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Third-bodies in tribology
Wear, 136 (1990)
29 - 45
THIRD-BODIES
29
IN TRIBOLOGY
MAURICE GODET Laboratoire de Me’canique des Contacts (CNRS URA 856), Institut App~~qu~es de Lyon, 69621 Vi~leurban~e Cedex (France)
National
des Sciences
Summary In the last decades, Tribology has moved, from the Tribology of Volumes, which attempted to produce friction and wear laws for different material combinations, through the Tribology of Surfaces, which rests strongly on surface science, to the Tribology of Interfaces which focusses on the role of the interface on friction and wear. Interfaces, or third-bodies can be defined in a material sense, as a zone which exhibits a marked change in composition from that of the rubbing specimens or in a kinematic sense, as the thickness across which the difference in velocity between solids is accommodated. The third-body or interface approach is useful as the third-body model presents all of Tribology, from thick film lubrication to dry friction, as a single science centered on the notion of flow. It also insists on the difference between wear and particle detachment mechanisms which are shown not to be equivalent. Interface kinematics in dry friction is presented in the light of “velocity accommodation sites and modes”. The effect of sites and modes on friction and wear are also discussed.
1. Tribology today, a mechanical view
1.1. Introduction Tribology is the science of contacts. Contacts are found in all assemblies [ 1, 2 ]. Industrial contacts see normal and tangential loads which may vary between a few milligrams in computers rigid discs [ 31 to thousands of tons in modem turbines [4] and generate pressures of gigapascals [ 51 in roller and gear applications. The tangential loads are usually associated with velocities which vary between zero and hundreds of meters per second, which in turn generate shear rates of up to 10’ 6’. These pressures and shear rates are the highest noted in technology. Contacts are thus strained to the highest extent, and mechanical engineers, surface and volume physicists and chemists - tribology is multidisciplinary - are called upon everyday to invent new ways to face up to these challenges. The answers to these lie in the application of basic theories. 0043-1648190/$3.50
@ Elsevier ~uoia/Printed
in The Netherlands
Tribology means different things to different men, and there is still today a concensus to divide it in two; thick film lubrication which is analysed theoretically [4, 61 and the “rest” [7 - lo] which includes everything from mixed and boundary lubrication to dry friction and which apparently refuses any form of general theory or classification. The purpose of this paper is to show that the distance between lubrication and the “rest” is not as large as it is believed to be, and that tribology can be presented under one single heading centered around interface or third-body flow or continuity concepts and third-body load carrying capacity [ 11 - 141. This paper will thus focus on the gap between thick film lubrication and the “rest” and attempt to reduce it. To have a chance of success it is important, right from the start, to be fully aware that thick film lubrication has been studied by mechanical engineers with a good mathematical background and that the “rest” has been tackled by material scientists. Thus, on top of the difference in complexity of both fields (thick film lubrication is notably simpler than the “rest”) the argument must take into account both mechanical and material concepts. For mechanical engineers who want to extrapolate what they have learned from thick film lubrication [6] : (1) the interface or third-body is characterized by its rheology, composition is indifferent; (2) boundary conditions between first and third bodies must be specified, surface activity is indifferent; (3) the velocity difference between first-bodies is accommodated across the interface which means that the interface possesses its own velocity field and dynamics; (4) load carrying capacity can be calculated if boundary conditions and rheology are known; (5) generalities overshadow material differences. For material scientists: (1) the interface is characterized by its chemical composition, rheology is indifferent; (2) the interface is looked upon as a static identity strongly attached to the rubbing surfaces; (3) velocity accommodation is not considered; (4) the qualitative notion of surface protection is substituted to the quantitative load-carrying concept; (5) material differences overshadow generalities in tribology. Unfortunately, even though the differences between the mechanical and material outlooks are strongly accentuated here they nevertheless remain and have to be considered if the gap between lubrication and the “rest” is to be reduced. 1.2. Contacts Loaded contacts generate stresses between rubbing solids or first-bodies in both thick film lubrication and in the “rest”. First-body contact mechan-
31
TABLE
1
Basic equations
of contact
Equilibrium equation Constitutive laws Lame equations Solutions are produced contact conditions
mechanisms
theory aij.j + fl = 0 Oij = hO6ij + 2/.lEij
for different
/.LAx~+ (h + /J.)dB/dxl + fi = 0 e.g. Boussinesq, Hertz, Mindlin,
etc..
Contact mechanisms theory is adequafe for normal loads it is not so good when tangential are introduced through Coulomb friction It does not take into account: Nor does it
effects r=pP -time - interface
(or third body)
provide satisfactory conditions
effects
boundary
its have been studied theoretically for over 100 years by Boussinesq [15] and Hertz [ 163 and more recently by Johnson [ 171 and Kalker [ 181. Table 1 lists the basic equations and symbols needed to derive the contact mechanics theory {19]. It should be noted that in relating stress to strain the law eliminates time and thus velocity effects. In the same way the acceleration term is dropped from the equilibrium equation. Written in terms of displacements the Lame equation satisfies compatibility requirements. In two-body contacts the Lame equation yields stress and displacement fields. Normal stresses are obtained directly while a friction law is needed to calculate tangential effects, The Hertz problem is a classical example of twobody contacts. Three-body contacts can be approached by considering either rigid firstbodies and by focusing only on third-body deformation (low pressure bearing lub~~ation is a classical example of this form of three-body contacts [6]), or deformable first-bodies and by focussing simult~eously on first and third-body deformation (elastohydrod~amics [ 201 illustrates this form of contacts). 1.3. Thick film lubrication As noted earlier, thick film lubrication is the only third-body contact which is clearly understood and formalized to such an extent that lubrication theory is a common design tool today. Further, oils or more generally viscous or near-viscous fluids are undoubtedly the best third-bodies available. Let us therefore identify the basic concepts and assumptions in lubrication theory and see if they can be transposed to or help to formalise the “rest”. Table 2 lists the basic equations and symbols which are needed to derive the complete Reynolds equation which governs thick film lub~~ation
32
TABLE 2 Basic equations of lubrication theory
Equilibrium Constitutive loads
Uij
For H/L < 10e3
=
(p
+
h0)6ij
ap -=
a --
aZli p_
axi
ax2 i ax2
1
Boundary condition
no slip at the wall
u(0) =
u(h) =
u1;
w(0) =
WI
Velocity
Flow:
u=
w(h) =
u2;
2fJgij
+
i= 1,3
w2
;j!;y(y-h)/ +~y+u,
w=...
ap
Divpu+z=O with: h = h(x, z) 6~ WI
Pressure:
P=
h,2
Load and friction (For plain bearings)
P-
hoZ
MUI,
91
6,uU12b ii?(W)
F =
Theory gives P, F and u(y) where u(y) is the velocity accommodation
function
[7]. The derivation of the equation is of interest in this presentation and a simplified version of the process which considers only incompressible, isoviscous, inertialess and unidirectional laminar flow is presented. The constitutive law specific to viscous third-bodies, which relates stress to strain-rates and not to strain itself, is introduced in the equilibrium equation to yield the Navier-Stokes equation. In this case, the equilibrium equation, which is general to all bodies includes an acceleration term. With the assumptions listed above, the Navier-Stokes equations reduce under thin film conditions to the three pressure gradients listed in Table 2. In the coordinate system chosen x2 is taken across the film. The velocity fields u and w are obtained after integrating these equations twice and introducing
33
boundary conditions which assume that there is “no slip at the wall”. u and w are then introduced in the continuity equation which is general and which states that mass is preserved; it cannot be created or destroyed. It is the pendant in fluid mechanics of the compatibility requirement in solid mechanics. The last operation yields the Reynolds equation which, in the form presented, is a non-linear differential equation with two unknowns, the pressure p and the film thickness h, which is given by the contact geometry. h is introduced in the Reynolds equation which is then solved for p, the integral of which over the contact area yields the load-carrying capacity P. Reynolds’ equation is a flow continuity relation [ll]. It should also be noted that the Reynolds equation can solve both static ( U1 = U, = V, = 0) and dynamic contact conditions. 1.4. The “rest” The difference in velocity between the two first-bodies cannot be accommodated across a body of zero thickness and it will be therefore assumed that the interface is not immaterial and that it possesses all the attributes of matter. Thus the equilibrium equation of Table 2 must be satisfied independently of the composition of the interface. Further, whether it acts as a whole or in parts, the interface must have one or many constitutive laws. The mass conservation law must also be obeyed at least locally if not over the entire contact. Finally, there is some interaction between first and third-bodies which must be expressed in terms of boundary conditions. One can measure now, the distance between what is known and what is needed to solve in quantitative terms the conditions met in the “rest”. Much is known about three-body chemical composition following the many Auger, Esca and Sims campaigns [21] which have been conducted, but little is known about third-body rheology. Further, first-third body interactions have not been studied in terms of boundary conditions. 1.5. Conclusions Two-body contact theory is applicable to all of tribology. Third-bodies modify the contact boundary conditions. This modification can be taken into account by introducing either a friction law, which governs tangential stresses, and maintaining the normal stress distribution given by two-body contact analysis, or a third-body element of known rheology, with well formulated first/third-body boundary conditions and solving simultaneously first and third-body equations. Friction laws however do not describe the physics of the problem [ 221. A lot of work must be done before third-body rheology and first/third body boundary conditions are understood and before the mechanical engineer can bridge the gap and be as efficient and pertinent in the “rest” as he is in thick film lubrication. The load-carrying concept must be extended to include materials other than viscous fluids. Static load-carrying materials, i.e. spacers or materials
which can separate even heavily loaded surfaces are many. Most of them however are unable to insure load-carrying under relative motion. Those which can are known here as load-carrying agents.
