Takadoum J. Materials and Surface Engineering in Tribology

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Surfaces 45

1.2.5.2. X-ray photoelectron spectroscopy

–

Primary particle: photon.

–

Secondary particle:electron.

–

Acronym: ESCA, XPS.

–

Characteristics of the technique:

- elemental analysis of materials,

- information about the environment of the atoms identified and the nature of

chemical bonds, and

- analysis of a surface of a few mm

to a depth of 0.1–2 nm.

OSSIBLE APPLICATIONS  Analysis of oxide films and corrosion layers in order to

determine the nature of chemical bonds of the main elements as well as that of

impurities; analysis of passivation layers; characterization of the state of chemical

bonds within polymers; and analysis of the core level and valence band.

1.2.5.3. Auger electron spectroscopy

–

Primary particle: electron.

–

Secondary particle: electron.

–

Acronym: AES.

–

Characteristics of the technique:

- elemental analysis of the top few-atom layers of solids. The depth of analysis

is 2 to 3 monolayers (of the order of a nanometer),

- local analysis (primary electron beam diameter less than 10 nm); the use of

an ion beam allows in-depth analysis alternating between analysis and ionic erosion

(down to several microns). This is also made possible by photoelectron spectroscopy

(XPS).

OSSIBLE APPLICATIONS Analysis of adsorbed layers. Analysis of thermal or

anodic oxide films. Characterization of thin deposits and analysis of segregated

layers on surfaces or within grain boundaries.

1.2.5.4. Glow discharge optical emission spectroscopy

–

Primary particle: ion.

–

Secondary particle: photon.

46 Materials and Surface Engineering in Tribology

– Acronym: GDOS.

–

Characteristics of the technique:

- simultaneous elemental analysis of dozens of elements. Analysis of all

elements, including hydrogen, possible with high sensitivity (10 ppm),

- sputtering analysis, a destructive technique which allows in-depth sample

analysis,

- analysis over large areas (of the order of cm

OSSIBLE APPLICATIONS Study of diffusion gradients. Analysis of thin films or

composition gradients. Identification of molecules adsorbed on a surface and

characterization of coatings. Analysis of iron and steel materials.

1.2.5.5. Rutherford backscattering spectroscopy

–

Primary particle: ion.

–

Secondary particle: ion.

–

Acronym: RBS.

–

Characteristics of the technique:

- the analysis of the energy of backscattered helium ions after elastic collision

with the sample’s surface atoms allows the determination of their mass,

- several elements can be simultaneously analyzed over a depth of a few

microns.

OSSIBLE APPLICATIONS Analysis of thin films. Determination of concentration

profiles. Suitable for all types of material.

1.2.5.6. Secondary ion mass spectroscopy

–

Primary particle: ion.

–

Secondary particle: ion.

–

Acronym: SIMS.

–

Characteristics of the technique:

- elemental and isotopic analysis of all elements in the periodic table,

- determination of concentration profiles of chemical elements to a depth of

several microns using ionic sputtering,

Surfaces 47

- detection of trace elements (ppm),

- can be used to obtain ionic images showing elemental distribution.

OSSIBLE APPLICATIONS Analysis of concentration profiles of bulk materials or

thin layers. For example, in the semi-conductors industry (analysis of silicon,

gallium arsenide or other semi-conductors; the aim is to control the dopant

concentration profiles, but also to localize and quantify impurities). Also used to

analyze metallurgical products heterogenity.

1.2.5.7. Infrared spectrometry

–

Primary particle: photon.

–

Secondary particle: photon.

–

Acronym: IR spectrometry

–

Characteristics of the technique:

- a method principally used for the analysis of organic materials,

- allows the determination of functional groups present in a material and the

nature of the different bonds in which the carbon atoms are involved,

- an essentially qualitative technique,

- allows the analysis of gaseous, liquid and solid samples, even in very small

quantities.

OSSIBLE APPLICATIONS Analysis of plastics and lubricants such as oils or greases.

Analysis of polymer-based coatings and thin films such as paints, varnishes or

electrodeposited polymers.

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Chapter 2

Tribology

2.1. Introduction

The word tribology is derived from the Greek word tribos, meaning friction. It

was first used in the UK in 1966 to describe the scientific and technical domains

studying friction, wear and lubrication.

Tribology is now a wide-ranging, multi-disciplinary field of study and research

aimed at:

 reducing material wear and increasing the lifetime and reliability of

mechanical and mechatronic systems; and

 controlling (or optimizing) friction (note that in some cases, e.g. vehicle

brakes, we aim for maximum friction, whereas in others, e.g. skiing and surfing, the

aim is to minimize its effects).

