It must be emphasized that a comparison in terms of dissipated energy already integrates the friction reduction factor. A similar analysis based on the Archard's approach (Figure 80), which reflects the ratio of the total wear volume to the product of the normal force by the total sliding distance, produces a more abrupt reduction of the wear rate as threshold temperature $T_t$ is exceeded ($\frac{K_{200^{\circ}C}}{K_{400^{\circ}C}} \approx 16$). Indeed, apart from decreasing the energy wear rate, the stabilized ‘glaze’ layer ($T>T_{gs}$) also decreases the amount of dissipated energy in the interface. Moreover, it is worth to notice that equally high linear correlation with the Archard's product (coefficient of determination $R^2$ and standard deviation $\sigma$ are $R^2_{200^{\circ}C}=0.98$ and $\sigma_{200^{\circ}C}=0.023 \text{ mm}^3$ and $R^2_{400^{\circ}C}=0.93$ and $\sigma_{400^{\circ}C}=0.003 \text{ mm}^3$ for $200^{\circ}C$ and $400^{\circ}C$, respectively) as with the above-discussed accumulated dissipated energy can be observed.

<figure><img src="image_81.png" /><figcaption>Figure 79: Total wear volume as a function of the accumulated dissipated energy at $200^{\circ}C$ and $400^{\circ}C$ for which the wide range of the mechanical loadings were investigated.</figcaption></figure>
<figure><img src="image_82.png" /><figcaption>Figure 80: Total wear volume as a function of the Archard's product at 200°C and 400°C for which the wide range of the mechanical loadings were investigated.</figcaption></figure>

# 4. ANALYTICAL CHARACTERIZATION OF THE INTERFACE

Different analytical techniques for characterization of the Jethete M152/A-286 interface were employed to complete the previous quantitative investigations and give the final answer regarding the process that controls the wear-protective layer development.

## 4.1. Scanning electron microscope investigations

At first, scanning electron microscope observations combining energy dispersive X-ray spectrometry analyses of the fretting scars were carried out. All investigations were conducted under 15 keV of the accelerating voltage of the electron beam. Prior to the observations the specimens were cleaned in ultrasonic bath so that remove the loose wear debris. Figure 81 shows the morphology of the fretting scar generated on to the A-286 specimen under the mechanical key point loading conditions at 23°C (i.e. below $T_t$). The local adhesive wear mechanism characterized by tearing out of the material was found to be predominant (Figure 81a). The local metal transfer and surface seizure might have induced a higher wear rate. The particulate nature of the
wear surface was revealed (Figure 81b-c). Tilted secondary electron images allowed the measurements of the pilled up third body layers to be carried out. The thickness of the third body was found to be in the 2-6 µm range (Figure 81d). It appears, therefore, that the 2-6 µm thick wear debris layers were flaked off under fretting loadings as a result of delamination process [Waterhouse et al. (1974)]. The continuing fretting action caused that they were crushed into the fine spherical particles within the interface.

The morphology of the fretting scar obtained under the mechanical key point loading conditions at the high temperature (400°C) (Figure 82) showed the features different from those characteristic of the low temperature. The large smooth load-bearing areas ('glaze' layers) were formed at discrete locations on to the wear surface (Figure 82a). Higher magnification images (Figure 82b-c) revealed linear grooves on the 'glaze' layers aligned in the sliding direction, which mean that above $T_t$ three body abrasive wear was dominant. Figure 82d depicts the image taken on the border of the scar where compacted particle regions can be observed. 'Glaze' layers were developed on the top of such areas as a result of burnishing of the agglomerations of particles adhered to each other during the test [Stott (1998)]. It is proved in high magnification picture (Figure 82c). It is apparent that the 'glaze' layers are very solidly compacted (characterized by a very high cohesion quality) on to the wear surface (Figure 82c) and elevate over the adjacent areas similar to those characteristic of adhesive wear mechanism observed at 23°C. These adjacent areas show, however, less particulate features than it was revealed at the lower temperature implying higher degree of particle compaction (i.e. higher cohesion). This seems to confirm that submission to the high local pressure and elevated temperature conditions favours the activation of the sintering process [Jiang et al. (1998), Kato et al. (2007)], promoting the formation of a compliant 'glaze' layer structure. The morphology of the wear scar generated at 200°C (Figure 83) revealed that most of its surface shows the features similar to those characteristic of the wear surface obtained at 23°C. Only somewhere the small 'glaze'-like patches could be noticed. The qualitative evaluation of the fretting scars produced at 200 and 400°C showed that it took up relatively smaller area at the former temperature than at the latter one. This therefore infers that $T_t=230°C$ is not the threshold temperature below which a 'glaze' structure cannot be formed, but it is the temperature below which a 'glaze' layer is unstable mechanically.
<figure><img src="image_83.png" /><figcaption>Figure 81: Characteristics of the wear surface formed on to the A-286 specimen at 23°C: (a) Low magnification image showing typical adhesive wear mechanism; (b) Tearing out of the material due to the local adhesive interactions; (c) High magnification image revealing the particulate nature of the third body; (d) Pilling up of third body layers.</figcaption></figure>

The elevated temperature (i.e. above $T_t$) facilitates wear particles compaction (i.e. increase of adhesion forces between wear particles [Yamamoto et al. (1981)]), so the formation of a very coherent wear-resistant load-bearing layers is promoted. As soon as a stable ‘glaze’ layer is developed in the interface ($T>T_t$) the load-bearing capacity is fully modified and resistance to wear increases around order of magnitude compared to the lower temperatures ($\frac{\bar{\alpha}_{kp\_T<T_t}}{\bar{\alpha}_{kp\_T>T_t}} \approx 13$). A virtue of the formation of a ‘glaze’ layer is that, when breakdown occurs locally and material is lost, the fretting action repairs the damage by rapid recreating the ‘glaze’ as high amount of wear particles is retained within the interface due to the increased particle adhesion.
<figure><img src="image_84.png" /><figcaption>Figure 82: Characteristics of the wear surface formed on to the A-286 specimen at 400°C: (a) Large load-bearing glaze layers; (b) Linear grooves on the glaze layers aligned in the sliding direction; (c) High magnification image depicting very high cohesion of the glaze layer that is elevated over the adjacent granular areas; (d) Compacted particle region observed on the border of the scar.</figcaption></figure>

Apart from the ordinary observations of the wear scars the cross-section investigations were carried out. The compacted third body layer overlying the substrate material was revealed in all cases. Figure 84 shows the cross-sectional view of the wear scar (Figure 84a) generated under the mechanical key point loading conditions at 400°C and associated EDX map of oxygen distribution (Figure 84b). The layered structure of the formed third body is clearly apparent as cracks parallel to the top surface can be observed. Some damaged areas apparent in the polished third body section show that the third body layer consists of the fine wear particles. The EDX map of oxygen distribution revealed a strong oxidation of the third body.
<figure><img src="image_85.png" /></figure>

Figure 83: Morphology of the wear scar generated on to the A-286 specimen under the mechanical key point loadings at 200°C; Adhesive wear mechanism is predominant, even though some small areas of glaze layers can be observed.

<figure><img src="image_86.png" /></figure>

Figure 84: (a) Cross-sectional view of the wear scar generated at 400°C on to the A-286 revealing layered structure of the formed third body and (b) the associated EDX map of oxygen distribution showing its strong oxidation.

Figure 85 depicts a comparison between the EDX spectrum obtained from the third body layer formed under the mechanical key point loading conditions at 400°C on to the wear surface of the Jethete M152 counter body and that acquired from the substrate. A diminution in iron and chromium content due to a strong oxidation (i.e. high amount of oxygen detected) and an increase in nickel content in the third body composition in relation to the substrate was observed. This implies that transfer of particles from the lower A-286 specimen (having high nickel content – see Table III) that are subsequently mixed with the Jethete M52 counter body material (having low
nickel content – see Table III) and the environmental component (i.e. oxygen) takes
place during the fretting experiments. The peaks from gold present on the spectra are
a consequence of depositing this element on the resin-encapsulated metal specimens
in order to ensure the conductivity of the electrons during the SEM observations. The
quantitative EDX analyses of the third body layers (performed at the surface, in the
centre and at the substrate) formed under the mechanical key point loading conditions
at different temperatures (23, 200 and 400°C) showed that the chemical composition
is homogenous across the third body thickness in the case of both counter-bodies at
the given temperature. Similar chemical composition of the third body could be
observed for all the considered temperatures for the individual counter bodies (Figure
86).

<figure><img src="image_87.png" /><figcaption>Figure 85: Comparison between EDX spectrum of the substrate (—) and the third body layer (——) formed on to the wear surface of the upper Jethete M152 specimen after test under the mechanical key point loadings at 400°C.</figcaption></figure>

Figure 87 shows the evolution of the thickness of the third body formed under the
mechanical key point loadings on to the wear surfaces of the Jethete M152 and A-286
counter body as a function of temperatures. As expected, it increases with
temperature. This implies that greater amount of wear particles is retained in the
interface what supports the hypothesis of the sintering process as a major factor
controlling the ‘glaze’ layer development [Jiang et al. (1998), Kato et al. (2007)].
Moreover, it must be noticed that the thickness increases practically in linear manner. If a thickness controlled the development of a stable effective wear-protective ‘glaze’ layer there should be revealed the discontinuities in its evolution at $T_t$ similar to those observed in friction and wear evolutions. It may therefore be implied that rather rheological properties of the interface, which change drastically with temperature variation, are in charge of effective ‘glaze’ layer development. At each the considered temperature the thickness of the third body developed on to the lower A-286 specimen was found to be greater than on to the Jethete M152 counter body. It is certainly due to gravity and a specificity of the studied contact geometry. Thus, the particles are easier retained within the wear scars of the lower specimens than on to the wear surfaces of the upper samples.

<figure><img src="image_88.png" /><figcaption>Figure 86: Evolution of oxygen (♦), iron (■), chromium (Δ) and nickel (×) content in the third body formed on to the (a) upper Jethete M152 and (b) lower A-286 specimen as a function of temperature.</figcaption></figure>

Hardness distribution conducted on the cross-sections through the wear scars produced on the A-286 specimen at 200 and 400°C under the key point loading conditions is shown in Figure 88. For the both temperatures a relatively high hardness of the compacted third body compared to the substrate material was found. In Figure 84 indentation marks can be observed. The conducted hardness measurements can be considered only in the qualitative way since the measured third body hardness may be
affected by the hardness of the substrate and the adjacent resin, especially at the lower temperatures as the thickness of the formed third body is relatively small.

<figure><img src="image_89.png" /><figcaption>Figure 87: Evolution of the thickness of the compacted third body layer formed on to the wear surface of the upper Jethete M152 (■) and lower A-286 (○) specimen as a function of temperature; Total thickness of the third body</figcaption></figure>

$$ (\Box-\Box)=(\Box-\bigcirc)+(\bigcirc-\bigcirc). $$

<figure><img src="image_90.png" /><figcaption>Figure 88: Hardness distribution performed on the cross-sections of the wear scars generated on the A-286 specimen at 200 (■) and 400°C (○) showing a high hardness of the third body layer in relation to the substrate.</figcaption></figure>

Generalizing from the SEM studies undertaken, at lower temperatures (T<Tt) severe adhesive wear mechanisms dominates (characterized by the high energy wear
coefficient), whereas at higher ones (T>Tᵢ) a third body abrasive process, involving
the formation of a compliant ‘glaze’ layer structure takes place (characterized by the
low energy wear coefficient). The compliant third body layer developed can be
considered as compacted oxidized wear particles originating from the two steel
surfaces. Where the ‘glaze’ areas have delaminated, the underlying material is of
granular appearance, however in cross-section it has a layered structure. It is
characterized by a high cohesion and elevated hardness, which enhances its load-
bearing properties. It all supports the tribo-sintering approach of the ‘glaze’
development [Jiang et al. (1998), Kato et al. (2007)].

In order to provide explicit clarification as to process(es) involved in ‘glaze’ layer
development, the structural analyses of the wear surfaces and wear debris were
carried out.

4. 2. X-ray diffraction study

X-ray diffraction (XRD) analyses, using a cobalt (Coα) lamp as a radiation source, of the wear scars on A-286 specimens did not reveal any oxide structures at 23 and 200°C. Similar XRD investigations performed for the fretting scar generated under the mechanical key point loadings at 400°C display small peaks, apart from high excitations from austenite, probably originating from Fe₂O₃ and/or Cr₂O₃ (Figure 89).