2. The interface 2.1 I Data This discussion focuses on the interface and on the evidence that has accumulated in the last few years essentially through visualization f23]. Experiments have been conducted on numerous material combinations which include polymers [24] (PMMA, PC etc.), elastomers [25], metals [26 281 (various steels, aluminium alloys, titanium alloys, copper etc.), ceramics [29] (A1203, Sic etc.), chalk [30], glass, sapphire, carbon etc. under both continuous and reciprocating motion and all have shown that debris is produced quasi immediately; it is then trapped in the contact for some time and finally eliminated. Many events were recorded on films, and interface dynamics could therefore be followed in detail. The size, morphology, and sometimes the composition of the debris eliminated are significantly different from those of the particles when detached from the first-bodies. Evidence therefore indicates that the original two-body contact is rapidly changed into a threebody contact which is an altogether different problem. Surprisingly enough, three-body tribology took some time to be accepted, because rubbing surfaces are always thoroughly cleaned before they are examined and all of the loose third-body or debris is eliminated during cleaning.
Fretting has provided good evidence of third”body effects. Figure 1 is a picture of glass rubbing against steel. Observations made every few runs show that damage starts at the first strokes and continues as time goes on. Debris is trapped and the situation moved from a, two-body (glass against steel) to a three-body (glass, debris bed or third-body and steel) contact. The early passage from a two- to a three-body contact is general, The results presented in Table 3 were obtained with three materials; two identical steel alloys (materials I and II) but quenched and tempered from different temperatures (TT) and a stainless steel (material III). Their composition in wt.% is listed below. Figure 2 [31] shows the change in coefficient of friction vs. both the number of cycles and the displacement during a characteristic cyclic wear test. The data presented, known as the “friction log” because of its shape, corresponds to a test run with material I. The friction log is divided in 4 parts : (1) elimination of the “natural” screens which pollute the specimen surfaces;
35
cycles
Load Amplitude Frequency
: 500 N : 5 50 vrn : 1 Hz
Fig. 1. Two- to three-body
TABLE
glass rubbing
on steel - material
I.
3
Chemical
I II III
contacts
composition
(wt.%) of test materials
C
Si
Mn
s
P
Ni
Cr
MO
TT
0.378 0.378 <.03
0.33 0.33
0.38 0.38
<103
0.011 0.011
3.77 3.77 12.5
1.65 1.65 17
0.29 0.29 2.75
600 “C 200 “C
<103
(2) increase in specimen (or first-body) interaction accompagnied by the corresponding first-body structural changes (strain hardening for instance for metals); (3) debris formation and gradual passage from a two- to a three-body contact; (4) three-body contact characterized by a continuous formation and ejection of debris. Steady state conditions prevail. It should be noted that parts 1 and 2 and the first part of 3 describe the particle detachment phase (Section 11.1). The second part of 3 corresponds to the trapping and part 4 to the elimination phase. Figures 3 - 5 show that the shape of the log depends on the following.
Fig. 2. Friction log obtained with material I defined in Table 1 (see ref. 2, p. 24).
Load Amplitude
: 500
Frequency
:1
N : 2 50 pm
Fig. 3. Effect material II.
Hz
of specimen preparation
(or cleaning) on friction log (see ref. 2, p. 41) -
( 1) Surface preparation: in Fig. 3(a), the steel specimens (material I) were cleaned first with acetone then with alcohol, while in Fig. 3(b), they were cleaned with alcohol alone.
37
Mat&at
I
i
Load Ampiitude Frequency : 1 HZ
-0
Fig. 4. Friction log obtained with three different materials for identical running conditions (see ref. 2, p. 45).
(2) Materials: Fig. 4 shows the effect of tempering temperature (I and II) and composition (III). (3) Frequency: Figs, 5fa - cl, illustrate the effect of frequency. Figures 2 - 5 suggest that: (1) phase 1 is controlled by surface physics; (2) material properties (toughness) govern phases 2 and 3; (3) machine dynamics control particle ejection and as such first-body protection. It should be noted that in all cases, steady state three-body conditions are reached after roughly 1000 cycles. The rest of the test is clearly governed by third-body dynamics.
2.3. Conclusions Visualization has helped in understanding third-body effects under both continuous and reciprocating tests. The basic phenomena (particle detachment, trapping and elimination) were identical in both cases. Twobody contacts are significantly different from three-body contacts and the experimental approach must therefore be different in each case.
38 0.1 Hz
:ct
amplitude Fig. 5. Effect
: f 50 pm of frequency
on the friction
log (see ref. 2, p. 60) -
material
III.
3. Theory 3.1.
Interface tribology The importance given recently to the study of interfaces [32] suggests that, in the last 40 years, the study of tribology has moved: - from the tribology of volumes (or bulk material) where material A was run against material B in elementary machines and empirical friction and wear laws were produced; - through the tribology of surfaces which insisted on the role of surface activity in contacts and introduced basic scientific concepts in the field; - to the tribology of interfaces or third-bodies which concentrates as well on the role of the interface as on that of the first-bodies. This constitutes a fairly radical change in the understanding of both friction and wear. 3.2. Friction Lubrication theory defines the friction force as the integral of the shear stresses generated in the lubricant on the driving surface. Figure 1 and the explanations advanced in Section 2.2 indicate that in the “rest” the material in which friction is generated can vary during a test and that under steady-
39
state conditions, after 1000 cycles, friction is generated within the debris bed or third-body. Figure 6 shows a debris bed taken during a steel against steel fretting test. Both rubbing specimens were removed from the machine and the contact was opened just before the picture was taken. The picture shows that a thin powder bed, neither uniform in distribution or composition, separates both first-bodies. Further, no indication as to how friction is generated is given as no information concerning velocity accommodation transpires from the picture, 3.3. Parameters which govern friction Clearly, progress in understanding and modeling friction in situations such as those pictured in Fig. 6 requires powder bed dynamics studies [33 361 and an identification of both modes (how is friction generated) and sites (where is friction generated) of velocity accommodation. This point will be taken up later but it is important to note at this stage that the friction force is governed by the debris bed which is very sensitive to many outside influences such as humidity, or environment in general, machine dynamics, contact shape etc.
3.4. Wear It is common to talk of wear mechanisms [37] and to list adhesive, abrasive and fatigue wear etc. This is contradictory to the succession of events described in the third-body approach (Section 3) which suggests that debris is first detached from the first bodies, then trapped for some time in the contact and finally eliminated from the track. Adhesion, abrasion, fatigue etc. are therefore not wear but particle detachment mechanisms. The difference between the two is of great importance. Indeed, in the original view, it is only possible to work on surface effects to control wear. In the third-body approach, wear can be controlled at any one of the three stages of wear. Powder beds, debris and thus third-bodies have load-carrying capacity. In most instances the protection afforded by debris beds is bene-
-
1.7 pm
Fig. 6. Debris bed.
