Tribol Lett (2015) 57:19 DOI 10.1007/s11249-014-0462-5
ORIGINAL PAPER
Tempering Temperature Effect on Sliding Wear at High Temperatures in Mottled Cast Iron O. A. Zambrano • J. J. Coronado • S. A. Rodrı´guez
Received: 2 July 2014 / Accepted: 6 December 2014 Ó Springer Science+Business Media New York 2015
Abstract This research analyses the effect of the microstructure of mottled cast iron on tribological behaviour using a high temperature pin-on-disc test with a steel disc oxidised at 1,200 °C ASTM A36 as a counterbody. Three different microstructures were obtained for the mottled cast iron pins by quenching and tempering at 400 °C and 600 °C. The test temperature was varied from 200 to 600 °C with the aim of approximating the temperatures reached on surface work rolls under industrial conditions. The oxidation of the ASTM A36 disc at 1,200 °C was used to reproduce a counterbody (calamine) similar to that occurring in the hot roll mill steel under industrial conditions. The other tribological test parameters were held constant (normal load of 20 N and sliding speed of 0.05 m/s). The experimental results at the lowest test temperature (200 °C) show that the wear strongly depends on the microstructure and that the greatest friction coefficients are present at this condition. However, at higher test temperatures (400 and 600 °C), the wear resistance depends on the pin oxide stability. The highest wear rate occurs at a test temperature of 400 °C, and the lowest wear rate occurs at 600 °C. The explanations for these phenomena are discussed. Keywords Sliding wear High temperatures Mottled cast iron Iron oxide
O. A. Zambrano (&) J. J. Coronado S. A. Rodrı´guez Research Group of Fatigue and Surfaces, Mechanical Engineering School, Universidad del Valle, Cali, Colombia e-mail:
[email protected]
1 Introduction Wear at high temperatures is an important phenomenon that affects several industries related to materials processing, and one of these is the hot rolling process. In this process, steel is generally processed at temperatures between 1,000 and 1,200 °C, and at these temperatures, the steel slab generates three iron oxide layers on the surface. The internal oxide consists of cubic wu¨stite (FeO), the intermediate oxide is cubic magnetite (Fe3O4), and the external oxide is rhombohedral hematite (a-Fe2O3) [1]. Their relative thicknesses (of the total scale thickness) correspond to 95 % wu¨stite, 4 % magnetite, and 1 % hematite. Wu¨stite (FeO) has low hardness and is known to display lubricant behaviour at high temperatures, thus reducing the wear rate and friction coefficient. Magnetite (Fe3O4) has an intermediate hardness and also plays a lubricant role, whereas hematite (a-Fe2O3) has a high hardness that promotes abrasive wear [2]. However, more specifically, these iron oxide layers have different tribological behaviours and relative thicknesses that depend on the temperature [3], atmosphere [4], and chemical composition of the alloys [5]. Furthermore, although a scale breaker exists in the hot rolling process, the high oxidation kinetics re-oxidise the surface in only 0.5–30 s [6], thus facilitating the formation of new oxide layers. However, the role of the microstructure at high temperatures is broadly varied. Because wear at high temperatures not only enables adhesion or abrasion mechanisms generated by the oxides, it also incurs oxidative wear, which could represent a predominant wear mechanism at elevated temperatures [7, 8]. Certain authors report a decrease in the wear and friction coefficients with increasing test temperature due to a continuous layer or glaze formation from debris compaction and sintering
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[9–13]. Others authors report an increase in the wear and friction coefficients with increasing test temperature due to oxidation and plastic deformation (i.e., ploughing) mechanisms [14, 15]. Transitions may appear between behaviours and different ranges of temperatures in the same test [16]. Thus, the interaction between the oxides and microstructure at high temperatures is strongly influenced by the mechanical stability of the oxides, which depends on (1) their chemical nature [17, 18]; (2) the temperature, which influences whether agglomeration and compaction of the wear debris could occur [10]; (3) load and sliding speed [19]; (4) the microstructure and hardness of the materials involved [5, 20]. Mechanical support of the oxides formed in each tribo-element may or may not be present; in other words, if the matrix does not have sufficient strength or hardness, the tribo-oxides will not reduce the wear [5, 20, 21]. However, the uniformity of oxidation on the microstructure also has a strong influence on the wear behaviour at high temperatures [5]. The role of oxides in the tribosystem also depends on whether the oxide occurs in compact form or in the form of free particles [2]. The previous considerations of the effect of microstructure on friction and wear behaviour demonstrate the complexity of predicting wear behaviour at high temperatures. The objective of this research is to elucidate and understand the effect of microstructure variation in the same material on the wear and friction coefficients at high temperatures when other test parameters are held constant.