<figure><img src="image_91.png" /><figcaption>Figure 89: XRD pattern of the wear scar generated under the mechanical key point
loading conditions at 400°C.</figcaption></figure>
The obtained result is in agreement with thermodynamics (α-Fe₂O₃ structure is a The elevated temperature (i.e. above Tt) facilitates wear particles compaction (i.e. stable phase above 400°C), but contradicts the hypothesis proposed by Hurricks (1972 and 1974) that above 200°C the Fe₃O₄ spinel oxides operate in the interface contributing to the friction and wear rate decrease. Taking into account the specificity of a standard XRD technique (problem to get a reliable result from the small area (i.e. the wear scar) on to the sample as the output may be affected by the information from outside the chosen regions (i.e. reference surface)) the result obtained can be explained in two ways. Either the signal acquired originated from outside the wear scar (i.e. from native oxides) or there was no transformation in oxide structure due to fretting action and Fe₂O₃ and/or Cr₂O₃ formed on to the wear surface. Thus, at the current stage of investigations it cannot be stated if the activation of the lubricating ‘glaze’ layer is controlled only by a tribo-sintering process or perhaps by a change in oxide structures either. In order to clarify the possible correlation between the oxide structural transformation and the glaze layer development a specific surface Raman analysis was undertaken.

4. 3. Raman investigations

Raman spectroscopy analysis of the A-286 specimens previously subjected to the
fretting tests under the mechanical key point loading conditions at 23 and 400°C was
performed. The analysis was conducted at room temperature. To avoid a heating
effect, the laser tuned at 785 nm was operated at 5 mW to excite the sample. The laser
beam was focused on the sample with a spot size of 2 µm. A 5 sec exposure time and
10 acc was applied to collect the Raman spectra. Figure 90 shows the spectra obtained
from the reference surfaces (i.e. from outside the wear scars). No characteristic peaks
from any oxide structures were revealed for the specimen after the fretting test at
23°C. Hence, it may be concluded that the layer of native oxides formed on to the
specimen's surface was very thin as the Raman spectrum was excited from the depth
of 2 µm underneath the top surface. In the case of the higher temperature (400°C)
thicker native oxides were formed on to the metal surface. Thus, several peaks on the
Raman spectrum originating from the formed native oxides could be observed. The
bands at 227, 294, 414, 502, 613 and 1320 cm⁻¹ correspond to α-Fe₂O₃ (hematite) [De
Faria et al. (1997)], while the feature at 671 cm⁻¹ is characteristic of Fe₃O₄ (magnetite)
[De Faria et al. (1997)] and other spinel-like structures (e.g. FeCr₂O₄ [Wang et al. (2004)], NiCr₂O₄ [Wang et al. (2003)] or NiFe₂O₄ [Kim et al. (2005)] etc.) possible in terms of chemical composition of the tested materials. No peaks from Cr₂O₃ were found, although from the standpoint of thermodynamics formation of this compound would be highly probable (Figure 32). Thus, the native oxides formed at 400°C are mainly consisted of α-Fe₂O₃ with the some addition of spinel structures. The result obtained is according to the thermodynamics (relation 22).

<figure><img src="image_92.png" /><figcaption>Figure 90: Comparison between Raman spectrum excited from outside the wear scar (i.e. native oxides) generated on to the lower A-286 specimen at 23°C (______) and 400°C (____).</figcaption></figure>

Figure 91 shows the spectra excited from the generated fretting wear scars. For the both temperatures (i.e. 23 and 400°C) the similar features can be observed. The strong broad features excited at 660 cm⁻¹ for 23°C and at 671 cm⁻¹ for 400°C imply that spinel structures are mainly formed on to the wear surface independently of the test temperature. The shift between the peaks may be explained by differences in oxide stechiometries. The weak features appearing between 220 and 500 cm⁻¹ as well as around 1320 cm⁻¹ prove the presence of small quantities of α-Fe₂O₃ in the formed oxide structures as well. Moreover, it cannot be excluded the presence of Cr₂O₃ as its strongest line is excited at 550 cm⁻¹, which may be either superimposed (23°C) by, or a shoulder (400°C) of, the broad peak from spinel-like oxides. The small excitations
found at 810 and 779 cm⁻¹, respectively for 23 and 400°C were not characterized to origin from any common oxides of Fe, Cr or Ni or nitrides of Cr. Further in-depth investigations should be undertaken to clarify this issue.

<figure><img src="image_93.png" /><figcaption>Figure 91: Comparison between Raman spectrum excited from the wear scar generated on to the lower A-286 specimen under the mechanical key point loading conditions at 23°C (___) and 400°C (___).</figcaption></figure>

While the result obtained at 23°C is in accordance with thermodynamics of iron oxidation (i.e. below 200°C Fe₃O₄ is the most thermodynamically stable oxide – relation 22), the result acquired at 400°C contradicts it (i.e. at 400°C α-Fe₂O₃ should be expected to form mostly). This implies that fretting action (at least at elevated temperature conditions) induces the unique transformation in oxide structure (for pure iron it would be α-Fe₂O₃ → Fe₃O₄) due to a complex stress-strain response of the
interface under loadings. Of course, in the case when high-alloyed steels are
investigated the transformation into more complex spinel-like compounds may be
possible (e.g. FeCr₂O₄, NiCr₂O₄, NiFe₂O₄ etc.). The Raman analyses have also
clarified the previously discussed XRD results indicating that the pattern obtained at
400°C was excited from outside the wear scar (i.e. native oxides were characterized).
Generalizing, the performed Raman spectroscopy analyses showed that both at the
low (23°C) and high (400°C) temperature spinel-like oxides were main compounds
formed on to the wear surfaces. The Raman technique is very sensitive to, and
provides a clear identification of, the Fe₂O₃ and Cr₂O₃ oxides, but does not allow an
unambiguous identification of spinels [Renusch et al. (1996)]. Thus, taking into
account chemical compositions of the mated materials (Table III) it may be concluded
that the formed products of tribo-oxidation are a mixture of different spinel oxides
rather than consist of individual specific compound. The invariable with temperature
interface in terms of structural composition implies that there is no correlation
between the abrupt decrease in wear rate observed above Tᵢ=230°C (Figure 75) and
formed oxide structures as it was suggested by Hurricks (1972 and 1974). Thus, it can
be stated that a modification of the rheological properties of the third body leading to
the development of a lubricating ‘glaze’ layer is controlled mainly by a tribo-sintering
process of oxidized wear particles.

In order to validate the Raman results transmission electron microscope (TEM)
investigations of generated wear debris were undertaken.

4. 4. Transmission electron microscope investigations

The compacted oxidized third body layer has been found to be made up of wear
debris generated during friction. Thus, chemical and phase composition of the former
is constituted by the composition of the latter. High resolution (HRTEM) and
conventional transmission electron microscope (TEM) observations combined with
selected area electron diffraction (SAED) and electron spectroscopic imaging (ESI)
analyses of numerous wear debris generated after fretting tests under the mechanical
key point loading conditions (δ*=± 100 µm, P=176 N and N=360000) at three
temperatures: 23, 200 and 400°C were carried out. The samples were prepared from
generated wear debris particles, which were collected straightaway after test on to the
copper mesh grid with Lacey carbon support film. Just after this, the sample was
placed into the microscope and analyzed. Accelerating voltage in the case of the
bright field imaging was 120 kV, however diffraction analyses were conducted at 100
kV excitation voltage.

High resolution observations showed that agglomerated wear debris was consisted of globular nano-particles of size from 10 to 20 nm, independently of fretting test temperature (Figure 92).

<figure><img src="image_94.png" /><figcaption>Figure 92: HRTEM bright filed image of wear debris revealing its nano-molecular structure.</figcaption></figure>

Figure 93 shows the bright filed image, the associated diffraction pattern and elemental ESI distribution maps of wear debris produced during the fretting experiment at 400°C. ESI analysis proved the presence of oxygen, iron, chromium and nickel elements in all investigated wear debris generated at different temperatures. Conducted diffraction analysis showed that all produced diffraction patterns had the same features (i.e. the same interplane distances could be determined for the produced annuluses), independently of the test temperature. The representative diffraction pattern is depicted in Figure 93b. Annuluses observed on the patterns signify that formed compounds have polycrystalline structures. Having knowledge of the chemical composition of the studied wear debris the produced annuluses characteristic of all temperatures were identified to be corresponding to the (311), (440), (511), (220) and (400) planes (giving the peaks of the highest intensities in reference XRD analysis) of γ-Fe₂O₃ and/or Fe₃O₄ and/or FeCr₂O₄ and/or NiCr₂O₄
<figure><img src="image_95.png" /><figcaption>Figure 93: TEM bright field image of the wear debris generated during the fretting test under the mechanical key point loading conditions at 400°C (a); the associated diffraction pattern (b); the associated ESI map showing distribution of iron (c), oxygen (d), chromium (e) and nickel (f).</figcaption></figure>
and/or NiFe₂O₄ and/or CrO compounds and to the (200), (111), (220) and (311) planes of NiO. Thus, many oxide compounds may be matched as they have the same cubic crystal structure with similar lattice constant (concerning the former group of possible oxides). In any case, the conducted XRD analysis proved the formation of spinel-like oxides. No evidence for the presence of α-Fe₂O₃ oxide in the wear debris generated at any temperature was shown, thereby, confirming previously obtained results of Raman analysis. While occurring the γ-Fe₂O₃ may be excluded based on the Raman analysis as it is a compound producing clearly distinguishable spectrum, the presence of the CrO and/or NiO oxides cannot be questioned since the Raman technique is insensitive to their identification [Renusch et al. (1996)].

Summarizing, from TEM investigations undertaken the following conclusion can be drawn. The generated wear debris was shown to be made up of globular nano-particles of size of 10-20 nm for all the considered temperatures. Spinel like-oxides (Fe₃O₄, and/or FeCr₂O₄ and/or NiCr₂O₄ and/or NiFe₂O₄) and/or CrO and/or NiO were found to be possible compounds formed as a result of tribo-oxidation process on to the wear surfaces, independently of the test temperature. This fact combined with the lack of evidence for the α-Fe₂O₃ presence once again casts doubt upon the hypothesis proposed by Hurricks (1972 and 1974), assuming oxides transformation as an essential factor explaining friction and wear decrease above around 200°C. Hence, it can be stated that the phenomenon that plays a crucial role for the development of the lubricating ‘glaze’ layer is a tribo-sintering process [Stott (1998), Kato et al. (2007)], whose the driving force is the increasing with temperature adhesion between oxidized wear particles. Summary of the performed analytical investigations of the interface is depicted in Figure 94.

<figure><img src="image_96.png" /><figcaption>Figure 94: Schematic illustration summarizing the results of the undertaken analytical investigations of the interface at different temperatures.</figcaption></figure>
5. EFFECT OF PRE-OXIDATION ON THE TRIBOLOGICAL BEHAVIOUR

In order to evaluate the effect of specimen pre-oxidation on the tribological behaviour
of the Jethete M152/A-286 contact below the severe to mild wear rate transition
temperature (Tt=220°C) three tests under the key point loading conditions (T=200°C,
δ*=± 100 µm, pm=25 MPa (i.e. P=176 N) and N=360000), using specimens
previously held in the set-up without fretting action for different time periods (1, 4.5
and 7.5 hours) at 400°C, were carried out.

Figure 95 shows the evolutions of the energy coefficients of friction as a function of test duration for the reference experimental conditions (the key point loadings) and two fretting tests, in which pre-oxidized in the time period of 1 and 7.5 hours specimens were used. Similar friction tendency for all the considered cases can be noticed. It turns out that there is no influence of the applied specific pre-treatment of specimens on the maximum and steady-state energy coefficients of friction as their values are very close to those characteristic of reference test (Figure 96). No effect on the evolution of the maximum energy coefficient of friction implies that under applied loading conditions the formed native oxide layer is destroyed immediately as the fretting action is being run [Maatta et al. (2001)].

<figure><img src="image_97.png" /><figcaption>Figure 95: Evolution of the energy coefficient of friction (μe) as a function of the test duration for the reference test conditions (the key point) (—) and two fretting experiments, in which pre-oxidized in the time period of 1 (—) and 7.5 (—) hours specimens were used.</figcaption></figure>
<figure><img src="image_98.png" /><figcaption>Figure 96: The evolution of the average steady-state and maximum energy coefficient of friction as a function of the time period of the applied pre-oxidation.</figcaption></figure>

Also wear response of the studied tribo-system appears not to be affected by the applied pre-oxidation process since a low deviation from the reference wear volume ($V_{ref} = 0.654 \text{ mm}^3$) not higher than $\pm 0.060 \text{ mm}^3$ (it constitutes around 9% of the $V_{ref}$) could be observed. Figure 97 shows the evolution of the total wear volume versus the applied time period of the pre-oxidation treatment.