40
ficial [38] even though some beds are abrasive [ 391. These aspects are ignored in the original view. A particle, eliminated from the contact, can stay in the wear track and be recirculated in multi-pass systems. It only becomes a bona-fide wear particle when it is eliminated from the track. Geometry, which is not discussed in the original view, controls recirculation and thus wear. 3.5. Parameters which govern wear As seen in Section 3.4, wear can be controlled at any one of the three stages presented in Section 2.2. Control of the first stage of wear or control of particle detachment is discussed in many papers; anti-wear coatings, surface treatments etc. are known to be effective and are commonly used industrially [9]. This section will therefore concentrate on the two other stages, trapping and elimination. Clearly, the same parameters often affect both factors, therefore the discussion will be grouped. Particle dwell time, or time during which a particle is trapped in the contact, which by definition governs the load-carrying capacity, is not conditioned solely by particle composition but also by the contact mechanical environment. Let us briefly recall the mechanics of interface elimination and note that particles are expelled from the contact through acceleration effects or body forces such as gravity or centrifugal action; Poiseuille flow is governed by the pressure distribution generated in the contact through its load-carrying action; Couette flow is controlled by surface motion which can drag particles outside of the contact and momentum effects transmitted from the first-bodies to the particles. Some of the factors which control elimination through any one of the processes described above are as follows. (1) Contact dynamics: powder bed dynamics [33 - 361 is a very complex subject and broad generalisations are dangerous. Nevertheless a quiet, smooth running new machine will generally trap particles better than a noisy worn and shaky device. (2) Open and closed contact: a spherical bearing traps practically all of the particles detached during the first few strokes. If, as is the case with some polymers, the particles form a protective bed [40], elimination is practically stopped and bearing life is long. Inversely, the trapping capabilities of a ball on plane contact are limited. It should be noted that if the track in a pin-and-disc machine is grooved, particle trapping can be enhanced. (3) Contact shape: the longer the contact, in the direction of motion [31] the longer will be the particle dwell time in the contact. Wide contacts limit particle side leakage. (4) Re-entry conditions (a particular aspect of contact shape): Section 3.5 states that detached particles can be recirculated if, between successive passes, they are held in the track as a trace and trapped at each new pass. Trapping action necessarily depends on entry conditions and results show that, in a pin-and-disc machine for instance, a small chamfer on the pin eases trace recirculation in the contact.
41
(5) Roughness: a protective layer, whether static or dynamic, must separate the two rubbing first-bodies. Therefore, the volume defined by the roughness voids between peak and valley must be filled before steady-state conditions are met. This can take between 1 and lo5 cycles depending on the material and the contact conditions and thus control internal flow in the contact and elimination rate. (6) Third-body rheology: the consistence of the interface, whether it is made out of loose powders or tacky substances, with high auto-adhesion between its particles, obviously governs the rate of elimination from the contact [ 411. (7) Boundary conditions: the boundary conditions between third- and first-body govern Couette flow, momentum transfer, and thus elimination rate. Clearly, surface effects, surface energy for instance, determine boundary conditions. 3.6. Conclusions Many parameters are known to govern friction and wear. Some are mechanical, and their effects can only be understood in the light of thirdbody theory. This great number of parameters explains why it is impossible to extrapolate friction and wear results from one application to another [42] or from laboratory tests to an industrial situation. Unless great care is taken in the simulation of the real situation, there will always be some difference between two contact conditions. Dynamic effects, to mention just one of the parameters, have been identified in lubrication [43,44] and it is therefore no surprise to see them appear as governing parameters in the “rest”.
4. Velocity accommodation 4.1. Three- body con tat t Figure 7 is a simple three-body contact model which is described in detail in refs. 45 and 46, discussed in refs. 41 and 47 and briefly recalled here. It includes the two first-bodies or rubbing specimens, the two thirdbody/first-body interfaces or screens, which have their own specific composition and the third-body bulk. Recall that third-bodies can be either natural (debris) or artificial (solid lubricants for example). 4.2. Velocity accommodation The manner in which the difference in velocity between rubbing solids is accommodated across the interface is defined here as the velocity accommodation mechanism (see Section 3.2.3). Velocity accommodation mechanisms, which govern friction and wear, have been identified during visualization tests. Figure 7 shows that in a three-body contact, for a given abcissa, the velocity can be accommodated at five different sites Si which include the
42
00
b) Modes
a) Sites
Fig. 7. Velocity
M,
accommodation.
two first-bodies Si and Ss , the two screens Sz and S4, and the third-body bulk S3, and according to four different modes Mj at each site which are the elastic M,, the rupture M2, the shear Ma and the rolling M4 modes. Thus 20 velocity accommodation mechanisms can be encountered. Each mechanism is identified by one SiMj code. S3M3 signifies for instance that the velocity is accommodated in the third-body bulk through shear. First-body or bulk accommodation will not be discussed in this paper which is centered on third-bodies which include both third-body bulk and screens. 4.3. Screen accommodation S2 and S4 Thin films are known to govern surface adhesion. They deform elastically S?M, and shear S2M3 [48]. They break up in lumps S2MZ, form rolls S2M4, which in turn can develop into homogeneous films [ 491. Their accommodation possibilities are unlimited after shearing or fracture. 4.4. Third-body bulk accommodation Third-body bulk rheology is a very weak term attempting to express the very many different types of behaviour encountered in a contact interface. Third-bodies deform elastically SaMi like all powder beds. Further, they fracture S3MZ, shear S3M3 and roll S3M4 as witnessed [45] by the motion pictures taken through one of the rubbing specimens or first-bodies which showed that graphite films fractured and iron oxides Fez03 beds sheared.
4.5. Conclusions
Identification of the velocity accommodation mechanisms in different applications is a necessary step to advance from a qualitative to a quantitative third-body approach. Looking again to lubrication theory for guidance, friction is calculated (Table 2) from the velocity distribution across the film thickness. Third-body shear S3M3 is the only mechanism present which significantly simplifies the problem.
43
5. Conclusions The third-body approach is the necessary step to reconcile mechanical engineers and physicists in tribology. Before, the mechanical engineer was ill at ease outside of lubrication as his basic concepts of equilibrium [50] and continuity were not taken into account. Further, the extension of the load carrying concept, from lubrication to tribology in general, introduces a new line of reasoning which, as in lubrication, focusses attention on third-body properties. The extension of the third-body approach to include velocity accommodation mechanisms is the necessary step to go from the qualitative to the quantitative exploitation of the third-body concept. It is also useful as it clearly situates lubrication with respect to the “rest” and points to the relative complexity of both areas of tribology. Recall that 20 accommodation mechanisms were identified in the “rest” while only one exists in thick film lubrication. Modeling of a general tribology problem is still out of reach today. It is clear, however, that in the future each mechanism will have to be modeled individually along with the conditions of its triggering and the limits of its application. There is a tremendous amount of work ahead and it has to be done in good harmony by mechanical engineers, material scientists, specialists of both surface and bulk physics, and applied mathematicians.
Acknowledgments The first papers on the third-body approach go back 20 years and many people have contributed to it. Thanks are due to D. Play who worked and published on the subject in the seventies and to Y. Berthier who contributed significantly to its advance in the eighties. Many useful discussions were held with other colleagues of the Laboratoire de Mecanique des Contacts and particularly with D. Berthe and L. Flamand. Outside of the laboratory, I wish to acknowledge J. Lancaster’s contribution, generous encouragement and remarkable ability to draw on a vast experience and understanding of things tribological. None of this work could have been done without the financial help provided by the French Ministries of Research (M. Grandvalet) and Defence (M. Durouchoux) and by various industries. Their trust in this work brought it to fruition.
References 1 J. R. Atkinson, J. Charnley, J. H. Dowling and D. Dowson, The wear of total replacement hip joints in the human body - a topographical survey of the surfaces of worn acetabular cups. In Wear of Non-Metallic Materials, Mechanical Engineering Publications, London, 1978, pp. 127 - 133. 2 D. Scott, Wear - Treatise of material science and technology, Vol. 113, Academic Press, New York, 1979.
