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# Fretting wear of the stainless steel / stainless steel contact under elevated temperature conditions

Radoslaw Rybiak

► To cite this version:

Radoslaw Rybiak. Fretting wear of the stainless steel / stainless steel contact under elevated temperature conditions. Engineering Sciences [physics]. Ecole Centrale de Lyon, 2008. English. NNT: 2008ECDL0013. tel-04309061

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Submitted on 27 Nov 2023

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## THESE EN COTUTELLE

### Ecole Centrale de Lyon – Université Polytechnique de Lodz

présentée devant

### L'ECOLE CENTRALE DE LYON

pour obtenir le titre de DOCTEUR

spécialité : Matériaux

par

### Radosław RYBIAK

## FRETTING WEAR OF THE STAINLESS STEEL/STAINLESS STEEL CONTACT UNDER ELEVATED TEMPERATURE CONDITIONS

### USURE PAR FRETTING D'UN CONTACT ACIER INOX/ACIER INOX SOUS HAUTES TEMPERATURES

Soutenance prévue le 27 Juin 2008 devant la commission d'examen de

M. Yves BERTHIER

Mme. Cécile LANGLADE-BOMBA

M. Léo VINCENT

M. Siegfried FOUVRY

M. Bogdan WENDLER

Mme. Bénédicte BONNET

Rapporteur

Rapporteur

Membre

Directeur de thèse

Directeur de thèse

Membre
# CONTENTS

INTRODUCTION.................................................................................................................. 4

CHAPTER 1: INDUSTRIAL ISSUES AND BIBLIOGRAPHY.................................. 7

1. FRETTING WEAR IN THE GE 90-115 B AERONAUTIC CIVIL ENGINE ........................ 7

1. 1. Working principle and structure of the GE 90-115 B turbofan engine .................................................. 7

1. 2. Variable Stator Vane system – presentation, working conditions and loads .................................................. 9

2. TRIBOLOGICAL PROCESSES.................................................................................................................. 12

2. 1. Historical outline of Tribology ................................................................................................................................. 13

2. 2. Destruction mechanisms involved in wear process .................................................................................................. 15

3. FRETTING DESTRUCTION PROCESS.................................................................................. 18

3. 1. Introduction .................................................................................................................................................................................. 18

3. 2. Contact conditions .................................................................................................................................................................................. 19

3. 3. Sliding conditions .................................................................................................................................................................................. 22

3. 4. Fretting maps .................................................................................................................................................................................. 25

3. 5. Transition criteria.................................................................................................................................................................................. 26

3. 6. Fretting damage mechanisms.................................................................................................................................................. 28

3. 6. 1. Fretting Cracking (i.e. endurance under Fretting Fatigue loading conditions).................................................. 29

3. 6. 2. Fretting Wear .................................................................................................................................................................................. 32

3. 7. Third body formation and transport.................................................................................................................................................. 40

3. 7. 1. Third body approach .................................................................................................................................................................................. 40

3. 7. 2. Tribologically transformed structure.................................................................................................................................................. 42

3. 7. 3. Flows and rheology notions .................................................................................................................................................. 44

3. 8. Fretting damage methodology .................................................................................................................................................. 47

3. 9. Palliatives in fretting.................................................................................................................................................................................. 48

4. INFLUENCE OF ENVIRONMENTAL CONDITIONS ........................................................................ 50

4. 1. Effect of elevated temperature .................................................................................................................................................. 50

4. 1. 1. Oxidation of metals and alloys.................................................................................................................................................. 50

4. 1. 2. Tribological behaviour of metals and alloys.................................................................................................................................................. 54

4. 1. 2. 1. Flash temperature .................................................................................................................................................................................. 54

4. 1. 2. 2. Generation of oxides during sliding wear.................................................................................................................. 56

4. 1. 2. 3. Establishment of wear-protective layers .................................................................................................................................................. 57

4. 1. 2. 4. Kinetics of in-situ oxidation .................................................................................................................................................. 63

4. 1. 2. 5. Oxide chemistry and structure.................................................................................................................................................. 66

4. 2. Effect of relative humidity.................................................................................................................................................................................. 67

5. OBJECTIVES OF THE WORK.................................................................................................................. 68

CHAPTER 2: STUDIED MATERIALS AND FRETTING EXPERIMENTS. 71

1. MATERIALS UNDER INVESTIGATION .................................................................................. 71

2. DEFINITION OF THE FRETTING PARAMETERS ........................................................................ 73

3. FRETTING WEAR EXPERIMENTS.................................................................................................................. 74

3. 1. Fretting apparatus .................................................................................................................................................................................. 74

3. 2. Contact geometry.................................................................................................................................................................................. 76

3. 3. Contact mechanics of the studied plane/plane configuration.................................................................................. 77

3. 4. Experimental conditions .................................................................................................................................................................................. 79

4. WEAR VOLUME EVALUATION.................................................................................................................. 79
# INTRODUCTION

Fretting wear is perceived as a plague in many industrial fields (aeronautics, nuclear engineering etc.) as degradation of mated surfaces due to wear is one of the principal problems resulting in necessity of repairing or replacing mechanical components. It is defined as a small displacement amplitude oscillatory motion between two nominally stationary solid bodies in contact under normal load. This process is usually observed in assemblies subjected to vibrations.

Within the framework of the present dissertation the elevated temperature conditions are being investigated to reproduce working conditions of the trunnion vane/bushing joints in the Variable Stator Vane system of the high pressure compressor of the GE90-115B two-spool high bypass turbofan engine. By analyzing the character of wear processes occurring in the VSV system a stationary bushing contacted with making torsional movements a vane trunnion can be considered as a joint subjected to fretting torsion. In this dissertation, however, the alternating fretting experiments under normal load equivalent to the airflow-induced interaction force between bushing and vane are being studied as it is much easier to implement in laboratory setups than fretting torsion by remaining similar loading conditions (i.e. pressure and relative sliding).

This work focuses on a few aspects. The origin of the low friction and wear ‘glaze’ layer is profoundly investigated. The fretting wear mapping of the ‘glaze’ layer activation as a function of temperature, displacement amplitude and pressure is plotted and discussed. Finally, the ‘composite’ wear law is developed, which allows the prediction of wear volumes under variable temperature and mechanical loading conditions.

The present Ph.D. dissertation is divided into four chapters. In Chapter 1 a bibliographic survey of the fretting issue is made and the relevant industrial issues described. The influence of environmental conditions on the tribological behaviour of alloy steels and superalloys is extensively discussed.

In Chapter 2 the materials used in the experiments and the fretting apparatus are presented. The contact mechanics of the considered contact geometry as well as the method used for wear volume evaluation is described.

In Chapter 3 the results of the investigations conducted under invariable loading conditions are discussed. Particular attention is paid to the impact of the temperature
on the tribological behaviour of the considered tribo-system. In-depth analytical investigations of the evolution of the interface as a function of temperature are also discussed. Moreover, the effect of the pre-oxidation is studied.

In Chapter 4 the fretting wear behaviour under variable temperature (adequate to those occurring in the VSV system) and mechanical loading conditions is investigated. The dynamics of the third body evolution under variable temperature conditions during a single fretting test is discussed. Fretting wear mapping of the ‘glaze’ layer activation as a function of temperature, displacement amplitude and pressure is elaborated. By considering the additive properties of the dissipated energy, the ‘composite’ energy wear formulation is developed to capture wear kinetics under variable loading conditions. It integrates the energy wear coefficient as a function of imposed loadings.
# CHAPTER 1

## INDUSTRIAL ISSUES AND BIBLIOGRAPHY
# CHAPTER 1: INDUSTRIAL ISSUES AND BIBLIOGRAPHY

## 1. FRETTING WEAR IN THE GE 90-115 B AERONAUTIC CIVIL ENGINE

### 1.1. Working principle and structure of the GE 90-115 B turbofan engine

A jet engine is an engine that discharges a fast moving jet of gases to generate a tremendous thrust to drive the plane forward.

Working principle of the jet engine can be summarized into the following points:

1. The engine sucks air in at the front. The inlet and fan pull the air in;

2. Air successively flows through the low pressure compressor then through the high pressure compressor in order to increase the air pressure;

3. The compressed air flows into a combustion chamber and is mixed with the fuel. An electric spark is used to light the mixture;

4. Burning gases are subsequently release in the turbine, which drives the compressor. Finally, the burning gases expand and blast out through the back of the engine. As the jets of gas shoot backward, the nozzle releases the gases and the aircraft is thrust forward.

<figure><img src="image_3.png" /><figcaption>Figure 1: Image of the GE90-115B two-spool high bypass turbofan engine.</figcaption></figure>

The GE90-115B civil engine (Figure 1) that some systems (e.g. low pressure compressor and part of the high pressure compressor) are designed and manufactured
by SNECMA is a two-spool high bypass turbofan engine (french ‘double-corps double-flux’) and is made up of 6 main components (Figure 2):

1. Fan;

2. Low Pressure Compressor (LPC);

3. High Pressure Compressor (HPC);

4. Combustion chamber;

5. Low Pressure Turbine (LPT);

6. High Pressure Turbine (HPT).

The turbofan engine generates dual airflow, the primary in the engine core, and the secondary in the bypass duct. To make it possible, a technology of a two-spool shaft is applied. It signifies that the engine is made up of two mechanically independent assemblies where the first is made up of the low pressure turbine driving the low pressure compressor and fan, however the second consists of the high pressure turbine, which drives the high pressure compressor. In this type of engine only some part of absorbed air participates in burning processes, giving so-called primary flow, which drives two-spool shaft system. The rest of absorbed airflow is accelerated in bypass duct by fan. The secondary flow produces around 80% of the thrust. The turbofan system is commonly used by airliners because it gives an exhaust speed that is better matched to subsonic airliner’s flight speed. A conventional turbojet engines generate an exhaust that ends up traveling very fast backwards, and this wastes energy. By emitting the exhaust so that it ends up traveling more slowly, better fuel consumption is achieved. In addition, the lower exhaust speed gives much lower noise. As regards dimensions, the fan of the GE90-115B engine measures more than 3 m of diameter and almost 5 m of length. The GE90-115B entered service in 2004 as the exclusive power plant for Boeing’s longer range 777-200LR and -300LR models.

The high pressure compressor, which cross-section is presented in Figure 3, is made up of rotor and stator. Rotor consists of several stages of rotor blades (RB) turning at high speed (more than 10000 revolutions per minute during take-off). That is exactly the rotor blades give a speed to airflow.

Stator of the GE90-115B two-spool high bypass turbofan engine is made up of stages of stator vanes placed between corresponding stages of rotor blades. Particular feature of its first 3 stages is that the vanes are of variable geometry. To be able to change and
control geometric settings of the vanes of these 3 stages as a function of working conditions of the engine, a complex VSV (variable stator vane) system is installed.

<figure><img src="image_4.png" /><figcaption>Figure 2: Cross-sectional view of the GE90-115B turbofan engine.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 3: Cross-section of the high pressure compressor of the GE90-115B engine.</figcaption></figure>

## 1. 2. Variable Stator Vane system – presentation, working conditions and loads

The function of the VSV system is to control the amount of air flowing through the compressor. To increase the operating capacity of the compressor the stator vane stages are designed with vanes that can rotate in around an axis that is in its longitudinal direction to adjust the angular orientation of the vane with respect to the airflow traveling through the compressor. The adjustment of the angular orientation allows changing the speed of airflow, thus optimizing the performance of the compressor. The VSV system is located approximately one third of the way back from the front of the engine. In case of the GE90-115B engine the VSV system
consists of an actuation system and 3 individual stages. Working temperature of the variable stator vanes at particular stages is different and fluctuates depending on the phase of the flight. At the first stage there is 114°C and 206°C, at the second 164°C and 274°C, and at the third 218°C and 350°C during the cruise and take-off, respectively. Movement of variable vanes is initiated by an actuator (fixed on the engine case), which induces turning of the actuation shaft. Subsequently, the latter transmits the movement to the actuation rings by means of adjustable turnbuckles. The levers, which are jointed to the actuation rings, turn around the axes of the vanes inducing their rotation. Figure 4 shows 3D view of the VSV system. The rest stages of stator (above 3rd stage) are consisted of fixed vanes. Besides, there is the other stage of variable settings, called Inlet Gas Vane (IGV), placed between the low pressure compressor and the high pressure compressor.

<figure><img src="image_6.png" /><figcaption>Figure 4: 3D view of the VSV system of the GE90-115B turbofan engine.</figcaption></figure>

The variable stator vane structure includes an outer trunnion disposed in a complementary mounting boss in the stator case for allowing rotation of the vane relative to the case. A lever arm is fixedly jointed to a coaxial stem extending outwardly from the vane trunnion. The distal end of the lever arm is operatively jointed to an actuation ring that controls the angle of the vane. All of the vane lever
arms in a single stage are joined to a common actuation ring for ensuring that all of the vanes are positioned relatively to the airflow in the compressor stage at the same angular orientation.

Variable stator vane assembly includes a bushing and washer disposed between a trunnion attached to a variable vane and a case. The bushing and washer have the task of decreasing the coefficient of friction between the trunnion and the case and thereby of facilitating rotation of the vane through the trunnion. The bushing and washer also help prevent wear of the trunnion and case, which are expensive to repair and/or replace. The vanes are made from titanium alloy in case of 'colder' stages and from stainless steel for 'hotter' ones, however bushings are made from carbon-based or metallic materials. The vane/bushings assemblies can be different depending on the engine and particular stages, but generally it is always one or two external bushings in the engine case and one mounted in the internal ring in the base of the VSV system. The vane/bushings joint is presented schematically in Figure 5.

<figure><img src="image_7.png" /><figcaption>Figure 5: The vane/bushings joint in the VSV system.</figcaption></figure>

Pressure present in the compressor increases with the stages and is always higher in the lower part of variable stator vanes than in the higher one. This compressed airflow exerts pressure on the vanes. Aerodynamic stresses (opposite to the airflow direction) are then induced in the vanes, which interact with the external bushings what results in wear in the vane trunnion/bushings contact. Another part of the VSV system
subjected to wear is the vane trunnion/internal bushing joint. Internal bushing is placed in the internal ring, freely mounted, which is positioned and maintained along the axis of the engine by the vane. This ring also participates in positioning the VSV. High pressure air present in the lower part of variable stator vanes causes pushing the internal ring towards the front direction of the engine, what consequently exerts pressure on the internal bushing and finally on the vane trunnion. Generated wear is of the same order as in the case of the external bushings.

When a bushing or washer system fails due to excessive wear, serious problems for the compressor may occur. The failure of the bushing and washer may create an increase in leakage of compressed air from the interior of the compressor through the variable stator vane assembly, which results in performance loss for the compressor. In addition, failure of the bushing and washer can result in contact between stator vane and the case, which causes wear and increases overhaul costs of the engine.

By analyzing the character of wear processes occurring in the VSV system a stationary either internal or external bushing contacted with making torsional movements a vane trunnion can be considered as a joint subjected to fretting torsion. In this dissertation, however, the alternating fretting experiments under normal load equivalent to the airflow-induced interaction force between bushing and vane are being studied as it is much easier to implement in laboratory set-ups than fretting torsion by remaining similar loading conditions (i.e. pressure and relative sliding).

## 2. TRIBOLOGICAL PROCESSES

Tribology is the science and technology of friction, lubrication, and wear. The name is derived from the Greek where *tribo* means 'I rub' or 'pertaining to friction' by rubbing and *logos* denotes 'science'. Tribology is an interdisciplinary subject, which to be understood well, necessities contributions from engineers, chemists, physicists, scientists, mathematicians as well as material and lubricant technologists. Tribology as a science was formally established slightly over 40 years ago. Previously, particular branches of Tribology were investigated by different scientific disciplines. And thus, issues of dry friction was a part of physics, boundary friction – physico-chemistry, lubrication – branch of petrol technology, wear – machine technology. The term 'Tribology' was introduced by British experts in 1966 in the report for Parliament
about state of lubricating technology [Jost (1966)]. It was defined as *the science and technology of interacting surfaces in relative motion and all practices related thereto*.

## 2. 1. Historical outline of Tribology

The world literature on lubrication, friction and wear has been growing steadily for over the past 100 years. And although the word Tribology was coined a short time ago, tribological knowledge and technology existed from the earliest time. Evidences of tribological issues could already be found in the third millennium BC. It is believed that lubricating materials were introduced in Egypt during the early civilizations period. In reference to Dowson (1998) it is possible to quote 3 main evidences of using lubricants in ancient Egypt. So, the first is that hydrated calcium sulphate (gypsum) was used to form the thin bed of viscid mortar to slide huge stone blocks for building of pyramids. The second indication is that water lubrication was used for transportation of heavy stone blocks. And lastly, the third proof, which demonstrates a chariot from about 1400 BC with traces of a lubricant (presumably, mutton or beef tallow) at its axle. Figure 6 shows the real painting preserved from around 2400 BC on which a man pouring water from a jar, presumably as a lubricant, is present in front of the sledge is presented.

<figure><img src="image_8.png" /><figcaption>Figure 6: A man pouring water from a jar, presumably as a lubricant, in front of the sledge with a statue of Ti in Saccara (Egypt), circa 2400 BC (after [Nosonovsky (2007)]).</figcaption></figure>

Dowson, inspired by the painting from El-Bersheh that shows 172 men dragging a giant statue (Figure 7), performed simple calculation and got a remarkable result. According to him, assuming an average force of a slave as 800 N, it could be achieved
a total drag force of 172 x 800 N = 137.6 kN. Presupposing the weight of the colossus 600 kN, it was then calculated the coefficient of friction as μ = 60/137.6 = 0.23, which was compared with that of wet wood-on-wood (μ=0.20). It allowed a conclusion that the sledge was indeed sliding over lubricated planks of wood.

<figure><img src="image_9.png" /><figcaption>Figure 7: Painting from El-Bersheh, circa 1880 BC, showing transportation of a huge statue (after [Nosonovsky (2007)]).</figcaption></figure>

Moreover, it was found that in Hebrew Bible the word oil appears very often (193 times) and is in conjunction with the verbs ‘to smear’ and ‘to slip’, indicating that it was utilized for tribological purposes [Nosonovsky (2007)].

Along with developing practical solutions within the scope of friction and lubrication, the first scientist studies were undertaken to write friction laws e.g. by Amonton (Amonton's law (1699)). However, it was not him who was named as a father of modern Tribology, but Leonardo da Vinci (1452-1519) who had studied incredibly manifold tribological subtopics (friction, bearing materials, plain bearings, lubrication systems, gears, screw-jacks and rolling-element bearings) already 150 years before Amonton's Law of Friction were introduced. Except Amonton, such names as Desanguliers, Euler and Coulomb should be mentioned. These pioneers brought Tribology into standards, and their laws are being still applied to many engineering problems even today.

Tribology is crucial to modern machinery which uses sliding and rolling surfaces. It has high economic importance. It was evaluated, in the report of Jost (1966), that around 515 billions pounds could have been saved by British industry if the correct use of tribological knowledge already existing had been made. It is generally believed that the economic losses resulting from ignorance of tribology reach around 6% of gross national product of the USA (and up to 4% of GNP in developed countries). It is approximately one third of world energy resources in present use appear as friction in
different forms. Thus, the main purpose of research in tribology is to minimize and eliminate losses caused by friction and wear at all levels of technology, where the rubbing of surfaces is involved.

## 2.2. Destruction mechanisms involved in wear process

Wear is the result of material removal by physical separation due to micro-fracture, by chemical dissolution, or by melting at the contact interface [Bhushan (2001)]. Most machines fail due to wear of their components, losing their durability and reliability. Hence, wear control is still being grown to be engineers' challenge for the advanced and reliable technology of the future.

There are several classifications of wear, however they all are related to the classifications previously proposed by Burwell and Strang (1952) and Archard and Hirst (1956). The former distinguished seven types of wear, whilst the latter envisaged only two. The latter classification of mild (characterized by low contact resistance) and severe (characterized by high contact resistance) wear was subsequently developed by Quinn (1962, 1967, 1983a, 1983b), who introduced an oxidational theory of wear, where mild wear was recognized as that, which involves reaction with the environment, in particular with oxygen.

According to the classification introduced by Burwell and Strang (1952) the following types of wear can be distinguished: adhesive wear, abrasive wear, corrosive wear, fatigue wear, fretting, cavitation and erosion. Among them first four wear processes are generally recognized as fundamental and major ones.

Wear mechanisms are described by considering complex changes during friction. The dominant wear mechanism may change from one to another for reasons that include changes in surface material properties and dynamic surface responses caused by among others: frictional heating, chemical film formation, and wear. Generally, wear does not take place through a single wear mechanism, but is a complex process involving different destruction modes at the same time. Thus, recognition and comprehension of particular wear mechanisms is important. Schematic drawings of four main wear mechanisms are illustrated in Figure 8.

Severe wear and mild oxidational wear classified by Quinn (1980) are corresponding to adhesive wear and corrosive wear by Burwell and Strang (1952), respectively.
Wear induced by fretting is the subject of this dissertation, thus it is discussed extensively afterwards in this chapter.