<figure><img src="image_99.png" /><figcaption>Figure 97: The evolution of the total wear volume as a function of the time period of the applied pre-oxidation.</figcaption></figure>
The pre-oxidation was recognized, in this study, as a treatment that does not produce any effect on the tribological behaviour of the Jethete M152/A-286 tribo-system even on the initial period of friction evolution (Figure 95 and 96). It therefore confirms the idea that it is not an oxide structure that controls the development of a stable effective ‘glaze’ layer, but a tribo-sintering process, which is activated by a synergetic effect of temperature and mechanical fretting loadings. Hence, considering that the post-oxidation fretting experiments were carried out under the key point loadings at 200°C (temperature below the severe to mild wear rate transition temperature ($T_t$)) the inability of the interface to produce a stable effectively acting ‘glaze’ layer is fully understandable. Moreover, it was reported by Glascott et al. (1985) that formed steady-state oxide scale resulted in the development of a wear-protective oxide surface during subsequent normal sliding at certain elevated temperature but not at room one. It was shown that, by contrast with the elevated temperature conditions, the low ambient temperatures favoured detachment and break-up of the oxide during sliding, which prevent the particle compaction and load-bearing oxidized layer development. Hence, it seems to be interesting to investigate pre-oxidation effect more extensively by verifying the impact of the higher fretting test temperatures (above $T_t$).

**6. SYNTHESIS OF THE CHAPTER**

The profound analysis of the impact of temperature (23-400°C) on the tribological behaviour of the Jethete M152/A-286 tribo-system under the key point loading conditions ($\delta^*=\pm 100$ µm, $p_m=25$ MPa (i.e. P=176 N) and N=360000) has been carried out. Friction and wear quantifications using a dissipated energy approach have been performed. It has been shown that the fretting wear of the Jethete M152/A-286 contact evolves in a series of stages with one event initializing another. The initial short running-in period (similar for all the considered temperatures) of adhesion and material transfer is followed by the intermediate transient period (characterized by high work hardening and degradation of the adhesion zones), within which the formation of the third body layers on to the wear surfaces takes place before the steady-state is established. It has been proved that independently of the temperature the wear occurs by a delamination process of flake-like wear debris, which are subsequently crushed into the fine spherical particles within the interface. A threshold
temperature $T_t=230°C$ has been established above which a stable lubricating ‘glaze’ layer is activated. Below and above $T_t$ different friction behaviour has been observed:

1) for $T<T_t$: there is a high and practically stable friction value (a mean value of the average steady-state energy wear coefficient $\overline{\overline{\mu}}_{e\_SS\_T<T_t} = 0.71$);

2) for $T>T_t$: a compliant ‘glaze’ layer is stabilized within the interface, promoting the lower friction coefficient ($\overline{\overline{\mu}}_{e\_SS\_T>T_t} = 0.49$).

The dissipated energy approach has provided a good formulation of the wear kinetics whatever the spectrum of the studied loading conditions (pressure, sliding amplitude, test duration). However, different energy wear coefficients have been found depending on the nature of the interface (i.e. below and above $T_t$):

1) for $T<T_t$: there is a high and almost constant energy wear coefficient (an average value of the energy wear coefficient $\overline{\alpha}_{kp\_T<T_t} = 5.44 \cdot 10^{-5} \text{ mm}^3 \cdot \text{J}^{-1}$);

2) for $T>T_t$: a low constant energy wear rate is observed ($\overline{\alpha}_{kp\_T>T_t} = 4.19 \cdot 10^{-6} \text{ mm}^3 \cdot \text{J}^{-1}$).

This variation of the energy wear coefficient indicates that different tribological processes are activated below and above the transition temperature $T_t$. As soon as a stable ‘glaze’ layer is activated (in fact there is a negligible 20°C temperature range for the transition) the low wear mechanisms is favoured. The load-bearing capacity is then fully modified and resistance to wear decreases around 13 times compared to lower temperatures.

SEM observations showed that below $T_t$ a typical severe adhesive wear dominates, whereas at higher ones ($T>T_t$) a third body abrasive process, involving the formation of a compliant ‘glaze’ layer structure, takes place. The compliant third body layers (the so-called lubricating glaze layers) developed can be considered as the compressed oxidized sub-microscopic wear particles originating from the two steel surfaces, which form solid compact layers, the tops of which are further burnished during the fretting action. The structural analyses of the wear surfaces using Raman and TEM techniques have shown that independently of the test temperature spinel-like ($Fe_3O_4$ and/or $FeCr_2O_4$ and/or $NiCr_2O_4$ and/or $NiFe_2O_4$) and possibly NiO and/or CrO oxides are main compounds formed. Hence, it is clear that the friction and wear rate decrease observed above $T_t$ is not associated with the change in the type of oxide generated during fretting (as was suggested by Hurricks (1972 and 1974)), but is
closely related to a modification of the surface energy of oxidized nano-particles present in the interface that causes drastic increase of the adhesion work between them [Yamamoto et al. (1981)] and favours a sintering process of the third body [Stott (1998), Kato et al. (2007)] leading to development of a lubricating ‘glaze’ layer.

It has been found that the fretting time to develop the compact wear-protective ‘glaze’ layers decreases with increasing temperature above the transition temperature $T_t$. Presumably it is associated with the synergetic effect of the faster rate of oxide production and increased adhesion between the generated wear particles at the higher temperature.

No effect of specimen pre-oxidation treatment under subsequently investigated fretting loading conditions on the tribological behaviour of the considered tribo-couple has been found. It indirectly supports the hypothesis that a tribo-sintering process, which is activated by a synergetic effect of temperature and mechanical fretting loadings generates the formation of a stable wear-protective ‘glaze’ layer.

The following questions are being arisen after analyzing the results obtained under the invariable loading conditions:

- What would be the dynamics of the third body evolution under variable loading conditions?;

- How can an energy wear approach be transposed to capture the wear kinetics under variable loading conditions?;

- Can the fretting wear behaviour of the studied tribo-couple be characterized by the two average energy wear coefficients associated with the found wear mechanisms in the range of the studied loadings?.

The responses to these questions are being attempted to be found in the next Chapter in which results of the investigations conducted under variable loading conditions are brought up for discussion.
# CHAPTER 4

## FRETTING BEHAVIOUR UNDER VARIABLE LOADING CONDITIONS
# CHAPTER 4: FRETTING BEHAVIOUR UNDER VARIABLE LOADING CONDITIONS

## 1. TRIBOLOGICAL BEHAVIOUR UNDER VARIABLE TEMPERATURE CONDITIONS

In practice, most mechanical systems operate under variable mechanical and environmental conditions. The investigated couple of materials is considered by Snecma to be applied to the vane/bushing joints of the third stage of the VSV system, where working temperature varies between 218 and 350°C (during cruise and take-off, respectively). The former temperature is below and the latter above the severe to mild wear rate transition temperature $T_t$ found in the previous Chapter (Figure 75). Hence, to be adequately evaluated, for the tribological behaviour of the considered tribo-system should be taken into account variable environmental conditions. Thus, the friction and wear behaviour under the variable temperature conditions within a single fretting tests are being discussed below.

### 1.1. Experimental methodology

A review of the literature shows that probably no attention has been paid to the tribological investigations under variable temperature conditions. Hence, a new methodology, taking into account the temperature variations within a test, was designed. A dozen experiments under variable temperature conditions (VT) during a single fretting test were carried out. They can be classified into two test configurations illustrated in Figure 98. The first type (the tests VT 1-7) consists of a different number of repeated blocks of 200°C-400°C, the second one (the tests VT 8-12) of 400°C-200°C. The other parameters were maintained as for the mechanical key point loading conditions ($p_m=25$ MPa (i.e. $P=176$ N) and $\delta^*=\pm100$ µm). The number of cycles within each step in the block in the given VT test was constant (the only exception is the test VT 7 – see Table VII). Between each temperature transition the fretting tests were suspended for a short time (less than 15 minutes) in order to adjust the new temperature value. During the treatment of cooling and heating the contact between specimens was always kept. In the case of the test VT 7, higher number of cycles was
imposed at the first step of the test in order to avoid the running-in and transient period and achieve well-stabilized steady-state conditions.

Details of all tests conducted under variable temperature conditions are provided in Table VII.

<figure><img src="image_100.png" /><figcaption>Figure 98: Pattern of the test under variable temperature conditions and the associated fretting log characteristic of experiments consisting of repeated blocks of: (a) 200 °C-400 °C (test VT 2) and (b) 400 °C-200 °C (VT 9).</figcaption></figure>

<table><caption>Table VII: Detailed data concerning conditions of the tests carried out under variable temperature conditions (VT).</caption><thead><tr><th rowspan="2">Tests<br>type VT</th><th colspan="8">N<sub>i</sub>,<br>with: N - number of cycles for the given temperature,<br>i - temperature value [°C].</th><th rowspan="2">Total<br>No.<br>of<br>cycles</th></tr><tr><th>N<sub>200</sub></th><th>N<sub>400</sub></th><th>N<sub>200</sub></th><th>N<sub>400</sub></th><th>N<sub>200</sub></th><th>N<sub>400</sub></th><th>N<sub>200</sub></th><th>N<sub>400</sub></th></tr></thead><tbody><tr><td>Test No.</td><td>N<sub>200</sub></td><td>N<sub>400</sub></td><td>N<sub>200</sub></td><td>N<sub>400</sub></td><td>N<sub>200</sub></td><td>N<sub>400</sub></td><td>N<sub>200</sub></td><td>N<sub>400</sub></td><td>ΣN<sub>i</sub></td></tr><tr><td>1</td><td>50k</td><td>50k</td><td>50k</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>150k</td></tr><tr><td>2</td><td>75k</td><td>75k</td><td>75k</td><td>75k</td><td>-</td><td>-</td><td>-</td><td>-</td><td>300k</td></tr><tr><td>3</td><td>50k</td><td>50k</td><td>50k</td><td>50k</td><td>50k</td><td>50k</td><td>-</td><td>-</td><td>300k</td></tr><tr><td>4</td><td>110k</td><td>110k</td><td>110k</td><td>110k</td><td>-</td><td>-</td><td>-</td><td>-</td><td>440k</td></tr><tr><td>5</td><td>180k</td><td>180k</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>360k</td></tr><tr><td>6</td><td>37.5k</td><td>37.5k</td><td>37.5k</td><td>37.5k</td><td>37.5k</td><td>37.5k</td><td>37.5k</td><td>37.5k</td><td>300k</td></tr><tr><td>7</td><td>30k</td><td>5k</td><td>5k</td><td>5k</td><td>5k</td><td>5k</td><td>5k</td><td>5k</td><td>65k</td></tr><tr><td>Test No.</td><td>N<sub>400</sub></td><td>N<sub>200</sub></td><td>N<sub>400</sub></td><td>N<sub>200</sub></td><td>N<sub>400</sub></td><td>N<sub>200</sub></td><td>N<sub>400</sub></td><td>N<sub>200</sub></td><td>ΣN<sub>i</sub></td></tr><tr><td>8</td><td>50k</td><td>50k</td><td>50k</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>150k</td></tr><tr><td>9</td><td>75k</td><td>75k</td><td>75k</td><td>75k</td><td>-</td><td>-</td><td>-</td><td>-</td><td>300k</td></tr><tr><td>10</td><td>50k</td><td>50k</td><td>50k</td><td>50k</td><td>50k</td><td>50k</td><td>-</td><td>-</td><td>300k</td></tr><tr><td>11</td><td>110k</td><td>110k</td><td>110k</td><td>110k</td><td>-</td><td>-</td><td>-</td><td>-</td><td>440k</td></tr><tr><td>12</td><td>180k</td><td>180k</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>360k</td></tr></tbody></table>
## 1. 2. Dynamics of third body evolution – friction behaviour

Figure 99 displays the evolution of the coefficient of friction for four fretting tests: VT 2, 3, 9 and 10. The experimental evolution is there compared with the theoretical response (the average steady-state energy coefficient of friction at the given temperature from Figure 67) obtained for the constant test situation. Quite a good correlation can be observed.

<figure><img src="image_101.png" /><figcaption>Figure 99: Evolution of the coefficient of friction versus the test duration for variable temperature conditions for the experiments: (a) VT 2, (b) VT 9, (c) VT 3 and (d) VT 10; Experimental evolution of the coefficient of friction under variable temperature conditions: ——; Evolution of the applied temperature: ————; Theoretical evolution of the coefficient of friction defined from the steady-state values obtained under</figcaption></figure>

200 (—) ($\bar{\mu}_{e\_SS}$ = 0.72) and 400°C (—) ($\bar{\mu}_{e\_SS}$ = 0.46).
This suggests that the interface evolves from one tribological regime to another (adhesive to abrasive involving the 'glaze' layer formation) very fast as the temperature changes. Indeed, practically perfect discontinuous transitions can be noticed, which indicates that the friction memory effect after temperature change may be neglected. The 'glaze' layer (activated above $T_t$) would appear to form instantaneously from the third body previously generated below $T_t$. A similar evolution is observed when the contact passes from a lubricating high temperature (400°C) system to a high friction low temperature (200°C) interface. The lubricating glaze layer degrades very fast below $T_t$. However, it must be noticed that the test parameters during the fretting experiments VT 1-6 and 8-12 were read out only every 5000 cycles. In order to get reliable assessment of the dynamics of the third body evolution under temperature variation within a single fretting test the experiment with short steps (5000 cycles) between temperature transitions and dense data acquisition (every 50 cycles) was carried out. To verify test reproducibility the test was repeated twice. Similar friction response illustrated in Figure 100a was always achieved. Figure 100b shows details of the evolution of the friction transitions. The number of cycles needed to establish new friction regime was determined. And thus, it turns out that for the transitions from 400 to 200°C it was always around $N_{t\_400-200°C}=500$ cycles, from 200 to 400°C $N_{t\_400-200°C}=600$ cycles. However, it must be mentioned that data acquisition during the test VT 12 was limited by the software performance as after test suspensions during successive runs early acquisition points were lost. The given values of the number of cycles needed to change friction regime were the first acquisition points recorded after the transitions. Thus, it infers that the friction response may indeed change immediately after temperature transitions.

