Interface Dynamics, Proceedings of the 14th Leeds-Lyon Symposium on Tribology

348 Pages·1987·14.648 MB·iii-vii, 3-395\348

by  D. Dowson, C.M. Taylor, M. Godet and D. Berthe (Eds.)

TRIBOLOGY SERIES 12
INTERFACE
DYNAMICS
edited by
D. DOWSON, C.M. TAYLOR, M. GODET AND D. BERTHE
Proceedings of the 14th Leeds-Lyon Symposium on Tribology,
held at The lnstitut National des Sciences Appliqukes, Lyon, France
8th-11 th September 1987
ELSEVIER Amsterdam - Oxford - New York - Tokyo 1988
For the Institute of Tribology, Leeds University
and
The lnstitut National des Sciences Appliqukes de Lyon
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VII
INTRODUCTION
The fourteenth Leeds-Lyon Symposium was - boundary conditions
held in Lyon on September 8-11th 1987. The - mechanisms
topic was “Interface Dynamics” and the call for
and 45 papers were presented, which left ample
papers specified that contributions could range
time for lively discussions.
from Interface Formation to Interface Elimina-
The social aspects were not neglected. The
tion. It included all factors, such as Contact
symposium started with the traditional ban-
stress fields, Interface rheology, Boundary slip,
quet, which included sweetbreads, and we con-
that controlled the passage from formation to
gratulate our friends from Great Britain for their
elimination. The topic was chosen for two rea-
courage in coping with some of the stranger as-
sons. First, it seemed timely: many tribologists
pects of French food. Europe in the making!
are today more or less explicitly concerned with
A concert was arranged on Wednesday night
interface action and not only with interface
and given by M. Michel Deneuve on a new in-
composition. The other reason was that some-
strument called “Cristal”, which amplifies
thing very specific had to be chosen to attract
sounds produced by rubbing glass rods. Music
delegates to Lyon after the July Institution of
ranging from Bach to Satie along with improv-
Mechanical Engineers meeting in London which,
isations was played and after a few minutes of
promised to be and was a great success.
surprise the audience settled down comfortably.
We were rewarded by the response of our
There were no cries of “heresy” during the per-
friends, who helped us contain the symposium
formance but a lot of questions came up after-
within the proposed topic. We were sorry to have
wards. A large barbecue followed by a sit-down
to turn down some very attractive papers which
dinner was arranged on Friday evening by Lab-
were definitely outside the scope of the call for
oratory staff. Songs, jokes and games lasted un-
papers. We were most happy with the number of
til early morning when the bus came to fetch
participants: 150 delegates from 23 countries.
those participating in the two-day week-end trip
Thirteen sessions were held on the following
to Alsace.
topics:
We were delighted to have a large delegation
- pictures in tribology from our friends from Leeds and we are looking
- fracture mechanics forward to joining them in September 1988 in
- lubricant rheology (2 sessions) Leeds for the XVth symposium and discussing
- powders “Tribological design of machine elements”.
- particle detachment
- load-carrying mechanisms (2 sessions) M. Godet
- stresses D. Berthe
- third-bodies (2 sessions)
3
Shear behaviour of an amorphous film with bubbles soap raft
model
D. Mazuyer, J.M. Georges and B. Carnbou
Wear and friction in boundary regime are often governed by the mechanical behavior of very thin
layers separating the two solids in sliding contact. Sometimes, these layers are amorphous.
Thanks to a bubble soap raft model, we simulate the sliding of two homogeneous rectangular
crystalline rafts separate? by an amorphous layer. The thickness and the length of this layer are
vsriable. The kinematic field of the plastic flow kith large displacements is experimentally
determine? in the same time as the record cf the tangential stress. Experimectal results show a
dependence of the sliding stress with the ratio thickness-length of the amorphous layer. At large
ratio, solid mechanical theories explain the behavior, but at small ratio, the effect of microsccpic
instabilities in the amorphous layer is dominant.
