4. Worn surfaces characterization after friction After friction at 150 ◦ C (high wear rate), OM images show that the first body surfaces are degraded at a large extent. The degradation consists of a lot of third body (1), torn off fibers (2) and degraded pyrocarbon (3) (Fig. 8a and c). Obviously, a high flow source (particles detachment) is dominating, with large size detached particles, as seen previously. After friction at 450 ◦ C (weak wear rate), the surfaces are bright, as if they were “polished”, with occurrence of mainly polished pyrocarbon (4), smooth fibers (5), small quantity of third body (6) and a few torn off fibers (Fig. 8b and d). The “polished” aspect of the surface is the result of small size detached particles. In this case, a low flow source is obviously dominating. 3.5. OM characterization of the pin–disc interface For both materials, sections perpendicular to the worn surfaces were performed in the pin-disc unit glued after friction experiments at 150 and 450 ◦ C. It is important to remind that such data on the interfaces are obtained after friction, so in static. It would be erroneous to interpret the OM images as images of
Fig. 9. OM image of G material: Characterization of the pin–disc interface and of the third body trapped after friction experiment at 150 ◦ C.
the interface during friction. For instance, the interface thickness could not remain constant during friction, i.e. in dynamic. Indeed, taking into account the composite heterogeneity, it is clear that the local pressure is highly non-uniform. The pressure variability induces strong deformations of the wearing surfaces. So, during friction, the interface thickness continually changes from one point to another and at every moment. Consequently, the transverse section of the worn surface is only an instant image of the real interface. In all cases, OM images highlight that the interface thickness fluctuates from one point to another and particles are not evenly
Fig. 10. OM images of the pin/disc interface observed in static. For both materials, the interface is thicker at low temperature (high wear rate): (a) G material after friction at 150 ◦ C, wear rate ≈27 m/min, (b) G material after friction at 450 ◦ C, wear rate ≈4 m/min, (c) NG material after friction at 150 ◦ C, wear rate ≈7 m/min and (d) NG material after friction at 450 ◦ C, wear rate ≈1 m/min.
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Fig. 11. G material after friction at 150 ◦ C. Characterization of the damages at the surface vicinity on polished section (SEM images): (a) fiber–matrix decohesions on a depth of about 40 m and (b) cracks on a depth of about 40 m.
distributed in the interfaces (Fig. 9). Let us recall that both the sawing and the polishing processes used for the sample preparation could be responsible for locally interface separation and for part of the particles observed in the interface. However, undoubtedly, the highest value of the interface thickness is related to the higher wear rate and thus to the local presence of third body particles. After friction at 150 ◦ C (high wear rate), the interface thickness is relatively significant for the G material, where it ranges up to 50 m. It is up to 30 m for the NG material (Fig. 10a and c). When the third body is present in the interface, it consists of small compacted and agglomerated particles and of first body fragments easily identifiable (fibers and matrix). It is important to note the large length of some fragments (up to 100 m) in the case of G material (Fig. 9). The high interface thickness at low temperature probably facilitates and accelerates the ejection of particles, once detached from the first body. In this case, the particles would not remain long enough in the contact to be completely crushed. Hence, source flow (detached particles) could be mainly directly transformed into wear flow (ejected particles). It can explain the existence of large size particles coming from the first body, easily recognizable in the wear flow. Moreover, large interface thickness corroborate large size agglomerates of third body ejected at low temperature. After friction at 450 ◦ C (lowest wear rate), the interface thickness is smaller for both materials. The highest (20 m) is observed for the G material, it is no more than 12 m for the NG material. The size of the particles present within the interface is also smaller (Fig. 10b and d). The weak interface thickness after friction at high temperature can be explained both by the weak flow source and by the smallness of the detached particles. Therefore, the ejection of detached particles is more difficult and would lead to more crushing, thus to smaller ejected particles.
Fig. 12. NG material after friction at 150 ◦ C. Fiber–matrix decohesion at the surface vicinity on a depth of about 40 m (SEM image).
thermo-mechanical stresses, which affect the “skin” of the material and may change the allowable stress (σ a ). It is probable that this mechanism is related to the “Tribological Transformations of Surface (TTS)” well studied and identified in the case of metals [21,22].
3.6. SEM characterization of the damages at the surface vicinity For both materials, SEM images of the surface vicinity were realized on the polished sections done perpendicularly to the worn surface. Various damages are observed, their predominance depends on the experiment temperature. They result from
Fig. 13. NG material after friction at 150 ◦ C. Damages observed at the vicinity of the disc surface: fiber–matrix decohesion: (1) and cracks into the matrix and (2) (SEM image).