<figure><img src="image_10.png" /><figcaption>Figure 8: Schematic drawings of four main wear mechanisms: (a) adhesive, (b) abrasive, (c) fatigue and (d) corrosive wear (after Bhushan (2001)).</figcaption></figure>

*Adhesive wear* consists in the formation of local adhesive nodes in the micro-areas of the surface layer deformation due to the molecular force interactions between asperity peaks, and their subsequent breaking associated with detachment and/or smearing of the particles on to the mated surfaces. The plastic deformation in the real contact area is a result of dislocations migration induced by high pressure and shearing. Due to such large deformation, a crack is initiated and propagated in the combined fracture process of tensile and shearing. When the cracks reach the contact interface, wear particles are formed and adhesive transfer is completed. Adhesive wear occurs especially in the contacts of metals characterized by high affinity. Elevated temperature intensifies the inclination for the formation of the adhesive junctions for the self-mated metals or for similar crystallographic structure metallic bodies being in contacts. Depending on the operating conditions and material properties, wear coefficient *K*<sub>ad</sub> (defined in the further part of Chapter 1 – relation 5) in adhesive wear of metals varies between 10<sup>-7</sup> and 10<sup>-2</sup> [Archard (1953), Hirst (1957)].

*Abrasive wear* takes place when wear of material is a result of ploughing of the weaker material by stronger one. It occurs if the contact interface between two surfaces has interlocking of an inclined or curved contact. Abrasive grooves can be then observed onto the weaker body. Moreover, some detached loosely moving or
immobilized, in one or both of the interacting surfaces, hard particles can also act as abrasive bodies. Abrasive wear usually proceeds very fast, and wear coefficient K<sub>ab</sub> for metals varies between 10<sup>-4</sup> and 10<sup>-1</sup> [Rabinowicz (1980)], depending on the contact conditions and material properties. Comparing K<sub>ab</sub> and K<sub>ad</sub> in adhesive wear, abrasive wear can be recognized as severe one.

Three different modes in abrasive wear, illustrated in Figure 9, can be distinguished: micro-cutting, wedge forming, and ploughing [Hokkirigawa et al. (1988)]. Generated wear particles form in different way and have different shapes depending on particular modes. In the micro-cutting mode, long and curled ribbon-like wear particles are formed (Figure 9a). This mode is characteristic of ductile materials. In the wedge-forming mode, a wedge-like wear particle is formed at the tip of the grooving asperity and stays there working as a kind of built-up wedge to continue grooving (Figure 9b). In the case of the ploughing mode, wear particles are generated as a result of repeated sliding passes and accumulation of plastic flow at the interface. Single pass of sliding produces only a shallow groove (Figure 9c).

<figure><img src="image_11.png" /><figcaption>Figure 9: Different modes of abrasive wear observed by SEM: (a) micro-cutting, (b) wedge-forming and (c) ploughing (from [Hokkirigawa et al. (1988)]).</figcaption></figure>

Corrosive wear is a tribochemical wear accelerated by corrosive media. It takes place when sliding proceeds in the environment of corrosive liquids or gases, where products of chemical or electrochemical reactions are formed on to the interacting surfaces. Such products may adhere strong to the surface and may exhibit different properties from the bulk material. If so, wear proceeds differently from that of the bulk material, and is mainly dominated by the reaction products formed by the interaction of solid materials with the corrosive environment. In this type of wear, tribochemical reaction produces a reaction layer on the surface. At the same time, such layer is removed by friction. Therefore, relative growth rate and removal rate
determine the wear rate of the reaction layers and, as a result, of the bulk material.
The most representative mode of corrosive wear is oxidative wear of metals.

*Fatigue wear* can be defined as a wear of solid surfaces caused by fracture from material fatigue. This kind of wear is produced during friction under repeated cycles of loading contacts. It leads to micro-cracks formation and propagation that evolves to macro-cracks and result in separating of material particles. The latter phenomenon is called spalling. In fatigue wear, high-cycle fatigue and low-cycle fatigue mechanisms can be distinguished.

# 3. FRETTING DESTRUCTION PROCESS

Fretting is defined as a reciprocating micro-displacement amplitude oscillatory motion between two nominally stationary solid bodies in contact under normal load. Depending on the loading conditions (displacement amplitudes, normal loads) different types of fretting damage mechanisms can be distinguished.

## 3. 1. Introduction

Fretting phenomena were first observed by Eden et al. (1911) when they found iron oxide debris in the steel grips of their fatigue machine in contact with a steel specimen. However, a definition and term 'fretting corrosion' was established by Tomlinson (1927) who conducted the quantitative study and concluded that relative movement had to occur to cause fretting. The successive investigations on the fretting phenomena were carried out among others by Godfrey and Bailey (1952) as well as by Halliday and Hirst (1956). They all demonstrated the significant impact of oxide particles that are present in the wear scar. In the 60s of the last century Wayson (1964) and Hurricks (1970) advanced the knowledge about mechanisms of fretting wear in metals. The latter concluded that the process can be divided into three stages, those of initial adhesion and metal transfer, the production of debris in a normally oxidized state and, finally, the steady-state wear condition. Moreover, he observed that abrasion as a cause of fretting damage is favoured only as a minor factor. Vingsbo and Soderberg (1988) were first who proposed the fretting maps to describe the relationship between wear and displacement amplitude, later developed by Vincent et al. (1992) by introducing the fretting regimes. Significant contribution
about the fretting fundamentals was brought by Waterhouse (1972) in the book "Fretting Corrosion".

Many nominally stationary joints of components in mechanical systems are subjected to vibrations and complex variable loading conditions. As a result, damage caused by fretting may take place what leads to the failure of the elements. Fretting is perceived as a plague in many industrial fields (aeronautics, nuclear engineering, automotive issues etc.). The degradation by fretting can be encountered for example in blade/disc joints in jet engines, steam generator tubes in a nuclear power plants, rolling bearings, riveted or screw joints, steel ropes, electric contacts or medical implants. Fretting is indeed a complex process, whose all involved mechanisms and kinetics are not completely identified and formalized yet. It was defined more than 50 factors that affect fretting [Collins (1981)], however this issues is still open to be complemented by other parameters like, e.g. impact of the magnetic field [Sato et al. (2000)].

## 3. 2. Contact conditions

Complexity of industrial tribo-systems does not often allow the straightforward transposition of their contact geometries to the simplified ones studied in laboratory conditions. Hence, three basic reference configurations are proposed and investigated (Figure 10):

- plane/plane,

- cylinder/plane,

- sphere/plane.

<figure><img src="image_12.png" /><figcaption>Figure 10: Three basic fretting contact geometries: (a) plane/plane, (b) cylinder/plane and (c) sphere/plane.</figcaption></figure>

The linear cylinder/plane and point sphere/plane contact geometries are the most often used to investigate the fretting phenomena due to their simplicity of contact
mechanics and ease of implementation. The stress distribution and elastic deformation for these two geometries can be determined analytically according to the Hertz's theory [Hertz (1882)]. His work basically summarizes how two axi-symmetric objects placed in contact will behave under loading. The model bases upon the classical theory of elasticity and continuum mechanics. More complex and profound information on contact mechanics can be found in works of Johnson (1985) and Hills et al. (1993).

However, above-mentioned contact geometries are poorly corresponding to the real vane/bushing contact occurring in the VSV system of the turbofan engine that is closer to the plane/plane contact. Even though the plane/plane configuration requires a specific alignment to guarantee the flat/flat contact, it allows maintaining a constant geometry of the contacted surfaces independently of the degree of surface wear by contrast with a conventional sphere/plane configuration. However, mechanical analysis of such geometry reveals discontinuity in the pressure distribution on the borders of the contact. Different types of plane/plane contact configurations were developed by Snecma, where the border effect was significantly reduced, so that reproduce the pressure field distribution that occurs in the contact blade/disc in the fan of the jet engine. At the beginning an axi-symmetrical pin type specimen had been tested, then two different pin type specimens (2D scale reduced and 2D scale 1 pin) were studied to better reproduce the real contact [Paulin (2006)] (Figure 11). The pressure profiles generated under such conditions were investigated by Alexandrov et al. (1986).

<figure><img src="image_13.png" /><figcaption>Figure 11: Different geometries to describe the plane/plane contact: (a) an axi-symmetrical, (b) 2D scale reduced and (c) 2D scale 1 pin type specimen.</figcaption></figure>
Two main test configurations are developed (Figure 12):

- *Fretting Fatigue test* is derived from a classical fatigue experiment where two pads (plan, cylinder or sphere) are pressed on the fatigue specimen. The pads are put perpendicularly in relation to the axis of the fatigue specimen. This specimen is here subjected to the cyclic tension. As a result, relative displacement ($\delta$) and cyclic tangential load (Q) are induced by the strain generated through the fatigue sample subjected to external loading (P). In this configuration cracks nucleates and subsequently propagates due to applied external loading. This type of experiments permits to quantify the influence of the contact and fretting on the specimen lifetime under fatigue by means of the Wöhler curve. In this type of test, fretting and fatigue loading are in phase;

- *Plain Fretting test* (also called fretting wear test) is equivalent to a classical reciprocating wear experiment, but sliding amplitude is here smaller than dimension of the contact. Micro-displacement is here generated by a relative motion between two bodies induced, for instance, by electro-dynamic shaker or hydraulic system. This type of configuration enables to analyze wear process and crack nucleation at the same time. Moreover, for this test, the influence of loading parameters is much easier to measure.

<figure><img src="image_14.png" /><figcaption>Figure 12: Fretting test configuration: (a) Fretting Fatigue and (b) Plain Fretting test.</figcaption></figure>

The most commonly used fretting test configuration in the tribology is ball-on-flat one. Blanpain et al. (1995) defined three fretting modes for this geometry (Figure 13):

- linear displacement (mode I),
- radial displacement (mode II),

- circumferential displacement (mode III).

<figure><img src="image_15.png" /><figcaption>Figure 13: Presentation of the three fretting modes with representative wear tracks; P – normal load, P<sub>r</sub> – rotation load, δ – displacement.</figcaption></figure>

Due to the simplicity of its operation and of the contact mechanics, mode I is the fretting mode readily explored in laboratories. Moreover, it is the most representative for the majority of industrial contacts. Variable normal load testing (mode II), also known as ‘false Brinelling’, is investigated less frequently, although it is a common problem encountered in ball bearings. Torsional relative displacement fretting mode III can be observed in the nuclear or fuel industry (heat exchangers or steam generators).

### 3. 3. Sliding conditions

It is generally stated that fretting process (mode I) occurs under alternating micro-displacement. It was reported that even for displacement amplitude lower than 1 µm damage caused by fretting can take place [Kennedy et al. (1983)]. Threshold value of displacement amplitude for transition from fretting to reciprocating sliding was variously interpreted and found to occur within a wide range of amplitudes between 50 and 300 µm [Halliday et al. (1956), Vaessen et al. (1968-1969), Ohmae et al. (1974), Gordelier et al. (1979)]. This problem was later clarified by Fouvry et al.
(1996), who related this limit to the contact dimension. He introduced the e coefficient, which is defined as a sliding ratio (relation 1):

$$e = \delta_g / a \qquad (1),$$

with: $\delta_g$ - the sliding amplitude that is different from the displacement amplitude due to the contact and test apparatus compliance, a - the contact radius.

<figure><img src="image_16.png" /><figcaption>Figure 14: Definition of sliding parameter e and identification of transition between fretting conditions and reciprocating regime (sphere/sphere contact).</figcaption></figure>

Figure 14 shows definition of sliding ratio and identification of transition between fretting regime and reciprocating sliding for the contact sphere/sphere. The boundary between fretting and reciprocating conditions is related to the limit value $e = 1$. When e remains lower than 1, an unexposed surface exists and fretting conditions take place whereas the system turns into the reciprocating regime when e is higher than 1 and all surface is exposed to the atmosphere. For a low value of tangential force, the micro-displacement between two bodies occurs. This displacement increases as the tangential force becomes higher what results in change of fretting contact conditions. Dynamic tangential force and displacement measurements during the fretting tests and some post-mortem metallographic examination allowed Vingsbo et al. (1988) to distinguish three different regimes of fretting:

- Stick regime: the interfacial sliding between two bodies does not occur as displacement is accommodated by elastic deformations. Stick domain is maintained
by locked asperities that can be plastically shared in the direction of micro-movement.
In this case, low damage fretting by very limited oxidation and wear can be observed.
For this regime the evolution Q=f(δ), called fretting loop or fretting cycle, takes form
of closed linear relation (Figure 15a);

-Stick-slip regime: occurs when displacement amplitude is higher than that in the stick regime. In this case the sliding does take place, however the stick zone is a dominating area in the contact. Increase of the displacement amplitude makes the stick zone smaller. Surface degradation is here characterized by cracking as a result of contact fatigue. If rough surfaces are subjected to contact the stick zone can be spread for a number of local single contacts. This regime is characterized by the closed Q – δ fretting cycle, which takes a characteristic shape of elliptic hysteresis (Figure 15b). The elastic analysis of the sphere/plane and cylinder/plane contact [Mindlin (1949)] allows the explanation of the pressure field and surface shearing. Considering the friction law of Coulomb it is $q(x, y) = μ · p(x, y)$ and $q(x, y) < μ · p(x, y)$ in the sliding and stick zone, respectively. For the elastic sphere/plane contact the size of the stick zone can be expressed by the sliding parameter (k):

$$k = \frac{c}{a} = \left( 1 - \frac{Q^*}{\mu \cdot P} \right)^{\frac{1}{3}} \quad (2),$$

with: c – the stick zone radius, a – the Hertzian contact radius, Q* - the tangential force amplitude, μ – the coefficient of friction operating within the sliding domain, P – the normal force.

-Gross slip regime: with still increasing displacement amplitude, the stick zone no longer occurs and entire contact area is subjected to sliding. Severe surface damage by wear, assisted by oxidation takes place. The Q – δ fretting loop characteristic of this regime is open and takes more quadratic shape (Figure 15c). Hence, the maximal tangential force Q* is here constant and do not depend on the sliding amplitude, what allows describing it by the classical Amonton's friction law: $Q^*=μ·P$ where μ – coefficient of friction and P – normal force.
<figure><img src="image_17.png" /><figcaption>Figure 15: Contact definitions and corresponding fretting loops for different fretting regimes: (a) stick regime, (b) stick-slip regime and (c) gross slip regime.</figcaption></figure>

### 3.4. Fretting maps

The concept of the fretting map was primarily introduced by Vingsbo et al. (1988) for a sphere/sphere contact geometry. They mapped fretting sliding domains based on relation between three fretting parameters: normal force, displacement amplitude and frequency. This approach was later developed by Vincent et al. (1992), who defined three fretting regimes for the running conditions recorded during fretting test:

- *Partial Slip Regime (PSR)*: corresponding to the condition when stick-slip sliding regime is maintained during the test, observed for the lowest values of displacement amplitudes;

- *Gross Slip Regime (GSR)*: corresponding to the condition when gross slip sliding regime is maintained through the interface during running test, characteristic of the highest values of displacement amplitudes;

- *Mixed Fretting Regime (MFR)*: corresponding to the condition when gross slip and partial slip regimes are occurring during the single fretting test, observed for intermediate values of displacement amplitudes.

Based on the above classification the Running Condition Fretting Map (RCFM) was put forward [Vincent et al. (1992)], where particular fretting regimes are mapped as a function of normal force and displacement amplitude (Figure 16). However, that map was incomplete because it did not take into account the material response and its degradation. This information was later supplemented by Blanchard et al. (1991) by
introducing the Material Response Fretting Map (MRFM) (Figure 16). Two main
damage mechanisms: cracking and wear, were there mapped in the same way by
depending on normal force and displacement amplitude. The RCFM maps are plotted
from the direct analysis of the fretting loops whereas the MRFM maps cannot be
made until after more profound metallographic analysis of the wear scars will carried
out. The MRFM map is especially important as it can be used by engineers and
designers to define the related wear mechanisms encountered in specific mechanical
systems under different loading conditions.

<figure><img src="image_18.png" /><figcaption>Figure 16: Fretting maps (RCFM and MRFM) representation

(after [Fouvry et al. (2000)]).</figcaption></figure>

**3. 5. Transition criteria**

Analyzing and verifying the single fretting cycle during the tests Fouvry et al. (1995a, 1996) introduced three criteria (Figure 17) that allowed a quantitative determination of the transition between partial and gross slip conditions for alternating loadings. These criteria were produced for the sphere/plane contact configuration assuming Mindlin’s hypotheses. Therefore, in turn the energy ratio, aperture ratio (also called
sliding ratio) and system free ratio criteria characterized respectively by the coefficients A, B and C were proposed. The transition values of the coefficients were determined as A<sub>t</sub> = 0.2, B<sub>t</sub> = 0.26 and C<sub>t</sub> = 0.77, below which partial slip conditions occur. The threshold values were found to be independent of the material properties. Nevertheless, computation of parameters A and B requires determination of the compliance of the system as they depend on the tangential accommodation of the fretting assembly. The aperture ratio and system free criterion are highly dependent on the sliding aperture (δ<sub>o</sub>) variation. Hence, it appears that the value of energy ratio A is the easiest to be accurately determined from among the above-mentioned criteria as dissipated energy for each cycle (E<sub>d</sub>) is less dependant on the data scattering than the sliding aperture (δ<sub>o</sub>) (also called sliding amplitude δ<sub>g</sub>).

<figure><img src="image_19.png" /><figcaption>Figure 17: Fretting loop analysis by quantitative parameters A, B and C to define the sliding transition (after [Fouvry et al. (1996)]).</figcaption></figure>

Transition between fretting and reciprocating sliding can be characterized throughout
analyzing the changes of friction coefficient, wear coefficient, wear volume, wear
scars profile or wear debris features before and after the boundary point. As an
example, for a sphere/plane self-mated steel contact wear coefficient and wear volume
were observed to be the most appropriate parameters for identifying the transition
criterion due to their quantitative values [Chen et al. (2001)].

**3. 6. Fretting damage mechanisms**

*Fretting Wear* (characteristic of Plain Fretting tests) and *Fretting Cracking*
(characteristic of Fretting Fatigue tests) are two main damage mechanisms that can
cause the catastrophic failure of the mated surfaces under fretting conditions.

*Fretting Cracking* is due to cyclic stresses resulting from the relative motion between
interacting bodies, which are conducive to crack nucleation and their propagation.
This type of damage appears as a consequence of local overstressing. The fretting
cracking is not a subject of this dissertation, thus it is being discussed briefly.

*Fretting Wear* is due to the interfacial shear work resulting from the relative motion between interacting bodies and is related to the debris formation and loss of material of contacting bodies. Fretting wear can be comprehended as a response of the tribo-system to the global overstraining of the surface.

Fretting Cracking and Fretting Wear are usually considered separately, however it
should be taken into account that under certain operating conditions they can be
identified as two competing processes, what is illustrated on the Material Response
Fretting Map in Figure 16. It accounts for why cracking can be observed under
fretting wear conditions and debris formation under fretting cracking regime
[Waterhouse (1981), Zhou et al. (1992)].

Fretting wear and fatigue concepts do not take into account the influence of the
interacting environment. In fact, pure fretting, when the chemical reactions do not
occur, is rather unusual rarely investigated process as the specific apparatus where
inert gases or vacuum must be used to produce neutral surrounding atmosphere.

Hence, the third mechanism of fretting damage – fretting corrosion – can be
distinguished. Indeed, the term of ‘fretting corrosion’ was originally used to define
destruction processes caused by fretting in air environment [Tomlinson (1927)], for
years considered as a synonym of fretting damage later. Corrosion appears in case of
oxidation process what can strongly affect the damage mechanisms. However, at
present it is treated as a secondary process in relation to fretting wear and fretting
fatigue. Fretting corrosion can be defined as a destruction process under fretting
regime stimulated by corrosive impact of the ambient atmosphere. Generated wear
products take usually form of metal oxides detached from the surface or oxidized
debris. In addition, fretting damage is here accelerated by stresses generated by
interacting solids, which increase the chemical reactivity of surfaces.

3. 6. 1. Fretting Cracking (i.e. endurance under Fretting Fatigue loading conditions)

Fretting Cracking under Fretting Fatigue loading conditions is observed mainly in the areas of stress concentration, e.g. in splines, shaft keys or cables. It usually takes place within or at the edge of the contact area. Then, the subjected component can be easily damaged if the crack propagates.

Under Fretting Fatigue loading conditions, materials performance can be characterized by a S-N curve (commonly used in characterizing the classical fatigue tests), also known as a Wöhler curve, which relate the number of cycles to failure (N) with maximal amplitude of cyclic stresses (S) (Figure 18). Plotting the Wöhler's curves allow an establishment of the endurance limit of materials, i.e. the maximal tension value at which the specimen failure will not occur even after great number of cycles (i.e. from the range 10⁸-10⁹ cycles or greater). It was shown that conjoined action of fretting and fatigue causes a significant decrease (from 2 to 5 times) of lifetime of the studied specimen in comparison with the pure fatigue test [McDowell (1953), Waterhouse (1992)].