1 INTRODUCTION 2 EXPERIMENTAL PROCEDURE
In the boundary lubrication regime, a thin The experimental configuration is shown in
discontinuous film separates the sliding fig. 1.Air at constant pressure is blown througk
surfaces. This film is created by adhesion and short capillaries to produce bubbles at the
packing of prodxts coming from the surfaces in surface of a soap solutior. (surface
contact and the reaction with an anti-wear tension : b;”= 6.9 N.m-’ ). If only a
additive 111. In this case, the mechanical capillary is used we obtain a raft with E
action of friction makes these films amorphcus crystalline structure. With two capillaries, we
(21. In addition, the tribochemical films obtain an amorphous raft, after mixing. The
undergo high pressure, in some cases high crystalline structure is made of 2.3 ma diameter
temperature and high shear rates in the contact. bubbles, and the amorphous structure is a
These effects are responsible for a duality mixture (45-55) of 2.3 ard 1.6 mm diameter
between a brittle behaviour and a ductile one in bubbles respectively. It is known that the
wear of the film by delamination 121. mechanical properties for an amorphous layer do
Two mechanical properties, the compressive not vary with the ratio of bubble sizes over a
and shearing strengths are essertial and large range 191. We create two rectangular
related. It is well known that in the static crystalline rafts which adhere to two parallel
situation the plastic yield strength of a layer frames a,n, , a2fi, (fig. 1). They are about
compressed between two rigid solids depends cn twelve bubbles thick. We separate the two
three factors : plastic properties of the layer, crystalline rafts by an amorphous layer whose
ratio of thickness to length called the Hill length and thickness are varied. The frame
nurrber 131 and adherence between the layer and WzA,is then moved at a constant low speed
the substrates 121. (1 mm/s), parallel to the frame ~,fi,c ausing a
Concerning the shearing behaviour, shear where the displacement is imposed. During
microsliding experiments show that different the test (about 20 seccnds), the diameter cf the
tribochemical films have almcst the same elastic butble is decreasing very slowly, howevtr the
properties, however their anti-wear properties variation is too small to affect the mechanical
are different 14). We are looking if these behaviour. The stiffness Gf the amorptous layer
properties are not more related to a plastic or is much lower than that of the crystalline layer
a viscoplastic behaviour. In order to understard 1101, so the whole deformation due to the
the shearing process in a ductile amorphous film impose? displaceaent occurs in the amorphous
in large deformation, we use a bubble soap raft film. During the experiment, the tangertial
model with which Bragg visualized defects in force is transmitted to the fixed frame End
materials 151, 161, 171. Bubble rafts provide B continLously recorded. By filming the experiment
useful two dimensional model for the study of on a video tape system and by photographing the
solids. An attractive repulsive potential test at regular two seconds time intervals, we
between particles is due to the surface tensior. czn determine the displacements in the an.orphcus
of the soap solutior. and the pressure inside the layer with a resolution corresponding to lezs
bubbles and governs their behwiour 181. With a than half a bubble. We neglect all the effects
uniform size of bubbles, we get a crystalline c,f the roughness. The boundary conditions are
lattice ; with two different sizes approprietaly determined by the crystalline rafts (adherence
mixed an amorphous structure. of the layer to the substrates).
The aim of this paper is to study the
evolution of the plastic flow for a large range
of the thickness to length ratio of the layer.
4
Figure 1 : Bubble raft used to simulate a sliding process. The displacement
of the frameol,qcauses a shearing of the amorphous layer.
The tangential force F is transmitted and measured on the
frame IX,~.
5
-
3 RESULTS AND LISCUSSION effective elastic shear mcdulus G = 1,2 lO-'N/m
which is jn agreemer.t with the Experimental
We call h the thickness of the layer and L values calculated from an inder.tatior test 191.
its length. DLring this period, we observe few local
movements of the bLbbles. Then, the stress is
3.1 Results for a giver. layer still increasing niore gradually, in proportion
to the defamation and reaches a const.ar?t
The mechanical behaviour of an amorphous limiting value TI. Ar0ur.d this mean balue, we
raft of bubbles is governed by local cotice small perturbations due to the numerous
displa.cemer.ts of the bubbles resulting from two mechar:ical instabilities. For every test, we
simultaneocj p-ocesses described by Argcn 1101. have observed that for a given Hill number, F
First, there is what Argon calls a diffuse Ehear is propcrtional to L, and we obtain a unique
causing the rotation of clusters of 6 bubbles. 1imit.ing stress fl =: Fl/L.