Summarizing, the transient periods to establish new friction regime were found to be shorter compared to the time required to generate the third body from a native interface (compare beginning of constant (Figure 55) and variable (Figure 100) fretting tests). In fact, for the invariable test at 200 and 400°C the number of cycles to establish steady-state is 20000 and 8000 fretting cycles, respectively (Figure 66). This infers that the friction evolution is not related to a progressive replacement of the third body by new one, but is controlled by the capability of the third body, which is already present in the interface, to reversible as a function of temperature change of its adhesive properties (elevated temperature conditions favours stronger adhesion between wear particles). No obvious influence of the order, number or duration of the
temperature sequences on the friction behaviour was found. Hence, it seems that rheological properties of the third body, which change drastically with temperature, play a vital role in the tribological behaviour as temperature variations below or above $T_t$ are applied.

To fully clarify the tribological response of the studied tribo-system under variable temperature conditions interrupted tests, also considering the impact of the test detentions, combined with an evaluation of a rheological quality of the interface should be conducted.

<figure><img src="image_102.png" /><figcaption>Figure 100: (a) Evolution of the coefficient of friction versus the test duration for the test VT 7; (b) zoom in of the evolution of the coefficient of friction showing details of the temperature transitions; Experimental evolution of the coefficient of friction under variable temperature conditions: ---; Evolution of the applied temperature: ----; Theoretical evolution of the coefficient of friction defined from the steady-state values obtained under 200 (___) and 400°C (___).</figcaption></figure>
### 1. 3. Wear behaviour

In the present dissertation (Chapter 3) the capacity of the energy wear approach to quantify the wear response of the considered contact for the given interface structure (i.e. the given temperature domain – see Figure 75 and 79) has already been demonstrated. However, a crucial question concerns its ability to predict the wear kinetics under variable temperature situations. Previous investigations have shown that, assuming a constant interface structure (i.e. a given wear mechanism), the energy wear approach is able to predict the wear kinetics under variable loading conditions. This has been extensively demonstrated for variable gross slip conditions [Paulin et al. (2005), Liskiewicz et al. (2005a)]. In the situation that is being discussed, a variation of temperature can drastically modify the interface and consequently the energy wear rate. This has been highlighted by temperature analysis (Figure 75). Under the mechanical key point loading conditions (i.e. $p_m=25$ MPa (i.e. $P=176$ N), $\delta*=\pm100$ µm and $N=360000$ cycles) two wear kinetics (i.e. the average energy wear coefficients) are activated depending on whether the temperature is below or above a threshold value $T_t=230$°C (i.e. if a stable wear-protective ‘glaze’ layer is activated or not). The friction investigations have indicated that the studied interface is highly reactive, displaying negligible memory effect. Hence, it appears that by using these two determined energy wear coefficients characteristic of the individual temperature domain (i.e. below and above $T_t$) the wear kinetics under the variable temperature conditions might be captured. In order to quantify it a ‘composite’ wear law integrating the energy wear coefficient as a function of the applied temperature is being introduced.

#### 1. 3. 1. Development of the ‘composite’ wear law

By considering the additive properties of the dissipated energy (i.e. energy is an extensive parameter), the ‘composite’ energy wear formulation is derived where the total wear response under variable temperature conditions (theoretical wear volume $V_{th.}$) is defined as a sum of the elementary wear contributions for each temperature sequence:

$$V_{th.} = \sum_{i=1}^{N} \alpha(T_{(i)}) \cdot Ed_{(i)} \qquad (44),$$
with: α(T<sub>(i)</sub>) - the energy wear coefficient at a given temperature T<sub>(i)</sub>, Ed<sub>(i)</sub> - the accumulated dissipated energy corresponding to the appropriate α(T<sub>(i)</sub>) value.

According to the results obtained at constant temperature conditions where an abrupt decrease of the energy wear coefficient (α) has been found above T<sub>t</sub>, the general formulation given above can be simplified by considering the following discontinuous evolution:

$$ \text{if } T < T_t, \text{ then } \alpha(T) = \bar{\alpha}_{kp\_T<T_t} = 5.44 \cdot 10^{-5} \text{ mm}^3 \cdot \text{J}^{-1} $$

$$ \text{and if } T > T_t, \text{ then } \alpha(T) = \bar{\alpha}_{kp\_T>T_t} = 4.19 \cdot 10^{-6} \text{ mm}^3 \cdot \text{J}^{-1}. $$

It leads to the formulation:

$$ V_{\text{th.}} = \bar{\alpha}_{kp\_T<T_t} \cdot \sum_{j=1}^{N_{T<T_t}} Ed_{(j)} + \bar{\alpha}_{kp\_T>T_t} \cdot \sum_{k=1}^{N_{T>T_t}} Ed_{(k)} \quad (45), $$

$$ V_{\text{th.}} = \bar{\alpha}_{kp\_T<T_t} \cdot \sum Ed_{T<T_t} + \bar{\alpha}_{kp\_T>T_t} \cdot \sum Ed_{T>T_t} \quad (46), $$

with: ΣEd<sub>T<T<sub>t</sub></sub> and ΣEd<sub>T<T<sub>t</sub></sub> - the accumulated dissipated energy obtained below and above T<sub>t</sub>, respectively.

For the studied conditions the relation 46 can be written as follows:

$$ V_{\text{th.}} = \bar{\alpha}_{kp\_T<T_t} \cdot \sum Ed_{200^{\circ}\text{C}} + \bar{\alpha}_{kp\_T>T_t} \cdot \sum Ed_{400^{\circ}\text{C}} \quad (47), $$

with: ΣEd<sub>200°C</sub> and ΣEd<sub>400°C</sub> - the accumulated dissipated energy obtained at 200 and 400°C, respectively.

### 1. 3. 2. 'Composite' wear law implementation

Figure 101 compares the experimental total wear volumes (V) obtained under variable temperature conditions, to the predicted wear volumes (V<sub>th.</sub>) extrapolated from the proposed 'composite' wear formulation (equation 47). An optimal prediction is achieved when the theoretical wear volumes are identical to the experimental ones. As Figure 101 illustrates, a rather good correlation is observed (most of the results are aligned along the theoretical dashed line depicting the perfect prediction with the slope equal to 1). The points were fitted linearly using the sum of the least squares and the result compared with the assumed perfect predictions. It turns out that the introduced 'composite' wear law produces a rather high convergence (1.04) with the
experimental results. Such a linear regression also displays high stability with the coefficient of determination R²=0.90. In order to take a measure of dispersion between experimental and theoretical results, a standard deviation analysis is applied:

$$ \sigma = \sqrt{\frac{\sum_{i=1}^{N} (X_i - \bar{X})^2}{Z}} \qquad (48), $$

with: σ - the square root of the variance of the experimental data, Xᵢ - the experimental wear data (V), Uᵢ - the theoretical wear data (V<sub>th.</sub>) according to equation 47, and Z - the number of samples (results) taken.

<figure><img src="image_103.png" /><figcaption>Figure 101: Wear extension under variable temperature conditions: comparison between experimental and theoretical (predicted from relation 47) wear volumes.</figcaption></figure>

The analysis gave σ<sub>VT</sub> = 0.041 mm³, which compared to the maximum experimental wear leads to a dispersion (σ/V<sub>max</sub> · 100%) less than 8%. For the experiments performed at the same total test duration but different order and number of temperature increments (VT 2, 3, 6, 9 and 10 – see Table VIII) showed very similar wear response. Once again it is, therefore, proved that the interface memory effect can be considered to be negligible. It must also be noticed that high reproducibility of the
test with short temperature sequences (VT 7) was obtained as very low dispersions of the results were achieved (less than ±12 and ±4% from the experimental and theoretical wear volume, respectively).

Detailed data concerning the wear analysis under variable temperature conditions are given in Table VIII.

<table><caption>Table VIII: Values of the accumulated dissipated energies obtained at 200 and 400°C, the associated theoretical (predicted from relation 47) and experimental wear volumes for variable temperature conditions.</caption><thead><tr><th>Test number</th><th>Total accumulated energy: ΣEd [J]</th><th>The portion of dissipated energy at 200°C: ΣEd<sub>200°C</sub> [J]</th><th>The portion of dissipated energy at 400°C: ΣEd<sub>400°C</sub> [J]</th><th>Theoretical total wear volume: V<sub>th.</sub> [mm<sup>3</sup>]</th><th>Experimental total wear volume: V [mm<sup>3</sup>]</th></tr></thead><tbody><tr><td>VT 1</td><td>5186</td><td>3692</td><td>1494</td><td>0.207</td><td>0.197</td></tr><tr><td>VT 2</td><td>8434</td><td>4879</td><td>3555</td><td>0.280</td><td>0.348</td></tr><tr><td>VT 3</td><td>9119</td><td>5300</td><td>3819</td><td>0.304</td><td>0.309</td></tr><tr><td>VT 4</td><td>13450</td><td>7848</td><td>5602</td><td>0.450</td><td>0.425</td></tr><tr><td>VT 5</td><td>12660</td><td>7338</td><td>5322</td><td>0.421</td><td>0.433</td></tr><tr><td>VT 6</td><td>9433</td><td>5450</td><td>3983</td><td>0.313</td><td>0.303</td></tr><tr><td>VT 7</td><td>1943±78</td><td>1599±50</td><td>344±28</td><td>0.088±0.003</td><td>0.107±0.013</td></tr><tr><td>VT 8</td><td>4722</td><td>1874</td><td>2848</td><td>0.114</td><td>0.113</td></tr><tr><td>VT 9</td><td>8543</td><td>4923</td><td>3620</td><td>0.283</td><td>0.318</td></tr><tr><td>VT 10</td><td>10095</td><td>5834</td><td>4261</td><td>0.335</td><td>0.422</td></tr><tr><td>VT 11</td><td>14320</td><td>8176</td><td>6144</td><td>0.471</td><td>0.528</td></tr><tr><td>VT 12</td><td>12230</td><td>7057</td><td>5173</td><td>0.406</td><td>0.355</td></tr></tbody></table>

Summarizing, in spite of its simplicity, the proposed ‘composite’ energy wear formulation allows the wear kinetics under variable temperature conditions (i.e. variable interface structure) to be predicted. This can be explained by the extensive property of the energy variable, but above all by the very high reactivity of the interface. The interface memory effect was found to be negligible for the investigated tribo-system as the order, the number of increments as well as the length of the imposed temperature sequences, play little importance. Therefore, the introduced ‘composite’ wear law seems to be a promising tool to predict the wear response under
variable temperature conditions. However, by imposing the wider spectrum of investigated temperature levels (i.e. temperature values close to $T_t$), the impact of the transient period (i.e. interface memory) should be higher and consequently the given 'composite' formulation may be assumed to be less stable. Further investigations should be considered to probe this aspect and perhaps to propose a different formulation, which better integrates the interface memory effect in wear modelling.

## 2. FRETTING WEAR MAPPING OF 'GLAZE' LAYER ACTIVATION

The investigations undertaken within the framework of the previous Chapter have demonstrated that under the mechanical key point loading conditions ($p_m$=25 MPa (i.e. $P$=176 N), $\delta^*=\pm100$ µm and $N$=360000 cycles) below and above the transition temperature $T_t$=230°C different wear mechanism with the associated average energy wear coefficient (Figure 75) is predominant. Moreover, series of experiments carried out at 200 and 400°C (i.e. below and above $T_t$) have shown that regardless of the imposed mechanical loadings (displacement amplitude, normal force and test duration) in the studied range of the conditions the considered tribo-system can be characterized for the given temperature by the single energy wear coefficient (Figure 79) (i.e. the given interface structure), whose value is pretty close to that of the average energy wear coefficient determined for the temperatures lower and higher than $T_t$ (Figure 75), respectively. Thus, in this place the following questions should be put:

- Does the change of predominant operating wear mechanism always take place at $T_t$=230°C, independently of the mechanical loadings?;

- If not, what is the influence of the displacement amplitude and mean pressure on the 'glaze' layer activation at different temperatures?.