<figure><img src="image_20.png" /><figcaption>Figure 18: Comparison of Wöhler curves for Fatigue and Fretting Fatigue tests.</figcaption></figure>
Apart from the tensile strain, the normal force and the displacement amplitude (induced by the specimen deformation under normal force and tangential stress) are two important parameters studied in fretting fatigue tests. Cracking behaviour of material is considered as a function of contact pressure and fatigue stresses. Thus, many authors showed that endurance limit diminished monotonously with increase of pressure in the contact [Endo (1976)]. On the other hand, Del Puglia et al. (1994) observed that the specimen lifetime reach some minimum for certain contact pressure. Waterhouse (1981) reported that the critical relative displacement amplitude for cracking phenomenon is comprised between 10 and 25 µm. Lower values of displacement were not sufficient to reduce specimen lifetime. In reverse, increase of displacement moves degradation process toward debris formation, where particles detachment eliminates the micro-cracks before they begin to propagate.

The point of first crack initiation and its direction are of great importance due to their industrial relevance. It was showed by Nakazawa et al. (1992), who investigated the plane/plane configuration that the point of crack nucleation within the contact area depends on the sliding conditions (Figure 19). Cracks are there expected to nucleate within the slip zone, most likely on the contact border as higher normal loading and smaller displacement amplitude conditions are imposed. With increase of slip zone in the contact some multi-cracks are observed.

The following four formulations can be applied to predict the crack initiation:

- Dang Van fatigue approach [Dang Van (1993)]: the crack nucleation process is a function of two macroscopic stresses: shear one and hydrostatic pressure. If these two variables reach the limit value then thee is a high risk of cracking on a critical grain;

- Crossland fatigue description [Crossland (1956)]: the macroscopic loading path is considered and crack nucleation risk is expressed as a combination of shear stress and hydrostatic pressure;

- McDiarmid fatigue formulation [McDiarmid (1991)]: identifies the maximal shear stress amplitude and indicates the critical plane where the crack is expected;

- Smith-Watson-Topper fatigue criterion [Smith et al. (1970)]: crack will initiate due to shear stress and will grow on a certain plane perpendicular to the direction of the principal stress.
<figure><img src="image_21.png" /><figcaption>Figure 19: Fretting damage mechanisms for plane/plane contact geometry

[Nakazawa et al. (1992)].</figcaption></figure>

In Fretting Fatigue test there can be encountered two forms of cracks: short (of the length of some tens of micrometers) and long ones that have propagated.

Micro-cracks appear very early in the lives of components. It was originally demonstrated by Forsyth (1961) that in ductile materials fatigue cracks propagate in two distinct stages (illustrated in Figure 20):

- Stage I: short cracks are generated, which orientation to the surface is comprised within the angle limits from 10° to 60° corresponding to the maximum shearing plane. The length of the crack varies and depends on the mechanical properties of the studied tribo-system. Initiation and propagation of short cracks are mainly controlled by the loading conditions of fretting;

- Stage II: during this stage the general plane of the previously generated short crack propagates perpendicularly to the direction of the maximum tensile stress. The evolution of long cracks is characterized by uniaxial fatigue strains in the material.

The presence of short and long cracks in a studied specimen suggests a complex fatigue strain and fretting loading at a time. However, there can be some conditions under which crack initiated by fretting do not propagate into the long one when so-called 'crack arrest' takes place. Hills et al. (1988) showed that the specimen lifetime can approach infinity in the presence of short cracks. Hence, it is important to
find a loading transition between fatigue strain and fretting. This transition can be
determined by using the Kitagawa-Takahashi diagram [Kitagawa et al (1976)].

<figure><img src="image_22.png" /><figcaption>Figure 20: A two stage process of fatigue crack propagation [Forsyth (1961)].</figcaption></figure>

3. 6. 2. Fretting Wear

By contrast with fretting fatigue damage where destruction by cracking takes place,
the wear phenomenon under fretting conditions is hardly formalized because it
involves mechanisms, which are considerably less quantifiable, such as:

- Material transfer;

- Modification of surface interface as a result of material removal;

- Flow of the wear debris within the interface;

- Mechanisms related to the impact of environmental conditions (oxidation, hydratation);

- Coupling between thermodynamic, mechanical and physico-chemical aspects.

There are different wear mechanisms and numerous factors affecting the tribological
processes. Hence, no single predictive equation or group of limited equations could be
found for general and practical use. Meng and Ludema. surveyed the journal *Wear*
between 1957 and 1992 and associated *Wear of Materials* (WOM) conferences from
1977 to 1991. They found 182 wear equations allowing wear quantification for the
many types of wear. Those models often had theoretical-empirical character, so many
tests had to be performed to determine related coefficients. Moreover, many of the
equations were deduced for specific tribo-systems. Consequently, their simple use is
limited and employment to the industrial issues impossible.
Review conducted by the authors [Meng et al. (1995)] showed that between 1947 and 1992 three schools in wear modelling successively developed can be distinguish.

- Years 1947 – 1970: During this period empirical equations were widely used. They based directly on the experimental results obtained under various conditions. For example, Rhee (1970) investigated the impact of normal force (P), sliding speed (Ṡ) and time (t) on the total wear of polymers. He proposed the following formulation:

$$ \Delta m = K \cdot P^a \cdot S^b \cdot t^c \quad (3), $$

with: Δm – the weight loss, K, a, b, c – the empirical constants.

Empirical models are applicable only within the range of parameters they are defined for, but are far more accurate than the theoretical relations developed under the same conditions.

- Years 1970 – 1980: Contact-mechanics-based equations were commonly developed within this time. The wear kinetics was then described by taking into account the real contact area and mechanical properties of the contacted materials as: Young's modulus or hardness.

The most representative formulation for this model group, nota bene commonly used in industrial application till these days, was elaborated by Archard (1953) (relation 4 and 5), who published well in advance of the later contact mechanics laws.

$$ V = K \cdot S \cdot A \quad (4), $$

$$ V = K \cdot S \cdot \frac{P}{H} \quad (5), $$

with: V – the total wear volume, K – the dimensionless wear coefficient, A – the real contact area, S – the sliding distance, P – the applied normal load, H – the hardness of the wearing material.

The wear coefficient K was interpreted by Archard as a probability to form a wear particle at each asperity encounter, however, the other authors proposed different interpretations of this coefficient [Shaw (1977), Hutchings (1992), Johansson (1993)]. Moreover, similar models were later proposed [Rabinowicz (1965), Moore (1980)].

- Years 1980 – 1992: Equations of wear kinetics based on the material failure mechanisms were evolved within this period. In this case, the wear resistance was no longer considered as an intrinsic property of materials, but was assumed to be closely related to the fatigue properties, shear failure defined by slip line analysis, dislocation mechanics brittle fracture properties or oxidation phenomena. In the last case, wear
was thought to be due to loss of oxide, e.g. the oxidational theory of wear [Quinn
(1967)] that is discussed afterwards.

Quantification of wear rate in the case of Fretting is more complicated in comparison
with, for example, sliding wear, because the former is strongly affected by debris
trapping within the friction interface, what results in a significant modification of the
interface as a result of debris flow and specific transfer of material.

Works concentrated on quantitative description of fretting problem were undertaken,
among others, by Klaffke (1994) and by the group of prof. Celis [Blanpain et al.
(1993)]. The first made a comparison of different surface treatments as function of
relative humidity using similar wear coefficient to that in the classical Archard's
model. The second related the wear resistance of different hard coatings to the sliding
distance, normal force and number of cycles (Figure 21). Recently, Goryacheva et al.
(2001) proposed to quantify the wear under partial slip regime by local formulation of
the Archard's law. The evolution of wear was there correlated with the modification
of the contact geometry during the fretting test followed by redistribution of the stress
field and deformation took place. This was connected with the wear volume by the
integration of the local Archard's law within the whole contact area.

<figure><img src="image_23.png" /><figcaption>Figure 21: Wear volume evolution of different coatings as a function of applied number of fretting cycles [Blanpain et al. (1993)].</figcaption></figure>

For recent 15 years an energy approach has been developed to describe fretting
behaviour. The damaging processes, which take place in the contact, can be assumed
to be driven by an increase in the contact temperature, material structure
transformations, debris generation or tribofilm formation. Indeed, all these processes involved in wear are activated and stimulated by frictional energy dissipated in the interface (Figure 22).

<figure><img src="image_24.png" /><figcaption>Figure 22: Dissipated energy concept as activating factor of wear (after [Fouvry et al. (1996)]).</figcaption></figure>

First attempt to provide a quantitative description of dissipated energy was carried out by Matveesky (1965). He put forward the concept of ‘Friction Power Intensity’ (Q<sub>F</sub>) to evaluate a degree of frictional heating occurring in the contact zones of rubbing surfaces:

$$Q_F = \frac{\mu \cdot P \cdot v_s}{A} \qquad (6),$$

with: μ – the coefficient of friction, P – the applied normal force, v<sub>s</sub> – the relative sliding velocity and A – the real area of contact.

This concept expresses the rate at which energy is generated by friction in the contact zone, but does not take into account the duration over which the energy is released to the mated bodies. Thirty years later, Plint (1995) developed the model of Matveesky and introduced the notion of ‘Energy Pulse’ (EP) as the product of the friction power intensity and the time for a point on the rubbing surfaces to transit through the contact zone:
$$EP = \frac{Q_F \cdot t_t}{2} = \frac{\mu \cdot P \cdot v_s \cdot t_t}{2A} \quad (7),$$

with: $t_t$ – the time of transit in the contact zone. In his model, author suggested that the amount of energy per unit of contact area dissipated at each encounter of the rubbing surfaces is closely related to the severity of contact conditions. This formulation was put forward for the case when two mated bodies are in motion and the energy generated in the contact zone flows at an equal instantaneous rate into the two contacting objects.

In the same year Fouvry et al. (1995b) and Mohrbacher et al. (1995) introduced the approach of accumulated dissipated energy for bidirectional sliding, appropriate for fretting phenomenon description. Dissipated energy (Ed) was formulated as a product of relative displacement ($\delta$) of two bodies in the contact and value of the tangential force (Q) taken from on-line recorded fretting loop (relation 8).

$$Ed = \sum Q \cdot \delta \approx 4 \cdot Q \cdot \delta^* \quad (8).$$

Recently, Huq and Celis [Huq et al. (2002)] used this concept to express the wear rate as a volumetric material loss per unit of dissipated energy in ball-on-disc unidirectional sliding. The following equation for dissipated energy was there presented:

$$Ed = \mu \cdot P \cdot v_s \cdot t \quad (9),$$

with: t – the duration of sliding test.

Numerous studies [Liskiewicz et al. (2006), Huq et al. (2002), Fouvry et al. (1997), Mohrbacher et al. (1995a), Wei et al. (1997)] showed that linear relationships between the wear volume and the accumulated dissipated energy calculated from the relation 8 can be plotted (Figure 23) and, from the slope of such evolutions, the so-called energy wear coefficient ($\alpha$) (relation 10) can be identified, what allows a comparison of wear resistance of different bulk materials and surface treatments.

$$\alpha = \frac{V}{\sum Ed} \quad (10).$$
<figure><img src="image_25.png" /><figcaption>Figure 23: Correlation between wear volume and the accumulated dissipated energy
(after [Fouvry et al. (1996)]).</figcaption></figure>

The energy approach, extensively validated for different couples of materials (TiN, steel) [Fouvry et al. (1997) and (2003), Liskiewicz et al. (2005)] was however found to be poorly applicable to describe the behaviour of the tribo-systems characterized by severe adhesion. For brittle materials like hard coatings or hardened steels, debris is obtained and easily ejected from the interface. Thus, the wear kinetics is linked to the input energy provided by the friction work and, linear evolutions between the accumulated dissipated energy and the wear volume extension are observed. When ductile materials like titanium or aluminium alloys are considered, in addition to the energy required to generate the debris, a given quantity of the friction energy is consumed in eliminating the debris from the interface. The higher the sliding amplitude, the faster the debris is ejected, and consequently the higher the energy wear coefficient. The relative impact of sliding on the energy efficiency of wear is therefore explained by the necessity to generate debris and successively eliminate it from the contact interface. The problem of the fretting behaviour of titanium alloys was undertaken and in-depth studied by the group of Fouvry [Fouvry et al. (2004), Paulin et al. (2005)]. They defined a unified fretting wear parameter (FW) (relation 11), expressed in Joules, which controls the wear kinetics of the Ti-6Al-4V alloy
under fretting loadings by weighting the accumulated dissipated energy (E<sub>d</sub>) by a
normalized sliding amplitude (δ<sub>g</sub>/δ<sub>g_ref</sub>).

$$
FW = \frac{\bar{\delta}_g}{\delta_{g\_ref}} \cdot \sum Ed \quad (11),
$$

with: δ̄<sub>g</sub> – the mean sliding distance of the test, δ<sub>g_ref</sub> – the reference sliding amplitude.

The wear volume (V) can be therefore written:

$$
V = \alpha_s \cdot FW \tag{12},
$$

with: α<sub>s</sub> – the sliding reduced energy wear coefficient.

A linear evolution between wear volume (V) and fretting wear parameter (FW) was
then observed for the invariable amplitude conditions for materials that are sensitive
to the adhesion phenomenon. By modifying the equation 11, a new formulation of the
sliding reduced energy wear factor was introduced (ΣEd<sub>s</sub>):

$$
\Sigma Ed_s = \sum_{i=1}^{N} \frac{\delta_{g(i)}}{\delta_{g\_ref}} \cdot Ed_{(i)} \quad (13),
$$

with: δ<sub>g(i)</sub> and Ed<sub>(i)</sub> – the sliding amplitude and the dissipated energy at the i<sup>th</sup> cycle.

Then, by using this modified fretting wear parameter it was possible to capture the
wear kinetics for variable sequential tests conditions:

$$
V = \alpha_s \cdot \Sigma Ed_s \tag{14}.
$$

The global energy analysis allows the wear coefficients to be determined more or less
independent of test conditions, thus a comparison of different palliatives can be
performed. Nevertheless, a change toward another contact configuration modifies the
established test conditions, what is a great obstacle to develop a general model. The
quantitative variables are defined globally while the wear volume related to the
accumulated dissipated energy does not consider the local aspects of degradation.
Hence, local energy approach put forward by Fouvry S. et al. (1997), appears to be a
reliable formulation to relate the local wear to the energy dissipated in the interface of
the contact area. Later, this concept was applied and developed by Liskiewicz and co-
authors [Liskiewicz et al. (2005a), (2005b) and (2005c)] to determine durability of the
hard coatings, which is classically related to the substrate reaching condition. Hence,
compared to a conventional wear volume analysis, wear depth quantification appears more suitable to predict the coating lifetime. By considering the dissipated energy as the controlling parameter of wear, it was assumed that the wear depth (h) is related to the cumulated dissipated energy density (ΣEdh) (i.e. energy per unit area). The wear depth extension can be therefore formalized through the following simple linear relationship:

$$h = \beta \cdot \sum Ed_h \quad (15),$$

with: β – the energy wear coefficient defined from the energy wear depth analysis.

<figure><img src="image_26.png" /><figcaption>Figure 24: TiC coating endurance for different sliding amplitudes: constant ones and variable; Fretting test conditions: RH= 50%, f = 5 Hz, P = 100N (after [Liskiewicz et al. (2005a)]).</figcaption></figure>

Hence, for a given coating thickness (e), it can be identified the critical dissipated energy density (Edhc) related to the moment when the substrate is reached:

$$Ed_{hc} = \frac{e}{\beta} \quad (16).$$

One fundamental conclusion from this relationship can be drawn, namely that the coating endurance is simply related to a critical energy density delivered to the tribo-system. Thus, it can be determined the critical number of cycles Nc to reach the substrate:
$$N_c = \frac{Ed_{hc}}{\overline{Ed}_h} \qquad (17),$$

with: $\overline{Ed}_h$ – the averaged energy density through the test.

An energy density-coating endurance chart (i.e. $\overline{Ed}_h$ – N curve) equivalent to the S-N fatigue Wöhler's representation was introduced. The coating endurance is then formalized as a function of the imposed mean energy density (Figure 24).

### 3.7. Third body formation and transport

#### 3.7.1. Third body approach

The third body approach was developed in the early 70s by Godet and his research group [Godet (1984), Colombie et al. (1984), Berthier et al. (1988), Vincent et al. (1992)]. This concept does not consider the dry contact through volumes of mated bodies, but through the interface notion. Indeed, from the standpoint of volumes or bulk solids, friction and wear are intrinsic properties of materials, whereas, from the standpoint of tribology of interface, friction and wear depend on the chemical composition and rheological properties of the interfaces. Thus, third body approach is based on the assumption that rather the quantity of the debris ejected outside the contact interface is as a factor that controls wear than quantitative determination of the total wear volume of the first bodies. Wear debris remaining in the contact is an operator that separates the first bodies protecting them against direct contact and participates in the process of loads transmission between the first bodies accommodating the greater part of their difference in speed. The third body can be introduced to the interface voluntary (grease, oil, nano-partices, etc.), or can results from wear process of the first bodies – debris film maintained within the contact area.

Third body load-carrying capacities under fretting conditions for steel-steel and chalk-glass contacts were studied by Colombie et al. (1984). They found that wear-protective third body formed from particles can develop even in the latter case (compacted chalk powder bed was formed between contacting bodies). Moreover, analytical characterization of wear debris and interfaces permitted them to propose theory of the third body formation that can be summarized in the following points:

1. Wear particles are formed following surface plastic deformation. Subsequently they are fragmented followed by their strong oxidation (Figure 26);
2. First body wear is governed by the formation and maintenance of the third body and by its abrasiveness;

3. Third body ejection depends on test machine dynamics and specimen shapes;

4. Identical behaviours are noted independently of the used first body material when the third body is formed.

Different aspects of the role of oxide wear debris were investigated by Varenberg et al (2002). They found that the role of oxide wear debris depends on the dominant wear mechanism of fretting wear. When adhesive wear mechanism is dominant the oxide wear particles act like a solid lubricant to reduce the damage caused by fretting. However, when the abrasive mechanism is prevailing the oxide wear particles facilitate the wear rather than protect against it. These results support the work of Colombie et al. (1984). It was shown by Iwabuchi (1991) that depending on normal load and slip amplitude artificially supplied particles of $Fe_2O_3$ can have either a beneficial effect, reducing wear, or a harmful one, facilitating wear. The former is caused by the quick formation of the compacted oxide layer, which acts as the third body load-carrying structure. It was also demonstrated that removing in-situ-formed wear debris from the interface prevents the severe to mild wear transition [Hiratsuka et al. (2005)].

Subsequent study on the friction interface allowed the third body concept to be progressively extended to the notion of velocity accommodation mechanisms [Berthier et al. (1989), Berthier (1990)]. Authors proposed formalism, which defines different sites and processes occurring at the interface (Figure 25). Contact is here defined by five sites ($S_i$) and four accommodation modes ($M_j$). The five identified sites are: two first bodies, a “bulk” third body and two third body films separating rubbing solids and bulk third body. However, four accommodation modes are represented by the elastic, breaking, shearing and rolling ones. The accommodation mechanism is defined by the couple of site and mode ($S_iM_j$) and 20 different configurations can be distinguished. It was shown by Vincent [Vincent et al. (1992)] that third body tribo-films ($S_2$ and $S_4$) are also activated under fretting conditions.

Thus, wear of the mated materials is defined by the quantity of wear particles ejected from the interface and can be calculated based on the determination of the flow of debris (w). For the case of a unidirectional contact this can be expressed by the following relation (18):
$$w = 1 \cdot \int_{0}^{h_d} u(y)dy \qquad (18),$$

with: 1 – the length of contact, h_d – the thickness of the debris film and u – the debris ejecting velocity distribution.

This model well describes real mechanisms of accommodation and damage, nevertheless it is difficult to formalize and does not allow a simple comparison of different tribo-systems. Analysis by means of this model allows an interpretation of the complex tribological phenomena related to impact of third body on decrease of the friction coefficient or its beneficial influence on wear kinetics. The third body and velocity accommodation notions permit also to better account for a big difference of wear kinetics observed for the contacts where debris is relatively easily trapped within the contact area (e.g. fretting) by contrast with the ones where wear particles are rapidly ejected from the interface (e.g. reciprocating sliding). Moreover, presented approach facilitates an analysis of the sliding regimes recognized in fretting. Thus, modification of accommodation site or mode can affect friction evolution and consequently transition from partial to gross slip regime.