Around these rotat.ing g,roups, there are small
amplitude trarslatione of lines of bLbbles. 3.2 Influence cf the Kill number cn the
These two locel trans formations create behzviow of the layer
aechar:ical instabilities whick are responsible
for a plastic strain. In order to describe the Figure 3 shc,ws the evolution c8f the sliding
behaviour in sliding, we define a two stress uith Hill numtser. It is interesting to
dimensional sheir stress 3 Eiven by the ratio observe thzt extrema occur for simrle values of
of the measured tangential force F t.o the 1engt.h h/L (respectively 0.15, 0.25, 0.5). Experiments
L of the layer. ., We assc,ciate to thips stress a made with cifferent sizes of bubtles give the
two-dimensiocal distortional strcin = U/h sarre curve.
where U is the.relative displacement of the twc,
a,n, fi2
frames and ciz end h the thickness of the
layer.
Hill Number h/L
Figure 7 : Influence of the Hill numter on the
plastic flow. Po is the limiting targential
stress for h/L = 1.
v
= (A ) : experj ment a1 points.
Shear strain U/h
We can distinguish two regions in the curve
(fig. 3) : a first for h/L greater than 0,25 acd
Figure 2 : Mechanical behaviour of the sliding E second for k/L less than 0.25. We later show
airorphous layer. that if h/L is greater than C.2E;, the plastic
A : the tangential stress Z is beha.viour can te explained ty the continuum
increEsing in porportion to the deformation. solids mechanics tut at h/L less than C.25, the
B : the tangential stress f is defects in the arrc'rptous layer are dominant.
reaching a limiting value characteristic fror.
- >
the plastic flow. 3.2.1 h/L 0,25
Figure 2 shows a typic21 record cf the WE visuzlize in figure 4, the displacement:
force F versus displacemert U. A t fir$t, the field, at the beginning of the linear increase.
stress increases in proportior. to the strain. In of the stress according to the sk.ear strain
sFite cf linearity this str,ain is not completely (figure 4A) and when the stress reaches its
reversible, however it is possible to define E limit (figure 4E).
"pseudo" elastic shear nloduluz characteristic These pictures are cbtained by
of small str2ins behaviour. Then we obtain an nhotographing the experiment, at regular time
6
,IA
=
Shear strain U/h
Figure 4 : Description on the evolution of the kinematic field
of the plastic flow, by superimposition of two
successive pictures of the layer, parallel to the
curve sliding stress versus shear deformation.
(A) : the tangential stress begins to increase
slowly in proportion to the displacement. The shear
band 2 appears between two lateral zones 1 and 3
respectively locked relative to the framew,qand the
frame ciz f$
(B) : the limiting stress ilis reached. The thickness
of the shear band increases while the thickness of the
two lateral zones (1, 3) remains constant at five
bubbles, the slip line becomes horizontal.
7
intervals (every two seconds) and by 3.2.1.1. h/L > 0.5
superimposing the photographs for two
consecutive times. Thanks to this visualization, We call h, the thickness of the shear
we can define three zones in the amorphous band,dh,is a normal elementary displacemect due
layer, when the tangential stress begins to to the sliding inside the plastic zone. As h
increase zlowly in proportion to the remains constant this small displacement must be
displacerrent. equilibrated by the elastic deformation of the
The first zone is close to the fixed two lateral zones. This displacement then causes
frame o,O, .Most of the bubbles are here a small variation of the normal stress given
stationnary and some of them have very small by[dh,/(h-h,)].E = do;,
disp1acement.s. If we regard the an:orphous layer We checked that h, doesn't depend on the
in a refereme moving with the speed of the Hill number, so this equztion shows that
lower crystalline raft, we observe a zone close a;, decreases if h increases and vice versa.