44 3 B. Bhushan and M. F. Doerner, Role of mechanical properties and surface texture in the real area of contact of magnetic rigid disks, ASME paper no. 88-Trib-39. (to be published in J. Tribol.). 4 0. Pinkus and B. Sternlicht, Theory of hydrodynamic lubrication, McGraw-Hill, New York, 1961. 5 B. J. Hamrock and D. Dowson, Isothermal elastohydrodynamic lubrication of point contacts, ASME/JOLT, 99 (1977) 264. 6 J. Frene, D. Nicolas, D. Berthe, M. Degueurce and M. Godet, Lubrification hydrodynamique: paliers et butees, Eyrolles, Paris, 1990. 7 J. A. Tichy, Modeling of dry and boundary lubricated contacts as seen from the hydrodynamicist’s perspective. In F. F. Ling and C. H. Pan (eds.), Approaches to Modeling of Friction and Wear, Springer-Verlag, New York, 1988, pp. 51 I 52. 8 F. P. Bowden and D. Tabor, Friction and Lubrication of Solids, Vols. I and II, Oxford University Press, Oxford, 1951 and 1964. 9 D. H. Buckley, Surface Effects in Adhesion, Friction, Wear and Lubrication, Tribol. Ser. 5, Elsevier, Amsterdam, 1985. 10 J. M. Georges, Microscopic Aspects of Adhesion and Lubrication, Tribol. Ser. 7, Elsevier, Amsterdam, 1982. 11 M. Godet and Y. Berthier, Continuity and dry friction: an Osborne Reynolds approach. In D. Dowson, C. M. Taylor, M. Godet and D. Berthe (eds.), Fluid Film Lubrication - Osborne Reynolds Centenary, Tribol. Ser. 11, Elsevier, Amsterdam 1987. 12 M. Godet, The third-body approach: a mechanical view of wear, Wear, ZOO (1984) 437 13 14 15
16 17 18 19 20 21 22
23
24
25 26
- 452.
H. Heshmat, 0. Pinkus and M. Godet, On a common tribological mechanism between interacting surfaces, STLE Transactions, 32 (1) (1989) 32 - 41. Y. Berthier, M. Brendle and M. Godet, Velocity accommodation in friction, STLE Tribol. Trans., 32 (1989) 4, 490 - 496. J. Boussinesq, Application des potentiels a l’btude de I’equilibre et du mouvement des solides Blastiques, Gauthier-Villars, Paris, 1885. H. Hertz, Miscellaneous Papers by H. Herts, Jones and Schott (eds.), Macmillan, London, 1896 (English translation). K. L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985. J. J. Kalker, Mathematical models of friction for contact problems in elasticity, Wear, 113 (1986) 61 - 77. A. S. Saada, Elasticity, Theory and Applications R.E. Krieder, Florida, 1983. D. Dowson and G. R. Higginson, Elostohydrodynamic Lubrication, 2nd edition, Pergamon, Oxford, 1977. D. H. Buckley, Surface Effects in Adhesion, Friction, Wear and Lubrication, Tribol. Ser. 5, Elsevier, Amsterdam, Chapter 2. R. Progri, B. Villechaise and M. Godet, Boundary conditions in a two-body contact formed by a rectangular polyurethane slab pressed against an araldite plane, Trans. ASME, J. Tribol. 107, (January 1985) 138 - 141. D. Play and M. Godet, Visuahsation of Chalk Wear. In D. D. Dowson, M. Godet, and C. M. Taylor (eds.), The Wear of Non-Metallic Materials, Mechanical Engineers, London, 1976, pp. 221- 229. L. Vincent and N. Dahmani, Interface dynamics in polymer friction. In D. D. Dowson, C. M. Taylor, M. Godet and D. Berthe (eds.), Interface Dynamics, Tribol. Ser. 12, Elsevier, Amsterdam, 1988. M. Godet, D. Play and D. Berthe, An attempt to provide an uniform treatment of tribology through load-carrying capacity, transport, and continuum mechanics, Trans ASME, J. Tribol. 102 (2) (April 1980). C. Chamont, Y. Honnorat, Y. Berthier, M. Godet and L. Vincent, Wear problems in small dispalcements encountered in titanium ahoy parts in aircraft turbomachines, 6th World Conf. on Titanium, Cannes, France, June 1988.
45 27 J. Sato, M. Shima and T. Sugawara, A fundamental study of fretting damage to glass using an improved apparatus, Wear, 106 (1985) 53 - 61. 28 J. S. Sheashy and G. R. Mount, The wear of copper in single pass sliding, Wear, 105 (1985) 235 - 246. 29 R. Trabelsi and Y. Berthier, Velocity accommodation between rubbing ceramics. Proc. 5th Int. Congress on Tribol., Helsinki, 1989, Vol. 4, pp. 48 - 54. 30 D. Play and M. Godet, Self-protection of high wear materials, ASLE Trans. 22 (1) (1979) 56 - 64. 31 Ch. Colombie, Y. Berthier, A. Floquet, L. Vincent, and M. Godet, Fretting: loadcarrying capacity of wear debris, Trans. ASME, J. Tribol. 106 (2) (3984) 185 - 194. 32 D. Dowson, C!. M. Taylor, M. Godet and D. Berthe (eds.), Interface Dynamics, Tribol. Ser. 12, Elsevier, Amsterdam, 1988. 33 R. S. Paranjpe and H. G. Elrod, Stability of chains of permeable spherical beads in an applied magnetic field, J. App. Phys. 60 (1986) 418 - 422. 34 H. G. Eirod, Granular flow as a tribological mechanism. In D. D. Dowson, C. M. Taylor, M. Godet and D. Berthe (eds.), Interface Dynamics, Tribal. Ser. 12, Elsevier, Amsterdam, 1988, pp. 75 - 89. 35 K. Craig, R. H. Buckhols and G. Domoto, Experiments on the rapid shear flow of metal powders. In D. D. Dowson, C. M. Taylor, M. Godet and D. Berthe (eds.), Interface Dynamics, Tribol. Ser. 12, Elsevier, Amsterdam, 1988, pp. 89 - 99. 36 B. J. Briscoe and P. D. Evans, The wear of polymers by particulate flows. In B. J. Briscoe and M. J. Adams (eds.), Triboiogy in Particulate Technology Adam Hilger, Bristol 1987, pp. 335 - 350. 37 J. T. Burwell, Survey of possible wear mechanisms, Wear, 1 (1957) 119 - 141. 38 Y. Berthier, Effet du comportement du troisieme corps sur i’usure des pafiers sees en mouvement alternatif, These Dr. Ing. INSA de Lyon, July 1982. 39 A. Misra and I. Finnie, An experimental study of three-body abrasive wear, Wear, 85 (1983) 57 - 69. 40 J. K. Lancaster, The formation of surface films at the transition between mild and severe wear, Proc. Roy. Sot. London, Ser. A, 273 (1963) 466 - 483. 41 Y. Berthier, L. Vincent and M. Godet, Velocity accommodation in fretting, Wear, 125 (1988) 25 - 38. 42 M. Godet, Extrapolation in tribology, Wear, 77 (1982) 29 - 44. 43 N. Abdul-Wabed, D. Nicolas and M. ‘I’. Pascal “Stability and unbalance response of large turbines”. ASME Trans., Lubr. Technol., 104 (January 1982) 66 - 75. 44 D. Bondoux, B. Bou-Said, G. Ferraris and M. Lalanne, Etude du comportement dynamique d’un prototype de pompe disphasique, M&z. Mate’riaux, Electr., 416 (May -June 1986) 38 - 41. 45 Y. Berthier, MQanismes et Tribologie, Th&e Dr.& Sciences, INSAlUCB Lyon, 1989. 46 Y. Berthier, Ex~rimen~l evidence for friction and wear modeling, fnt. Conf. on Wear of Materials, Denver, 1989 (to be published). 47 Y. Berthier, M. Brendle and M. Godet, Boundary conditions: adhesion in friction. In D. D. Dowson, C. M. Taylor, M. Godet and D. Berthe teds.), fnterface Dynamics, Tribol. Ser. 12, Elsevier, Amsterdam, 1988, pp. 19 - 25. 48 B. J. Briscoe, B. Scrutton and R. F. Willis, Shear strength of thin lubricant films, Proc. Roy. Sot. London, Ser., A 333 (1973) 99 - 114. 49 D. Tabor, The role of surface and intermolecular forces in thin film lubrication. In J. M. Georges (ed.), Microscopic Aspects of Adhesion and Lubricants, Tribol. Ser. 7, Elsevier, Amsterdam, (1982) pp. 651 - 677. 50 M. Godet, Mechanics versus or with materials in the understanding of tribology, Lubric. Eng., 40 (7) (1984) 410 - 414.