This dual objective requires an approach that combines contact mechanics with

the physico-chemistry of surfaces and interfaces.

We will discuss these two aspects of tribology in this chapter, and present results

that illustrate the coupling and interaction between mechanics and physico-

chemistry in problems of friction and wear. However, before we enter into a detailed

treatment of these effects, we first review a few basic notions of plasticity.

50 Materials and Surface Engineering in Tribology

2.2. Elements of solid mechanics

2.2.1. The stress vector

When a surface dS with normal

(see Figure 2.1) is subject to a force

at the

point P, the stress vector

at P is defined by the relation:

dF TdS

[2.1]

The stress vector

is the force per unit area, written as

(P,

), corresponding

to the stress vector at P acting on the face of normal

can be decomposed into

two parts:



[2.2]

where

is the normal stress and

the shear stress.

Figure 2.1. The stress vector

2.2.2. The stress tensor

To establish the state of stresses at a point P, it is sufficient to know the

components of the stress tensor

at this point.

xxyxz

yx yy yz

xzyzz

VVV

VVVV

VVV

§·

¨¸

©¹

[2.3]

Tribology 51

If we consider a parallelepiped of sides dx, dy, dz in equilibrium as shown in

Figure 2.2, each component ı

represents the stress parallel to the direction i applied

to the face with normal j. ı

xx,

and ı

are tension stresses, whereas the six other

components of the tensor are shear stresses. They are often written as Ĳ instead of ı,

noted as Ĳ

, Ĳ

Because the body is isotropic and in equilibrium, we can write:

= ı

The tensor

therefore reduces to six components, and can be diagonalized in the

following form:

§·

¨¸

©¹

[2.4]

where ı

, ı

and ı

III

are the principal stresses expressed in this new orthonormal

frame and the new axes are referred to the principal directions.

In the principal frame, the stress tensor therefore reduces to three components ı

and ı

III

Figure 2.2. Components of the stress tensor

52 Materials and Surface Engineering in Tribology

A given state of stress described in the principal frame by the tensor

can

therefore be decomposed into two terms

00 00 0 0

00000 0

00 00 0 0

ImIm

II m II m

II m III m

VVVV

VV VV



§·§·§ ·

¨¸¨¸¨ ¸



¨¸¨¸¨ ¸



©¹©¹© ¹

The first term is referred to as the spherical part of the tensor

and it

corresponds to a hydrostatic pressure. The second term represents the deviatoric

stress and corresponds to the shear component of tensor

2.2.3. Yield criteria

Yield criteria are expressed as a series of equations defining particular conditions

on the components ı

of the stress tensor. They are noted in the form:

()0

[2.6]

where f is a known function. When this condition is satisfied, yield will occur.

Equation [2.6] can be expressed as a function of the principal stresses in terms of

a new function f':

'( , , ) 0

IIIIII

VV V

[2.7]

2.2.3.1. The Tresca criterion

The Tresca criterion is a maximum shear stress criterion based on the notion that

yielding occurs when the maximum shear stress attains a threshold value.

Taking ı

 ı

III

, we can write this criterion:

max

IIII



[2.8]

When Ĳ

max

is greater than or equal to the yield shear stress for a state of pure

stress k, yielding occurs. Y gives the yield stress obtained from a tensile (or

compression) test.

[2.5]

Tribology 53

2.2.3.2. The von Mises criterion

This criterion is based on the notion that plastic deformation occurs when the

stored distortion strain energy attains a critical value.

Using Y and k defined above, the von Mises criterion is expressed in the

principal frame by:

()



()

II III



222

()26

III I



[2.9]

The two criteria have been superimposed in Figure 2.3, and we can note that the

maximum separation (E) between the two is equal to:

EY 

, [2.10]

a maximum difference of around 15%.

Figure 2.3. Representation of the Tresca and von Mises criteria in the principal frame

2.3. Elements of contact mechanics [JOH 85, WIL 94]

2.3.1. Hertz contact theory

Figure 2.4 shows three different contact geometry configurations. In the case of

elastic contact, Hertz’s theory allows us to describe the stress distribution on and

below the surface.

Hexagone de Tresca

III

Cercle

de von Mises

Von Mises

circle

Tresca hexagon

54 Materials and Surface Engineering in Tribology

a) b) c)

Figure 2.4. Different types of contacts:

a) point; b) linear; c) surface

We take a simple case of point contact, illustrated by a sphere of radius R

pushing on a plane surface under the action of a force F (see Figure 2.5).

P(x)

Figure 2.5. Sphere-plane contact