2 Experimental Procedure 2.1 Materials The tested material is a mottled cast iron (MCI) with a chemical composition (determined using an optical emission ARL 3460 Advantage spectrometer) of 3–3.6 % C, 1.4–2.1 % Cr, 4.1–4.8 % Ni, 0.25–0.7 % Mo, 0.09 % V, and 3 % Ti ? Nb. This material is currently used in the manufacturing of rolling-mill rolls used in the hot rolling process. The MCI was austenitised at 930 °C and cooled in air. After quenching, selected samples were tempered at 400 and 600 °C for 30 h and cooled in a furnace, and for the pin samples, / 3 mm 9 40 mm samples were cut using an electro-discharge machining. 2.2 X-Ray Diffraction Analyses The MCI samples from each heat treatment were analysed via XRD to determine the weight percentages of martensite and retained austenite. The XRD data were obtained at room temperature using a PANalytical diffractometer with Bragg-Brentano geometry and Cu ka radiation (45 kV,
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40 mA). The samples were scanned over 2h angles between 10° and 100°, and the 2h scan step was 0.02°. The weight percentages of the phases were calculated by applying the Rietveld method [22], and the refinements were produced using the GSAS program [23]. 2.3 Tribological Test Wear tests were performed on a pin-on-disc tribometer at high temperature. Sliding wear tests were carried out using an MCI pin against a ASTM A36 steel disc previously oxidised in a furnace at 1,200 °C for 4 h with a roughness of 3.90 ± 0.64 lm of Ra, thickness of 733.82 ± 70.17 lm, and HV50f hardness of the external layer of 975.5 ± 62.7. This oxidation test was performed with the aim of obtaining industrial calamine formation on the surface of the steel similar to that formed when it is rolled in the range of approximately 1,150–1,200 °C in industrial conditions. The applied parameters were a constant tangential speed of 0.05 m/s; test temperatures of 200, 400, and 600 °C (selected to reproduce the range of maximum temperatures reached on hot work roll surfaces in industrial conditions [3, 24] ); a normal load of 20 N (lower loads do not produce mass loss, and higher loads break up the oxide formed on the AISI A36 disc); a total sliding distance of 120 m. Three repetitions were performed for each condition, and the test errors were determined with 95 % confidence (the error bars in all figures represent the confidence interval at 95 % for each condition, i.e. the mean values correspond to the central point of the bars in the figures and the vertical line represent the confidence interval). For each pin, a stage of superficial homogenisation was produced using abrasive paper of alumina 600 grit. Finally, the mass losses of the pins were measured using an analytical scale with 0.1-mg resolution. In general, the mass loss at high temperatures is analysed according to the measure of topography using laser interferometry to calculate the volume removed. Nevertheless, the use of the gravimetric method to measure the mass loss at high temperatures dependent on the specific conditions of the tribosystem is also possible [5, 21, 25–27]. In this case, the used of the gravimetric technique to measure the mass loss at high temperatures was employed for two main reasons: (1) the abrasiveness of the oxide formed on the ASTM A36 continuously produced wear on every pin surface, thus making it impossible to obtain an initial image and another image of the wear track using laser interferometry or other techniques to calculate the missing volume. (2) The static and dynamic oxidation of the pins produces a negligible mass gain or mass loss. In the first case, static oxidation of the pins for 20 and 60 min at 200, 400, and 600 °C showed high oxidation resistance (negligible values in mass gain) as show in the Tables 1 and 2, respectively. In the second case, using normal loads
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Table 1 Static oxidation of the pins for 20 min at different temperatures Temperature of static oxidation (°C)
Mean initial mass (g)
Mean final mass (g)
Mass gain (g)
Mass gain (mg)
200
1.3435 ± 0.0001
1.3436 ± 0.0001
*0
*0
400
1.3511 ± 0.0001
1.3510 ± 0.0001
*0
*0
600
1.3476 ± 0.0001
1.3477 ± 0.0001
*0
*0
Table 2 Static oxidation of the pins for 60 min at different temperatures Temperature of static oxidation (°C)
Mean initial mass (g)
Mean final mass (g)
Mass gain (g)
Mass gain (mg)
200
1.3525 ± 0.0001
1.3525 ± 0.0001
*0
*0
*0
*0
400
1.3500 ± 0.0001
1.3501 ± 0.0001
600
1.3666 ± 0.0001
1.3668 ± 0.0001
0.0002
0.2
\20 N and test durations of 40 min at these temperatures, produced no mass loss or mass gain. These findings imply that the wear mass loss presented in the tests performed is not influenced by the static oxidation and the gravimetric method could be used. 2.4 Hardness Test Macro-hardness testing was performed on the heat-treated samples using a Rockwell C instrument. Micro-hardness testing was performed on heat-treated samples using a Vickers indenter at 50 gf for 10 s. To obtain the microhardness after wear testing, each pin was cold-mounted in resin, transversely (to the wear surface) ground down to grit 1,500, and mechanically polished using 1-, 0.3-, and 0.05-lm alumina for 30 s to obtain a flat surface without removing the deformed layer. The test errors were determined with 95 % confidence.