These questions are being investigated in this paragraph as a new fretting wear mapping concept defining the 'glaze' layer activation conditions as a function of temperature, displacement amplitude and mean pressure is being discussed.

### 2.1. Experimental methodology

An innovative test methodology where the considered parameter (displacement amplitude or mean pressure) was increasing stepwise (IS) within a single fretting experiment was designed. By using such a fast test procedure the fretting mapping of
‘glaze’ layer activation as a function of temperature, displacement amplitude and pressure might be plotted without necessity of carrying out numerous time-consuming invariable tests. In order to verify it the results obtained under variable conditions are compared to those under constant conditions defined in Table VI.

Experiments under parameters increasing stepwise within a single fretting test were performed at different temperatures in the 23-400°C range, where for tests type DIS (displacement amplitude increasing stepwise) the displacement amplitude was increasing from ±50 to ±200 µm with the 50 µm step at maintaining constant mean pressure p<sub>m</sub>=25 MPa (i.e. P=176 N), whereas in the case of tests type PIS (pressure increasing stepwise) the mean pressure was generally augmenting from 5 to 50 MPa (i.e. form P=35 N to P=352 N) in five steps at maintaining constant sliding amplitude δ<sub>g</sub>=77±4 µm (i.e. that obtained at the key point loading conditions). For the tests type DIS the number of cycles within each step in the given test was constant: 100000 fretting cycles. The required value of the time-varying parameter (i.e. displacement amplitude and mean pressure, respectively) was automatically adjusted by a data acquisition platform.

Figure 102 shows a pattern of the test DIS 4 and the associated fretting log showing
the evolution of the fretting loops.

<figure><img src="image_104.png" /><figcaption>Figure 102: Pattern of the test DIS 4 (the fretting experiment under displacement amplitude increasing stepwise at 300°C) and the associated fretting log.</figcaption></figure>

Detailed data concerning conditions of the test carried out under stepwise increasing
displacement amplitude and pressure is given in Table IX.
<table><caption>Tests type DIS (displacement amplitude increasing stepwise)</caption><thead><tr><th rowspan="2">Test No.</th><th rowspan="2">Test temperature [°C]</th><th colspan="4">N<sub>i</sub>,<br/>with: N - number of cycles for the given<br/>displacement amplitude,<br/>i - displacement amplitude value [µm].</th><th rowspan="2">Total No. of cycles</th></tr><tr><th>N<sub>50</sub></th><th>N<sub>100</sub></th><th>N<sub>150</sub></th><th>N<sub>200</sub></th></tr></thead><tbody><tr><td>1</td><td>23</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>400k</td></tr><tr><td>2</td><td>200</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>400k</td></tr><tr><td>3</td><td>250</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>400k</td></tr><tr><td>4</td><td>300</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>400k</td></tr><tr><td>5</td><td>400</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>400k</td></tr></tbody></table>

<table><caption>Tests type PIS (pressure increasing stepwise)</caption><thead><tr><th rowspan="2">Test No.</th><th rowspan="2">Test temperature [°C]</th><th colspan="7">N<sub>i</sub>,<br/>with: N - number of cycles for the given<br/>mean pressure,<br/>I - mean pressure value [MPa].</th><th rowspan="2">Total No. of cycles</th></tr><tr><th>N<sub>5</sub></th><th>N<sub>10</sub></th><th>N<sub>17.5</sub></th><th>N<sub>25</sub></th><th>N<sub>37.5</sub></th><th>N<sub>50</sub></th><th>ΣN<sub>i</sub></th></tr></thead><tbody><tr><td>1</td><td>23</td><td>60k</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>-</td><td>460k</td></tr><tr><td>2</td><td>200</td><td>135k</td><td>100k</td><td>100k</td><td>100k</td><td>-</td><td>-</td><td>435k</td></tr><tr><td>3</td><td>225</td><td>60k</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>560k</td></tr><tr><td>4</td><td>250</td><td>50k</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>550k</td></tr><tr><td>5</td><td>300</td><td>50k</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>550k</td></tr><tr><td>6</td><td>400</td><td>60k</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>100k</td><td>560k</td></tr></tbody></table>

Table IX: Detailed data concerning conditions of the tests carried out under stepwise increasing displacement amplitude (DIS) and pressure (PIS).

## 2. Definition of the threshold values of tribo-magnitudes for ‘glaze layer activation

To make possible plotting the fretting wear mapping of ‘glaze’ layer activation, the threshold values of tribo-magnitudes (the average steady-state energy coefficient of friction and energy wear coefficient) for the formation of stable wear-protective ‘glaze’ layer must be defined. The analysis of the evolution of the average steady-state energy coefficient of friction and energy wear coefficient defined from the mechanical key point loadings (p<sub>m</sub>=25 MPa (i.e. P=176 N), δ*=±100 µm and N=360000 cycles) versus temperature (Figure 67 and 75, respectively) has shown that a stable effective wear-protective ‘glaze’ layer (defined to occur above T<sub>t</sub>=230°C) produces the mean value of the average steady-state energy coefficient of friction $\bar{\bar{\mu}}_{e\_SS\_T>T_t} = 0.49$ and the average energy wear coefficient
$\bar{\alpha}_{kp\_T>T_t} = 4.19 \cdot 10^{-6} \text{ mm}^3 \cdot \text{J}^{-1}$. However, it should also be taken into account the result obtained within the $T_{ga}<T<T_{gs}$ range of temperature (i.e. at 225°C) for which an unstable, in terms of effectiveness, ‘glaze’ layer has been found to form (Figure 68), characterized by $\bar{\mu}_{e\_SS\_225°C} = 0.67$ and $\alpha_{225°C} = 1.27 \cdot 10^{-5} \text{ mm}^3 \cdot \text{J}^{-1}$. Hence, because between 225°C and $T_{gs}$ there may take place a formation of a stable ‘glaze’ layer the threshold value of the average steady-state energy coefficient of friction ($\bar{\mu}_{thr\_e\_SS\_gs}$) and energy wear coefficient ($\alpha_{thr\_gs}$) for a stable effective wear-protective ‘glaze’ layer formation is determined as follows:

$$ \bar{\mu}_{thr\_e\_SS\_gs} = \bar{\mu}_{e\_SS\_T>T_t} + \frac{\bar{\mu}_{e\_SS\_225C} - \bar{\mu}_{e\_SS\_T>T_t}}{2} = 0.58 \quad (49), $$

$$ \alpha_{thr\_gs} = \bar{\alpha}_{kp\_T>T_t} + \frac{\alpha_{225C} - \bar{\alpha}_{kp\_T>T_t}}{2} = 8.44 \cdot 10^{-6} \text{ mm}^3 \cdot \text{J}^{-1} \quad (50). $$

Thus, in further considerations it is assumed that $\bar{\mu}_{thr\_e\_SS\_gs} = 0.58$ and $\alpha_{thr\_gs} = 8.44 \cdot 10^{-6} \text{ mm}^3 \cdot \text{J}^{-1}$ is the threshold value of the average steady-state energy coefficient of friction and energy wear coefficient, respectively, below which a stable effective ‘glaze’ layer is established in the interface.

## 2. 3. Evaluation of the dynamics of the third body evolution under variable loading conditions through analyzing the friction evolution

The evolution of the coefficient of friction for all fretting experiments carried out under displacement amplitude (tests type DIS) and mean pressure (tests type PIS) increasing stepwise at different temperatures is shown in Figure 103 and 104, respectively.

The experimental evolution is there compared with the theoretical response (an average steady-state energy coefficient of friction at the given conditions – see Table X) obtained for the certain adequate constant test situations. In general, rather a good correlation can be observed as the steady-state conditions are established.

For the test DIS 1 and 2 (Figure 103a and b) and PIS 1 (Figure 104a) the changes of the related parameter during the test do not affect the friction evolution, which is established practically at constant high level ($\mu_e \approx 0.70 \pm 0.05$ for tests type DIS,
$\mu_e \approx 0.75 \pm 0.05$ for the test type PIS), characteristic of adhesive wear regime for the whole test duration.

In the case of the test DIS 3 and 4 (Figure 103c and d) and PIS 2-4 (Figure 104b-d) the significant discontinuities in friction evolution (characterized by the abrupt increase of the coefficient of friction) at the displacement amplitude and pressure transitions can be observed. For these all tests the evolution of the coefficient of friction during the first sequence is similar to that characteristic of experiments conducted above $T_{ga}$ (Figure 57), where after certain maximum within the transient stage the asymptotic decrease down the stabilized value, generally lower than $\bar{\mu}_{thr\_e\_SS\_gs} = 0.58$ can be observed. It suggests that an effective ‘glaze’ layers are developed under such conditions. For the test DIS 3 the stabilization of the coefficient of friction ($\mu_e \approx 0.59$) takes place slightly above $\bar{\mu}_{thr\_e\_SS\_gs}$, but the experiment performed under the adequate invariable conditions (Figure 105 and Table X) shows that also in this situation the low friction and wear regime is predominant. Of course, it is observed that the higher the temperature the less time is required to establish the low friction regime (25000 and 40000 cycles for the tests DIS 4 and 3; 20000 and 60000 cycles for the tests PIS 4 and 2, respectively). Such behaviour has already been discussed in Chapter 3. The stabilization of the coefficient of friction at the level characteristic of high wear adhesive regime occurs after longer time period (at later displacement amplitude or pressure transition) as test temperature increases. At the earlier transitions the abrupt increase of the coefficient of friction up to the high friction regime (generally up to $\mu_e \approx 0.70$; the only exception is test PIS 2) is followed by its progressive decrease below $\bar{\mu}_{thr\_e\_SS\_gs} = 0.58$. The perfect discontinuous transitions observed suggest that the increase of the displacement amplitude or mean pressure causes an immediate degradation of the previously formed ‘glaze’ layer as more severe conditions are imposed. The ‘glaze’ re-forms later as $\mu_e$ progressively decreases after a time period shorter than observed for the adequate constant test situations. For example, it takes up about 60000 and 50000 cycles during the test DIS 3 (Figure 103c) and PIS 4 (Figure 104d) after the transition from 50 to 100 µm and from 17.5 to 25 MPa, respectively, in comparison to 130000 cycles during the adequate invariable test under $\delta^*=\pm100$ µm and $p_m=25$ MPa (i.e. $P=176$ N) at 250°C (Figure 105a). Thus, once again it is shown that during the tests
under the time-varying parameters after successive transitions the establishment of a
'glaze' layer that forms from already the present third body, which has partially
accommodated the loads. Though it should be expected that with the increase of the
investigated parameter (displacement amplitude or pressure) at the given temperature
more time will be required to establish a stable effective 'glaze' layer (as has been
observed at 200 and 400°C - Figure 72) it is not obvious after analyzing the friction
evolution obtained under variable conditions. Also the other invariable experiments at
different temperatures showed that the lower the loadings the faster the formation of a
stable effective 'glaze' layer. It is demonstrated in Figure 105a and 106a as the
evolution of the coefficient of friction versus test duration for different displacement
amplitudes at 250°C and different mean pressures at 225°C is shown, respectively.
The transitions to the high friction regime characteristic of adhesive wear mechanism
are characterized by perfect discontinuities implying the high interface reactivity.
Destruction of the 'glaze' layer takes place immediately and the imposed loadings are
no longer favourable to a 'glaze' reconstruction as the coefficient of friction reaches
values higher compared to $\bar{\mu}_{thr\_e\_SS\_gs} = 0.58$ for the rest test duration (i.e. to the end
of the experiment). Practically constant high friction level is maintained in the case of
the test DIS 3 and 4 after the transition from 100 to 150 µm and from 150 to 200 µm,
respectively. A slight increase in the friction evolution after the transition from 150 to
200 µm during the test DIS 3 being the response of the interface to more severe
loading imposed can be observed. However, the coefficient of friction stabilizes very
fast as new loading is accommodated. The invariable test performed under 150 µm of
displacement amplitude at 250°C (Figure 105a) and under 200 µm at 300°C (Table X)
confirms

that under such conditions adhesive high friction and wear regime is operating for
whole test duration (tests at N=360000 cycles). Such long tests suggest that these
results are representative of the applied conditions. In the case of the tests type PIS
when after transition the adhesive high friction regime (higher than
$\bar{\mu}_{thr\_e\_SS\_gs} = 0.58$) is longer operated the coefficient of friction generally increases
slightly with each consecutive transitions what is in good agreement with the results
obtained under the adequate invariable test situations (e.g. 0.624 at 17.5 MPa and
0.763 at 50 MPa - Figure 106a and Table X). The value of the coefficient of friction
within the individual sequence is practically stable.
<figure><img src="image_105.png" /><figcaption>Figure 103: Evolution of the coefficient of friction versus the test duration for the experiments under displacement amplitude increasing stepwise (DIS): (a) DIS 1 at 23°C, (b) DIS 2 at 200°C, (c) DIS 3 at 250°C, (d) DIS 4 at 300°C, (e) DIS 5 at 400°C;

Experimental evolution of the coefficient of friction under variable displacement amplitude conditions: ______; Evolution of the applied displacement amplitude: ______;

Theoretical evolution of the coefficient of friction defined from the steady-state values obtained for certain the adequate constant test situations (______).</figcaption></figure>
<figure><img src="image_106.png" /></figure>

<figure><img src="image_107.png" /></figure>

<figure><img src="image_108.png" /></figure>

<figure><img src="image_109.png" /></figure>

<figure><img src="image_110.png" /></figure>

<figure><img src="image_111.png" /></figure>

Figure 104: Evolution of the coefficient of friction versus the test duration for the experiments under pressure increasing stepwise (PIS): (a) PIS 1 at 23°C, (b) PIS 2 at 200°C, (c) PIS 3 at 225°C, (d) PIS 4 at 250°C, (e) PIS 5 at 300°C, (f) PIS 6 at 400°C;

Experimental evolution of the coefficient of friction under variable pressure conditions: ______; Evolution of the applied mean pressure: ______; Theoretical evolution of the coefficient of friction defined from the steady-state values obtained for certain the adequate constant test situations (______).
For the test DIS 5 (Figure 103e) and PIS 5 and 6 (Figure 104 e and f) after the transition period occurring at the beginning of each test the low coefficient of friction is established for whole test duration, in which evolution only small short disturbances can be observed at the parameter transitions. These disturbances are displayed by abrupt friction increase (generally slightly above $\bar{\mu}_{thr._e(SS\_gs)} = 0.58$), which practically immediately decreases after transitions. It therefore seems that though a stable ‘glaze’ layer is perturbed during transition it re-forms very quickly as high temperature conditions favour higher oxidation rate and higher adhesion forces between wear particles.