<figure><img src="image_27.png" /><figcaption>Figure 25: Accommodation mechanisms at the interface [Berthier et al. (1990)].</figcaption></figure>

### 3. 7. 2. Tribologically transformed structure

Further in-depth study on determination of phenomena related to debris formation in the friction interface permitted a development of third body generation law. Moreover, it was shown that metallic contacts subjected to fretting wear tend to generate a specific transformed layer underneath the surface interface [Blanchard et al. (1991), Zhou et al. (1997), Sauger et al. (2000)]. This specific layer is called the tribologically transformed structure (TTS) and forms following plastic deformations induced by a relative movement of two solid bodies under normal load during the
very first fretting cycles. Authors proposed two-stage wear mechanism where first accumulation of plastic deformation (without wear and TTS) takes place, after which rapid formation of TTS (its formation is finished) and wear by removal of material resulting in formation of wear debris occurs (Figure 26). Thickness of the formed TTS remains constant, while total thickness of worn surface increases (Figure 27). Tribologically transformed structure appears as a nanocrystalline structure, corresponding to the chemical composition of the initial material and made of the more stable structure according to the equilibrium diagram. Its Young modulus is like that of the original metallic structure, but its hardness is significantly higher. By contrast with the compacted debris layer, the TTS contains a very small amount of oxygen, similar to that observed in the bulk material what permits a conclusion that oxygen is not the controlling factor for TTS generation.

<figure><img src="image_28.png" /><figcaption>Figure 26: Formation and evolution of the third-body through the contact interface
[Blanchard et al. (1991)].</figcaption></figure>
Evidence in favour of TTS existence was presented based on investigations on the self-mated contacts. However, Rigney et al. (1984) investigated heterogeneous materials in the contact. They put forward a theory of mechanically mixed layer (MML). It was shown that local contacts cause large plastic strains in either or both solid components. The plastic deformation changes the near-surface microstructure and makes the material unstable to local shear. As a result, transfer of particles that are further deformed and mixed with counter-face material and/or environmental components is produced and ultrafine-grained material called MML is generated. The very fine microstructure in this transfer material is stabilized by the mixing in (mechanical alloying) of a second phase.

<figure><img src="image_29.png" /><figcaption>Figure 27: Thickness evolution versus accumulated local dissipated energy: (a) TTS; (b) total worn surface [Sauger et al. (2000)].</figcaption></figure>

Transformations of these superficial layers (TTS and MML) modify the initial properties and thereby behaviour of the contacted materials. Thus these phenomena have to be considered in analyses of debris formation. However, even if we realize that the surface processes induced by the plastic deformation play a crucial role in comprehension of the third body approach, it is still very complicated to integrate this factor into a quantitative model.

### 3.7.3 Flows and rheology notions

Flows and rheology concepts are used for analyzing and structuring dynamic phenomena created by contacts and their interaction with the environment, in the physico-chemical and mechanical sense [Descartes et al. (2002)]. These notions
enable the progression and evolution of solid third bodies (properties, localisation, etc.) to be formalized during their migrations in and outside the contact. The flows of the third body represent the tribological circuit approach (Figure 28). This approach was introduced by Berthier (1990) and defines the different flows of the third body activated in the contact. This is a mechanical approach similar to that used in 'lubrication', i.e. with fluid third bodies, which leads to correlating the changes in friction to the rheology and flows of the solid third bodies circulating in the contact.

The possible flows of the third body that can be activated in an elementary two-dimensional contact are illustrated in Figure 28.

The internal source flow ($Q_i$) corresponds to the detachment of particles due to TTS, cracking, adhesion, etc. It leads to the formation of the natural third body. The external source ($Q_e$) flow stems from the introduction of the artificial third body between first bodies. The internal flow is the flow of the third body that circulates between the first bodies (trapped particles). The external flow is the flow of the third body that escapes from the contact. It splits into a recirculation flow ($Q_r$) and a wear flow ($Q_w$). The re-circulation flow is composed of the third body re-introduced into the contact. However, wear flow is composed of the third body that has been definitively ejected from the contact and can no longer participate in velocity accommodation.

<figure><img src="image_30.png" /><figcaption>Figure 28: Tribological circuit for an elementary two-dimensional contact
(from [Descartes et al. (2002)]).</figcaption></figure>

Rheology notion of solid third body permits, among others, a relative characterization on the basis of their 'cohesion' and 'ductility'. These two properties are determined
by observations of the third body and are related to its morphologies and texture. In
this case the word texture is not used in the metallurgical sense but more classically
refers to the orientation of the third body layers or the third body particles, their size,
shape and arrangement. The term cohesion is chosen by analogy with cohesion of
powder mixture. The qualitative comparison of different third body cohesions for the
scale of observation chosen is depicted in Figure 29. Third body of very low cohesion
is very powdery and composed of small particles (Figure 29a) by contrast with highly
cohesive third body that is very compact and appears to be more compressed (Figure
29c).

<figure><img src="image_31.png" /><figcaption>Figure 29: Relative cohesion of the solid third body (SEM images):</figcaption></figure>

(a) very low; (b) low; (c) high (from [Descartes et al. (2002)]).

The term ductility chosen by analogy with plastic flow characteristics of metals and it
expresses the ease with which third body spreads and extrudes in the contact. Low
ductility means that the third body spreads little and only covers a small area of the
contact (Figure 30a). On the contrary, high ductility means that third body spreads
easily and covers a large part of the contact are (Figure 30c).

<figure><img src="image_32.png" /><figcaption>Figure 30: Relative ductility of the solid third body (SEM images):</figcaption></figure>

(a) low; (b) not very high; (c) high (from [Descartes et al. (2002)]).
### 3.8. Fretting damage methodology

Fretting can have dangerous repercussions for the operation of mechanical systems. Particularly perilous is damage caused by cracking as it often cannot be detected before the subjected component ruptures completely. Hence, it is of great importance to predict dominating mechanism of fretting damage and determine the risk of the component failure.

<figure><img src="image_33.png" /><figcaption>Figure 31: Illustration of the methodology developed for the fretting damage analysis (after [Fouvry et al. (1996)]).</figcaption></figure>

In order to predict the fretting damage the methodology elaborated by Fouvry et al. (1996) was proposed (Figure 31). It consists in an identification of sliding condition through the quantitative parameters A, B, C, which define the transition between partial and gross slip regimes. When the fretting regime is defined the main mechanism responsible for surface process degradation can be indicated. If it is the partial slip, the cracking phenomenon is expected and nucleation condition can be precisely determined and quantified by one of the fatigue approaches, e.g. by means of multiaxial fatigue analysis of Dang Van [Dang Van (1993)]. However, gross slip conditions favour material removal and debris formation as a principle material
surface degradation process. In this case damage can be quantitatively described by
referring the loss of material to the energy dissipated in the contact (e.g. as in Figure
23).

3. 9. Palliatives in fretting

Considering the economical and social losses that may be caused under fretting
loadings, some appropriate steps should be taken in order to eliminate or at least to
limit the adverse effects of fretting. The overview of various palliative strategies
including different treatments such as lubricants, low friction coatings, soft thick
coatings, shot peening and hard ceramics were performed by Fouvry et al. [2006].

Protection against fretting has to be taken into account already during design stage of the fretting couple. By designing the appropriate contact geometry of nominally stationary junction, the concentration of the stresses and consequently cracking by fretting fatigue can be avoided. Construction treatment can also contribute to reduction of reciprocal displacement amplitude [Guzowski (1998)]. Nevertheless, damage by fretting cannot be completely avoided as this kind of destruction process was reported to take place even under displacement amplitude lower than 1 µm [Kennedy et al. (1983)].

Another very important aspect allowing fretting damage to be reduced is adequate
material selection for mated components. In general, tribo-systems with polymers are
characterized by higher fretting resistance compared to e.g. steel/steel ones, and hard
steel has higher resistance than the soft one. Polymers display lower Young modulus,
thus under fretting loadings most of the displacement is accommodated by elastic
deformation rather than by sliding. This can explain why with polymers smaller wear
is observed. Of course, there are always some exceptions like high chromium steel
where brittle and hard oxides formed on its surface contribute to increase of wear rate
[Varenberg et al. (2002)].

Appropriate surface engineering treatments can provide an effective protection against fretting. Thus, the following methods with adequate processes increasing fretting resistance can be enumerated [Harris et al. (1985), Labedz (1988), Waterhouse (1988), Fu et al. (2000)]:

- *Induce a residual compressive stresses:* one of the most effective way to decrease damage caused by fretting fatigue (e.g. by shot-peening, nitriding,
carburizing, ion implantation, etc.). Fridrici et al. (2001) showed that compressive residual stresses have an important effect by limiting crack propagation. By contrast, Kubiak et al. (2005) observed only negligible impact of shoot-peening on crack behaviour. Indeed, influence of shoot-peening on crack initiation and its propagation is directly related to the imposed contact loadings. Thus, large sliding can relax the compressive stresses very fast diminishing significantly the positive effect of that kind of surface treatment;

- Decrease of coefficient of friction: lower value of friction forces leads to lower shear stresses and related destruction response. This effect can be produced by introducing solid lubricants or applying different surface treatment techniques PVD, CVD, nitriding, carburizing, etc.;

- Increase of the surface hardness: this action prevents the adhesive and abrasive wear in fretting (e.g. by nitriding, shot-peening, PVD and CVD techniques, etc.);

- Control of surface chemistry: tribochemical reactions that proceed onto the interacting surfaces can produce lubricating layers (e.g. oxide or nitride layers) and significantly improve fretting resistance.

An effective method to decrease the coefficient of friction and wear rate is to apply lubricants [Kalin et al. (1997), Zhou et al. (1999)]. However, on certain conditions such as low sliding speed, low sliding amplitude or high pressure, lubricating does not always bring desirable effects. Shima et al. (1997) reported that for small strokes, i.e. for conditions approaching almost complete ‘stick’ regime, values of the coefficient of friction values under oil lubrication were well in excess of double those observed without it. These high values were accounted for by the fact that the oil was unable to penetrate into the fretting contact region, but did maintain a shield around it, so that metal-on-metal contact was maintained under oxygen deprived conditions. Thus, an effective lubricating is possible in case of fretting only if constant inflow of grease or oil can be maintained within the contact area. Moreover, it should be noticed that for certain mechanical systems an application of liquid oils is not possible, e.g. at elevated temperature working conditions, and then other palliative solutions has to be introduced e.g. solid lubricating coatings.
## 4. INFLUENCE OF ENVIRONMENTAL CONDITIONS

Apart from mechanical loadings the environmental factors: temperature and relative humidity can strongly affect the tribological behaviour of contacted components, so their influence has to be taken into account with particular care as well. Many industrial tribo-systems have to withstand elevated temperature conditions or frequent changes in ambient humidity for long hours without failure. For example, stator vane/bushing joints in turbofan engines, electrical contacts in car engines or nuclear power plants are exposed to the elevated temperature conditions. Hence, comprehension of the effect of the environmental factors is a crucial issue for engineers and researchers, who put a lot of effort into finding adequate material treatment solutions to upgrade the resistance to wear of machine components working even under very high temperatures.

In the present dissertation dry contacts subjected to fretting wear under elevated temperature conditions are being studied, thus effect of temperature is discussed extensively whereas of humidity only briefly.

### 4.1. Effect of elevated temperature

The elevated temperature in the contact area of interacting bodies can be induced either by frictional heat during room temperature tests (e.g. for unidirectional sliding) or by external heat (typically for reciprocating sliding). External heat is important in high-temperature sliding, such as can be encountered in jet engines. Elevated temperature conditions promote oxidation process that may drastically change tribological response of the systems. Thus, static oxidation and tribo-oxidation processes of metals and alloys are precisely described below.

#### 4.1.1. Oxidation of metals and alloys

The type of oxides formed as a result of tribochemical processes that takes place in the interface of contacting bodies cannot be deduced without considering the aspect of static oxidation of metals. This, in turn, cannot be studied without employing thermodynamic and kinetic bases of the possible reactions. Thermodynamics and kinetics provide a good background for the prediction and comprehension of the static oxidation results. During oxidation process metals may react with oxygen to produce
an oxide at the surface. There is interest in three aspects of this reaction: the ease with which the metal oxidizes, the nature of the oxide film that forms, and the rate at which oxidation occurs [Askeland (1998)].

The ease with which oxidation may occurs is given by the Gibbs free energy of formation of the oxide. The overall equation for oxidation of a metal (Me) may be represented as follows:

$$x\text{Me(s)} + \frac{1}{2}\text{yO}_2\text{(g)} \leftrightarrow \text{Me}_x\text{O}_y\text{(s)} \quad (19).$$

The driving force for this reaction is the Gibbs free energy change ($\Delta G(T)$) associated with the formation of oxide from the reactants at the temperature T and it can be written as:

$$\Delta G(T) = \Delta G^0(T) + R \cdot T \cdot \ln Q \quad (20),$$

with: $\Delta G^0(T)$ – the standard Gibbs free energy, R – the universal gas constant, T – the temperature in Kelvin and Q – the reaction quotient.

The standard Gibbs free energy of formation of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of that substance from its component elements, at their standard states (the most stable form of the element at 25°C and 1 bar). At equilibrium, when $\Delta G(T) = 0$ the equation 20 becomes:

$$\Delta G^0(T) = -R \cdot T \cdot \ln K \quad (21),$$

with: K – the equilibrium constant for any reversible reaction at equilibrium.

The ease with which different metals tend to form oxides can be read off the Ellingham diagram (Figure 32 [Ellingham (1944)]), which depicts standard Gibbs free energy change ($\Delta G^0$) for the oxidation reaction as a function of the temperature. The higher is the negative $\Delta G^0$ the higher is the tendency of a metal to spontaneous formation of an oxide in alloy. Thus, the noble metals, which are easily reduced, occur at the top of the diagram, while the more reactive metals are at the bottom. However, some of the metals with high tendencies to oxidation (Al, Ti) resist oxidation from room temperature up to certain elevated temperatures due to the impermeability of the coherent compact oxide film that forms first. The protective nature of formed oxide layers can be qualitatively assessed by using Pilling-Bedworth law [Askeland (1998)]. The related parameter, so-called Pilling-Bedworth ratio defined as a ratio of oxide volume grown to unoxidized material consumed in oxidation, can be determined. And thus, if the Pilling-Bedworth ratio is less than one,
the oxide occupies a smaller volume than the metal from which it formed. The oxide coating is therefore porous and oxidation continues rapidly – typical of metals such as magnesium. If the ratio is one or two, the volumes of the oxide and metal are similar, and an adherent, nonporous, protective film forms – typical of, above mentioned aluminium and titanium. If the ratio exceeds two, the oxide occupies a large volume and may flake off the surface, exposing fresh metal that continues to oxidise – typical of iron.

Oxide layer or scale on the surface of metal or alloy can give protection by acting as a barrier between metal and reactive gas (oxygen). However, effectiveness of such barrier is, among others, a function of temperature-dependent diffusion rate of the reactants across the barrier and defect nature of the barrier. Typical oxides in metals are Al₂O₃, NiO, Cr₂O₃, SiO₂, MgO, FeO, Fe₂O₃. However, oxide scale formed on metal is not often uniform, but consists of different type of oxides of the same element within thickness. For example, in case of pure iron there is thin inner layer of Fe₂O₃ on the surface above which there grows outer more defective layer of Fe₃O₄ and at higher temperature (above 570°C) FeO phase that is very defective poor barrier to diffusion becomes stable [Dobrzanski (1999)]. As it can be got from Ellingham diagram (Figure 32) Fe₃O₄ has the lowest standard Gibbs free energy, so it tends to form easier than Fe₂O₃. In order to predict the oxidation results the stability of particular oxides at given temperature has to be taken into account as well. And thus, magnetite (Fe₃O₄) is known to undergo the following phase transformation with temperature increase [De Boer et al. (1954), Goto (1964),]:

$$ \mathrm{Fe_3O_4}(\text{magnetite}) \xrightarrow{200^{\circ}\text{C}} \gamma-\mathrm{Fe_2O_3}(\text{maghemite}) \xrightarrow{400^{\circ}\text{C}} \alpha-\mathrm{Fe_2O_3}(\text{hematite}) \quad (22). $$

In case of alloys, there may take place selective oxidation. It means that some alloying elements (Cr, Ti, Al, Si etc.) of an alloy, have a higher affinity for oxygen than other alloying elements (Ni, Fe, Co, Cu etc.), and consequently, may oxidize earlier (according to thermodynamic aspect, see Ellingham diagram (Figure 32)) and more rapidly. Thermodynamics allows prediction of the final equilibrium state for a reaction, but gives no information about reaction rate. Kinetics expresses the speed of the oxidation process. Reaction rates depend on a number of factors, such as temperature, oxygen pressure, dwell time, surface area or surface pre-treatment. The corresponding kinetics equations can be written assuming an adequate oxidation law
<figure><img src="image_34.png" /><figcaption>Figure 32: Ellingham diagram (after [Ellingham (1944)]); Alloying elements, which are the components of the investigated in the present dissertation alloys, are presented in colours.</figcaption></figure>
(i.e. parabolic, logarithmic etc.). As regards the effect of alloying elements on
oxidation rate, Al, Si and Cr form stable oxides with low diffusion coefficients for
oxygen. Even though, they all have high affinity with oxygen, when formed, the thin
compact oxide layer resists oxygen diffusion and limits further oxidation of the alloy.
Some other metals such as Ni, Fe, Co, W, Ti do not form protective oxide layers and
their oxidation rate is high. For example, in case of high temperature oxidation in air
of Ni-20%Cr alloy (typical gas turbine alloy) complex oxides are formed, i.e. thin
protective barrier layer of Cr₂O₃ at the base of the NiO-rich scale, containing spinel-
type NiCr₂O₄ oxide [Stott (1998)].

4. 1. 2. Tribological behaviour of metals and alloys

Although there is good understanding of static oxidation of metals and alloys as well
as mechanisms of oxide formation, this is not entirely clear (e.g. kinetics of oxidation)
in situations when relative motion under load occurs between contacting bodies. The
oxides can be considered as in-situ solid coatings for applications that involve high
temperature conditions or where the application of engineered solid coatings is either
difficult or impossible. It was shown that even at room temperature, the development
of oxides within the area of the contact may lead to the reduction to some extent
metal-to-metal interactions and, hence wear rate, giving mild wear conditions. Higher
temperature of the contact area promotes higher oxidation rate what may support the
development of wear-protective oxide layers onto contacting surfaces as a result of
tribo-sintering of oxide particles. However, these oxides are not always effective in
reducing the wear of metals. The beneficial effect of in-situ formed oxides depends on
their chemistry and structure.

4. 1. 2. 1. Flash temperature

Transformation of a part of frictional energy to heat is responsible for increase in the
temperature of sliding bodies, especially in real contact regions (at the peaks of
contacting asperities). Calculation of this temperature and prediction of its distribution
is very difficult due to a complexity of the problem where a number of interfacial
properties, usually undetermined in details, affect the generation of frictional heat in
tribo-contact. For example, in fretting wear, the mechanical and thermal properties of
interface are constantly changing due to its tribochemical transformations what makes them impossible to determine exactly.

The review of different models for calculating temperature rise (called flash temperature) for dry ball (silicon nitride)-on-flat (steel) contact under fretting conditions was performed by Kalin et al. (2001). The authors showed significant discrepancies between the results that can be obtained for the same contact and loadings using different models. Figure 33 shows the average and maximum temperature rise obtained according to different models at 88 N normal load, 50 µm displacement amplitude and 210 Hz frequency of oscillation where no variation of influencing factors was employed. It can be observed that the temperatures calculated using the same input parameters vary quite significantly, by about a factor of 3. Moreover, the temperature of contact area was shown to increase with displacement amplitude due to increasing sliding speed. By using different methods for determination of the real contact area or different input values for the thermal conductivity the calculated flash temperature during dry fretting can vary by as much as dozen hundreds of degrees Celsius. Such large mismatch suggests that severe limitations in accuracy must be considered and care in the interpretation of results taken. Notwithstanding, it must be noticed that in this consideration [Kalin et al. (2001)] tests were performed under very high frequency of oscillation (210 Hz), which results in fast heat generation and accumulation in small contact dimension.

<figure><img src="image_35.png" /><figcaption>Figure 33: Results of various models for the average and maximum temperature rise under unlubricated fretting at 50 µm displacement amplitude (from [Kalin et al. (2001)]); Symbols: AR=Archard, HM=Holm, TK=Tian-Kennedy, GG=Greenwood-Greiner, AS=Ashby-Abulawi-Kong.</figcaption></figure>
Low frequency (10 Hz) fretting experiments for unlubricated ball-on-flat steel (AISI 52100) self-mated contact was studied by Kolodziejczyk et al. (2007). Authors calculated that the flash temperature for the most severe test conditions investigated (2 GPa maximal Herzian pressure and 150 µm displacement amplitude) did not exceed the value of 30 K above the test temperature. Thus, the structural changes of the material in the contact were interpreted to be hardly probable due to frictional heat, but more likely due to mechanical transformations [Sauger et al. (2000)].

Another authors [Glascott et al. (1985)] investigated the low-speed reciprocating sliding (peak-to-peak amplitude 2.5 mm) of dry Jethete M152 self-mated contact under a load of 1.5 kg. They demonstrated that a relatively high number of load-carrying junctions occur in the interface between plastically deformed, wear-protective oxide layers, so load supported by any one junction is quite small. Hence, the mean, surface, flash temperature rise during sliding would be expected to be relatively small. That was confirmed by their computation (using Archard's model), which gave a value of mean temperature rise at a typical oxide-oxide junction as low as 2°C.