29 - 45
THIRD-BODIES
29
IN TRIBOLOGY
MAURICE GODET Laboratoire de Me’canique des Contacts (CNRS URA 856), Institut App~~qu~es de Lyon, 69621 Vi~leurban~e Cedex (France)
National
des Sciences
Summary In the last decades, Tribology has moved, from the Tribology of Volumes, which attempted to produce friction and wear laws for different material combinations, through the Tribology of Surfaces, which rests strongly on surface science, to the Tribology of Interfaces which focusses on the role of the interface on friction and wear. Interfaces, or third-bodies can be defined in a material sense, as a zone which exhibits a marked change in composition from that of the rubbing specimens or in a kinematic sense, as the thickness across which the difference in velocity between solids is accommodated. The third-body or interface approach is useful as the third-body model presents all of Tribology, from thick film lubrication to dry friction, as a single science centered on the notion of flow. It also insists on the difference between wear and particle detachment mechanisms which are shown not to be equivalent. Interface kinematics in dry friction is presented in the light of “velocity accommodation sites and modes”. The effect of sites and modes on friction and wear are also discussed.
1. Tribology today, a mechanical view
1.1. Introduction Tribology is the science of contacts. Contacts are found in all assemblies [ 1, 2 ]. Industrial contacts see normal and tangential loads which may vary between a few milligrams in computers rigid discs [ 31 to thousands of tons in modem turbines [4] and generate pressures of gigapascals [ 51 in roller and gear applications. The tangential loads are usually associated with velocities which vary between zero and hundreds of meters per second, which in turn generate shear rates of up to 10’ 6’. These pressures and shear rates are the highest noted in technology. Contacts are thus strained to the highest extent, and mechanical engineers, surface and volume physicists and chemists - tribology is multidisciplinary - are called upon everyday to invent new ways to face up to these challenges. The answers to these lie in the application of basic theories. 0043-1648190/$3.50
@ Elsevier ~uoia/Printed
in The Netherlands
Tribology means different things to different men, and there is still today a concensus to divide it in two; thick film lubrication which is analysed theoretically [4, 61 and the “rest” [7 - lo] which includes everything from mixed and boundary lubrication to dry friction and which apparently refuses any form of general theory or classification. The purpose of this paper is to show that the distance between lubrication and the “rest” is not as large as it is believed to be, and that tribology can be presented under one single heading centered around interface or third-body flow or continuity concepts and third-body load carrying capacity [ 11 - 141. This paper will thus focus on the gap between thick film lubrication and the “rest” and attempt to reduce it. To have a chance of success it is important, right from the start, to be fully aware that thick film lubrication has been studied by mechanical engineers with a good mathematical background and that the “rest” has been tackled by material scientists. Thus, on top of the difference in complexity of both fields (thick film lubrication is notably simpler than the “rest”) the argument must take into account both mechanical and material concepts. For mechanical engineers who want to extrapolate what they have learned from thick film lubrication [6] : (1) the interface or third-body is characterized by its rheology, composition is indifferent; (2) boundary conditions between first and third bodies must be specified, surface activity is indifferent; (3) the velocity difference between first-bodies is accommodated across the interface which means that the interface possesses its own velocity field and dynamics; (4) load carrying capacity can be calculated if boundary conditions and rheology are known; (5) generalities overshadow material differences. For material scientists: (1) the interface is characterized by its chemical composition, rheology is indifferent; (2) the interface is looked upon as a static identity strongly attached to the rubbing surfaces; (3) velocity accommodation is not considered; (4) the qualitative notion of surface protection is substituted to the quantitative load-carrying concept; (5) material differences overshadow generalities in tribology. Unfortunately, even though the differences between the mechanical and material outlooks are strongly accentuated here they nevertheless remain and have to be considered if the gap between lubrication and the “rest” is to be reduced. 1.2. Contacts Loaded contacts generate stresses between rubbing solids or first-bodies in both thick film lubrication and in the “rest”. First-body contact mechan-
31
TABLE
1
Basic equations
of contact
Equilibrium equation Constitutive laws Lame equations Solutions are produced contact conditions
mechanisms
theory aij.j + fl = 0 Oij = hO6ij + 2/.lEij
for different
/.LAx~+ (h + /J.)dB/dxl + fi = 0 e.g. Boussinesq, Hertz, Mindlin,
etc..
Contact mechanisms theory is adequafe for normal loads it is not so good when tangential are introduced through Coulomb friction It does not take into account: Nor does it
effects r=pP -time - interface
(or third body)
provide satisfactory conditions
effects
boundary
its have been studied theoretically for over 100 years by Boussinesq [15] and Hertz [ 163 and more recently by Johnson [ 171 and Kalker [ 181. Table 1 lists the basic equations and symbols needed to derive the contact mechanics theory {19]. It should be noted that in relating stress to strain the law eliminates time and thus velocity effects. In the same way the acceleration term is dropped from the equilibrium equation. Written in terms of displacements the Lame equation satisfies compatibility requirements. In two-body contacts the Lame equation yields stress and displacement fields. Normal stresses are obtained directly while a friction law is needed to calculate tangential effects, The Hertz problem is a classical example of twobody contacts. Three-body contacts can be approached by considering either rigid firstbodies and by focusing only on third-body deformation (low pressure bearing lub~~ation is a classical example of this form of three-body contacts [6]), or deformable first-bodies and by focussing simult~eously on first and third-body deformation (elastohydrod~amics [ 201 illustrates this form of contacts). 1.3. Thick film lubrication As noted earlier, thick film lubrication is the only third-body contact which is clearly understood and formalized to such an extent that lubrication theory is a common design tool today. Further, oils or more generally viscous or near-viscous fluids are undoubtedly the best third-bodies available. Let us therefore identify the basic concepts and assumptions in lubrication theory and see if they can be transposed to or help to formalise the “rest”. Table 2 lists the basic equations and symbols which are needed to derive the complete Reynolds equation which governs thick film lub~~ation
32
TABLE 2 Basic equations of lubrication theory
Equilibrium Constitutive loads
Uij
For H/L < 10e3
=
(p
+
h0)6ij
ap -=
a --
aZli p_
axi
ax2 i ax2
1
Boundary condition
no slip at the wall
u(0) =
u(h) =
u1;
w(0) =
WI
Velocity
Flow:
u=
w(h) =
u2;
2fJgij
+
i= 1,3
w2
;j!;y(y-h)/ +~y+u,
w=...
ap
Divpu+z=O with: h = h(x, z) 6~ WI
Pressure:
P=
h,2
Load and friction (For plain bearings)
P-
hoZ
MUI,
91
6,uU12b ii?(W)
F =
Theory gives P, F and u(y) where u(y) is the velocity accommodation
function
[7]. The derivation of the equation is of interest in this presentation and a simplified version of the process which considers only incompressible, isoviscous, inertialess and unidirectional laminar flow is presented. The constitutive law specific to viscous third-bodies, which relates stress to strain-rates and not to strain itself, is introduced in the equilibrium equation to yield the Navier-Stokes equation. In this case, the equilibrium equation, which is general to all bodies includes an acceleration term. With the assumptions listed above, the Navier-Stokes equations reduce under thin film conditions to the three pressure gradients listed in Table 2. In the coordinate system chosen x2 is taken across the film. The velocity fields u and w are obtained after integrating these equations twice and introducing
33
boundary conditions which assume that there is “no slip at the wall”. u and w are then introduced in the continuity equation which is general and which states that mass is preserved; it cannot be created or destroyed. It is the pendant in fluid mechanics of the compatibility requirement in solid mechanics. The last operation yields the Reynolds equation which, in the form presented, is a non-linear differential equation with two unknowns, the pressure p and the film thickness h, which is given by the contact geometry. h is introduced in the Reynolds equation which is then solved for p, the integral of which over the contact area yields the load-carrying capacity P. Reynolds’ equation is a flow continuity relation [ll]. It should also be noted that the Reynolds equation can solve both static ( U1 = U, = V, = 0) and dynamic contact conditions. 1.4. The “rest” The difference in velocity between the two first-bodies cannot be accommodated across a body of zero thickness and it will be therefore assumed that the interface is not immaterial and that it possesses all the attributes of matter. Thus the equilibrium equation of Table 2 must be satisfied independently of the composition of the interface. Further, whether it acts as a whole or in parts, the interface must have one or many constitutive laws. The mass conservation law must also be obeyed at least locally if not over the entire contact. Finally, there is some interaction between first and third-bodies which must be expressed in terms of boundary conditions. One can measure now, the distance between what is known and what is needed to solve in quantitative terms the conditions met in the “rest”. Much is known about three-body chemical composition following the many Auger, Esca and Sims campaigns [21] which have been conducted, but little is known about third-body rheology. Further, first-third body interactions have not been studied in terms of boundary conditions. 1.5. Conclusions Two-body contact theory is applicable to all of tribology. Third-bodies modify the contact boundary conditions. This modification can be taken into account by introducing either a friction law, which governs tangential stresses, and maintaining the normal stress distribution given by two-body contact analysis, or a third-body element of known rheology, with well formulated first/third-body boundary conditions and solving simultaneously first and third-body equations. Friction laws however do not describe the physics of the problem [ 221. A lot of work must be done before third-body rheology and first/third body boundary conditions are understood and before the mechanical engineer can bridge the gap and be as efficient and pertinent in the “rest” as he is in thick film lubrication. The load-carrying concept must be extended to include materials other than viscous fluids. Static load-carrying materials, i.e. spacers or materials
which can separate even heavily loaded surfaces are many. Most of them however are unable to insure load-carrying under relative motion. Those which can are known here as load-carrying agents.
