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 ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 P.O. Box 21 1, 1000 AE Amsterdam, The Netherlands Distriburors for rhe hired Srares and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY INC. 52, Vanderbilt Avenue New York, NY 10017, USA. ISBN 0-444-70487-6 (Vol. 12) ISBN 0-444-41677-3 (series) Q.' Elsevier Science Publishers B.V., 1988 All rights reserved. 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Printed in The Netherlands 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.