In the present dissertation low frequency fretting experiments are being investigated. Thus, by taking into account above discussion on the flash temperature aspect the effect of the frictional heat on the temperature rise in the studied contacts can be assumed to be negligible.

### 4. 1. 2. 2. Generation of oxides during sliding wear

The mechanisms of oxide generation under low-speed reciprocating sliding at elevated ambient temperatures were investigated extensively by the group of prof. Stott [Glascott et al. (1985), Stott (1998), Jiang et al. (1998)]. Three limiting cases for the generation of oxide were identified [Stott (1998)]:

1. Oxides may be formed by oxidation of the metal asperities while in contact. At the same time, more general oxidation of all the apparent area of contact occurs. Oxides from both sources may be removed completely during subsequent traversals, exposing clean metal to the environment that is reoxidized in the next traversal. This is similar to the mild oxidational wear model [Quinn (1967, 1983a, 1983b)]. The resulting wear debris may be ejected from the contact or cause abrasion of the metal substrate,
increasing wear, or may be compacted between the sliding surfaces to give wear-protection. This was termed an ‘oxidation-scrape-reoxidation’ mechanism.

2. Some particular conditions like high ambient temperature may lead to the following scenario. The oxides developed during sliding (or present on the surface prior to sliding) may be removed only partially or not at all by the sliding action and continue to thicken with time. This wear situation was termed a ‘total oxide’ mechanism. Such mechanism associated with deformation of the oxides can give protection against further wear.

3. Another possible source of oxides during sliding is oxidation of metallic debris. Such wear debris particles, produced in the early stages of the test, may be broken up and fragmented under sliding action, thereby exposing fresh areas of clean metal for further oxidation. This wear situation was termed ‘metal debris’ mechanism. During sliding, the oxidation process is promoted by the heat of deformation and the increased energy of the particles due to the increased defect density and surface energy. Moreover, if the heat of oxidation released is taken into account, fine metallic particles may be oxidized spontaneously and completely. Hence, a significant amount of oxides can be generated during low-speed sliding, even at low temperatures. The resulting oxide debris can develop into a wear-protective layer, as considered later.

### 4. 1. 2. 3. Establishment of wear-protective layers

It was already mentioned that wear particles generated in the interface can strongly affect tribological behaviour of metals. In case of reciprocating sliding or alternating fretting the wear debris can be retained on the contacting surfaces as shown schematically in Figure 34 [Stott (1998)]]]. Although, some are lost, resulting in wear, others are maintained within the scars where they are comminuted by repeated plastic deformation and fracture while moving freely between the sliding surfaces. However, once they are reduced to a sufficiently small size, they can be agglomerated at certain locations, particularly in grooves, due to adhesion forces between solid surfaces arising from surface energy, and develop compact layers that eventually become load-carrying (Figure 34c). An adhesion between solids can be represented by a nominal tensile stress parameter ($σ_a$). To break the N pairs of particle contacts adhered together the $σ_a$ can be expressed by the following relation [Jiang et al. (1998)]:
$$ \sigma_a = k \cdot D^{-1} \cdot \gamma \qquad (23), $$

with: k – the constant of proportionality, D – the particle diameter, γ - the surface energy between two solid surfaces.

According to the relation 23, the adhesion strength of particle agglomerates increases with decrease in particle size. The rise of temperature leads to increase of surface energy between solids, thus of adhesion as well. Consequently, fine particles are sintered together to some extent to form more solid layers. The sintering process of fine particles was reported to occur at temperatures only slightly above 20°C [Zhou et al. (1989)], but of course is more significant at higher temperatures. This reduces

<figure><img src="image_36.png" /><figcaption>Figure 34: Schematic diagram showing the processes of development of wear debris particle layers and ‘glaze’ layers during dry sliding wear (after [Stott (1998)]); (a) Generation of metallic wear debris; (b) Comminution, oxidation and agglomeration of debris particles; (c) Compaction of agglomerated debris particles; (d) development of ‘glaze’ layer over compacted particle layer under some conditions; (e) Breakdown of wear-protective layers and development of new protective layers in other areas.</figcaption></figure>
material loss since newly formed debris particles are recycled into the layers while, as the particles are heavily deformed and oxidized, the layers are hard and give protection against wear damage. As sliding progress, two competitive processes take place: break-down of the layers (Figure 34e) and sintering between particles, which consolidate the layer (Figure 34d). The latter process is accelerated as temperature in the contact area elevates. When the surface becomes solid before break-down occurs, wear is low due to formation of so-called ‘glaze’ layer on top of the compacted debris particles. On the other hand, if there are weak sintering bondings in particles layers, the loose hard oxide particles are removed more easily resulting in higher wear.

The conclusion from above discussion is that the elevated temperature conditions promote formation of the wear-protective glaze layers. It was reported that there is a certain critical value of temperature required to establish a ‘glaze’ surface under a given set of conditions [Stott (1998)], depending also on investigated materials [Glascott et al. (1985)]. Summarizing, the sliding wear process at different temperatures can be depicted schematically as in Figure 35.

<figure><img src="image_37.png" /><figcaption>Figure 35: A diagram showing the wear model for dry sliding wear of metals at various temperatures (from [Jiang et al. (2004)]).</figcaption></figure>

On the basis of the above description of a wear process, a mathematical model accounting for the establishment of such wear-protective layers was developed [Jiang et al. (1995)]. In the model it was assumed that the wear rate of the wear-reducing
layers is negligible compared to that of other areas and wear debris particles are only produced from unprotected zones. Thus, the wear volume after sliding time (t) is expressed by the following equation:

$$V(t) = \frac{\pi}{6} \int_{0}^{t} \left\{ A(t) \cdot N(t) \cdot [1 - C_{e}(t)] \int_{0}^{\infty} [D^{3} \cdot f(D) \cdot P_{r}(D)] dD \right\} dt \quad (24),$$

with: $N(t)$ – the number of wear debris particles formed per unit time at time t, $A(t)$ – the apparent area of the wear scar at time t, $C_e(t)$ – the effective coverage by wear-protective layers at time t, $f(D)dD$ – the percentage of newly generated particles that fall in the diameter range of D to (D + dD), and $P_r(D)$ – the probability that a wear particle of diameter D is removed from the wear track.

The volume of wear debris particles retained within the rubbing surfaces at time t ($V_{retained}(t)$) is as follows:

$$V_{\text{retained}}(t) = \frac{\pi}{6} \int_{0}^{t} \left\{ A(t) \cdot N(t) \cdot [1 - C_{e}(t)] \int_{0}^{\infty} D^{3} \cdot f(D) \cdot [1 - P_{r}(D)] dD \right\} dt \quad (25),$$

with: [1 - $P_r(D)$] – the probability that a wear particle of diameter D will be retained in the interface.

If all particles retained within the rubbing surfaces are assumed to be compacted eventually to form wear protective layers and the average thickness of these layers is $\delta$, then the coverage of the wear surface by such compact wear particle layers ($C_{compact}$) is related to the volume of the retained particles ($V_{retained}(t)$), as follows:

$$C_{\text{compact}} = \frac{V_{\text{retained}}(t)}{A \cdot \delta} \quad (26).$$

These layers are particularly effective if a ‘glaze’ oxide of critical thickness ($\delta(c)$) can be established on their surfaces. The oxidation kinetics of the wear debris can be expressed in terms of a scale thickness (x) as:

$$x = g(t) \quad (27),$$

with: $g(t)$ – the relevant function of time.

Hence, the critical time ($t(c)$) for a ‘glaze’ of critical thickness ($\delta(c)$) to develop on the compacted debris is:

$$t(c) = g^{-1}(\delta(c)) \quad (28),$$

with: $g^{-1}(\delta(c))$ – the inverse function of $g(t(c))$.
If an area of compacted particle layer $dA_c(\tau)$ is established at time $\tau$, then an area of 'glaze' equal to $dA_c(\tau)$ should have developed after a further period $(t(c))$, i.e. at a time $(\tau+t(c))$. Thus, the coverage of the apparent wear surface by 'glaze' layers ($C_{glaze}$) at time $t$ is [Jiang et al. (2004)]:

$$C_{glaze}(t) = \int_{0}^{t-t_c} \frac{dA_c(\tau)}{A(t)} \qquad (29)$$

Thus, it is obvious that both a compacted particle layer and a 'glaze' layer may coexist. They are both protective but the latter is more effective. The fractional coverage of the wear surface by 'glaze' layer needed to cause the severe to mild wear transition is much less than that by non-'glaze' compact particle layer.

When both types of wear protective layers are present, the concept of an equivalent protective coverage of the wear surface ($C_e$) can be introduced (relation 30).

$$C_e = \frac{C_{compact}}{C_{compact\_limit}} + \frac{C_{glaze}}{C_{glaze\_limit}} \qquad (30)$$

with: $C_{glaze}$ – the surface coverage of glaze layers, $C_{compact\_limit}$ (found to be 0.4-0.6) and $C_{glaze\_limit}$ (found to be 0.2) – the critical coverage of compact and glaze layers, respectively, beyond which the wear surfaces become completely protected and wear transitions from a high rate to a low one occur.

The model discussed above was successfully implemented to predict the wear and surface coverage of wear protective layers formed on Nimonic 80A alloy under various loads at 20°C and 400°C (Figure 36). Wide agreement between calculated results and reported experimental observations was obtained. Later, the model was developed to study the effect of partial pressure of oxygen on the generation rate of wear debris particles [Jiang et al. (2004)]. This effect was found to be in two ways. On the one hand, an increase in partial pressure of oxygen leads to a decrease in particle size, which facilitates the development of compact wear-protective layers, therefore reduces wear. On the other hand, the generation rate of wear debris increases with increase in partial pressure of oxygen, which promotes wear. Also there, a reasonable agreement between calculated results and experimental investigations was achieved.
<figure><img src="image_38.png" /><figcaption>Figure 36: The calculated plots of wear versus sliding time under different loads at (a) 20°C and (b) 400°C (from Jiang et al. (1995)).</figcaption></figure>

A ‘glaze’ layer formation was also reported by Inman et al. [Inman et al. (2005), Inman et al. (2006)]. The authors studied profoundly the impact of temperature and sliding speed on wear behaviour of supперalloys (the Nimonic 80A/Stellite 6 contact). They showed that low speed (0.314 m/s) sliding conditions accompanied by the high temperature (between 510°C and 750°C) favour compaction of particles and their sintering to form a wear protective nano-structured ‘glaze’ layer. The rapid formation of this glaze layer from primarily cobalt-chromium debris transferred from (and also back to) the surface of the Stellite 6, kept wear of both the Nimonic 80A and Stellite 6 to very low levels. However, increasing the sliding speed to 0.905 m/s suppressed glaze formation with only a patchy, unstable glaze forming on the Stellite 6 counter-face and an absence of glaze development on the Nimonic 80A sample. The high amount of oxide debris generated at 0.905 m/s instead acted as a loose abrasive assisting wear of especially the Nimonic 80A. This behaviour was attributed to a change in oxide chemistry (due to the dominance of nickel and chromium oxides
generated from the Nimonic 80A) resulting in poor oxide sintering characteristics, in combination with increased mobility and reduced residency of the oxide debris at 0.905 m/s. The obtained results allowed the authors to compose a simple wear map (Figure 37) detailing the effects of sliding speed and temperature on the wear of the investigated contact [Inman et al. (2006)].

<figure><img src="image_39.png" /><figcaption>Figure 37: Sliding speed versus temperature wear map for the Nimonic 80A/Stellite 6 contact (after [Inman et al. (2006)]).</figcaption></figure>

4. 1. 2. 4. Kinetics of in-situ oxidation

In the beginning parabolic oxidation rate characteristic of static oxidation was assumed to take place at the contact area during sliding, e.g. in the oxidational theory of wear [Quinn (1967)]. This is controlled by the diffusion of metal or oxygen ions through the oxides. In the oxidational theory of wear, Quinn (1967) produced an expression for the wear rate under mild wear conditions, based on the equation. He modified Archard's interpretation by assuming that (1/K) encounters are necessary to produce a critical oxide thickness (ξ) at the real area of contact (A) and obtained the following expression for the wear rate under mild conditions:
$$W_{\text{theory}} = \left[ \frac{\frac{d \cdot A_p \cdot e^{-Q_p / RT_f}}{\xi^2 \cdot \rho_0^2 \cdot f_0^2 \cdot v}} \right] \cdot A \qquad (31),$$

where: $W_{\text{theory}}$ – the wear rate predicted by oxidational wear theory, d – the distance of sliding contact at an asperity, $A_p$ – the Arrhenius constant for parabolic oxidation, Q – the oxidational activation energy for parabolic oxidation, R – the molar gas constant, $T_f$ – the temperature of the real area of contact between the pin and the disc, $\rho_0$ – the average density of the oxides formed at the real areas of contact, $f_0$ – the mass fraction of oxide film which is oxygen, v – the speed of sliding at the contact zone.

He showed that if the sliding speed is comparatively slow or the loads are light the frictional heating is negligible and then the development of the contacting plateau of oxides is not sufficiently large for it to be the preferred contact region. This is describing a mechanism of severe wear. When temperature of the real area of the contact is high enough (under high speed or loads conditions) to provide sufficient amount of frictional heating, then the contacting plateau is oxidized preferentially to the other plateaux and the remainder of the surface. When the plateau reaches a critical oxide film thickness, the film becomes unstable and breaks up to form flakes, and eventually, wear debris. Afterwards the contact is displaced to the other plateau, and the virgin surface revealed is oxidized again to form another oxide film. Therefore, in this case the wear rate is related to the rate of oxidation.

Notwithstanding, the feasibility of using parabolic oxidation was questioned later by some researchers [Krause (1971), Childs (1980)]. Indeed, relative motion between interacting bodies results in oxide cracking what provides more rapid transport of metal and oxygen ions. Hence, it was suggested that linear oxidation is more appropriate during sliding [Childs (1980)]. Oxide cracking phenomenon supports the linear oxidation theory. Hong et al. [Hong et al. (1988)] proposed that linear oxidation, which results from cracking and detachment of the oxide layer, better describes tribo-oxidation. Figure 38 [Hong (2002)] depicts quantitative models of static-oxidative and tribo-oxidative scale growth and removal from substrate. Curve 3 represents mild tribo-oxidative kinetics under which the oxide layer is protective.
<figure><img src="image_40.png" /><figcaption>Figure 38: Quantitative models of static-oxidative and tribo-oxidative scale growth and removal from suitable substrates based on: (1) static-parabolic oxidation; (2) static-paralinear oxidation; (3) mild tribo-oxidative, and (4) severe tribo-oxidative kinetics (from [Hong (2002)]).</figcaption></figure>

Quinn's linear oxidational wear model for pin-on-disc can be expressed as follows:

$$V = \frac{A[A_p \exp(-Q/RT_f)] \cdot t}{f_0 \cdot \rho_0} \quad (32),$$

with: V – the total wear volume, Q – the oxidational activation energy for linear oxidation, t – the sliding time.

A modified version of relation 32, as a function of dissipated energy (Ed) for the ball-on-flat configuration was proposed by Huq et al. (2002). So, the total wear volume (V) can be expressed by the following relation:

$$V = \frac{A}{f_0 \cdot \rho_0} \cdot Ed \quad (33).$$

The above equation expresses the wear volume is linearly related to dissipated energy, but changes of tribochemistry in the contact results in a modification in the wear rate. It was shown that volumetric wear loss versus dissipated energy gives a good estimation about wear rate in comparison to wear rate expressed in terms of wear loss per unit time.

Friction causes chemical reactions to proceed much faster than they would otherwise. Formation of the material defects in the plastic zones under complex stress-strain loadings is, apart from flash temperature, one of the mechanisms by which friction
increases chemical reactivity on the interface. Hong et al. (1988) showed the reduction of activation energy during wear assuming linear kinetics and oxide-oxide contact. The tribo-oxidation energy of 316 stainless steel was there reported to be significantly lower (19.1 kJ/mole) compared to static activation energy (160 kJ/mole).

### 4. 1. 2. 5. *Oxide chemistry and structure*

Oxides formed at the contact area under sliding conditions are then removed as a result of repeated contacts. Due to the stress build-up between the oxides and substrates, the oxides become unstable when the oxides reach a certain thickness, especially if the Pillings-Bedworth ratio is high (> 2) [Askeland (1998)]. The type of oxides formed during tribo-oxidation has a substantial effect in producing wear- and friction-reducing oxide layers. Relatively soft and deformable oxides would facilitate development of such wear-protective surfaces. Next very influential factors are oxide cohesion and oxide/substrate adhesion. When the cohesion and adhesion are strong enough the retention of such protective layers can be facilitated. However, low friction and wear necessitate reasonably easy fracture of oxide-oxide asperity junctions between the surface oxide layers, resulting in an optimum ductility for an effective wear-protective oxide [Glascott et al. (1985)].

Relatively more ductile rather than very brittle oxides should be more amenable to plastic deformation, which suggests that $Co_3O_4$ or NiO should more readily form wear-protective oxide surfaces than $Cr_2O_3$, as was found at low ambient temperatures. Hence, if it could be possible to control the growth of oxides the development of NiO rather than $Cr_2O_3$ on Ni-Cr alloys or of FeO or $Fe_3O_4$ rather on Fe-Cr alloys would be expected to be more conducive to formation of a wear-protective oxide surface during wear [Glascott et al. (1985)].

Elevated temperature fretting behaviour of mild steels was studied by Hurricks (1972, 1974). Changes in the oxide structure was there thought to be responsible for an abrupt decrease in wear rate once the temperature was raised beyond 200°C [Hurricks (1974)]. According to the author the observed decrease of wear rate is believed to be due to the transformation in oxide structure, where a spinel $Fe_3O_4$ (magnetite) becomes more thermodynamically stable above 200°C than a rhombohedral $\alpha-Fe_2O_3$ (hematite). It is generally known that the former is porous and can be easily sheared off, however the latter is hard and has an abrasive character [Buckley (1981)]. Hence,
$Fe_3O_4$ seems to reduce friction and wear more effectively than $\alpha-Fe_2O_3$. Crystallographic structures of both oxides are shown in Figure 39.

<figure><img src="image_41.png" /><figcaption>Figure 39: Crystallographic structure of (a) magnetite ($Fe_3O_4$) (after [Haavik et al. (2000)]) and (b) hematite ($\alpha-Fe_2O_3$) (after [Pauling et al. (1925)]).</figcaption></figure>

Structural impact of the third body and the associated oxide nature on the friction and wear behaviour was also shown by Kato [Kato (2003), Kato et al. (2007)] to be very influential who explored the effect of artificially supplied particles. He found that mild wear transition can be explained by the sintering rate of the supplied oxide particles. When the supplied oxide was highly diffusive ($Fe_2O_3$, $SnO_2$ or CuO), the tribofilm formation rate was high and the mild wear transition occurred after a shorter sliding distance. By contrast, no severe to mild wear transition was observed for poorly diffusive particles like $Al_2O_3$, $TiO_2$ or $SiO_2$. In the case of $Fe_2O_3$ particles, the sliding distance from the severe to mild wear transition was decreased when finer particles were supplied.

## 4. 2. Effect of relative humidity

The effect of relative humidity on the unlubricated wear of steel was studied extensively by many authors. Liew (2006) showed that wear increased nearly 1.5 orders of magnitude for steel/steel contact when relative humidity of the surrounding air decreased from 80 to 28% (Figure 40). The low humidity conditions promoted both delamination and adhesive wear, while the mild wear occurring at high humidity
levels was due to inhibition of these wear mechanisms by the formation of interfacial layers such as iron hydroxide and ferri-oxide-hydrates, and the adsorption of water on the worn surface in addition to the normal atmospheric oxidation.

<figure><img src="image_42.png" /><figcaption>Figure 40: The effect of humidity on the wear rate of steel and aluminium pins (pin-on-disc test) (from [Liew (2006)]). Test conditions were as follows: velocity of 6 m/min, nominal load of 5N and sliding distance of 500 m.</figcaption></figure>

Besides, it was reported that the sliding speed had significant influence on the effect of humidity on wear of steel [Tsuji et al. (1975)]. At low speed, the wear increased with a decrease in humidity. By contrast, high sliding speed results in an increase of wear with humidity. The impact of normal load was investigated by Bregliozzi et al. (2003, 2004). Wear and coefficient of friction of stainless steel were found to increase when relative humidity decreased for loads higher than 2 N, while under lower normal load the effect of humidity was contrary and higher coefficient of friction with the humidity increase was observed.

## 5. OBJECTIVES OF THE WORK

Within the framework of the present dissertation the elevated temperature investigations are being undertaken to reproduce the working conditions of the trunnion vane/bushing joints in the Variable Stator Vane system. It has been shown in the bibliographic survey that environmental conditions may significantly affect tribological behaviour of alloy steels and superalloys. This has been associated to the significant modification of the interface. It has also been demonstrated that using
energy approach and assuming constant interface structure (i.e. given wear mechanism) the energy approach is able to predict the wear kinetics by a single energy wear coefficient independently of mechanical loadings (test duration, displacement, normal force) and even under variable loading conditions. Moreover, defining the objectives of the present work it must be taken into account an aspect that VSV system is subjected to variable temperature conditions during a flight of a plane.