Fig. 1 Micrograph of MCI quenched from 930 °C
3 Results 3.1 Microstructure and Retained Austenite The microstructure of the quenched MCI is shown in Fig. 1 and is composed of M3C carbides, niobium carbides (NbC), graphite, martensite, and retained austenite. The microstructures of the tempered samples at 400 and 600 °C are shown in Figs. 2 and 3, respectively. These microstructures are composed of ferrite and fine spherical carbides produced during tempering from transformation of the retained austenite [28]. The main differences among these three microstructures are related to the retained austenite, as shown in the following section.
Fig. 2 Micrograph of MCI tempered at 400 °C
The retained austenite and ferrite-a (Fe-a represents the amount of both martensite and ferrite phases because the peaks of both phases are not distinguishable in the XRD
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Tribol Lett (2015) 57:19 Table 3 Quantitative amount of retained and martensite with heat treatment
Fig. 3 Micrograph of MCI tempered at 600 °C
pattern) can be observed graphically in the XRD pattern if Fig. 4. The retained austenite reduction is related to the (111) peak, which decreases with tempering temperature,
Fig. 4 XRD results of the mottled cast iron at 3-quenched, 2-tempered at 400 °C, and 1-tempered at 600 °C
Fig. 5 Relationship between mass loss and test temperature for each condition of the mottled cast iron
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Sample
c-Fe (wt%)
a-Fe and BCT Fe (wt%)
Quenched
43.2
56.8
Tempered at 400 °C
20.7
79.3
Tempered at 600 °C
7.0
93.0
and the a-ferrite is related to the (110) peak, which increases with tempering temperature. The quantitative XRD analysis is presented in Table 3. The maximum amount of retained austenite was observed in the quenched sample, and the sample tempered at 600 °C exhibited the greatest reduction of the austenite content. 3.2 Tribological Test The mass losses of the pins for each test temperature are shown in Fig. 5. The results show that at a test temperature of 200 °C, the quenched sample showed higher wear resistance, followed by the tempered sample at 400 °C and the tempered sample at 600 °C. At 200 °C, the mass loss is controlled by the content of retained austenite and the initial hardness (Table 3; Fig. 9, respectively). On the other hand, at a test temperature of 400 °C the results are different; the quenched sample showed almost the same wear resistance as the tempered sample at 600 °C, despite the broad difference in hardness and retained austenite (Fig. 9; Table 3, respectively) and the tempered sample at 400 °C showed higher wear resistance because of lower softening of the matrix, which in some grade improve the support of the tribo-oxide layer to reduce wear [21]. These results showed that at this temperature neither hardness nor retained austenite is responsible for the wear resistance, but the formation and
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Tempered at 600°C Tempered at 400°C
Running-in Period (m)
100
Quenched
80
60
40
20
0
200°C
400°C
600°C
Sliding wear test temperature
Fig. 7 Running-in periods versus sliding wear for test temperature and microstructures
1
Quenched
Stable fricon coefficients
0.9 Tempered at 400°C
0.8
Tempered at 600°C
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
200°C
400°C
600°C
Sliding wear test temperature
Fig. 8 Stable friction coefficients versus sliding wear test temperature for each microstructure
Fig. 6 Relationships among the friction coefficient, sliding distance, and test temperature for the mottled cast iron: a quenched, b tempered at 400 °C, and c tempered at 600 °C
stability of the tribo-oxides are controlling the wear behaviour. Finally, at a test temperature of 600 °C the samples showed higher wear resistance compared with the other test temperatures (independent of the matrix strength), which is due to a continuous layer or glaze formation, which prevent the interaction of both surfaces and reduce the wear [10]. Figure 6 presents the progress of the friction coefficient with the sliding distance for different temperature tests. Figures 6 and 7 show the three main behaviours: (1) the lowest mass loss and the lowest friction coefficients were observed at the highest test temperature (600 °C) for all microstructures, (2) the lowest test temperature (200 °C) produced intermediate mass loss and the highest friction coefficients, and (3) the intermediate test temperature (400 °C) resulted in the highest mass loss and intermediate friction coefficients. The friction curves (Fig. 6) show the running-in periods, which refer to the initial period of changes in the friction coefficient during the stabilisation and homogenisation of