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Fig. 14. (a) G material and (b) NG material after friction at 450 ◦ C. Damages at the vicinity of the disc surface: “exfoliation” within the matrix on a depth of about 2 m (SEM images).
After friction at 150 ◦ C, the predominant degradations are fiber–matrix decohesions and cracks, visualized at the fiber–matrix interface and within the matrix. The first body depth damage is about 40 m (Figs. 11a and b, 12 and 13). These degradations lead to detachment of large size particles. After friction at 450 ◦ C, the predominant degradations are “exfoliations” occurring within the pyrocarbon matrix. They damage the materials on about 2 m in depth (Fig. 14a and b). Micro-cracks are also observed close to the rubbing surface, within fibers, on about 1 m in depth (Figs. 15 and 16). Taking into account these relatively low depth damages, they are obviously at the origin of small size particle detachment (micrometric), leading to a “polished” aspect of the first body surfaces. 3.7. Effect of the heat treatment on the wear of carbon/carbon composite Both materials (G and NG) exhibit similar behavior, with regard to the thermal evolution of worn surface aspect, the wear rate, the CO2 production in the contact and the ejected particle size. For similar friction experiments, the G material (heat
Fig. 16. NG material after friction at 450 ◦ C. Image illustrating damages of longitudinal fibers, on a depth of about 1 m (SEM image).
treated over 2000 ◦ C) is characterized by a higher wear rate, a weakness of the fiber–matrix interface, particles of larger size. As a consequence of the thermal treatment, G material is characterized by a higher flow source and therefore higher CO2 concentration than NG material, this latter being densified without further treatment. 4. Conclusion
Fig. 15. G material after friction at 450 ◦ C. Image illustrating damages of transversal fiber and “exfoliation” within the matrix (SEM image).
This investigation allowed, for the first time, a (semi) quantitative study of the CO2 production during carbon/carbon composite friction and its relationships with the detached particle size and the wear mechanisms. The amount of CO2 produced in the contact closely depends on the wear rate (i.e. on the amount of third body formed during friction), on the size of the detached particles formed in the contact and also on the experiment temperature. At low temperature (150 ◦ C), the in situ gas exchange analysis indicates a high CO2 production. Paradoxically, the ratio CO2 concentration over wear unit (i.e. over the wear flow) is the weakest, especially for the G material. These data are explained by the larger size of the particles formed at low temperature,
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which limits their oxidation. Characterizations of the worn surfaces and of the sections perpendicular to the rubbing surface show that, fiber–matrix decohesions and cracks can damage the material up to 40 m in depth, leading to the detachment of large particles (up to 100 m in length in G material), thus to important surface degradations. These phenomena result in a high flow source, dominant during friction at low temperature. At high temperature (450 ◦ C), the in situ gas analysis displays a low CO2 production. However, the ratio CO2 concentration over wear unit (i.e. over wear flow) is the highest, especially for the NG material. The particles formed are smaller, hence more sensitive to oxidation. “Exfoliation” occurring in the matrix and micro-cracks affecting the fibers damage the materials on a depth of 1–2 m. In addition, taking into account the interface analysis after friction, its average thickness decreases together with the wear rate and with the size of detached particles. Furthermore, the interface thickness could influence the particles ejection (wear flow): the thicker the interface is, the easier is the particles ejection. A low flow source appears to be the major phenomenon during friction at high temperature. In fact, the various modes of the source flow could coexist together within a same contact, with fluctuations in space and time. Depending on friction conditions, one is statistically preponderant on the other. As well seen by mass spectrometry, carbon oxidation is governed by the wear processes. In order to better understand the carbon oxidation, our perspectives are, on one hand, to characterize the structure and texture of the third body (MET, DRX and BET). On the other hand, to perform modeling of chemical reactions occurring in the contact, in order to quantify the lost of carbon by oxidation. Acknowledgments The authors greatly thank Caroline No¨el for the OM characterization and the image processing of the ejected particles and Annie Richard (Centre de Microscopie e´ lectronique, Universit´e d’Orl´eans) for her kind help in SEM imaging. References [1] K.-J. Lee, H.-Z. Cheng, J.-S. Chen, Effect of densification cycles on continuous friction behavior of carbon–carbon composites, Wear 260 (2006) 99–108. [2] X. Xiong, B.-Y. Huang, J.-H. Li, H.-J. Xu, Friction behaviors of carbon/carbon composites with different pyrolytic carbon textures, Carbon 44 (2006) 463–467. [3] S. Ozcan, P. Filip, Microstructure and wear mechanisms in C/C composites, Wear 259 (2005) 642–650. [4] T.-J. Hutton, D. Johnson, B. McEnaney, Effects of fiber orientation on the tribology of a model carbon–carbon composite, Wear 249 (2001) 647–655.
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