In order to clarify the aspect of the dynamics of the third body evolution after the consecutive parameter transitions during the tests under displacement amplitude and mean pressure increasing stepwise the interrupted experiments combined with post-mortem analytical investigations of the interface, involving rheological evaluation of its properties should be performed.

In order to complete the study on the wear mapping of glaze layer activation certain the complementary invariable tests must have been performed. The evolution of the energy coefficient of friction versus the test duration for the experiments under different displacement amplitudes (50, 100 and 150 µm) at 225°C (constant $p_m=25$ MPa (i.e. P=176 N) and N=360000 cycles) is shown in Figure 105b, under 5 MPa of mean pressure at 150°C (constant $\delta_g=77\pm4$ µm and N=360000 cycles) in Figure 106b. As it can be observed, the tests at 100 and 150 µm are characterized by the higher energy coefficient of friction than $\bar{\mu}_{thr._e(SS\_gs)} = 0.58$. The analysis of the associated energy wear coefficients (Table X) confirmed that under such conditions the adhesive high friction and wear regime is predominant. In the case of the test under 50 µm of the displacement amplitude at 225°C the obtained average steady-state energy coefficient of friction was exactly as $\bar{\mu}_{thr._e(SS\_gs)} = 0.58$ and the associated energy wear coefficient $\alpha=3.78\cdot10^{-6} \text{ mm}^3\cdot\text{J}^{-1}$ (lower than $\alpha_{thr\_gs} = 8.44 \text{ mm}^3\cdot\text{J}^{-1}$). Thus, the considered conditions favour the activation of the formation of a stable effective ‘glaze’ layer. The experiment under 5 MPa (i.e. P=35 N) of the mean pressure at 150°C was found to produce $\bar{\mu}_{e(SS)}$ lower then $\bar{\mu}_{thr._e(SS\_gs)} = 0.58$ (Table X). Hence, it
<figure><img src="image_112.png" /></figure>

Figure 105: Evolution of the coefficient of friction versus the test duration for the invariable test under 50 (____), 100 (____) and 150 µm (____) of displacement amplitude (constant $p_m=25$ MPa (i.e. $P=176$ N) and $N=360000$ cycles) at (a) 250°C and (b) 225°C.

<figure><img src="image_113.png" /></figure>

Figure 106: Evolution of the coefficient of friction versus the test duration for the invariable test performed at (a) 225°C under 10 (____), 17.5 (____), 25 (____) and 50 MPa (____) of mean pressure and at (b) 150°C under 5 MPa of mean pressure; the rest loading conditions for all these tests were: constant $\delta_g=77\pm4$ µm and $N=360000$ cycles.
<table><thead><tr><th rowspan="3">Tribo-magnitudes</th><th colspan="10">Temperature: T [°C]</th></tr><tr><th colspan="3">23</th><th colspan="2">150</th><th colspan="5">200</th></tr><tr><th>δ* [μm]</th><th>δ* [μm]</th><th>δ* [μm]</th><th>p<sub>m</sub> [MPa] (P [N])</th><th>δ* [μm]</th><th colspan="3">p<sub>m</sub> [MPa] (P [N])</th><th colspan="3">p<sub>m</sub> [MPa] (P [N])</th></tr><tr><th></th><th>100</th><th>100</th><th>100</th><th>5 (35)</th><th>50</th><th>100</th><th>150</th><th>200</th><th>10 (70)</th><th>37.5 (264)</th><th>50 (352)</th></tr></thead><tbody><tr><td>μ<sub>e SS</sub></td><td>0.71</td><td>0.70</td><td>0.68</td><td>0.54</td><td>0.62</td><td>0.71</td><td>0.66</td><td>0.69</td><td>0.70</td><td>0.73</td><td>0.74</td></tr><tr><td>α [10<sup>5</sup> mm<sup>3</sup>/J]</td><td>5.71</td><td>6.08</td><td>5.51</td><td>6.66</td><td>1.19</td><td>4.92</td><td>6.94</td><td>7.29</td><td>5.01</td><td>5.54</td><td>5.44</td></tr><tr><th rowspan="3">Tribo-magnitudes</th><th colspan="10">Temperature: T [°C]</th></tr><tr><th colspan="3">215</th><th colspan="2">225</th><th colspan="5">250</th></tr><tr><th>δ* [μm]</th><th colspan="2">δ* [μm]</th><th>p<sub>m</sub> [MPa] (P [N])</th><th>δ* [μm]</th><th colspan="3">p<sub>m</sub> [MPa] (P [N])</th><th colspan="3">p<sub>m</sub> [MPa] (P [N])</th></tr><tr><th></th><th>100</th><th>50</th><th>100</th><th>150</th><th>10 (70)</th><th>17.5 (122)</th><th>50 (352)</th><th>50</th><th>100</th><th>150</th><th>37.5 (264)</th></tr><tr><td>μ<sub>e SS</sub></td><td>0.73</td><td>0.58</td><td>0.67</td><td>0.72</td><td>0.52</td><td>0.62</td><td>0.76</td><td>0.54</td><td>0.53</td><td>0.63</td><td>0.79</td></tr><tr><td>α [10<sup>5</sup> mm<sup>3</sup>/J]</td><td>4.98</td><td>0.38</td><td>1.27</td><td>5.80</td><td>0.54</td><td>2.94</td><td>5.13</td><td>0.41</td><td>0.36</td><td>3.20</td><td>5.71</td></tr><tr><th rowspan="3">Tribo-magnitudes</th><th colspan="10">Temperature: T [°C]</th></tr><tr><th colspan="3">275</th><th colspan="2">300</th><th colspan="2">350</th><th colspan="5">400</th></tr><tr><th>δ* [μm]</th><th colspan="2">δ* [μm]</th><th>δ* [μm]</th><th>δ* [μm]</th><th colspan="3">p<sub>m</sub> [MPa] (P [N])</th><th colspan="3">p<sub>m</sub> [MPa] (P [N])</th></tr><tr><th></th><th>100</th><th>100</th><th>200</th><th>100</th><th>50</th><th>100</th><th>150</th><th>200</th><th>37.5 (264)</th><th>50 (352)</th><th>-</th></tr><tr><td>μ<sub>e SS</sub></td><td>0.49</td><td>0.46</td><td>0.66</td><td>0.51</td><td>0.45</td><td>0.46</td><td>0.51</td><td>0.47</td><td>0.55</td><td>0.55</td><td>-</td></tr><tr><td>α [10<sup>5</sup> mm<sup>3</sup>/J]</td><td>0.42</td><td>0.36</td><td>4.15</td><td>0.46</td><td>0.58</td><td>0.50</td><td>0.34</td><td>0.69</td><td>0.68</td><td>0.79</td><td>-</td></tr></tbody></table>

Table X: Values of tribo-magnitudes (the average steady-steady energy coefficient of friction (μ<sub>e SS</sub>) and energy wear coefficient (α)) obtained for invariable test situations under different displacement amplitudes (constant p<sub>m</sub>=25 MPa (i.e. P=176 N) and N=360000 cycles) and mean pressures (constant δ<sub>g</sub>=77±4 μm and N=360000 cycles) at different temperatures (in the 23-400°C range) used as a reference response of the interface as compared to the response under the adequate loading conditions for experiments under variable conditions (tests type DIS and PIS).

preliminarily could be assumed that the considered test conditions would support the activation of a stable effective ‘glaze’ layer. However, the associated energy wear coefficient (Table X) revealed the value much higher compared to α<sub>thr._gs</sub>, close to
that characteristic of adhesive wear regime $\bar{\alpha}_{kp\_T<T_t} = 5.44 \cdot 10^{-5} \text{ mm}^3 \cdot \text{J}^{-1}$, explicitly indicating the predominant wear mechanism occurring under the considered conditions.

Summarizing from above discussion, as there is no friction memory effect found after the parameter transitions under variable test conditions the applied innovative experimental methodology can successfully be used to investigate the impact of the mechanical loadings at different temperatures on the tribological response of the considered tribo-system and find threshold conditions for the formation of a stable effective ‘glaze’ layer without necessity of performing numerous time-consuming invariable tests. Obviously, there is always a need to carry out certain complementary invariable experiments to resolve on unclear situations that may arise as the friction evolution under variable test conditions is considered. Then, throughout analyzing the energy wear coefficient an explicit verification on the predominant wear mechanism occurring under the given loading conditions can be done. It has been shown that the energy wear coefficient is more sensitive to the interface changes, thereby more reliable in determining the operating wear regime than the energy coefficient of friction.

## 2. 4. Displacement amplitude and pressure versus temperature maps of the ‘glaze’ layer activation

Based on the results obtained under variable and invariable conditions discussed above

the threshold value of the displacement amplitude (at constant $p_m=25$ MPa (i.e. $P=176$ N)) and mean pressure (at constant $\delta_g(\delta^*, P)= \pm 77$ µm) at the given temperature for adhesive high wear ($\delta^*_{thr._adh.} (T)$ and $p_{mThr._adh.}(T)$, respectively) and low wear ($\delta^*_{thr._gs} (T)$ and $p_{mThr._gs}(T)$, respectively), associated with the activation of ‘glaze’ layers, regime occurrence has been determined. It has been found that for $\delta^* \ge \delta^*_{thr._adh.} (T)$ and $p_m \ge p_{mThr._adh.}(T)$ the adhesive wear mechanism is predominant, however for $\delta^* \le \delta^*_{thr._gs} (T)$ and $p \le p_{mThr._gs}(T)$ the abrasive wear mechanism, involving activation of ‘glaze’ layers takes place. Thus, the fretting wear mapping of wear mechanisms can be plotted, illustrated in Figure 107. Displacement amplitude versus temperature map (under constant $p_m=25$ MPa (i.e. $P=176$ N)) is
shown in Figure 107a, and mean pressure versus temperature (under $\delta_g(\delta*, P)= \pm 77$ µm) in Figure 107b. As it can be observed the intermediate temperature domain between high friction and wear adhesive interface and low friction and wear 'glaze' layer interface as a function of pressure is quasi vertical (Figure 107b). It therefore infers that the pressure impact is rather inconsiderable and the activation of a stable 'glaze' layer is mainly controlled by temperature. The more influential parameter seems to be the displacement amplitude (Figure 107a). Figure 108 shows the width of the intermediate temperature domain ($\Delta T_{gs}$) between high friction and wear adhesive interface and low friction and wear 'glaze' layer interface (determined from Figure 107) versus displacement amplitude and mean pressure. It is clearly seen that in the case of the pressure impact $\Delta T_{gs}$ is low (<30°C) and practically independent of the studied loading (Figure 108b). Situation is different when the displacement amplitude impact is considered. In this case, low $\Delta T_{gs}$ =25°C is maintained only below the critical value of the displacement amplitude $\delta*_{cr\_gs}=\pm 100$ µm. Above this critical displacement the intermediate temperature domain shows an abrupt increase and at 200 µm of displacement amplitude $\Delta T_{gs}=100$°C (Figure 108a). It suggests that larger displacement amplitudes than $\delta*_{cr\_gs}=\pm 100$ µm may significantly interact on the stability of 'glaze' layers, retarding the formation of stable wear-protective structures. Further analysis of fretting wear maps shows that, as expected, the higher the temperature the greater the value of the displacement amplitude (Figure 107a) and mean pressure (Figure 107b) can be imposed at maintaining low friction and wear response of the interface (i.e. due to the activation of stable effective 'glaze' layers). It is certainly related to rheological properties of third body remaining in the interface. As high temperature increases adhesion forces between wear particles [Yamamoto et al. (1981)] a tribo-sintering process of the third body is favoured [Jiang et al. (1998), Kato et al. (2007)]. Thus, the rheology of the third body changes as the cohesion of the third body increases with temperature (it has been shown in Chapter 3). High cohesion quality of the third body makes it more effective in load-bearing action. Moreover, at high temperatures the debris ejection outside the contact may be limited as bigger particles are easier oxidized and incorporated in the third body. Then, due to the retention of greater amount of wear particles within the interface the thicker third body layer may be generated. That might bear the loads more effectively, even though a thickness of the third body layer does not seems to be an essential factor that controls the process of the development of a stable effective 'glaze' layer.
<figure><img src="image_114.png" /></figure>