Hence, the two main research objectives of this dissertation are:

1. Profound characterization of the tribological behaviour of the considered tribo-system under invariable and variable loading conditions using energy approach, allowing the fretting wear mapping of wear regimes as a function of temperature, displacement amplitude and pressure to be plotted;

2. Development of a 'composite' wear formulation allowing a prediction of wear volume under variable loading conditions.

To fulfill the objectives the following question have to be answered:

- What is the impact of temperature on the evolution of the energy coefficient of friction and energy wear coefficient?

- What is the evolution of the interface versus temperature; What is the change of its tribo-chemical and rheological properties?

- Is there any influence of pre-oxidation on the tribological behaviour?

- What is the dynamics of third body evolution under variable temperature test conditions corresponding to the real ones occurring in VSV system?

- Is it possible to make a map of wear regimes using an innovative variable loading conditions methodology?

- What is the impact of the mechanical loading conditions on the tribological behaviour and the associated interface?

- How energy wear approach can be transposed to capture wear volume under variable loading conditions?
# CHAPTER 2

## STUDIED MATERIALS AND FRETTING EXPERIMENTS
## 1. MATERIALS UNDER INVESTIGATION

The Jethete M152/A-286 tribo-system is being explored within the framework of the present dissertation. The characterization of the materials is presented below using information obtained from SNECMA.

Jethete M152 (UNS-S64152, AIR-Z12CNDV12) is a member of the Fe-12 Cr family alloys, with the additions of Ni and Mo. This alloy belongs to the class of martensitic stainless steels (morphology of the structure is shown in Figure 41a) and has a combination of properties, which include good ductility at high strength levels, uniform properties throughout thick sections and favourable strength at elevated temperatures. It also features outstanding fracture toughness and good oxidation resistance up to approximately 550°C. These all features, together with its favourable coefficient of thermal expansion (see Table III), make the alloy attractive for use for steam turbine components and compressor parts in gas turbine applications.

A-286 (UNS-S66286, AIR-EZ6NCT25) is an iron-base austenitic precipitation-hardened superalloy (classified as a stainless steel by SNECMA) with high content of Ni and Cr. Its structural morphology is shown in Figure 41b. It is used in situations when high strength up to 700°C is required as well as for cryogenic applications. Invoking the data provided by steel manufacturers [ATI Allvac (2001), Special Metals (2004)], the tensile strength of A-286 alloy decreases only by 90 MPa between room temperature and 400°C. A-286 alloy has an excellent oxidation resistance up to 982°C. Its corrosion resistance in many environments is similar to that characteristic of austenitic stainless steels. Moreover, it has superior corrosion resistance to nickel-base alloys when exposed to sulphurous atmospheres at elevated temperatures. Applications of A-286 include jet engines, supercharger, and missile components comprising: wheels and blades, casings, afterburner and sound suppressor parts, fuel nozzles, fasteners, extraction tooling, miscellaneous hardware.

The main precipitating phases identified in A-286 alloy are γ' [Ni₃(Ti,Al)] and η (Ni₃Ti). The γ' is the major hardening phase in A-286, and is the most important intermetallic compound due to its natural morphology with small interparticle distance, preference for general precipitation and large volume percent. Other
favourable factors include the high ductility of the phase compared with minor precipitates and the coherency with the austenitic matrix because of close lattice matching. It forms as spherical precipitates that have a low surface energy. In the approach to equilibrium, the γ' transition phase is replaced by hexagonal η phase. As a cellular precipitate, forming in the range of 399°-982°C, it is nucleated at grain boundaries and can be detrimental to notched stress-rupture strength. Precipitation may also occur as Windmanstatten intergranular η which reduces hardness, strength, and physical properties, but not ductility. The presence of boron and aluminium in A-286 retards both modes of formation. The alloying elements such as: Mo, Cr and B are solid-solution strengtheners, at the same time the last is extremely potent and markedly improves stress-rupture properties [Muraca et al. (1972)].

<figure><img src="image_43.png" /><figcaption>Figure 41: Morphology of the studied materials: (a) tempered martensite of Jethete M152 stainless steel and (b) spherical precipitations of γ' phase in austenitic matrix of A-286 superalloy; Royal water etching solution (mixture of concentrated nitric and hydrochloric acids in the ratio of one to three) was used to reveal morphology of the studied alloys.</figcaption></figure>

The mechanical properties of the studied alloys are listed in Table I, the physical and surface ones in Table II, and their chemical compositions in Table III.

<table><caption>Table I: The mechanical properties of the studied materials.</caption><thead><tr><td>Materials</td><td>Hardness</td><td>Young's Modulus [GPa]</td><td>Tensile Strength [MPa]</td><td>0.2% Yield Strength [MPa]</td><td>Poisson's ratio</td></tr></thead><tbody><tr><td>Jethete M152</td><td>344 HB</td><td>216</td><td>1150</td><td>900</td><td>0.30</td></tr><tr><td>A-286</td><td>311 HB</td><td>201</td><td>1035</td><td>698</td><td>0.30</td></tr></tbody></table>
<table><caption>Table II: The physical and surface properties of the studied materials.</caption><thead><tr><th>Materials</th><th>Average Surface Roughness: R<sub>a</sub> [µm]</th><th>Density [g*cm<sup>-3</sup>]</th><th>Thermal Expansion<sup>x</sup> [10<sup>-6</sup>*m/(m*°C)]</th><th>Thermal Conductivity [W/(m*°C)]</th></tr></thead><tbody><tr><td>Jethete M152</td><td>0.40</td><td>7.75</td><td>12.0</td><td>30.0</td></tr><tr><td>A-286</td><td>0.40</td><td>7.94</td><td>17.2</td><td>12.7</td></tr><tr><td colspan="5">x – between 20° and 400°C at 400°C</td></tr></tbody></table>

<table><caption>Table III: The chemical compositions of the studied alloys: Jethete M152 and A-286.</caption><thead><tr><th rowspan="2">Material</th><th colspan="7">Compound average nominal wt. %</th></tr><tr><th>C</th><th>Cr</th><th>Ni</th><th>Mo</th><th>Si</th><th>Mn</th><th>-</th></tr></thead><tbody><tr><td rowspan="3">Jethete M152</td><td>0.12</td><td>11.70</td><td>2.70</td><td>1.70</td><td>0.20</td><td>0.80</td><td>-</td></tr><tr><td>V</td><td>N</td><td>P</td><td>S</td><td>Fe</td><td>-</td><td>-</td></tr><tr><td>0.30</td><td>0.04</td><td>0.013</td><td>0.013</td><td>Remainder</td><td>-</td><td>-</td></tr><tr><td rowspan="3">A-286</td><td>C</td><td>Cr</td><td>Ni</td><td>Mo</td><td>Si</td><td>Mn</td><td>Ti</td></tr><tr><td>0.04</td><td>14.80</td><td>25.50</td><td>1.25</td><td>0.50</td><td>1.50</td><td>2.10</td></tr><tr><td>V</td><td>Al</td><td>B</td><td>P</td><td>S</td><td>Fe</td><td>-</td></tr><tr><td></td><td>0.30</td><td>0.20</td><td>0.006</td><td>0.015</td><td>0.015</td><td>Remainder</td><td>-</td></tr></tbody></table>

## 2. DEFINITION OF THE FRETTING PARAMETERS

Quantifying the fretting process is possible owing to an on-line recording of fretting cycles (also called fretting loops) during the test. The fretting loop is defined as a representation of the tangential loading as a function of displacement (Figure 42). Several parameters can be derived from the recorded fretting cycle. They are described below.

*The displacement amplitude (δ*)*, maintained by the control system, corresponds to the maximum displacement amplitude imposed. The value of this parameter differs from the maximum amplitude achieved by the relative displacement of the two contacted bodies what is a consequence of the test assembly compliance.

*The sliding amplitude (δ<sub>g</sub>)* is defined as a residual displacement when the tangential force is equal to 0. Applying this parameter any interactions induced by the tangential accommodation of the system on the displacement value (δ*) can be controlled.
The maximum tangential force amplitude (Q*) represents the maximum recorded value of the tangential effort transmitted by the contact. It is representative of the conventional coefficient of friction (μ = Q*/P) of the two contacted bodies under gross slip fretting conditions.

The dissipated energy of cycle (Ed) is characterized by the area of the fretting loop. The value of this parameter can be approximately quantified as a product of the maximal tangential force (Q*) and sliding distance (4·δg) during the cycle of the alternating fretting (relation 34):

$$Ed = 4 \cdot \delta_g \cdot Q^* \quad (34).$$

<figure><img src="image_44.png" /><figcaption>Figure 42: The fretting loop recorded during fretting test.</figcaption></figure>

# 3. FRETTING WEAR EXPERIMENTS

## 3. 1. Fretting apparatus

Tests were carried out using an electrodynamic shaker activating a specific fretting rig manufactured by DeltaLab (United Kingdom) and upgraded in LTDS (Laboratory of Tribology and Dynamics of Systems) (France) illustrated in Figure 43.

Data acquisition platform created under LabView software was used for on-line collection and control of fretting parameters. The required value of the normal force (P) was maintained during fretting tests by a precise brushless engine, while the tangential force (Q) and displacement (δ) were recorded. Thus, the fretting loop Q-δ (Figure 41) could be drawn to extract quantitative variables, including the dissipated energy (Ed), the sliding amplitude (δg), the tangential force amplitude
(Q*) and the displacement amplitude (δ*). A developed acquisition module allowed also conducting the tests at constant sliding amplitude owing to automatic adjusting the displacement amplitude at maintaining a demanded value of the normal force. The relative displacement was determined by optical sensors, the tangential force by a piezoelectric sensor and the normal force by a strain gauge sensor. A reciprocating movement with a constant frequency was always imposed. All fretting tests were carried out in a closed chamber where the relative humidity was controlled as close as possible to the contact using a humidity sensor. The elevated temperature conditions were reached using heating elements placed into the lower holder. The temperature was measured by means of a thin thermocouple placed at top of the flank surface of the lower specimen as close as possible to the fretting contact. The rubbing surface of the upper specimen was heated by the lower specimen as a result of thermal conductivity. In order to maintain the required temperature in the contact, it was surrounded by a thermo-insulating fabric limiting the dissipation of heat and homogenizing the temperature.

<figure><img src="image_45.png" /><figcaption>Figure 43: (a) Diagram and (b) photograph of the specific fretting apparatus.</figcaption></figure>
## 3. 2. Contact geometry

The contact geometry used in the study was a plane/plane configuration. The upper axi-symmetrical pin type Jethete M152 specimen with 3 mm diameter of the contact surface rubbed against the lower rigidly fixed cylindrical A-286 sample (Figure 44). The pin type specimen had a chamfer machined at a 45° angle between circular surface of the contact and cylinder that it was turned from. The applied contact geometry corresponded to about 7 mm² of flat apparent area of the contact (A ap) that allowed low pressure conditions to be investigated. By contrast with a conventional sphere/plane configuration, it required a specific alignment to guarantee the flat/flat contact, but permitted practically constant pressure conditions independently of the surface wear. Illustrations of the contact configuration and specimens used in the study are presented in Figure 45.

<figure><img src="image_46.png" /><figcaption>Figure 44: Diagram of the fretting contact geometry used in the study.</figcaption></figure>

<figure><img src="image_47.png" /><figcaption>Figure 45: (a) Picture of the contact geometry applied in the study, (b) The specimens used in the tests: cylindrical A-286 and axi-symmetrical pin type Jethete M152 sample.</figcaption></figure>
### 3.3. Contact mechanics of the studied plane/plane configuration

It was mentioned previously (i.e. in Chapter 1) that the plane/plane contact configuration produces discontinuities in the pressure distribution on the borders of the contact. Finite element analysis based on the created elastic finite element 2D axi-symmetric model was used in order to quantify pressure distribution of the studied contact configuration of the Jethete M152/A-286 tribo-system. Figure 46 illustrates the developed model and mesh of 10 µm elements. The computation of the pressure distribution was performed for three values of the normal force: 88, 176 and 352 N. The pressure distribution profiles obtained at 88 and 352 N, where the maximum pressure peaks can be observed on the borders of the contact, are shown in Figure 47. However, it was demonstrated by Mary et al. (2007) and Paulin et al. (2008) that due to wear processes, the surfaces in the contact are modified in such a way that the pressure peaks yield to the flattening effect (related to the increase of the surface conformity) and the pressure profile evolves towards a homogeneous distribution. It can therefore be assumed that after a few cycles of fretting test the contact depicts a quasi flat constant pressure distribution that will promote a homogeneous evolution of the wear damage.

<figure><img src="image_48.png" /><figcaption>Figure 46: Developed 2D axi-symmetric model with mesh of 10 µm elements.</figcaption></figure>
<figure><img src="image_49.png" /><figcaption>Figure 47: Pressure distribution characteristic of the studied contact configuration computed for the investigated Jethete M152/A-286 tribo-system under two values of the normal force: 88N (—) and 352 N (—).</figcaption></figure>

The computed values of maximum pressures ($p_0$) as well as of mean pressures ($p_m$) (defined as a ratio of the applied normal force (P) to the apparent initial contact area ($A_{ap}$)) in the contact are given in Table IV.

<table><caption>Table IV: Maximum pressure ($p_0$) (obtained from finite element analysis), mean pressure ($p_m$) and semi-width of the contact ($a$) obtained under three considered normal forces for the applied plane/plane contact configuration for the Jethete M152/A-286 tribo-system.</caption><thead><tr><th>Tribo-couple</th><th>Normal<br>force<br>P [N]</th><th>Maximum<br>pressure in the<br>contact p<sub>0</sub> [MPa]</th><th>Mean pressure<br>in the contact<br>p<sub>m</sub>=P/A<sub>ap</sub> [MPa]</th><th>1/2 width of<br>the contact<br>a [mm]</th></tr></thead><tbody><tr><td rowspan="3">Jethete M152/<br>A-286</td><td>88</td><td>57</td><td>12.5</td><td>1.5</td></tr><tr><td>176</td><td>113</td><td>25</td><td>1.5</td></tr><tr><td>352</td><td>227</td><td>50</td><td>1.5</td></tr></tbody></table>
### 3. 4. Experimental conditions

All fretting wear experiments were carried out under reciprocating sliding motion (alternating fretting) at a frequency (f) of 13 Hz and 10 ± 2% relative humidity (RH). Dry conditions without externally added lubricant are being investigated within the framework of the present dissertation. All applied loadings promoted gross slip conditions. The constant heating speed equal to 20°C/min was always applied in order to achieve the required value of the elevated temperature.

Within the framework of the present dissertation both invariable and variable, during a single fretting test, loading conditions are being investigated. They are described in details in the relevant Chapters (i.e. invariable conditions in Chapter 3, variable in Chapter 4).

### 4. WEAR VOLUME EVALUATION

Specimens from the Jethete M152/A-286 contact were ultrasonically cleaned in acetone for a time period of 10 min each before and after tests in order to remove surface contamination and loose debris particles, respectively.

The wear volume of the studied tribo-couple was determined indirectly by converting the mass loss of the specimens, measured by means of precise laboratory balance equipment (measurement accuracy: ±0.01 mg), and assuming the densities of each material as in Table II.

In the present dissertation, the wear analysis is limited to the total wear volume (V) of the studied tribo-system defined as the sum of the upper (Vupper) and lower (Vlower) wear volumes (relation 35).

$$V = V_{\text{upper}} + V_{\text{lower}} \qquad (35).$$

An important aspect that must be taken into account when elevated temperature conditions are investigated is to consider a volume gain of specimens due to static oxidation of metal materials occurring in the contact. Thus, for tests performed at 300°C and higher temperatures, a correction resulting from the static oxidation of Jethete M152 and A-286 specimens was introduced (for lower temperatures it was unmeasurable or so small, below 3% of the total wear volume, that neglected). Hence, the determined wear volume of metal specimens was increased by the volume gain
(V<sub>g</sub>) (converted from the mass loss, assuming an iron oxide density of 5.24 g/cm<sup>3</sup>) obtained after static oxidation tests (specimens in the contact but without fretting action) in a time period corresponding to that of the conducted fretting tests. However, on account of considerable amount of fretting tests carried out at different number of cycles at 400°C (including tests at variable loading conditions, defined in Chapter 4) as well as limited number of specimens supplied for thesis realization, it was not possible to carry out all corresponding static oxidation tests. Hence, to provide data needed for accurate wear evaluation, oxidation curves of the Jethete M152/A-286 contact at 400°C (Figure 48), based on a few results obtained from static oxidation tests, were plotted and associated equations extracted. For both specimens static oxidation was found to proceed according to a parabolic law, where for the upper Jethete M152 and lower A-286 specimen it can be described by the relation 36 and 37, respectively.

$$V_{g\_upper} = -1.44 \cdot 10^{-8} \cdot t^2 + 1.97 \cdot 10^{-5} \cdot t \quad (36),$$

$$V_{g\_lower} = -4.87 \cdot 10^{-8} \cdot t^2 + 6.45 \cdot 10^{-5} \cdot t \quad (37),$$

with: V<sub>g\_upper</sub> and V<sub>g\_lower</sub> – the volume gain due to native oxide formation on the surfaces of the upper Jethete M152 and lower A-286 specimen, respectively; t – the time period corresponding to that of the performed fretting test.

<figure><img src="image_50.png" /><figcaption>Figure 48: Static oxidation curves obtained at 400°C for the upper Jethete M152 (—) and lower A-286 (---) specimen contacted as during fretting test.</figcaption></figure>
Upper specimen from the contact (Jethete M152)

<table><thead><tr><th rowspan="2">Number of cycles / corresponding time period of static oxidation: N / t [min]</th><th colspan="3">Gain volume V<sub>g_upper_JetheteM152</sub> [mm<sup>3</sup>] at temperature:</th></tr><tr><th>300°C</th><th>350°C</th><th>400 °C</th></tr></thead><tbody><tr><td>20000 / 26</td><td>-</td><td>-</td><td>0</td></tr><tr><td>50000 / 64</td><td>-</td><td>-</td><td>0.001</td></tr><tr><td>100000 / 128</td><td>-</td><td>-</td><td>0.003<sup>x</sup></td></tr><tr><td>150000 / 192</td><td>-</td><td>-</td><td>0.004<sup>x</sup></td></tr><tr><td>180000 / 231</td><td>-</td><td>-</td><td>0.005</td></tr><tr><td>220000 / 282</td><td>-</td><td>-</td><td>0.006<sup>x</sup></td></tr><tr><td>360000 / 462</td><td>0.001</td><td>0.003</td><td>0.005</td></tr><tr><td>400000 / 513</td><td>0.001</td><td>-</td><td>0.007<sup>x</sup></td></tr><tr><td>560000 / 718</td><td>0.002</td><td>-</td><td>0.007</td></tr></tbody></table>

Lower specimen from the contact (A-286)

<table><caption>Table V: Volume gains of the metal specimens from the Jethete M152/A-286 tribo-system obtained after static oxidation tests conducted at different temperatures in time periods corresponding to those of fretting experiments; Values marked with (x) denotes corrections calculated using equation 36 and 37 for the upper Jethete M152 and lower A-286 specimen, respectively.</caption><thead><tr><th rowspan="2">Number of cycles / corresponding time period of static oxidation: N<sub>cyc</sub> / t [min]</th><th colspan="3">Gain volume V<sub>g_lower_A-286</sub> [mm<sup>3</sup>] at temperature:</th></tr><tr><th>300°C</th><th>350°C</th><th>400 °C</th></tr></thead><tbody><tr><td>20000 / 26</td><td>-</td><td>-</td><td>0.002</td></tr><tr><td>50000 / 64</td><td>-</td><td>-</td><td>0.006</td></tr><tr><td>100000 / 128</td><td>-</td><td>-</td><td>0.007<sup>x</sup></td></tr><tr><td>150000 / 192</td><td>-</td><td>-</td><td>0.011<sup>x</sup></td></tr><tr><td>180000 / 231</td><td>-</td><td>-</td><td>0.014</td></tr><tr><td>220000 / 282</td><td>-</td><td>-</td><td>0.014<sup>x</sup></td></tr><tr><td>360000 / 462</td><td>0.007</td><td>0.011</td><td>0.017</td></tr><tr><td>400000 / 513</td><td>0.008</td><td>-</td><td>0.020<sup>x</sup></td></tr><tr><td>560000 / 718</td><td>0.010</td><td>-</td><td>0.022</td></tr></tbody></table>

Using equation 36 and 37 the missing values of the volume gain of the metal specimens from the Jethete M152/A-286 contact were calculated, by assuming that time periods of the lacking static oxidation tests corresponds to those of conducted fretting experiments. For tests conducted under variable loading conditions (defined in Chapter 4) a time period of static oxidation was considered as a sum of the
individual time contributions at 400°C. For simplification, the correction for these tests was determined assuming continuous character of oxidation as that for experiments at constant temperature.

Detailed data concerning the correction values (i.e. volume gains) introduced to compensate for a static oxidation of the metal specimens are listed in Table V.