to the mobile crystalline raft where the bubbles The geometrical representation of the stress
don't move relative to the moving frawe. Between tensor with the evolution of f,(fig.5 A'- B')
t,hese two regions, there is a middle zone wl-.ich shows that an increase of q, is related to a
is atout ten bcbbles thick for every Hill decrease of the sliding stress , which
number. Here, the bubbles have displacement of proves that if h/L > 0.5, tlvaries in the same
large amplituc'e relative to both the fixed acd way as h/L ratio.
the mcsving frame. These motiocs are numerous
and discrdered. We zlso notice that the 3.2.1.2. 0.25 < h/L < 0.5
direction caf the bznd depenc's c.n the K i l l number
and corrrspocds to,a slip line. The shear bard, The shear band hits the upper crystalline
where the plastic deformatior. is localised raft, therefore since the crystalline raft is
>
crosses the whole layer if h/L 0.5 and hits much more rigid than the amorphous structure, we
<
one of the crystalline rafts wher. h/L 0.5. impose a sliding in the horizor.ta1 direction.
These different configurations are related to
differences in mechanical behaviour. Further in The sides are cot free anymore and a
the test, wher. the sliding streEs reack-,es its normal stress waZ can appear. The description by
limit, we find again the three zoces that WE a Mohr representation in Fig. 5 C' shows that as
hzve just described (figure 4B) with the sare the sliding direction is horizontal, P, must
el
characteristics. But, the rr.iddle z.or,e increases reach the plasticity criterion. is then
its thickness and its direction becomes greater than for Hill number more than 0.5. From
k-orizontal, while the thickness of the two continLurr1 solid mechenics, we can find again the
lateral zoces is decreasing to a minimwn value experimental curve cf the evolution of the
of abcut five bubtles. We note that aromc' the limiting stress for Hill number great,er than
sides c.f the layer, the paths c.f the bubbles are 0.25.
not in E straight line but circular.
Green 1111 observed such pher.omena in a 3.2.2. h/L < 0.25
plastic sheared junction for which the Hill
number is less than 1.47 and divided the By coL*nting the instabilities in the
junction into a piddle zone ur.dergoing a pure layer,we plot the distribution of instabilities
shearing surrobnded. by two lateral zones in pure in the amorpkous film (Fig. 6).
torsion. Frorr. our experimental results comtined This curve confirms the preceeding results
>
with a simFle mechanical approach based cn a for h/L 0.25, particularly the existence of
Mohr dezcriptioc, we can Explain the evolution two locked zones respectively close to the fixed
of the stress f, chxacteristic from the and the moving frame zurrounding a middle zone
plastic flow for kligh kill nurrber. where the bubbles have disordered and numerc.us
We first define, for the bubble rafts, movetxer.ts. But if h/L is less than 0.25 we
a plasticity criterion ty : observe a change in the distribution of the
u tg'P+ c = r ,w here c is the cokesion of the instabilities : the distribution is not centered
rr.ateria1 (c = 17.8 K/m for our bLbble scap around x = h/2 anymore and the number of
rafts) and (r is a normzl stress associated kith instabilities doesrt't stop increasing frorr. the
a recessary reorganizing of the butbles inside fixed frame to the moving frame. These numerous
the sliding layer in large displacerr.ents. \re n:icroscopic instabilities are responsible for
represer.t the stress field by the tensor bour.dary effects (large deformatioc of the
( 5T 1 97 % ) azsuming that the stress field is sides) which didn't occur for high Hill number.
uniform in the layer except at its lateral We cannot explain the mechanical behaviour
sides. Displacements in the r.ormal direction are with the theory used for Hill number grezter
r.ot possible because of the rigidity of the than 0.25. For small Hill number, the thickness
crystalline rafts 191 so the aecharical of the layer corresponds to the dimensions of
instabilities can only cccur with an increase of the clusters of bubbles around which the local
.
the ncrrnal stress q, Depending cn whether hjL instabilities occur. Therefore, the effects due
is greater than 0.5 or not the shear band to these motions are dominant and the plastic
crosses the whole layer or hits the fixed flow is not only dependant on the Hill number
crystalline raft. anymore but also on the thickness h.
c
8
'
I I
A ' B' C'
I i
Hill Number h/L
Figure 5 : Mohr representation of the stress tensor inside the
layer for different configurations to describe the
evolution of ZL for high Hill numbers (A', B', C').