<figure><img src="image_115.png" /></figure>

Figure 107: Displacement versus temperature (a) and mean pressure versus temperature (b) map of fretting wear regimes; Evolution of the δ*<sub>thr._adh.</sub> (T) (a) and p<sub>m thr._adh.</sub> (T) (b) determining the threshold conditions for high wear regime occurrence in the studied range of loadings: (—); Evolution of the δ*<sub>thr._gs</sub> (T) (a) and p<sub>m thr._gs</sub> (T) (b) determining the threshold conditions for low wear regime occurrence in the studied range of loadings: (—).
<figure><img src="image_116.png" /><figcaption>Figure 108: Width of the intermediate temperature domain between high friction and wear adhesive interface and low friction and wear ‘glaze’ layer interface ($\Delta T_{gs}=T(=)$ -$T(=)$: from Figure 107) versus (a) displacement amplitude and (b) mean pressure.</figcaption></figure>

## 2.5. Wear prediction under variable displacement and mean pressure conditions

To predict wear volume under variable displacement amplitude and pressure conditions at different temperatures, already the introduced ‘composite’ wear law is employed. For the studied situation the formulation 44 can be written as follows:

$$V_{\text{th.}} = \sum_{i=1}^{N} \alpha((\delta^*, p_m, T)_{(i)}) \cdot Ed_{(i)} \quad (51),$$

with: $\alpha((\delta^*, p_m, T)_{(i)})$ - the energy wear coefficient at a given displacement amplitude $\delta^*_{(i)}$, mean pressure $p_{m(i)}$ and temperature $T_{(i)}$, $Ed_{(i)}$ - the accumulated dissipated energy corresponding to the appropriate $\alpha((\delta^*, p_m, T)_{(i)})$ value.

By using the displacement amplitude versus temperature and the pressure versus temperature maps of the fretting wear regimes (Figure 107) and assuming that the individual wear regime is characterized by the associated single energy wear coefficient (defined in Chapter 3 – Figure 75) in the range of the studied loadings the general formulation (relation 51) can be simplified by considering the following discontinuities:
if $\delta^* \ge \delta^*_{thr._adh.}$ (T) (for tests type DIS – at constant $p_m=25$ MPa (i.e. P=176 N) and $p_m \ge p_{m\_thr._adh.}$ (T) (for tests type PIS – at constant $\delta_g(\delta^*, P)= \pm 77$ µm),

then $\alpha((\delta^*, p_m, T)_{(i)}) = \bar{\alpha}_{kp\_T<T_t}$

and if $\delta^* \le \delta^*_{thr._gs}$ (T) (for tests type DIS) and $p_m \le p_{m\_thr._gs}$ (T) (for tests type PIS),

then $\alpha((\delta^*, p_m, T)_{(i)}) = \bar{\alpha}_{kp\_T>T_t}$.

It leads to the formulation:

$$V_{\text{th.}} = \bar{\alpha}_{kp\_T<T_t} \cdot \sum_{j=1}^{N_{\delta^* \ge \delta^*_{thr._adh.}(T) \atop p_m \ge p_{m\_thr._adh.}(T)}} \text{Ed}_{(j)} + \bar{\alpha}_{kp\_T>T_t} \cdot \sum_{k=1}^{N_{\delta^* \le \delta^*_{thr._gs}(T) \atop p_m \le p_{m\_thr._gs}(T)}} \text{Ed}_{(k)} \quad (52),$$

$$V_{\text{th.}} = \bar{\alpha}_{kp\_T<T_t} \cdot \sum_{\substack{p_m \ge p_{m\_thr._adh.}(T) \\ \delta^* \ge \delta^*_{thr._adh.}(T)}} \text{Ed}_{(T)} + \bar{\alpha}_{kp\_T>T_t} \cdot \sum_{\substack{p_m \le p_{m\_thr._gs}(T) \\ \delta^* \le \delta^*_{thr._gs}(T)}} \text{Ed}_{(T)} \quad (53),$$

with: $\sum_{\substack{p_m \ge p_{m\_thr._adh.}(T) \\ \delta^* \ge \delta^*_{thr._adh.}(T)}}$ – the accumulated dissipated energy obtained at the given

temperature for the displacement amplitudes $\delta^*$ and mean pressure $p_m$ superior or equal to $\delta^*_{thr._adh.}(T)$ and $p_{m\_thr._adh.}(T)$ for tests type DIS and PIS, respectively and $\sum_{\substack{p_m \le p_{m\_thr._gs}(T) \\ \delta^* \le \delta^*_{thr._gs}(T)}}$ – the accumulated dissipated energy obtained at the given

temperature for the displacement amplitudes $\delta^*$ and mean pressure $p_m$ inferior or equal to $\delta^*_{thr._gs}(T)$ and $p_{m\_thr._gs}(T)$ for tests type DIS and PIS, respectively.

Comparison of the experimental (V) and theoretical (Vth.) (i.e. determined from relation 53) wear volumes obtained under variable displacement amplitude (tests type DIS) and mean pressure (tests type PIS) conditions at different temperatures is shown in Figure 109a and 109b, respectively. The experimental results obtained under mean pressure increasing stepwise, in general, correspond well to those determined on the basis of the ‘composite’ wear formulation (the only exception is the test PIS 4). For the tests type DIS, however, higher dispersion with the ‘composite’ wear model can be observed. Very poor correlation for the test DIS 3 and 4 is found (the relative error $((V - V_{th.}) / V) \cdot 100\%$) is 125 and 60%, respectively). The greater dispersion observed as the impact of the displacement amplitude is investigated is related to the fact that the
<figure><img src="image_117.png" /><figcaption>Figure 109: Comparison of the experimental (□) and theoretical (■) (predicted from relation 53) wear volumes obtained under variable: (a) displacement amplitude (tests type DIS) and (b) mean pressure (tests type PIS) conditions.</figcaption></figure>

<table><caption>Table XI: Values of the accumulated dissipated energies obtained under severe (adhesive wear mechanism is predominant) and mild (activation of load-bearing 'glaze' layers) fretting wear regime, the associated theoretical (predicted from relation 53) and experimental wear volumes for variable displacement amplitude (tests type DIS) and mean pressure (tests type PIS) conditions.</caption><thead><tr><th>Test type and number</th><th>ΣEd [J]</th><th>ΣEd<sub>δ*≥δ*<sub>thr_adh.</sub> (T)</sub><br>P<sub>m</sub>≥P<sub>m_thr_adh.</sub> (T)<br>[J]</th><th>ΣEd<sub>δ*≤δ*<sub>thr gs</sub> (T)</sub><br>P<sub>m</sub>≤P<sub>m_thr gs</sub> (T)<br>[J]</th><th>V<sub>th.</sub><br>[mm<sup>3</sup>]</th><th>V<br>[mm<sup>3</sup>]</th></tr></thead><tbody><tr><td>DIS 1</td><td>18401</td><td>18401</td><td>-</td><td>1.001</td><td>1.201</td></tr><tr><td>DIS 2</td><td>18100</td><td>18100</td><td>-</td><td>0.985</td><td>1.197</td></tr><tr><td>DIS 3</td><td>21903</td><td>16670</td><td>5233</td><td>0.929</td><td>0.422</td></tr><tr><td>DIS 4</td><td>17284</td><td>8055</td><td>9229</td><td>0.477</td><td>0.299</td></tr><tr><td>DIS 5</td><td>14278</td><td>-</td><td>14278</td><td>0.060</td><td>0.089</td></tr><tr><td>PIS 1</td><td>13520</td><td>13520</td><td>-</td><td>0.735</td><td>0.774</td></tr><tr><td>PIS 2</td><td>7559</td><td>6736</td><td>823</td><td>0.370</td><td>0.363</td></tr><tr><td>PIS 3</td><td>19857</td><td>18384</td><td>1473</td><td>1.006</td><td>0.933</td></tr><tr><td>PIS 4</td><td>18735</td><td>13196</td><td>5539</td><td>0.741</td><td>0.451</td></tr><tr><td>PIS 5</td><td>17291</td><td>-</td><td>17291</td><td>0.072</td><td>0.073</td></tr><tr><td>PIS 6</td><td>17656</td><td>-</td><td>17656</td><td>0.074</td><td>0.059</td></tr></tbody></table>
displacement amplitude affects the transition between high wear adhesive and low
wear ‘glaze’ layer interface to a greater extent than pressure (Figure 108). Particularly
for the displacement amplitudes larger than $\delta_{cr\_gs} \pm 100$ µm, larger the intermediate
temperature domain (implying higher instability of a ‘glaze’ layer) will produce a
higher dispersion with the ‘composite’ prediction. By contrast, in the case of the
pressure impact the intermediate temperature domain is narrow, so the dispersion is
lower and the correlation with the ‘composite’ model better for the tests type PIS.
Moreover, it should be noticed that the comparison between experimental and
predicted wear volumes for all tests do not display any tendencies (individual
dispersion for the given test).

Detailed data concerning the wear analysis under variable displacement amplitude
(tests type DIS) and mean pressure (tests type PIS) conditions are provided in Table
XI.

### 3. GLOBAL USE OF THE 'COMPOSITE' WEAR LAW

The last part of the present dissertation is devoted to answering the question: can the
fretting wear behaviour of the studied tribo-system be characterized by the two
average energy wear coefficients (Figure 75) associated with the revealed wear
mechanisms in the range of the studied loadings?. To answer this question the
'composite' wear law developed above (relation 53) on the basis of the fretting wear
maps (Figure 107) is here employed in order to predict the wear volumes of all tests
carried out within the framework of the present dissertation (i.e. under invariable and
variable loading conditions).

The results can be observed in Figure 110 that compares the experimental total wear
volumes (V) to the predicted wear volumes (Vth.) extrapolated from the proposed
'composite' wear formulation (relation 53). Tests of each group under variable
conditions (VT, DIS and PIS) are differently marked. It turns out that the used
'composite' wear law produces a very high convergence (0.99) with the experimental
results. Such a linear regression also displays fairly high stability with the coefficient
of determination $R^2=0.89$. In order to take a measure of dispersion between
experimental and theoretical results, a standard deviation analysis is applied (relation
<figure><img src="image_118.png" /><figcaption>Figure 110: Global application of the developed ‘composite’ wear law: comparison between experimental and theoretical (predicted from relation 53) wear volumes for all experiments carried out within the framework of the present dissertation; Tests under invariable conditions: ◇; Tests under variable conditions type VT: ◆, DIS: ◆ and PIS: ●.</figcaption></figure>

48). It gives $\sigma=0.161 \text{ mm}^3$, which compared to the maximum experimental wear leads to a dispersion in the range of studied loadings ($\frac{\sigma}{V_{\max}} \cdot 100\%$) less than 9%. The worst fitting can be observed for the invariable experiments performed at high values of the displacement amplitude and intermediate temperatures (tests under constant $p_m=25 \text{ MPa}$ (i.e. $P=176 \text{ N}$) and $N=360000$ cycles: $\delta^*=\pm200$, $T=300^\circ\text{C}$; $\delta^*=\pm200$, $T=200^\circ\text{C}$; $\delta^*=\pm225$, $T=200^\circ\text{C}$; $\delta^*=\pm150$, $T=250^\circ\text{C}$). It is therefore clearly shown that the stability of the developed ‘composite’ approach is degraded for higher displacement amplitudes. It is due to that above $\delta^*_{cr\_gs}=\pm100 \text{ µm}$ the intermediate temperature domain between adhesive high wear regime and low wear ‘glaze’ layer interface is critically enlarged (Figure 108a). For the higher displacement amplitudes due to the activation of a rapid third body ejection process a ‘glaze’ layer becomes unstable. Thus, this once again implies that the studied interface is more sensitive to changes of the displacement amplitude (in terms of the produced wear kinetics) than
mean pressure, at least in the investigated range of loadings. This seems to be
confirmed by investigations under variable conditions during a single fretting tests, as
for the experiments type DIS higher differences between experimental and theoretical
wear volumes have been found compared to the tests type PIS (Figure 109).
Moreover, quite a poor fitting is seen for the variable test DIS 3 and PIS 4 at 250°C as
well as for the invariable experiment under the mechanical key point loadings at
225°C. It is certainly due to the fact that at these intermediate temperatures a
competing formation of the two different interfaces (adhesive and abrasive one,
involving formation of ‘glaze’ layers) takes place as the main factor that controls the
development of a stable ‘glaze’ layer is temperature. For the invariable experiment
under the mechanical key point loadings at 225°C it has been clearly demonstrated in
the previous Chapter (see Figure 67, 68 and 75).