Summarizing, the total wear volume of the considered tribo-system (V) is here determined as a sum of the wear volumes of the upper Jethete M152 and lower A-286 specimen, increased by the corrections resulting from the static oxidation phenomenon (relation 38).

$$V = V_{\text{upper}} + V_{\text{g\_upper}} + V_{\text{lower}} + V_{\text{g\_lower}} \quad (38),$$

<figure><img src="image_51.png" /><figcaption>Figure 49: The relative error between the wear volume determined using mass loss method (V) and that measured by 3D profiler ($V_{3D\_pr.}$) for a few fretting scars generated on the A-286 specimens tested against Jethete M152 material at different temperatures under the mechanical key point loading conditions ($\delta*=\pm100 \mu m, p_m=25 MPa$ (i.e. $P=176 N$), and $N=360000$ cycles).</figcaption></figure>

In order to assess the reliability of results obtained using indirect mass loss method the wear volumes of a few fretting scars obtained under invariable test situations at different temperatures on to the A-286 plane specimens were also estimated by means of 3D VEECO-Wyko NT9300 interferometric profiler. The relative error between the wear volume determined using mass loss method (V) and that measured by 3D
profiler (V<sub>3D_pr.</sub>) was found to be low, less than 15% (Figure 49). Thus, considering
such a good correlation as well as high operational costs of 3D profiler, use of mass
loss method for wear evaluation is fully justified. Moreover, it provides an equivalent
wear description of the upper axi-symmetric pin type (for which wear evaluation using
3D profiler is difficult and time-consuming) and lower plane counter-bodies. Figure
50 shows 3D profiles of the fretting scars generated on the A-286 specimens at 23 and
400°C.

<figure><img src="image_52.png" /><figcaption>Figure 50: 3D profiles of the scars generated on the A-286 specimens tested against Jethete M152 material under the mechanical key point loading conditions at two temperatures:(a) 23°C and (b) 400°C.</figcaption></figure>
# CHAPTER 3

## FRETTING BEHAVIOUR UNDER
CONSTANT LOADING CONDITIONS
# CHAPTER 3: FRETTING BEHAVIOUR UNDER CONSTANT LOADING CONDITIONS

In the present Chapter of the dissertation the influence of the temperature on the fretting wear behaviour and physico-chemical response of the associated interface of the Jethete M152/A-286 tribo-system under invariable loading conditions are being discussed.

## 1. LOADING CONDITIONS

The key point loading conditions with reference to the real situation occurring in the vane/bushing joint were defined as follows: p_m=25 MPa (i.e. P=176 N), δ*=±100 µm, number of cycles N=360000 cycles and T=200°C. The reference conditions produced the sliding amplitude δ_g=±77 ± 4 µm during the test. The corresponding fretting log showing the evolution of the fretting loops during the experiment performed under the key point conditions is illustrated in Figure 51.

<figure><img src="image_53.png" /><figcaption>Figure 51: Illustration of the fretting log recorded for the test conducted under the key point loading conditions.</figcaption></figure>

To evaluate the impact of temperature, the single mechanical key point loading conditions (i.e. p_m=25 MPa (P=176 N), δ*=±100 µm and N=360000 fretting cycles) were studied at different temperatures from 23 to 400°C.

To quantify the wear response as a function of the pressure, displacement amplitude and test duration, a cross-experimental strategy centred on the mechanical key point
conditions was applied (Figure 52). Based on these reference loading conditions, the impact of pressure was evaluated by imposing the normal load from 88 to 352 N (i.e. from $p_m=12.5$ to $p_m=50$ MPa). The displacement amplitude ranging from $\pm 50$ to $\pm 225$ $\mu$m and the test duration ranging from 500 to 360000 fretting cycles were also studied. It must be noted that iso-sliding amplitude conditions corresponding to the key point value were maintained during the pressure effect analysis by monitoring the applied displacement amplitude in order to compensate for the tangential elastic accommodation. This complete investigation was carried out for the two temperatures: 200 and 400$^{\circ}$C. The former is below while the latter above the severe to mild wear rate transition temperature.

<figure><img src="image_54.png" /><figcaption>Figure 52: Illustration of the cross-experimental strategy studied at 200 and 400$^{\circ}$C; Tests conducted at the both temperatures (●), only at 200$^{\circ}$C (○) and only at 400$^{\circ}$C (○); Logarithmic scale was applied to depict test duration loadings.</figcaption></figure>

Moreover, several dozen tests at certain values of the displacement amplitude in the range from $\pm 50$ to $\pm 200$ $\mu$m (at maintaining constant $p_m=25$ MPa (i.e. $P=176$ N) and $N=360000$ cycles) and pressure in the range from 5 to 50 MPa (i.e. from $P=35$ N to $P=352$ N) (at maintaining constant $\delta_g=\pm 77 \pm 4$ $\mu$m and $N=360000$ cycles) at different
temperatures in the 150-400°C range, but others than 200°C, were carried out. The results obtained are being taken into consideration as the investigations under variable loading conditions are being discussed in the next Chapter.

Three experiments under the mechanical key point conditions (p<sub>m</sub>=25 MPa (i.e. P=176 N), δ*=±100 µm and N=360000 cycles) at 200 and 400°C were performed to verify test reproducibility. Then, mean values of all recorded variables and wear volumes were determined for use in further considerations. A high reproducibility of the tests was obtained as very low dispersions of the results were achieved (basically less than ±15%). For the rest loading conditions only a single fretting experiment was performed.

Matrix of all tests carried out at different temperatures, displacement amplitudes and pressures at constant number of cycles (N=360000) is shown in Table VI.

<table><caption>Table VI: Matrix of all tests conducted at different temperatures, displacement amplitudes and pressures (at constant N=360000 cycles) for the Jethete M152/A-286 tribo-system; The cross ‘x’ in the cell denotes that test at the given parameters was carried out.</caption><thead><tr><th rowspan="2">Temperature<br>T [°C]</th><th colspan="8">Displacement amplitude: δ* [µm]<br>(p<sub>m</sub>=25 MPa (i.e. P=176 N) and<br>N=360000)</th><th colspan="6">Pressure: p<sub>m</sub> [MPa]<br>(δ<sub>g</sub>=±77 µm, N=360000)</th></tr><tr><th>50</th><th>75</th><th>100</th><th>125</th><th>150</th><th>200</th><th>225</th><th>5</th><th>10</th><th>12.5</th><th>17.5</th><th>37.5</th><th>50</th></tr></thead><tbody><tr><td>23</td><td>-</td><td>-</td><td>x</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>100</td><td>-</td><td>-</td><td>x</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>150</td><td>-</td><td>-</td><td>x</td><td>-</td><td>-</td><td>-</td><td>-</td><td>x</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>200</td><td>x</td><td>-</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td><td>-</td><td>x</td><td>x</td><td>-</td><td>x</td><td>x</td></tr><tr><td>215</td><td>-</td><td>-</td><td>x</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>225</td><td>x</td><td>-</td><td>x</td><td>-</td><td>x</td><td>-</td><td>-</td><td>-</td><td>x</td><td>-</td><td>x</td><td>-</td><td>x</td></tr><tr><td>250</td><td>x</td><td>-</td><td>x</td><td>-</td><td>x</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>x</td><td>-</td></tr><tr><td>275</td><td>-</td><td>-</td><td>x</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>300</td><td>-</td><td>-</td><td>x</td><td>-</td><td>-</td><td>x</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>350</td><td>-</td><td>-</td><td>x</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>400</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td><td>x</td><td>-</td><td>-</td><td>-</td><td>x</td><td>-</td><td>x</td><td>x</td></tr></tbody></table>
## 2. FRICTION BEHAVIOUR

### 2.1. Development of the energy coefficient concept

Typical gross slip fretting loops were observed during the tests (Figure 53). A slight tangential force increase with displacement amplitude during the cycle observed under all studied conditions. This behaviour is probably related to continuous work hardening of contacted metal materials under fretting loadings. It is well known that especially steel materials having austenitic structure (A-286 superalloy) are susceptible to that type of strengthening mechanism [Peckner et al. (1977)]. Moreover, small tangential force peaks at the maximum displacement amplitude were noticed. This phenomenon, which is not observed for hard steel or hard coating contacts, is characteristic of ductile materials such as aluminium [Elleuch et al. (2002)] and titanium [Fouvry et al. (2004)] alloys. It may be associated to plastic draughts generated at the inlets contact borders which promotes surface interferences when the maximum displacement is reached [Fouvry et al. (2004)]. Such a ploughing effect might then explain the tangential force peaks observed on the fretting cycles.

<figure><img src="image_55.png" /><figcaption>Figure 53: The characteristic fretting loop observed during all experiments.</figcaption></figure>
<figure><img src="image_56.png" /><figcaption>Figure 54: Comparison between evolution of the conventional (μ) (—) and energy (μe) (—) coefficient of friction for the key point loading conditions.</figcaption></figure>

Hence, to characterize a friction law which is representative of the wear phenomena for the Jethete M152/A-286 tribo-system, the normalized or conventional tangential force ratio (μ = Q*/P) is therefore no longer appropriate, and an average value needs to be introduced. Based on an energy description, an energy coefficient of friction (μe) is considered (relation 39):

$$ \mu_e = \frac{Ed}{4 \cdot P \cdot \delta_g} \qquad (39). $$

Figure 54 compares the evolution of the conventional and energy coefficient of friction under the key point loading conditions. As it can be observed the former continuously increases with time duration as Q* grows as a result of above-mentioned phenomena, however the latter is characterized by stable evolution as the steady-state is reached.

## 2. 2. Impact of temperature

Figure 55 shows the evolution of the energy coefficient of friction for two temperatures (200 and 400°C) under the mechanical key point loading conditions (i.e.
$p_m=25$ MPa ($P=176$ N), $\delta^*=\pm100$ µm and $N=360000$ fretting cycles). For both the considered temperatures an initial stage (first a few hundreds cycles) of the friction evolution is similar. The difference in the friction behaviour can be observed, however, during next stages as tests are being proceeded for longer time duration. The evolution of the energy coefficient of friction depicted in Figure 55 for 200°C is characteristic of the experiments conducted at the temperatures lower than $T_{ga}=220$°C (temperature of ‘glaze’ layer activation), for 400°C of those carried out above $T_{ga}$.

In-depth analysis of the friction behaviour, where all essential friction-related parameters are defined is being discussed below.

<figure><img src="image_57.png" /><figcaption>Figure 55: Evolution of the energy friction coefficient ($\mu_e$) as a function of the test duration for two tests carried out under the mechanical key point conditions at 200 (______) and 400°C (______).</figcaption></figure>

### 2. 2. 1. Analysis of the evolution of the energy coefficient of friction

The evolution of the energy coefficient of friction demonstrating a tendency characteristic of the experiments carried out under the mechanical key point loading conditions below and above $T_{ga}$ is illustrated in the form of friction pattern in Figure 56 and 57, respectively.

Analyzing both graphs three stages in friction evolution can be distinguished, independently of test temperature. At the beginning of each test a running-in period
<figure><img src="image_58.png" /><figcaption>Figure 56: Friction pattern showing evolution of the energy coefficient of friction characteristic of tests carried out below transient temperature $T_{ga}=220^{\circ}C$.</figcaption></figure>

<figure><img src="image_59.png" /><figcaption>Figure 57: Friction pattern showing evolution of the energy coefficient of friction characteristic of tests carried out above transient temperature $T_{ga}=220^{\circ}C$.</figcaption></figure>

(initial short state taking up first a few hundreds cycles) characterized by a sharp increase of the energy coefficient of friction (where the highest energy friction coefficient ($\mu_{e\_max}$) within entire test duration at certain critical number of cycles ($N_{\_max}$) is achieved) followed by a drastic decrease in its evolution (down a
minimum friction value ($\mu_{e_min}$) at $N_{min}$ number of cycles) can be observed. Subsequently, an intermediate transient state occurs. The evolution of the coefficient of friction within this stage characteristic of fretting tests carried out below $T_{ga}$ proceeds as follows (Figure 56). The energy coefficient of friction increases asymmetrically from $\mu_{e_min}$ before stabilizes at a high steady-state friction value reached at $N_{ss}$ number of cycles. The transient period is different for experiments conducted at temperatures higher than $T_{ga}$ (Figure 57). The monotonic increase observed below $T_{ga}$ is here replaced by a heterogeneous evolution where the initial increase from $\mu_{e_min}$ up to some maximum $\mu_{e_tran}$ is followed by an asymptotic decrease down the more or less stabilized value achieved at $N_{ss}$. For all the considered temperatures the steady-state regime is determined by a mean steady-state energy coefficient of friction ($\bar{\mu}_{e SS}$).

### 2. 2. 1. 1. Running-in period characterization

A sharp increase in the evolution of the energy coefficient of friction ($\mu_e$) observed for all the considered temperatures within the initial stage is related to strong adhesion and metal transfer phenomena as two similar metal materials are contacted [Hurricks (1972 and 1974), Kayaba et al. (1981-1982)]. Many researchers reported that even the seizure effect can then occur [Boas et al. (1977), Goto (1995), Maatta et al. (2001)]. The material transfer was confirmed by an energy dispersive X-ray spectroscopy (EDX) analysis of the fretting scar generated after short test (500 cycles) at 200°C. Figure 58 compares EDX spectrum obtained from outside the scar and that excited from the wear scar produced on the upper Jethete M152 specimen. An increase in nickel content after fretting experiment was found, thereby implying material transfer from the lower A-286 specimen on to the upper one (A-286 superalloy contains significantly higher amount of nickel in its composition compared to Jethete M152 stainless steel – see Table III). Moreover, oxygen was detected in the scar what signifies that fretting action activates processes that favours oxidation phenomenon. Figure 59a shows scanning electron microscope (SEM) picture of flake-like wear debris transferred on to the Jethete M152 counter-body what is in good agreement with literature where fretting wear is believed to be caused predominantly by the
formation of flake-like debris that is subsequently crushed into smaller spherical
fragments (Figure 59b) [Kayaba et al. (1981)].

<figure><img src="image_60.png" /><figcaption>Figure 58: Comparison of EDX spectrum obtained from outside (——) and from the wear scar (——) generated on to the upper Jethete M152 specimen after short test (500 cycles) at 200°C.</figcaption></figure>

<figure><img src="image_61.png" /><figcaption>Figure 59: (a) Flake-like wear debris observed after the short (500 cycles) fretting experiment at 200°C; (b) Fine spherical wear debris particles observed after the long test (360000 cycles) at 200°C.</figcaption></figure>

The impact of temperature on the adhesion during a running-in period is shown in
Figure 60. As it can be observed there is no temperature influence and almost constant
value of maximum energy coefficient of friction ($\mu_{e\_max}$) is kept through a wide range of the studied temperatures (comprises between 1.10 and 1.30), even though it would be expected to decrease with temperature increase as higher temperature produces thicker layer of native oxides on to the mated surfaces that might prevent the formation of strongly adhesive metal-to-metal junctions [Glascott et al. (1985), Maatta et al. (2001)]. Hence, independence of the evolution of the maximum energy coefficient of friction ($\mu_{e\_max}$) on the applied temperature may be explained by the fact that not thick enough layer of oxides is formed on to the mated surfaces even at 400°C to protect against strong adhesion. As a result of the fretting action a native oxide layer is immediately damaged and removed, what in consequence leads to the metal-to-metal interface. A decrease in number of cycles needed to reach $\mu_{e\_max}$ (N\_max) with temperature increase was observed (Figure 60). This tendency is probably related to the susceptibility of the contacted materials to the plastic deformation, which increases with temperature. Thus, less amount of energy provided for the interface (less number of cycles) at the higher temperatures promotes similar adhesive behaviour as for lower ones.

<figure><img src="image_62.png" /><figcaption>Figure 60: Maximum energy coefficient of friction ($\mu_{e\_max}$) and associated number of cycles (N\_max) at which it is reached as a function of temperature under the mechanical key point loading conditions.</figcaption></figure>
<figure><img src="image_63.png" /><figcaption>Figure 61: Arithmetical mean surface roughness (R_a) of the scars generated on to the lower A-286 specimens after interrupted tests with reference to the related friction evolution for the key point loading conditions (i.e. p_m=25 MPa (P=176 N), δ*=±100 µm, N=360000 cycles and T=200°C).</figcaption></figure>

After a sharp increase a drastic drop down μ_e_min at N_min in the friction evolution within a running-in period takes place. The abrupt decrease of the coefficient of friction observed for all temperatures can be related to the roughness evolution (Figure 61) of the contacted surfaces (determined by means of 3D VEECO-Wyko NT9300 interferometric profiler) that significantly increases at N_min in relation to its initial value (before test R_a=0.4 μm) due to formation of post-adhesive prows and hollows. Indeed, two contradictory effects of roughness on adhesion exist. On the one hand for two surfaces stuck together the roughness increases the force needed to peel them apart, on the other hand for two solids placed in the contact roughness reduces a pull-off force [Singer et al. (1992)]. Though, it must be mentioned that roughness analysis was performed after ultrasonic cleaning of the contacted specimens. Thus, loose wear debris operating in the interface is not considered in the proposed hypothesis. This, however, was taken into account in the work of Merhej (2008) who studied dry self-mated 100 C6 steel contact at room temperature conditions and observed similar friction evolution (i.e. for T<TGA). According to his observations, illustrated in Figure 62, after the peak value (μ_e_max) the surface layer of material,
<figure><img src="image_64.png" /><figcaption>Figure 62: Schematic description of the interface evolution of the self-mated 100 C6 steel contact versus the test duration explaining the successive stages of the friction evolution (after [Merhej (2008)]).</figcaption></figure>

<figure><img src="image_65.png" /><figcaption>Figure 63: Minimum energy coefficient of friction ($\mu_{e\_min}$) and associated number of cycles ($N_{\_min}$) as a function of temperature under the mechanical key point loading conditions.</figcaption></figure>
which supports severe plastic strain, starts to generate the first wear debris that are
immediately oxidized. A consequence of the formation of this first debris within the
interface is a separation of the adhering first bodies by limiting the metal-metal
interactions, and consequently a sharp decrease of the coefficient of friction (Figure
62 D). The minimum of the coefficient of friction (μ<sub>e_min</sub>) was found by him to be
established thanks to the operating third body displaying powder structure. It may
therefore be implied that probably synergetic effect of roughness increase and
rheological properties of the formed third body contributes to the abrupt decrease of
the coefficient of friction after a few hundred cycles of fretting test.

Like in the case of the μ<sub>e_max</sub> the minimum energy coefficient of friction (μ<sub>e_min</sub>)
seems to keep more or less steady value (μ<sub>e_min</sub>=0.52±0.05) independently of the
temperature, while a conclusion as to the associated number of cycles needed to reach
it (N<sub>_min</sub>) is not so obvious as it shows high scattering (Figure 63).

2. 2. 1. 2. Characterization of the transient and steady state

Transient state can be defined as an intermediate period occurring between a running-
in period and steady-state. Within this stage a conditioning period characterized by a
high work hardening as well as degradation and dispersal of the adhesion zones takes
place. Debris is then generated, promoting the formation of a third body layer and the
establishment of the steady-state regime. Comminution and dispersal of the adhesion
zones is proved as roughness of the contacted surfaces decreases in the transient stage
following its increase during adhesive stage (Figure 61). Afterwards, when a
conditioning period comes to the end the roughness starts to grow as the crucial role
plays then debris formation deciding which kind of wear regime will be promoted. On
the other hand, the increase of the coefficient of friction within the transient state was
reported by Merhej (2008) to be related to the formation of compacted third body
(agglomerated structure), which was supposed to be less compliant than the powder
structure observed as the minimum coefficient of friction was reached (Figure 62).

As it has already been mentioned above the evolution of the coefficient of friction
within the transient state differs significantly for fretting experiments performed
below and above T<sub>ga</sub>. It suggests that the third body formed in the interface evolves
differently within the transient stage and displays different properties below and
above T<sub>ga</sub>. At temperatures higher than T<sub>ga</sub> the energy coefficient of friction reaches some maximum (defined as a maximum transition energy coefficient of friction (μ<sub>e_tran</sub>)) at N<sub>tran</sub> number of cycles followed by its decrease down the stabilized value (μ<sub>e_ss</sub>). The value of the μ<sub>e_tran</sub> and associated number of cycles needed to achieve it (N<sub>tran</sub>) generally decreases as the applied test temperature increases (Figure 64). Similar situation can be observed if we consider a time period that is taken up by transient stage before steady-state is established.

Figure 65 shows the evolution of the energy friction coefficients (μe) for two temperatures 250 and 400°C (both above Tga) under the mechanical key point loading conditions. It is clearly seen that steady-state is reached at less number of cycles at higher temperature. It can also be concluded that the higher the temperature the lower the stabilized friction value (μe_ss) is.