2. The interface 2.1 I Data This discussion focuses on the interface and on the evidence that has accumulated in the last few years essentially through visualization f23]. Experiments have been conducted on numerous material combinations which include polymers [24] (PMMA, PC etc.), elastomers [25], metals [26 281 (various steels, aluminium alloys, titanium alloys, copper etc.), ceramics [29] (A1203, Sic etc.), chalk [30], glass, sapphire, carbon etc. under both continuous and reciprocating motion and all have shown that debris is produced quasi immediately; it is then trapped in the contact for some time and finally eliminated. Many events were recorded on films, and interface dynamics could therefore be followed in detail. The size, morphology, and sometimes the composition of the debris eliminated are significantly different from those of the particles when detached from the first-bodies. Evidence therefore indicates that the original two-body contact is rapidly changed into a threebody contact which is an altogether different problem. Surprisingly enough, three-body tribology took some time to be accepted, because rubbing surfaces are always thoroughly cleaned before they are examined and all of the loose third-body or debris is eliminated during cleaning.
Fretting has provided good evidence of third”body effects. Figure 1 is a picture of glass rubbing against steel. Observations made every few runs show that damage starts at the first strokes and continues as time goes on. Debris is trapped and the situation moved from a, two-body (glass against steel) to a three-body (glass, debris bed or third-body and steel) contact. The early passage from a two- to a three-body contact is general, The results presented in Table 3 were obtained with three materials; two identical steel alloys (materials I and II) but quenched and tempered from different temperatures (TT) and a stainless steel (material III). Their composition in wt.% is listed below. Figure 2 [31] shows the change in coefficient of friction vs. both the number of cycles and the displacement during a characteristic cyclic wear test. The data presented, known as the “friction log” because of its shape, corresponds to a test run with material I. The friction log is divided in 4 parts : (1) elimination of the “natural” screens which pollute the specimen surfaces;
35
cycles
Load Amplitude Frequency
: 500 N : 5 50 vrn : 1 Hz
Fig. 1. Two- to three-body
TABLE
glass rubbing
on steel - material
I.
3
Chemical
I II III
contacts
composition
(wt.%) of test materials
C
Si
Mn
s
P
Ni
Cr
MO
TT
0.378 0.378 <.03
0.33 0.33
0.38 0.38
<103
0.011 0.011
3.77 3.77 12.5
1.65 1.65 17
0.29 0.29 2.75
600 “C 200 “C
<103
(2) increase in specimen (or first-body) interaction accompagnied by the corresponding first-body structural changes (strain hardening for instance for metals); (3) debris formation and gradual passage from a two- to a three-body contact; (4) three-body contact characterized by a continuous formation and ejection of debris. Steady state conditions prevail. It should be noted that parts 1 and 2 and the first part of 3 describe the particle detachment phase (Section 11.1). The second part of 3 corresponds to the trapping and part 4 to the elimination phase. Figures 3 - 5 show that the shape of the log depends on the following.
Fig. 2. Friction log obtained with material I defined in Table 1 (see ref. 2, p. 24).
Load Amplitude
: 500
Frequency
:1
N : 2 50 pm
Fig. 3. Effect material II.
Hz
of specimen preparation
(or cleaning) on friction log (see ref. 2, p. 41) -
( 1) Surface preparation: in Fig. 3(a), the steel specimens (material I) were cleaned first with acetone then with alcohol, while in Fig. 3(b), they were cleaned with alcohol alone.
37
Mat&at
I
i
Load Ampiitude Frequency : 1 HZ
-0
Fig. 4. Friction log obtained with three different materials for identical running conditions (see ref. 2, p. 45).
(2) Materials: Fig. 4 shows the effect of tempering temperature (I and II) and composition (III). (3) Frequency: Figs, 5fa - cl, illustrate the effect of frequency. Figures 2 - 5 suggest that: (1) phase 1 is controlled by surface physics; (2) material properties (toughness) govern phases 2 and 3; (3) machine dynamics control particle ejection and as such first-body protection. It should be noted that in all cases, steady state three-body conditions are reached after roughly 1000 cycles. The rest of the test is clearly governed by third-body dynamics.
2.3. Conclusions Visualization has helped in understanding third-body effects under both continuous and reciprocating tests. The basic phenomena (particle detachment, trapping and elimination) were identical in both cases. Twobody contacts are significantly different from three-body contacts and the experimental approach must therefore be different in each case.
38 0.1 Hz
:ct
amplitude Fig. 5. Effect
: f 50 pm of frequency
on the friction
log (see ref. 2, p. 60) -
material
III.
3. Theory 3.1.
Interface tribology The importance given recently to the study of interfaces [32] suggests that, in the last 40 years, the study of tribology has moved: - from the tribology of volumes (or bulk material) where material A was run against material B in elementary machines and empirical friction and wear laws were produced; - through the tribology of surfaces which insisted on the role of surface activity in contacts and introduced basic scientific concepts in the field; - to the tribology of interfaces or third-bodies which concentrates as well on the role of the interface as on that of the first-bodies. This constitutes a fairly radical change in the understanding of both friction and wear. 3.2. Friction Lubrication theory defines the friction force as the integral of the shear stresses generated in the lubricant on the driving surface. Figure 1 and the explanations advanced in Section 2.2 indicate that in the “rest” the material in which friction is generated can vary during a test and that under steady-
39
state conditions, after 1000 cycles, friction is generated within the debris bed or third-body. Figure 6 shows a debris bed taken during a steel against steel fretting test. Both rubbing specimens were removed from the machine and the contact was opened just before the picture was taken. The picture shows that a thin powder bed, neither uniform in distribution or composition, separates both first-bodies. Further, no indication as to how friction is generated is given as no information concerning velocity accommodation transpires from the picture, 3.3. Parameters which govern friction Clearly, progress in understanding and modeling friction in situations such as those pictured in Fig. 6 requires powder bed dynamics studies [33 361 and an identification of both modes (how is friction generated) and sites (where is friction generated) of velocity accommodation. This point will be taken up later but it is important to note at this stage that the friction force is governed by the debris bed which is very sensitive to many outside influences such as humidity, or environment in general, machine dynamics, contact shape etc.
3.4. Wear It is common to talk of wear mechanisms [37] and to list adhesive, abrasive and fatigue wear etc. This is contradictory to the succession of events described in the third-body approach (Section 3) which suggests that debris is first detached from the first bodies, then trapped for some time in the contact and finally eliminated from the track. Adhesion, abrasion, fatigue etc. are therefore not wear but particle detachment mechanisms. The difference between the two is of great importance. Indeed, in the original view, it is only possible to work on surface effects to control wear. In the third-body approach, wear can be controlled at any one of the three stages of wear. Powder beds, debris and thus third-bodies have load-carrying capacity. In most instances the protection afforded by debris beds is bene-
-
1.7 pm
Fig. 6. Debris bed.