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Fig. 9 Relationship between micro-hardness before and after the wear test and test temperature for each condition of the mottled cast iron
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Micro Hardness Vickers (50gr-10s)
19
800
Quenched
750
Tempered at 400°C
700
Tempered at 600°C
650 600 550 500 450 400 350 300
Before wear
200°C
400°C
600°C
Sliding wear test temperature
the surface. The ends of the running-in periods were determined in terms of the intersection point resulting from drawing the slopes in the stable zone and the transition zone of the friction versus the sliding distance curve for the three microstructures and three temperature tests. These values are shown in Fig. 7, and the stable friction coefficients are shown in Fig. 8. Figure 7 shows that at a test temperature of 200 °C, all microstructures show the lowest sliding distance required to stabilise the friction coefficient, and this observation can be explained by a poor or null influence of oxidation at this temperature. At this temperature, the running-in period may depend on the plastic strain, which can occur over less time than the oxidative process. At a test temperature of 600 °C, the running-in period is extended for all microstructures, which implies a longer process of surface stabilisation between the asperities of both surfaces due to a dominant oxidative process that interferes with the direct plastic strain of asperities. Figure 8 shows the linear change in the friction coefficient at steady state as a function of test temperature for the three microstructures. The highest values of the friction coefficients occur at a test temperature of 200 °C because of the contact metal oxide or no layer formation (NL) [16], as is deduced from the high strain hardening of the matrix (due to the contact interaction of the asperities of the counterbody with the pin surface) and the wear mechanisms (see Sect. 4.1). The lowest friction coefficient values at steady state are found at 600 °C and are due to the pin oxide layer that plays the role of a solid lubricant (which is formed by the test temperature favouring sintering of the oxides and wear debris [29] ) as is deduced from the reduction of wear mass loss (formation of an oxide film prevents metal-metal contact and thus lowers wear and friction [30] ), softening of the matrix, and wear mechanisms (see Sect. 4.3). This behaviour is comparable to that found by Milan et al. [12] in a similar range of temperatures. Finally, at a test temperature
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of 400 °C the friction coefficient values show an intermediate behaviour between the friction coefficients at 200 and 600 °C. The significant scatter or oscillation of the friction coefficients between genuine replications could have its origin in the high roughness of the counterbody (oxidised ASTM A36 steel) [31, 32], but the decrease of the friction coefficients with increasing test temperature is clear for the three microstructures. 3.3 Hardness Test The macro-hardnesses of materials that were quenched, tempered at 400 °C, and tempered at 600 °C were 58.7 HRC ± 0.6, 57.3 HRC ± 0.6, and 47.1 HRC ± 0.5, respectively. The sample tempered at 400 °C does not present a drastic decrease in hardness with respect to the quenched sample because of the secondary hardening generated by the precipitation of fine carbides [28]. The micro-hardness of the M3C carbide was 1017.1 ± 56.4 HV50gf, which is in accordance with the values reported in the literature [5, 33]. The matrix microhardness before and after the wear tests are shown Fig. 9. The samples tested at 200 °C showed matrix hardening of 15.3, 5.7, and 4.3 % for materials that were quenched, tempered at 400 °C, and tempered at 600 °C, respectively. The amount of work hardening decreases with the increases in the tempering temperature due to the decrease in the content of retained austenite, which is primarily responsible for the higher matrix hardening. The matrix hardening explains the mass loss differences between microstructures (Fig. 5). For a test temperature of 400 °C, the materials quenched and tempered at 600 °C showed a greater decrease in hardness (-17.2 and -11.8 %, respectively), whereas those tempered at 400 °C showed negligible softening (-1.4 %) because of the precipitation of fine carbides (secondary hardening [28] ).