<figure><img src="image_119.png" /><figcaption>Figure 111: Replotted Figure 110 showing the comparison between experimental and theoretical (predicted from relation 53) wear volumes for all experiments carried out within the framework of the present dissertation except the results obtained under the displacement amplitudes higher than $\delta^{*}_{cr\_gs}=\pm100$ µm; Tests under invariable conditions: ◇; Tests under variable conditions type VT: ◆, DIS: ◆ and PIS: ●.</figcaption></figure>
Figure 111 shows a replotted Figure 110 without the results obtained under the displacement amplitudes higher than $\delta^{*}_{cr\_gs}=\pm100$ µm, however Figure 112 a replotted Figure 110 without the results obtained under the displacement amplitudes higher than $\delta^{*}_{cr\_gs}=\pm100$ µm and for DIS 3, PIS 4 and the invariable experiment under the mechanical key point loadings at 225°C results (called intermediate temperature outliers). The standard deviation analysis gives $\sigma_{w\_\delta\_>\delta^{*}_{thr\_gs}} = 0.127$ mm³ and $\sigma_{w\_T_{outl\_\delta\_>\delta^{*}_{thr\_gs}}} = 0.071$ for the situation in Figure 111 and Figure 112, respectively. Thus, it is observed that the dispersion is reduced around 20% in Figure 111 and 60% in Figure 112 in relation to the dispersion obtained in Figure 110.

<figure><img src="image_120.png" /></figure>

Figure 112: Replotted Figure 110 showing the comparison between experimental and theoretical (predicted from relation 53) wear volumes for all experiments carried out within the framework of the present dissertation except the results obtained under the displacement amplitudes higher than $\delta^{*}_{cr\_gs}=\pm100$ µm and for DIS 3, PIS 4 and the invariable experiment under the mechanical key point loadings at 225°C;

Tests under invariable conditions: ◇; Tests under variable conditions type

VT: ◆, DIS: ◆ and PIS: ●.
Generalizing from the study undertaken, the previously developed ‘composite’ energy wear formulation (relation 53), integrating the two average energy wear coefficients (determined in Chapter 3 – Figure 75) as a function of the loading conditions, allows a good prediction of the wear kinetics even under variable loading conditions. However, there is a limitation of its application for the displacement amplitudes larger than $\delta^{*}_{cr\_gs}=\pm100$ µm and for certain experiments performed in the intermediate 225-250°C temperature range. Such a high predictability presented by the ‘composite’ wear model implies that the investigated Jethete M152/A-286 tribo-system could be characterized by the two energy wear coefficients ($\bar{\alpha}_{kp\_T<T_t} = 5.44 \cdot 10^{-5}$ and ($\bar{\alpha}_{kp\_T>T_t} = 4.19 \cdot 10^{-6}$ mm³·J⁻¹) each associated with the predominant wear mechanism (adhesive and abrasive, involving formation of effective ‘glaze’ layer, respectively).

# 4. SYNTHESIS OF THE CHAPTER

The experiments under variable temperature conditions adequate to those occurring in the Variable System Vanes have been performed. The interface memory effect has been found to be negligible for the investigated tribo-system as practically perfect transitions (implying high interface reactivity) from one wear regime to another have been observed. No obvious influence of the order, number or duration of the temperature sequences on the friction behaviour has been revealed. Hence, it seems that rheological properties of the third body, which change drastically with temperature, play a vital role in the tribological behaviour as temperature variations below or above $T_t$ are applied.

The innovative experimental methodology consisting in conducting the experiments under displacement amplitude and mean pressure increasing stepwise conditions has been introduced. It has been demonstrated that this new experimental methodology allows a fast plotting of the fretting wear mapping of ‘glaze’ layer activation as a function of temperature, displacement amplitude and pressure merely by considering the friction evolution, practically without necessity of performing numerous time-consuming invariable experiments.

The plotted fretting wear mapping (displacement amplitude and normal force versus temperature map) of wear regimes has shown that the most determining factor for the
formation of a stable ‘glaze’ layer is temperature. Mechanical parameters (i.e. displacement amplitude and pressure) play a minor role. Pressure has a quasi negligible effect as the intermediate temperature domain between adhesive high wear and low wear ‘glaze’ layer interface as a function of pressure is practically vertical (Figure 107b). Moreover, the width of the intermediate temperature domain (ΔTgs) is in the case of the pressure very low (<30°C) and practically independent of the studied loading (Figure 108b). The relatively low dispersion between the experimental results and those obtained from the proposed ‘composite’ wear model has been found. This all implies that pressure plays a minor impact on either the activation or the degradation of a ‘glaze’ layer. Displacement amplitude (i.e. sliding amplitude) is more influential parameter than pressure. Until the critical value of the displacement amplitude δ*cr._gs=±100 µm its impact is small (narrow the intermediate temperature domain – Figure 108a) as there is small effect of loading history. The relatively low dispersion between the experimental and the predicted wear volumes has then been observed (compare Figure 110 and 111). The larger displacement amplitudes (i.e. above δ*cr._gs=±100 µm) critically interact on the stability of a ‘glaze’ layer. Such more severe conditions tend to prevent the formation of a stable ‘glaze’ layer. This induces a wider intermediate temperature domain between established high wear and low regime. Under such conditions the impact of the loading history is more significant and, in consequence, the dispersion between experimental and predicted from the ‘composite’ wear model results is higher. Moreover, it has been observed that the higher the temperature the greater the value of the mechanical loadings can be imposed at maintaining low friction and wear response of the interface (i.e. due to the activation of stable effective ‘glaze’ layers). Such a tendency can be explained by rheological properties of the third body layer formed in the interface. Elevated temperature conditions intensify a tribo-sintering process of the third body. In that way a cohesion quality of the third body increases, so it can bear higher loadings.

The stability of the proposed ‘composite’ wear model to predict the wear volume even under variable loading conditions has been confirmed as a good forecast of the wear kinetics has been achieved. However, the developed formulation has represented certain limitations of its application. It has been demonstrated that the model is less stable as the displacement amplitudes larger than δ*cr._gs=±100 µm are studied and for certain experiments performed in the intermediate 225-250°C temperature range (i.e.
for the test DIS 3, PIS 4 and for the invariable experiment under the mechanical key
point loadings at 225°C).

The results obtained from the study on the fretting wear mapping and the ‘composite’
wear model indirectly confirm the origin of a ‘glaze’ layer from a tribo-sintering
process of the third body. It is outlined by the fact that above a threshold displacement
amplitude the third body (‘glaze’ layer) is more easily ejected and then the interface
displays an unstable response.
# GENERAL CONCLUSIONS

Fretting wear behaviour of the Jethete M152/A-286 tribo-system under elevated temperature conditions has been investigated within the framework of the present dissertation.

The following conclusions can be drawn from the presented research work:

- Fretting wear mapping of wear regimes as a function of temperature, displacement amplitude and mean pressure in the contact has been elaborated. It has been demonstrated that depending on the loading combination different wear mechanism is predominant: high wear adhesive one or low wear abrasive, involving the formation of the lubricating ‘glaze’ layer.

- These two wear mechanism has been found to be associated to the specific evolution of the energy coefficient of friction.

- The temperature has been found to be the most determining factor for the formation of the stable wear-protective ‘glaze’ layer. The transition from the high to low wear interface is very sharp (i.e. in the narrow range of 20°C) (Figure 113a). Mechanical parameters (i.e. displacement amplitude and pressure) have been shown to play a minor role, where the displacement amplitude (i.e. sliding amplitude) has been found to be the more influential

<figure><img src="image_121.png" /><figcaption>Figure 113: (a) The abrupt transition of the predominant wear regime as $T_i$ is exceeded; (b) The influence of the displacement amplitude on the interface response.</figcaption></figure>
parameter than the pressure. The critical displacement amplitude has been established (δ*cr\_gs=±100 µm) above which the interaction on the stability of the ‘glaze’ layer critically increases (Figure 113b).

- In-depth analytical investigations of the interface have shown that independently of the temperature conditions the third body layer developed on the wear surfaces can be considered as compacted oxidized wear nano-particles originating from the two alloy surfaces. It has also been revealed that spinel-like (Fe₃O₄ and/or FeCr₂O₄ and/or NiCr₂O₄ and/or NiFe₂O₄) and possibly CrO and NiO oxides are main compounds formed.

- The development of the wear-protective ‘glaze’ layer has been found to be closely associated with a tribo-sintering process of the third body. The load-bearing properties of the ‘glaze’ layer are a consequence of its high cohesion quality and elevated hardness.

- High temperature intensifies oxidation rate of wear particle and promotes a tribo-sintering process of the third body, which favour the development of the stable effective ‘glaze’ layer. The higher the temperature the faster the development of the wear-protective ‘glaze’ structures.

- It has been shown that the higher the temperature the greater the value of the mechanical loadings can be imposed at maintaining low wear response of the interface (i.e. due to the activation of stable effective ‘glaze’ layers).

- The pre-oxidation treatment has been found to have no effect on the tribological behaviour of the considered system. It therefore indirectly confirms the origin of the ‘glaze’ layer as the structure produced as a result of a tribo-sintering process, which is activated by a synergetic effect of the temperature and the mechanical fretting loadings.

- The innovative test methodology where the considered mechanical parameter is increasing stepwise during a single fretting experiment at different temperatures has been proposed. It has been demonstrated that it allows a considerably faster plotting of the fretting wear mapping of the wear regimes
without necessity of performing numerous time-consuming invariable experiments.

- Under the related variable mechanical loading test conditions after the parameter transitions the ‘glaze’ layer degradation takes place very fast followed by its subsequent re-formation if the imposed new loadings are still favourable to the development of a stable ‘glaze’ layer.

- The experiments under variable temperature conditions adequate to those occurring in the Variable Stator Vane system have been performed. The interface memory effect has been found to be negligible for the investigated tribo-system implying that rheological properties of the third body change drastically with the temperature transitions.

- Using the additive properties of the dissipated energy the ‘composite’ wear law integrating the energy wear coefficient as a function of the predominant interface (i.e. adhesive or ‘glaze’ layer) has been developed. The stability of the proposed ‘composite’ wear formulation to predict the wear volume even under variable loading conditions has been demonstrated as a good forecast of the wear kinetics has been achieved. It infers that the investigated tribo-system can be characterized by the two energy wear coefficients each associated with the different predominant wear mechanism. However, the model has been

<figure><img src="image_122.png" /><figcaption>Figure 114: The ‘composite’ model applied to (a) all studied loading conditions and (b) all excluding the tests in the intermediate domains.</figcaption></figure>
found to represent certain limitations of its application for the loading conditions in the intermediate domain (for the displacement amplitudes larger than $\delta^{*}_{cr\_gs}=\pm100$ µm and for the certain experiments performed in the intermediate 225-250°C temperature range) before the stable ‘glaze’ is formed (Figure 114a). The model has shown the high stability if it is applied to the loadings (temperature, displacement amplitude, pressure) from outside the intermediate domains (Figure 114b).

Though within the framework of the present dissertation the tribological behaviour of the considered tribo-system has profoundly been described both under invariable and variable loadings there are still some interesting aspects worth additional work. The further investigations should be undertaken to develop the following areas:

- Evaluation of the quantitative rheological properties of the third body (i.e. nano-hardness and Young modulus) under elevated temperature conditions in order to determine how its mechanical properties evolve with temperature;

- To fully clarify the tribological response of the studied tribo-system under variable loading conditions, interrupted tests after the parameter transitions combined with an evaluation of a rheological quality of the interface should be conducted;

- The developed ‘composite’ wear formulation seems to be a promising tool to predict the wear response under variable loading conditions. However, the model should be improved for the large displacement amplitude and the intermediate 225-250°C temperature domain conditions (i.e. for the intermediate transient domain). Further investigations should be undertaken to probe this aspect and perhaps to propose a different formulation which better integrates the transient response of the interface in wear modelling.
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