40
ficial [38] even though some beds are abrasive [ 391. These aspects are ignored in the original view. A particle, eliminated from the contact, can stay in the wear track and be recirculated in multi-pass systems. It only becomes a bona-fide wear particle when it is eliminated from the track. Geometry, which is not discussed in the original view, controls recirculation and thus wear. 3.5. Parameters which govern wear As seen in Section 3.4, wear can be controlled at any one of the three stages presented in Section 2.2. Control of the first stage of wear or control of particle detachment is discussed in many papers; anti-wear coatings, surface treatments etc. are known to be effective and are commonly used industrially [9]. This section will therefore concentrate on the two other stages, trapping and elimination. Clearly, the same parameters often affect both factors, therefore the discussion will be grouped. Particle dwell time, or time during which a particle is trapped in the contact, which by definition governs the load-carrying capacity, is not conditioned solely by particle composition but also by the contact mechanical environment. Let us briefly recall the mechanics of interface elimination and note that particles are expelled from the contact through acceleration effects or body forces such as gravity or centrifugal action; Poiseuille flow is governed by the pressure distribution generated in the contact through its load-carrying action; Couette flow is controlled by surface motion which can drag particles outside of the contact and momentum effects transmitted from the first-bodies to the particles. Some of the factors which control elimination through any one of the processes described above are as follows. (1) Contact dynamics: powder bed dynamics [33 - 361 is a very complex subject and broad generalisations are dangerous. Nevertheless a quiet, smooth running new machine will generally trap particles better than a noisy worn and shaky device. (2) Open and closed contact: a spherical bearing traps practically all of the particles detached during the first few strokes. If, as is the case with some polymers, the particles form a protective bed [40], elimination is practically stopped and bearing life is long. Inversely, the trapping capabilities of a ball on plane contact are limited. It should be noted that if the track in a pin-and-disc machine is grooved, particle trapping can be enhanced. (3) Contact shape: the longer the contact, in the direction of motion [31] the longer will be the particle dwell time in the contact. Wide contacts limit particle side leakage. (4) Re-entry conditions (a particular aspect of contact shape): Section 3.5 states that detached particles can be recirculated if, between successive passes, they are held in the track as a trace and trapped at each new pass. Trapping action necessarily depends on entry conditions and results show that, in a pin-and-disc machine for instance, a small chamfer on the pin eases trace recirculation in the contact.
41
(5) Roughness: a protective layer, whether static or dynamic, must separate the two rubbing first-bodies. Therefore, the volume defined by the roughness voids between peak and valley must be filled before steady-state conditions are met. This can take between 1 and lo5 cycles depending on the material and the contact conditions and thus control internal flow in the contact and elimination rate. (6) Third-body rheology: the consistence of the interface, whether it is made out of loose powders or tacky substances, with high auto-adhesion between its particles, obviously governs the rate of elimination from the contact [ 411. (7) Boundary conditions: the boundary conditions between third- and first-body govern Couette flow, momentum transfer, and thus elimination rate. Clearly, surface effects, surface energy for instance, determine boundary conditions. 3.6. Conclusions Many parameters are known to govern friction and wear. Some are mechanical, and their effects can only be understood in the light of thirdbody theory. This great number of parameters explains why it is impossible to extrapolate friction and wear results from one application to another [42] or from laboratory tests to an industrial situation. Unless great care is taken in the simulation of the real situation, there will always be some difference between two contact conditions. Dynamic effects, to mention just one of the parameters, have been identified in lubrication [43,44] and it is therefore no surprise to see them appear as governing parameters in the “rest”.
4. Velocity accommodation 4.1. Three- body con tat t Figure 7 is a simple three-body contact model which is described in detail in refs. 45 and 46, discussed in refs. 41 and 47 and briefly recalled here. It includes the two first-bodies or rubbing specimens, the two thirdbody/first-body interfaces or screens, which have their own specific composition and the third-body bulk. Recall that third-bodies can be either natural (debris) or artificial (solid lubricants for example). 4.2. Velocity accommodation The manner in which the difference in velocity between rubbing solids is accommodated across the interface is defined here as the velocity accommodation mechanism (see Section 3.2.3). Velocity accommodation mechanisms, which govern friction and wear, have been identified during visualization tests. Figure 7 shows that in a three-body contact, for a given abcissa, the velocity can be accommodated at five different sites Si which include the
42
00
b) Modes
a) Sites
Fig. 7. Velocity
M,
accommodation.
two first-bodies Si and Ss , the two screens Sz and S4, and the third-body bulk S3, and according to four different modes Mj at each site which are the elastic M,, the rupture M2, the shear Ma and the rolling M4 modes. Thus 20 velocity accommodation mechanisms can be encountered. Each mechanism is identified by one SiMj code. S3M3 signifies for instance that the velocity is accommodated in the third-body bulk through shear. First-body or bulk accommodation will not be discussed in this paper which is centered on third-bodies which include both third-body bulk and screens. 4.3. Screen accommodation S2 and S4 Thin films are known to govern surface adhesion. They deform elastically S?M, and shear S2M3 [48]. They break up in lumps S2MZ, form rolls S2M4, which in turn can develop into homogeneous films [ 491. Their accommodation possibilities are unlimited after shearing or fracture. 4.4. Third-body bulk accommodation Third-body bulk rheology is a very weak term attempting to express the very many different types of behaviour encountered in a contact interface. Third-bodies deform elastically SaMi like all powder beds. Further, they fracture S3MZ, shear S3M3 and roll S3M4 as witnessed [45] by the motion pictures taken through one of the rubbing specimens or first-bodies which showed that graphite films fractured and iron oxides Fez03 beds sheared.
4.5. Conclusions
Identification of the velocity accommodation mechanisms in different applications is a necessary step to advance from a qualitative to a quantitative third-body approach. Looking again to lubrication theory for guidance, friction is calculated (Table 2) from the velocity distribution across the film thickness. Third-body shear S3M3 is the only mechanism present which significantly simplifies the problem.
43
5. Conclusions The third-body approach is the necessary step to reconcile mechanical engineers and physicists in tribology. Before, the mechanical engineer was ill at ease outside of lubrication as his basic concepts of equilibrium [50] and continuity were not taken into account. Further, the extension of the load carrying concept, from lubrication to tribology in general, introduces a new line of reasoning which, as in lubrication, focusses attention on third-body properties. The extension of the third-body approach to include velocity accommodation mechanisms is the necessary step to go from the qualitative to the quantitative exploitation of the third-body concept. It is also useful as it clearly situates lubrication with respect to the “rest” and points to the relative complexity of both areas of tribology. Recall that 20 accommodation mechanisms were identified in the “rest” while only one exists in thick film lubrication. Modeling of a general tribology problem is still out of reach today. It is clear, however, that in the future each mechanism will have to be modeled individually along with the conditions of its triggering and the limits of its application. There is a tremendous amount of work ahead and it has to be done in good harmony by mechanical engineers, material scientists, specialists of both surface and bulk physics, and applied mathematicians.
Acknowledgments The first papers on the third-body approach go back 20 years and many people have contributed to it. Thanks are due to D. Play who worked and published on the subject in the seventies and to Y. Berthier who contributed significantly to its advance in the eighties. Many useful discussions were held with other colleagues of the Laboratoire de Mecanique des Contacts and particularly with D. Berthe and L. Flamand. Outside of the laboratory, I wish to acknowledge J. Lancaster’s contribution, generous encouragement and remarkable ability to draw on a vast experience and understanding of things tribological. None of this work could have been done without the financial help provided by the French Ministries of Research (M. Grandvalet) and Defence (M. Durouchoux) and by various industries. Their trust in this work brought it to fruition.
References 1 J. R. Atkinson, J. Charnley, J. H. Dowling and D. Dowson, The wear of total replacement hip joints in the human body - a topographical survey of the surfaces of worn acetabular cups. In Wear of Non-Metallic Materials, Mechanical Engineering Publications, London, 1978, pp. 127 - 133. 2 D. Scott, Wear - Treatise of material science and technology, Vol. 113, Academic Press, New York, 1979.