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Table 4 Energy dispersive X-ray spectrometry (EDS) of pin surfaces found in a sample quenched tested at 200 °C (Fig. 10a) Chemical elements
Fe
Zone 1
93.02
Zone 2
79.96
Zone 3
92.44
O – 14.15 –
Cr
Ni
Si
Mn
–
5.37
1.61
–
–
4.34
1.55
–
4.86
–
–
2.70
temperature was lower than that of the other temperature condition. This behaviour is explained by the formation of a stable layer of oxide on the pin surface; this layer avoids pure metal contact between the body and counterbody surfaces, and mass loss is prevented in this manner. Although the continuous oxide decreases the heat transfer generated by frictional heat, the test temperature produces a large decrease in the hardness of the matrices (softening by restoration). 3.4 Wear Mechanisms
Fig. 10 Scanning electron microscopy images of the wear surfaces tested at 200 °C for samples: a quenched, b tempered at 400 °C, and c tempered at 600 °C
Finally, for a test temperature of 600 °C, all samples showed softening of the matrix that was higher than that occurring at 400 °C. The samples showed decreases in hardness of -24.3, -20.4, and -29.7 % for materials quenched, tempered at 400 °C, and tempered at 600 °C, respectively. However, the wear rate of all samples at this
Figure 10 presents the wear surface of pins tested at 200 °C, and Table 4 lists the results of the EDS analysis of points 1, 2, and 3 shown in Fig. 11a. The wear mechanisms observed in the microstructures tested at a test temperature of 200 °C were wedge formation and micro-ploughing (Fig. 10). Figure 10a displays the plastic strain adjacent to the groove caused by the passage of an abrasive particle in the metallic surface and a metallic prow formed at the end of the groove. The wedge formation can be observed in Fig. 10b, and micro-ploughing is present in Fig. 10c. The EDS analysis of the samples at this test temperature shows selected oxide zones (zone 2) on the overall surface, implying that the oxidation at this test temperature is not relevant. There is no oxidative wear, but it is clear that the interaction between the abrasive (oxides on the disc) and metal (pin surface) materials is responsible for the highest strain hardening of the matrix at this test temperature. Figure 11 shows the wear surface of pins tested at 400 °C. The wear mechanisms observed were oxidation and micro-cracking, and the latter is shown in additional detail in Fig. 12. The wear surface presents a discontinuous oxide with compact and porous zones. Figure 13 shows a fracture of the pin oxide that exposes the metallic surface. At this temperature, the oxide (formed by wear debris and common oxide growth) cannot display mechanical stability, which means that the oxide is not completely compacted and sintered and is susceptible to fracture or breakdown, which is consistent with the results of EDS analysis (Table 5) in which the composition of the points 1, 2, and 3 are presented in Fig. 13. At a test temperature of 600 °C, all microstructures show a compact oxide layer on the pin surface (Fig. 14). In this condition, the microstructure is covered with a
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Fig. 12 Scanning electron microscopy images of the pin surface tested at 400 °C in which a an oxide flake becomes detached from the surface and b fracture of the pin oxide can be observed
Fig. 11 Scanning electron microscopy images of the wear surfaces tested at 400 °C for samples: a quenched, b tempered at 400 °C, and c tempered at 600 °C
mechanically stable oxide that blocks contact with the counterbody and aids in reducing the wear rate and friction coefficient. The wear mechanism observed at a test temperature of 600 °C was oxidative for the microstructures tested.