<figure><img src="image_66.png" /><figcaption>Figure 64: Maximum transition energy coefficient of friction (μe_tran) and associated number of cycles (N_tran) needed to reach it as a function of temperature under the mechanical key point loading conditions.</figcaption></figure>
<figure><img src="image_67.png" /><figcaption>Figure 65: Evolution of the energy friction coefficient ($\mu_e$) as a function of the test duration for two temperatures 250 (—) and 400°C (—) under the mechanical key point loading conditions.</figcaption></figure>

The number of cycles needed to reach steady-state ($N_{ss}$) was determined based on the friction evolution and increment of the dissipated energy recorded during the tests. Figure 66 shows that for $T<T_{ga}$ and $T>T_{ga}$ different tendencies can be observed. The number of cycles needed to establish steady-state below $T_{ga}$ is practically independent of temperature ($N_{ss}=20000$ cycles), however above $T_{ga}$ a decrease of $N_{ss}$ according the Arrhenius law as temperature increases is observed. Thus, it is clearly demonstrated that the third body formed below and above $T_{ga}$ interacts in different manner. For the temperatures higher than $T_{ga}$ thermal processes appear to be activated that lead to the modification of the third body structure.
<figure><img src="image_68.png" /><figcaption>Figure 66: Number of cycles needed to reach steady-state energy coefficient of friction versus temperature below (—) and above (—) T<sub>ga</sub>.</figcaption></figure>

The average steady-state energy coefficient of friction (μ̄<sub>e SS</sub>) is defined by averaging the friction value μ<sub>e</sub> over the last (N-N<sub>SS</sub>) cycles of the fretting tests when the stabilized friction response is systematically achieved (relation 40):

$$ \bar{\mu}_{e\_ss} = \frac{1}{N - N_{\_ss}} \cdot \sum_{i=N_{\_ss}}^{N} \mu_{e(i)} \quad (40), $$

with: N – the total number of cycles (360000), N<sub>ss</sub> – the number of cycles needed to reach a steady-state (Figure 66) and μ<sub>e(i)</sub> – the energy coefficient of friction at i th number of cycles.

Figure 67 plots the evolution of the average steady-state energy coefficient of friction (μ̄<sub>e SS</sub>) as a function of temperature. Three domains, indeed, can be identified. Below a threshold temperature established at T<sub>ga</sub>=220°C (temperature of ‘glaze’ layer activation) a high friction regime, corresponding to the conventional steel/steel behaviour under ambient conditions, is observed. Above T<sub>ga</sub> a decrease of the coefficient of friction is observed. Hence, it can be concluded that the higher the temperature, the more complete the formation of the lubricating third body layer. At this stage of the investigations, however, it is not possible to say if this evolution is related to the partial constitution of the ‘glaze’ layer (i.e. the interface displays a
composite structure including ‘glaze’ layer islands and non-lubricating domains) or if
the interface consists of a continuous third body that has not reached lubricating
properties yet. The coefficient of friction decreases in a quasi-linear manner down to a
second threshold temperature Tgs= 240°C (temperature of ‘glaze’ layer stabilization).
Above Tgs an effective ‘glaze’ layer is generated within the interface, promoting a low
and practically stable coefficient of friction. The very long duration of the tests
(360000 cycles) suggests that this trend is representative of the steady-state behaviour
of the interface.

<figure><img src="image_69.png" /><figcaption>Figure 67: Evolution of the average steady-state energy friction coefficient ($\bar{\mu}_{e\_SS}$) as a function of the applied temperature for the key point conditions.</figcaption></figure>

Furthermore, it must be noticed that at 225°C (just above T<sub>ga</sub>) the value of the average steady-state energy coefficient of friction is close to the values characteristic of lower temperatures (i.e. below T<sub>t</sub>). It is due to the fact that some disturbances in the friction evolution at 225°C within the steady-state characterized by sharp peaks are occurring (Figure 68). Thus, it appears that under the studied mechanical loadings at 225°C the formed ‘glaze’ layer, though activated, is yet unstable to be capable of bearing the load effectively. Found disturbances in the friction evolution imply that the activated ‘glaze’ layer is subjected to the destruction process straightaway after its formation.
<figure><img src="image_70.png" /><figcaption>Figure 68: Evolution of the energy coefficient of friction at 225°C under the mechanical key point loading conditions.</figcaption></figure>

Taking into account above discussion and the fact that the transition between high and low friction regime takes place in a narrow temperature range of 20°C ($T_{ga}<T<T_{gs}$) the transition temperature $T_t = \frac{(T_{ga} + T_{gs})}{2} = 230°C$ is defined to simplify our considerations. It is then assumed that only the two friction domains exist, where below $T_t$ the interface with different than ‘glaze’ layer properties is predominantly developed, while above $T_t$ a stable lubricating ‘glaze’ layer is formed. Quantifying (excluding the transition result at 225°C), the mean value of the average steady-state energy coefficient of friction ($\bar{\mu}_{e\_ss}$) below and above the transition temperature $T_t$ is $\bar{\mu}_{e\_ss\_T<T_t} = 0.71$ and $\bar{\mu}_{e\_ss\_T>T_t} = 0.49$, respectively.

It must be recalled that coefficient of friction is controlled by the generated interface, so by the third body and its structure. Taking into account a state of the art of tribological issues under elevated temperature conditions the observed difference in friction evolution as $T_t=230°C$ is exceeded could be explained in two ways. On the one hand, it must be considered a tribo-chemical aspect as above $T_t$ porous oxides ($Fe_3O_4$) are believed to act as a solid lubricants [Hurricks (1974)], on the other hand a tribo-sintering process [Jiang et al. (1998), Kato et al. (2007)] of wear particles as adhesion between them increases with temperature [Yamamoto et al. (1981)] leading to the formation of a load-bearing ‘glaze’ layer should be mentioned. Thus, high
coefficient of friction observed below $T_t$ can be due to either brittle and hard oxides ($Fe_2O_3$) operating in the interface or poor adhesion between wear particles preventing the formation of the compact 'glaze' layer before they are ejected outside the contact. Furthermore, to explain the friction behaviour as a function of temperature a synergetic effect of tribo-chemical transformation and sintering process of the wear debris cannot be excluded. The response to the arising question: which of the above-mentioned phenomena plays a crucial role in the friction behaviour is being discussed extensively in the next paragraphs as wear behaviour and analytical investigations of the interface (providing its detailed physico-chemical characterization) are being analyzed.

### 2.3. Impact of the mechanical loadings at 200 and 400°C

Analysis of the friction behaviour for all tests performed at the different mean pressures and displacement amplitudes at 200 and 400°C are being discussed in this section.

The evolutions of the maximum, minimum, maximum transition (only above $T_t$, i.e. at 400°C) and steady-state energy coefficients of friction as well as related number of cycles needed to reach them versus mean pressure and displacement amplitude for 200 and 400°C are shown in Figure 69, 70, 71 and 72, respectively. In general, each individual friction parameter and the associated value of the number of cycles considered appears to increase slightly as the mean pressure or displacement amplitude increases. The only exception is the evolution of the number of cycles needed to achieve the maximum and maximum transition energy coefficient of friction versus displacement amplitude where it tends to decrease as the parameter increases.

The increase of the maximum energy coefficient of friction ($\mu_{e\_max}$) as the displacement amplitude increases (Figure 69) can be explained qualitatively in terms of the probability of asperity collisions between the contacting surfaces. At the larger fretting amplitudes an asperity has a higher probability of interacting with many adjacent opposing asperities than it can be expected for smaller displacement. This, in consequence, may lead to higher adhesive contact as higher displacement amplitude is imposed [Aldham et al. (1985)]. The impact of the mean pressure (i.e. constant, corresponding to the normal force) can be similarly considered, namely area of the
real contact is directly proportional to the load [Singer et al. (1992)], thereby as the mean pressure increases the probability of asperities interactions grows.

<figure><img src="image_71.png" /><figcaption>Figure 69: Maximum energy coefficient of friction ($\mu_{e\_max}$) and related number of cycles needed to reach it ($N_{\_max}$) as a function of the mean pressure at (a) 200°C and (c) 400°C and displacement amplitude at (b) 200°C and (d) 400°C.</figcaption></figure>

The maximum of the energy coefficient of friction corresponds to the situation when there is a maximum metal-metal interaction. It can be observed that the number of cycles ($N_{\_max}$) to reach maximum energy coefficient of friction decreases as the imposed displacement amplitude increases. It infers that the faster the elimination of native oxides and spreading of the metal-metal interaction the faster the $\mu_{e\_max}$ reaching. The larger the displacement the higher the amount of interlocking asperities, so faster elimination of native oxides and smaller $N_{\_max}$ at which maximum energy coefficient of friction is established. More difficult is to interpret the mean pressure effect, where the number of cycles to reach $\mu_{e\_max}$ increases with the parameter. If it
is assumed that $N_{max}$ is a function of the total elimination of native oxides, then a
following hypothesis should be verified. The greater the normal force (mean pressure)
the larger the real contact area, so the longer the process of elimination of native
oxides.

<figure><img src="image_72.png" /><figcaption>Figure 70: Minimum energy coefficient of friction ($\mu_{e\_min}$) and related number of cycles needed to reach it ($N_{\_min}$) as a function of the mean pressure at (a) 200°C and (c) 400°C and displacement amplitude at (b) 200°C and (d) 400°C.</figcaption></figure>

As the steady-state is established the tribological behaviour is no longer controlled by
the first bodies but by the third body occurring in the interface. The increase of the
mean pressure or displacement amplitude causes generation of more severe working
conditions, which produce higher coefficient of friction ($\bar{\mu}_{e\_SS}$) (Figure 72).

In case of the increased mean pressure and displacement amplitude the removal
probability of the wear debris from the rubbing surfaces increases [Jiang et al.
<figure><img src="image_73.png" /><figcaption>Figure 71: Maximum transition energy coefficient of friction ($\mu_{e\_tran}$) and related number of cycles needed to reach it ($N_{\_tran}$) at 400°C as a function of the (a) mean pressure and (b) displacement amplitude.</figcaption></figure>

<figure><img src="image_74.png" /><figcaption>Figure 72: Average steady-state energy coefficient of friction ($\bar{\mu}_{e\_SS}$) and related number of cycles needed to reach it ($N_{\_SS}$) as a function of the mean pressure at (a) 200°C and (c) 400°C and displacement amplitude at (b) 200°C and (d) 400°C.</figcaption></figure>
(1995)]. Moreover, it was reported that the depths of deformation layers on the wear surfaces increase with load, thus larger wear debris particles are produced [Soda et al. (1976)]. Bigger particles are more difficult to oxidize, thus the probability of their incorporation into the third body layer decreases. Hence, more time (higher number of cycles N<sub>ss</sub>) is needed to establish the steady-state as more severe loadings are imposed (Figure 72).

## 3. WEAR BEHAVIOUR

### 3. 1. Criteria introduced for wear resistance analysis

In the present Chapter two wear criteria are considered to evaluate and compare the fretting wear resistance of the studied tribo-systems as a function of temperature.

#### 3. 1. 1. Archard's wear criterion

Transposed to the studied gross slip fretting conditions the classical Archard's product (P·S) previously discussed in Chapter 1 can be expressed by the following relationship:

$$P \cdot S = \sum_{i=1}^{N} 4 \cdot P_{(i)} \cdot \delta_{g(i)} \quad (41),$$

with: N - the number of cycles, P<sub>(i)</sub> - the normal force and δ<sub>g(i)</sub> - the sliding amplitude at the i<sup>th</sup> cycle.

Thus, the Archard's wear coefficient (K) where total wear volume (V) is compared to the Archard's product can be written as follows:

$$K = \frac{V}{P \cdot S} = \frac{V}{\sum_{i=0}^{N} 4 \cdot \delta_{g(i)} \cdot P_{(i)}} \quad (42).$$

#### 3. 1. 2. Energy wear approach

This approach permits a comparison of the total wear volume with the accumulated friction work dissipated through the interface (Chapter 1). The dissipated energy corresponds to the accumulated energy (ΣEd) determined from the sum of the fretting cycle area:
$$ \sum Ed = \sum_{i=1}^{N} Ed_{(i)} \qquad (43), $$

with: N- the number of cycles and $Ed_{(i)}$ - the dissipated energy of the ith cycle.

Thus, the energy coefficient of friction (α) is defined as a ratio of the total wear volume to the accumulated energy dissipated in the interface (relation 10).

### 3. 2. Impact of temperature

Figure 73 shows the evolution of the total wear volume as a function of the temperature for the mechanical key point loading conditions (i.e. $p_m=25$ MPa (i.e. $P=176$ N), $δ*=±100$ µm and $N=360000$ fretting cycles). The abrupt drop in the wear evolution can be observed as temperature exceeds the temperature $T_{ga}=220°C$. For $225°C$ (i.e. $T_{ga}<T<T_{gs}$) an intermediate value of the wear volume is observed. In the range of $20°C$ (i.e. between $T_{ga}$ and $T_{gs}$) the wear response is therefore found to be reduced around 11 times above $T_{gs}$ compared to the temperatures lower than $T_{ga}$. Simplifying our considerations above the threshold temperature $T_t$ low wear response can be observed.

<figure><img src="image_75.png" /><figcaption>Figure 73: Evolution of the total wear volume obtained at the mechanical key point loading conditions as a function of temperature.</figcaption></figure>
<figure><img src="image_76.png" /><figcaption>Figure 74: Replot of the evolution of the total wear volume obtained under the mechanical key point loading conditions as a function of temperature (Figure 73), according to Arrhenius relationship.</figcaption></figure>

To explain the evolution of the total wear volume versus temperature the oxidational wear theory cannot be applied because, according to its assumption, wear should increase with temperature due to the increased oxidation rate (relation 31). On the other hand, the beneficial effect of the formation of a wear-protective ‘glaze’ layer promoted only by the increased temperature cannot also account for the obtained results. Attempting to find the response regarding the mechanism of a ‘glaze’ layer development, Figure 73 is replotted according to an Arrhenius relationship between wear and temperature (Figure 74). The activation energy for the wear process as the severe to mild wear rate transition takes place is here found to be approximately 33 kJ/mol. This value is of the same order of magnitude as the tribo-oxidation energy characteristic of the stainless steel [Hong et al. (1988)]. It is also consistent with the activation energy for the development of adhesion between contact asperities in the ‘stick-slip’ static friction process [Jiang et al. (1995)]. Hence, it signifies that either the tribo-oxidation or the tribo-sintering process cannot be excluded as that by which the development of the wear-protective ‘glaze’ layer is controlled. Moreover, perhaps a synergetic effect between tribo-oxidation and tribo-sintering should be considered. Such an assumption might be supported through the fact that both phenomena intensify with temperature. The beneficial effect of the higher oxidation rate is the faster wear particles oxidation as well as higher probability that larger debris would
be completely oxidized and incorporated into a ‘glaze’ layer. Hence, as temperature increases those both processes may favour the faster development of a ‘glaze’ layer of better lubricating properties.

Figure 75 plots the evolution of the energy wear coefficient defined from the mechanical key point loading conditions ($\alpha_{kp}$) as a function of the applied temperature. Similarly to the friction behaviour (Figure 67) three domains can be identified. Below the temperature $T_{ga}=220^{\circ}C$ an almost constant high energy wear coefficient can be found, between $T_{ga}$ and $T_{gs}$ an intermediate value of $\alpha_{kp}$ can be observed, however above $T_{gs}=240^{\circ}C$ a quasi constant low energy wear coefficient is maintained. As the establishment of the low friction and wear interface takes place in a narrow range of temperature (20$^{\circ}C$) the severe to mild wear rate transition temperature $T_t=230^{\circ}C$ is introduced in order to simply our considerations. It is then assumed that a change of the tribological response occurs at $T_t$. Below $T_t$ high wear regime is predominant, while above $T_t$ low wear regime is activated. Quantifying (excluding the result at 225$^{\circ}C$), the average value of the energy wear coefficient ($\bar{\alpha}_{kp}$) below and above the transition temperature $T_t$ is $\bar{\alpha}_{kp\_T<T_t} = 5.44 \cdot 10^{-5}$ and $\bar{\alpha}_{kp\_T>T_t} = 4.19 \cdot 10^{-6} \text{ mm}^3 \cdot \text{J}^{-1}$, respectively. Thus, the energy wear coefficient is reduced by a factor of 13 above $T_t$.

<figure><img src="image_77.png" /><figcaption>Figure 75: Evolution of the energy wear coefficient defined from the mechanical key point conditions ($\alpha_{kp}$) as a function of temperature.</figcaption></figure>
Though the friction analysis shows that at 225°C ($T_{ga}<T<T_{gs}$) the value of the coefficient of friction is close to those characteristic of lower temperatures (Figure 67), the energy wear response is characterized by a sharp decrease (Figure 75). It suggests that even if the lubricating properties of the ‘glaze’ layer are not fully developed within $T_{ga}<T<T_{gs}$, an immediate modification of wear response is activated. It therefore seems to be fully justified that only two wear regimes can be considered. Above $T_t$ the dissipated energy at the interface is no longer consumed through a severe two body damage process, but involves the third body ‘glaze’ layer accommodation of shear work. Less energy is then available to produce debris and consequently the energy wear rate is reduced.

The above discussion on the effect of temperature on the wear evolution did not give the explicit answer regarding the process (tribo-chemical or tribo-sintering), which is responsible for friction and wear decrease as the transition temperature $T_t$ is exceeded, but provided the clue that increasing adhesion interaction between particles with temperature enhanced by a tribo-oxidation process might be an essential factor for the development of the wear-protective ‘glaze’ layer. Results of the analytical analyses of the interface are being talked about in the next paragraph of the present dissertation in order to clarify the mechanism of ‘glaze’ layer formation.

Moreover, after the analysis of wear evolution versus temperature it arises a question: if the two found average energy wear coefficient are characteristic of the individual ranges of temperatures (below and above $T_t$), independently of the applied loading conditions? This aspect is being discussed extensively in the paragraph dedicated to fretting wear mapping of the ‘glaze’ layer activation.

### 3.3. Impact of the mechanical loadings at 200 and 400°C

The wear behaviour at two different temperatures, this below (200°C) and that above (400°C) the severe to mild wear rate transition as a function of various loading conditions (defined in Figure 52) are being contemplated in this section. Figure 76, 77 and 78 shows the evolution of the total wear volume versus, respectively, the applied displacement amplitude, mean pressure and test duration for both the considered temperatures. As it can be observed for all cases the total wear volume increases with the value of the individual parameter. As a function of the displacement amplitude and mean pressure it appears to take a linear tendency, whereas a quasi-parabolic
trend characterizes the wear evolution versus number of cycles (during the running-in and conditioning period a higher wear rate can be observed).

Figure 79 depicts the evolution of the total wear volume as a function of the accumulated dissipated energy for the two considered temperatures. For each temperature a high linear correlation with the dissipated energy can be observed (coefficient of determination R² and standard deviation σ are R²₂₀₀°C=0.96 and σ₂₀₀°C=0.034 mm³ and R²₄₀₀°C=0.90 and σ₄₀₀°C=0.003 mm³ for 200°C and 400°C, respectively). Assuming a constant interface structure (i. e. a constant temperature condition), the energy variable appears as a single factor whatever the imposed mechanical conditions such as pressure, sliding amplitude and test duration. This correlation is verified for the studied loading range (Figure 52) and contact geometry. Linear approximations are therefore considered, allowing the energy wear coefficient (α) to be identified (according to relation 10). Quantifying the energy wear coefficient gives α₂₀₀°C = 6.50·10⁻⁵ and α₄₀₀°C = 5.62·10⁻⁶ mm³·J⁻¹ at 200 and 400°C, respectively. Thus, the energy wear coefficient determined for all imposed mechanical loadings at the temperature 400°C (i.e. above the severe to mild wear rate transition temperature Tᵢ=220°C) is reduced by a factor of about 12 compared to that established at 200°C (i.e. temperature below Tᵢ). The value of the decrease found is practically the same as for the comparison of the average energy wear coefficients determined in the previous section. Relative error between the average energy wear coefficient below (ᾱₖp_T<Tᵢ = 5.44·10⁻⁵ mm³·J⁻¹) and above (ᾱₖp_T>Tᵢ = 4.19·10⁻⁶ mm³·J⁻¹) the severe to mild wear transition and the energy wear coefficient at 200 (α₂₀₀°C = 6.50·10⁻⁵ mm³·J⁻¹) and 400°C (α₄₀₀°C = 5.62·10⁻⁶ mm³·J⁻¹) determined for the wide range of the mechanical loadings is 15 and 25%, respectively. From the standpoint of tribological wear assessment such differences do not appear as very high, thus the assumption suggesting that the fretting wear behaviour of the studied tribo-couple as a function of temperature might be characterized by the two above-determined average energy wear coefficients in the studied range of loadings seems to be fully rationalized.
<figure><img src="image_78.png" /><figcaption>Figure 76: Evolution of the total wear volume versus the imposed displacement amplitude at (a) 200°C and (b) 400°C.</figcaption></figure>

<figure><img src="image_79.png" /><figcaption>Figure 77: Evolution of the total wear volume versus the imposed mean pressure at (a) 200°C and (b) 400°C.</figcaption></figure>

<figure><img src="image_80.png" /><figcaption>Figure 78: Evolution of the total wear volume versus the studied test duration (number of cycles) at (a) 200°C and (b) 400°C.</figcaption></figure>