(A') : h/L = 1 : Reference configuration.
(B') : 0.5 < h/L < 1 : the normal stress increases and
elbecomes smaller than for h/L = 1.
(C') : 0.25< h/L CO.5 : the normal stress appears,
the slip line is horizontal then 'E is greater than
1
for 0.5< h/L< 1.
9
In addition, for large Hill number the Bibliography
deformztior. is localised in a shear tar.d with a
privilegied direction : this process is related Ph. KAPSA, "Etude microscopique et
to a minimization of the er.ergy. For low Hill macroscopique de l'usure en regime de
number, the thickness is too small and the slip lubrification limite", Th&se d'Etat 8219,
line is necessarily horizontal, so there is ar Universitd Claude Bernard Lyon, p. 54
increase of the deformation energy, which can (1982).
explain the steep increase of the limiting shear J.M. GEORGES, J.M. MARTIN, "Quelques
<
stress if h/L 0.25. relations entre les structures et les
propridtes mdcaniques des films de
lubrification limite", Eurotrib 85,
VO~. 11, 5.2.1, p. 8-10.
HILL, "Mathematical theory of plasticity",
Claredcn Press, Oxford, p. 226-235
(1950).
A. TONCK, Ph. KAPSA, J. SABOT, "Mechanical
behavior of tribochemical films under a
cyclic tangential load flat-contact" ,
Trans. ASME, vol. 108, p. 117-122
(1986).
L. BRAGG, J.F. NYE, "A dynamical model of
a crystal structure I", Proc. Roy. SOC.,
A190, p. 474 (1947).
L. BRAGG, W.M. LOMER, "A dynamical model
i of a crystal structure II", Proc. Roy.
SOC., A.196, p. 171 (1949).
W.M. LOMER, "A dynamical mcdel of a
*.12 crystal structure III", Prcc. Roy.
SOC., A. 196, p. 182 (1949).
0
A.S. ARGON, L.T. SHI, "Simulation of
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 plastic flow and distribLted shear
relaxation by means of the amorphous Bragg
x/h
bubble raft", Conf. Proc. Met. SOC.
AIME, p. 279 (1982).
J.M. GEORCES, G. MEILLE, J.L. LOUBE?',
Figure 6 : Distribution of instab-iliti es in the A.M. TOLEN, "Bubble raft mcdel for
amorphous layer for h/L = 0.5 ( ) ard for indentation with adhesion", Nature, vol.
h/L = 0.25 t---*). 320, p. 342-344 (1986).
x/h = C : bcundary between the layer arZ the A.S. AF-GON, H.V. KUO, "Plastic flok in
fixed crystalline raft. disordered bcbble raft", Materials
x/b = 1 : boundary between the layer and the science and Engineering, p. 107 (1979).
moving crystalline raft. A.P. GREEN, "The plastic yielding of metal
junctions due to comtBined shear and
4 COICLUSION pressbre", Jourr a1 of the Mechsnical
Physics of solids, vol. 2, p. 202
With the bubble soap raft mcdel, we could (1954).
determine the shear behaviour of an amorphous
layer adi-ering to two rectangular crystalline
rafts. For large disFlacements the tangential
stress reaches a ccnstant limiting value z, ,
which chatacterizes the plastic flow of the
layer and dependE on the Hill nunber. For large
>
Hill nun,ber (h/L 0.25) a mechanical apprcach
based on the cbservatior. of the kinematic field
cf the plastic flow can explain the behaviour of
the layer. But for small Hill nLmber, the
macrosccpic behsviour of the amorphous film is
gcvernc-d by physic21 effects due to the motions
of small clusters of five cr six bubbles.
5 ACKNOhLEDGMENTS
We are grateful to G. MEILLE for his help
during this work.