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Fig. 13 Scanning electron microscopy images of partial fracture of the pin oxide found in a sample tempered at 400 °C and tested at 400 °C
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Table 5 Energy dispersive X-ray spectrometry (EDS) results of the wear scar of a partial fracture in pin oxide found in a sample tempered at 400 °C and tested at 400 °C Chemical elements
Fe
O
Cr
Ni
Si
Zone 1
78.38
15.50
–
4.36
1.76
Zone 2
78.33
14.23
1.12
5.02
1.30
Zone 3
92.38
–
5.84
1.78
–
3.5 Wear Debris In every case, the wear debris contains a large amount of iron oxides followed by nickel–iron oxides and nickel– chrome–iron oxides. The iron oxides could have originated from the body and/or from the counterbody (oxidised ASTM A36 disc). Figure 15 and Table 6 show the morphology of the generated debris and EDS analysis, respectively.
4 Discussion 4.1 At a Test Temperature of 200 °C The predominant contact is metal oxide, given the (1) high friction coefficients observed in all microstructures of MCI tested at this temperature (Fig. 6), (2) the high strain hardening of the matrix (Fig. 9), and (3) the predominant wedge formation and micro-ploughing wear mechanisms for all pins at this test temperature (Fig. 10). In this condition, the wear behaviour depends almost exclusively on the matrix hardness, and the results are comparable with those found by Coronado et al. [34] at room temperature. There are no oxides to block the contact of both surfaces that allows the matrix strain hardening. We thus conclude that for all running-in periods of all microstructures tested (quenched and tempered at 400 and 600 °C), the minimum running period was observed at 200 °C. 4.2 At a Test Temperature of 400 °C Severe wear occurred at this condition compared with that at other test temperatures. This observation is explained by the loss of stability of the pin oxide at this temperature. Oxidative wear that occurs from the dynamic behaviour of the pin oxide (oxidation, formation of compact pin oxide, the breakdown or fracture of pin oxide, new material surface exposed and oxidised again) facilitates the removal of material from the surface, as evidenced in the mass loss (Fig. 5) and the discontinuous oxide observed in Fig. 13.
Fig. 14 Scanning electron microscopy images of the wear surfaces tested at 600 °C for samples: a quenched, b tempered at 400 °C, and c tempered at 600 °C
Nickel–iron oxides were found in the wear debris (pin oxides) (Fig. 15; Table 6), which supports the fact that the oxidative mechanism is the predominant mechanism.
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Fig. 15 Wear debris of the sample tested at 400 °C for MCI tempered at 400 °C
Table 6 Energy-dispersive X-ray spectrometry (EDS) results of wear debris for the condition tested at 400 °C for MCI tempered at 400 °C Chemical elements
Fe
O
Cr
Ni
Si
Spectrum 1
72.75
22.46
1.69
3.10
–
Spectrum 2
77.73
14.23
–
–
–
Spectrum 3
74.42
23.05
1.69
5.84
0.82
Spectrum 4
72.17
22.76
–
4.26
0.81
4.3 At a Test Temperature of 600 °C In this condition, the oxide displayed stable behaviour and formed a protective layer on the pin surface against subsequent wear damage. Evidence of this observation is the low friction coefficients (Fig. 6), low wear loss in all tests (Fig. 5), and compact and continuous oxides observed from SEM (Fig. 14). This behaviour is consistent with the effect of sintering and compactness of wear debris reported by Stott [9, 10, 13] in which it was necessary to achieve a specific value of temperature to favour this phenomenon. In this research, a transition temperature exists between 400 and 600 °C. The longer running-in periods were found at 600 °C because of the initial oxidation and later growth of stable or meta-stable oxide layers in the interface, directly affecting the time required for plastic accommodation of the surfaces in contact.
5 Conclusions This research analysed the high temperature tribological behaviour of an MCI sliding on oxide formed at 1,200 °C for 4 h on ASTM A36 steel. The results support the following conclusions:
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At low temperature, the mass loss is inversely proportional to the amount of retained austenite in the matrix. In this case, the strain hardening of the matrix has a great influence on the wear behaviour. If the temperature is increased, the wear rate increases and the friction coefficient decreases because of the formation of an oxide layer. At high temperature, the wear behaviour depends more strongly on the stability of the oxide and less on the microstructure (retained austenite). A transition temperature exists at which a stable oxide layer is formed and produces lower friction coefficient values and a drastic decrease in mass loss. The running-in periods are prolonged when the test temperature is increased because of the initial oxidation and later growth of a stable or meta-stable oxide layer in the interface, which directly affects the time required for plastic accommodation of the surfaces in contact. Acknowledgments The authors acknowledge Universidad del Valle for support from project no. CI 2652.
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