44 3 B. Bhushan and M. F. Doerner, Role of mechanical properties and surface texture in the real area of contact of magnetic rigid disks, ASME paper no. 88-Trib-39. (to be published in J. Tribol.). 4 0. Pinkus and B. Sternlicht, Theory of hydrodynamic lubrication, McGraw-Hill, New York, 1961. 5 B. J. Hamrock and D. Dowson, Isothermal elastohydrodynamic lubrication of point contacts, ASME/JOLT, 99 (1977) 264. 6 J. Frene, D. Nicolas, D. Berthe, M. Degueurce and M. Godet, Lubrification hydrodynamique: paliers et butees, Eyrolles, Paris, 1990. 7 J. A. Tichy, Modeling of dry and boundary lubricated contacts as seen from the hydrodynamicist’s perspective. In F. F. Ling and C. H. Pan (eds.), Approaches to Modeling of Friction and Wear, Springer-Verlag, New York, 1988, pp. 51 I 52. 8 F. P. Bowden and D. Tabor, Friction and Lubrication of Solids, Vols. I and II, Oxford University Press, Oxford, 1951 and 1964. 9 D. H. Buckley, Surface Effects in Adhesion, Friction, Wear and Lubrication, Tribol. Ser. 5, Elsevier, Amsterdam, 1985. 10 J. M. Georges, Microscopic Aspects of Adhesion and Lubrication, Tribol. Ser. 7, Elsevier, Amsterdam, 1982. 11 M. Godet and Y. Berthier, Continuity and dry friction: an Osborne Reynolds approach. In D. Dowson, C. M. Taylor, M. Godet and D. Berthe (eds.), Fluid Film Lubrication - Osborne Reynolds Centenary, Tribol. Ser. 11, Elsevier, Amsterdam 1987. 12 M. Godet, The third-body approach: a mechanical view of wear, Wear, ZOO (1984) 437 13 14 15
16 17 18 19 20 21 22
23
24
25 26
- 452.
H. Heshmat, 0. Pinkus and M. Godet, On a common tribological mechanism between interacting surfaces, STLE Transactions, 32 (1) (1989) 32 - 41. Y. Berthier, M. Brendle and M. Godet, Velocity accommodation in friction, STLE Tribol. Trans., 32 (1989) 4, 490 - 496. J. Boussinesq, Application des potentiels a l’btude de I’equilibre et du mouvement des solides Blastiques, Gauthier-Villars, Paris, 1885. H. Hertz, Miscellaneous Papers by H. Herts, Jones and Schott (eds.), Macmillan, London, 1896 (English translation). K. L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985. J. J. Kalker, Mathematical models of friction for contact problems in elasticity, Wear, 113 (1986) 61 - 77. A. S. Saada, Elasticity, Theory and Applications R.E. Krieder, Florida, 1983. D. Dowson and G. R. Higginson, Elostohydrodynamic Lubrication, 2nd edition, Pergamon, Oxford, 1977. D. H. Buckley, Surface Effects in Adhesion, Friction, Wear and Lubrication, Tribol. Ser. 5, Elsevier, Amsterdam, Chapter 2. R. Progri, B. Villechaise and M. Godet, Boundary conditions in a two-body contact formed by a rectangular polyurethane slab pressed against an araldite plane, Trans. ASME, J. Tribol. 107, (January 1985) 138 - 141. D. Play and M. Godet, Visuahsation of Chalk Wear. In D. D. Dowson, M. Godet, and C. M. Taylor (eds.), The Wear of Non-Metallic Materials, Mechanical Engineers, London, 1976, pp. 221- 229. L. Vincent and N. Dahmani, Interface dynamics in polymer friction. In D. D. Dowson, C. M. Taylor, M. Godet and D. Berthe (eds.), Interface Dynamics, Tribol. Ser. 12, Elsevier, Amsterdam, 1988. M. Godet, D. Play and D. Berthe, An attempt to provide an uniform treatment of tribology through load-carrying capacity, transport, and continuum mechanics, Trans ASME, J. Tribol. 102 (2) (April 1980). C. Chamont, Y. Honnorat, Y. Berthier, M. Godet and L. Vincent, Wear problems in small dispalcements encountered in titanium ahoy parts in aircraft turbomachines, 6th World Conf. on Titanium, Cannes, France, June 1988.
45 27 J. Sato, M. Shima and T. Sugawara, A fundamental study of fretting damage to glass using an improved apparatus, Wear, 106 (1985) 53 - 61. 28 J. S. Sheashy and G. R. Mount, The wear of copper in single pass sliding, Wear, 105 (1985) 235 - 246. 29 R. Trabelsi and Y. Berthier, Velocity accommodation between rubbing ceramics. Proc. 5th Int. Congress on Tribol., Helsinki, 1989, Vol. 4, pp. 48 - 54. 30 D. Play and M. Godet, Self-protection of high wear materials, ASLE Trans. 22 (1) (1979) 56 - 64. 31 Ch. Colombie, Y. Berthier, A. Floquet, L. Vincent, and M. Godet, Fretting: loadcarrying capacity of wear debris, Trans. ASME, J. Tribol. 106 (2) (3984) 185 - 194. 32 D. Dowson, C!. M. Taylor, M. Godet and D. Berthe (eds.), Interface Dynamics, Tribol. Ser. 12, Elsevier, Amsterdam, 1988. 33 R. S. Paranjpe and H. G. Elrod, Stability of chains of permeable spherical beads in an applied magnetic field, J. App. Phys. 60 (1986) 418 - 422. 34 H. G. Eirod, Granular flow as a tribological mechanism. In D. D. Dowson, C. M. Taylor, M. Godet and D. Berthe (eds.), Interface Dynamics, Tribal. Ser. 12, Elsevier, Amsterdam, 1988, pp. 75 - 89. 35 K. Craig, R. H. Buckhols and G. Domoto, Experiments on the rapid shear flow of metal powders. In D. D. Dowson, C. M. Taylor, M. Godet and D. Berthe (eds.), Interface Dynamics, Tribol. Ser. 12, Elsevier, Amsterdam, 1988, pp. 89 - 99. 36 B. J. Briscoe and P. D. Evans, The wear of polymers by particulate flows. In B. J. Briscoe and M. J. Adams (eds.), Triboiogy in Particulate Technology Adam Hilger, Bristol 1987, pp. 335 - 350. 37 J. T. Burwell, Survey of possible wear mechanisms, Wear, 1 (1957) 119 - 141. 38 Y. Berthier, Effet du comportement du troisieme corps sur i’usure des pafiers sees en mouvement alternatif, These Dr. Ing. INSA de Lyon, July 1982. 39 A. Misra and I. Finnie, An experimental study of three-body abrasive wear, Wear, 85 (1983) 57 - 69. 40 J. K. Lancaster, The formation of surface films at the transition between mild and severe wear, Proc. Roy. Sot. London, Ser. A, 273 (1963) 466 - 483. 41 Y. Berthier, L. Vincent and M. Godet, Velocity accommodation in fretting, Wear, 125 (1988) 25 - 38. 42 M. Godet, Extrapolation in tribology, Wear, 77 (1982) 29 - 44. 43 N. Abdul-Wabed, D. Nicolas and M. ‘I’. Pascal “Stability and unbalance response of large turbines”. ASME Trans., Lubr. Technol., 104 (January 1982) 66 - 75. 44 D. Bondoux, B. Bou-Said, G. Ferraris and M. Lalanne, Etude du comportement dynamique d’un prototype de pompe disphasique, M&z. Mate’riaux, Electr., 416 (May -June 1986) 38 - 41. 45 Y. Berthier, MQanismes et Tribologie, Th&e Dr.& Sciences, INSAlUCB Lyon, 1989. 46 Y. Berthier, Ex~rimen~l evidence for friction and wear modeling, fnt. Conf. on Wear of Materials, Denver, 1989 (to be published). 47 Y. Berthier, M. Brendle and M. Godet, Boundary conditions: adhesion in friction. In D. D. Dowson, C. M. Taylor, M. Godet and D. Berthe teds.), fnterface Dynamics, Tribol. Ser. 12, Elsevier, Amsterdam, 1988, pp. 19 - 25. 48 B. J. Briscoe, B. Scrutton and R. F. Willis, Shear strength of thin lubricant films, Proc. Roy. Sot. London, Ser., A 333 (1973) 99 - 114. 49 D. Tabor, The role of surface and intermolecular forces in thin film lubrication. In J. M. Georges (ed.), Microscopic Aspects of Adhesion and Lubricants, Tribol. Ser. 7, Elsevier, Amsterdam, (1982) pp. 651 - 677. 50 M. Godet, Mechanics versus or with materials in the understanding of tribology, Lubric. Eng., 40 (7) (1984) 410 - 414.