Mechanics of Coatings (Tribology Series 17)

MECHANICS OF COATINGS TRIBOLOGY SERIES 17 MECHANICS OF COATINGS edited by D. DOWSON, C.M.TAYLOR and M. GODET Proce...

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MECHANICS OF COATINGS

TRIBOLOGY SERIES 17

MECHANICS OF COATINGS

edited by

D. DOWSON, C.M.TAYLOR and M. GODET Proceedingsof the 16th Leeds-Lyon Symposium on Tribology held at The lnstitut National des SciencesAppliquees, Lyon, France 5th 8th September 1989

-

ELSEVIER Amsterdam -Oxford

- New York -Tokyo

1990

For the Institute of Tribology, Leeds University and The lnstitut National des Sciences Appliquees de Lyon

ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 P.O. Box 211,lOOOAE Amsterdam,The Netherlands Distributors for the United States and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY INC. 655Avenueof the Americas NewYork, NY 10010

ISBN 0-444-88676-1(VOI. 17) ISBN 0-444-41677-3 (Series) QElsevier Science Publishers B.V., 1990 All rights reserved. No part of this publication may be reproduced, stored i n a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./Physical Sciences and Engineering Division, P.O. Box 1991, 1000 BZ Amsterdam, The Netherlands. Special regulations for readers i n the U.S.A. - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be in the U.S.A. All other copyright questions, including photocopying outside of the U.S.A., should be referred to the copyright owner, Elsevier Science Publishers B.V., unless otherwise specified. No responsibility is assumed by the Publisher for any injury and/or damage t o persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained i n the materials herein. pp. 15-26, 63-72, 183-192, 295-302, 337-350, 371-378: copyright not transferred. This book is printed on acid-free paper. Printed in the Netherlands.

CONTENTS Introduction Epitaph Session I

Session I1

Session I11

Session IV

Session V

Session VI

Session VII

ix xi

Conference themes On the elastic constants of thin solid lubricant films M.N. GARDOS Frictional properties of lubricating oxide coatings M.B. PETERSON, S.J. CALABRESE, S.Z. LI and X.X. JIANG Elastic and viscoelastic analysis of two multiply layered cylinders rolling over each other with coulomb friction J.J. KALKER Theory Analysis of damage mechanism using the energy release rate P. DESTUYNDER and T. NEVERS Integrity of wear coating subjected to high-speed asperity excitation F.D. JU and J.-C. LIU Coating design methodology M. GODET, Y. BERTHIER, J.-M. LEROY, L. FLAMAND and L. VINCENT Experiments Reduction in friction coefficient in sliding ceramic surfaces by in-situ formation of solid lubricant coatings A. GANGOPADHYAY, S. JAHANMIR and B.E. HEGEMANN In-situ engineered oxide coatings H-S HONG and W.O. WINER A morphological study of contact fatigue of TiN coated rollers H.S. CHENG, T.P. CHANG and W .D. SPROUL Soft coatings 1 A full solution to the problem of film thickness prediction in natural synovial joints D. DOWSON and J. YAO Finite element analysis of EHD lubrication of rubber layers A. GABELLI and B. JACOBSON Analyses of shear deformations between cylinders with and without surface films J.W. K A " E L and T.A. DOW Solid lubricants Effects of microstructure and adhesion on performance of sputter-deposited MoS, solid lubricant coatings P.D. FLEISCHAUER, M.R. HILTON and R. BAUER Role of transfer films in wear of MoS, coatings S. FAYEULLE, P.D. EHNI and I.L. SINGER Assessing the durability of organic coatings M.J. ADAMS, B.J. BRISCOE, A.L. CARTER and P.J. TWEEDALE Rough coated surfaces Effect of surface coatings in a rough normally loaded contact Ph. SAINSOT, J.M. LEROY and B. VILLECHAISE Elastic behaviour of coated rough surfaces J.I. McCOOL Hardness Scratch tests on hard layers A.G. TANGENA, S. FRANKLIN and J. FRANSE A theoretical approach of hardness distribution in rigid perfectly plastic coated materials M.L. EDLINGER and E. FELDER Damage mechanisms of hard coatings on hard substrates: a critical analysis of failure in scratch and wear testing R. REZAKHANLOU and J. von STEBUT

3 15

27 37

45 53

63 73

81

91 I03 111

121 129

139 151

157 169

175

I83

VI

Session VIII

Session IX

Session X

Session XI

Session XI1

Session XI11

Session XIV

Multilayer theory Stress determination in elastic coatings and substrate under both normal and tangential loads J.M. LEROY and B. VILLECHAISE A survey of cracks in layers propelled by contact loading D.A. HILLS, D. NOWELL and A. SACKFIELD A statistical approach for cracking of deposits : determination of mechanical properties A. MEZIN, R. RAMBUARINA and J. LEPAGE Young’s modulus Young’s Modulus of TiN and T i c coatings L. CHOLLET and C. BISELLI A method for in situ determination of Young’s modulus of deposits J.P. CHAMBARD and M. NIVOIT Biomechanics Use of a polyelhylene coating to improve the biotribology of a hemiarthroplasty implant M. LABERGE, G. DROUIN, J.D. BOBYN and C.H. RIVARD Comparison of theoretic 31 and experimental values for friction of lubricated elastomeric surface layers under transient conditions J.R. GLADSTONE and J.B. MEDLEY A preliminary investigation of the ‘cushion bearing’ concept for joint replacement implants D.D. AUGER, J.B. MEDLEY, J. FISHER and D. DOWSON Soft coatings 2 The influence of elastic deformation upon film thickness in lubricated bearings with low elastic modulus coatings D. DOWSON and Z. JIN Frictional mechanism in uncoated and zinc-coated steel sheet forming - theoretical and experimental results V. SAMPER and E. FELDER Effect of nitrogen ion implantation on the friction and wear properties of some plastics M. WATANABE, H. SHIMURA and Y. ENOMOTO Failure mechanisms The effect of continuous Au sputter deposition on the enhancement of growth of transfer particles K. HIRATSUKA, L.L. HU and T. SASADA Elasto-plastic finite element analysis of axisymmetric indentation using a simple personal computer M. GUEURY, P. BAGUR, R. REZAKHANLOU, J. von STEBUT Oxides The oxide film and oxide coating on steels under boundary lubrication Y-W ZHAO, J-J LIU and L-Q ZHENG New tools and models A survey of research in acoustic microscopy applied to metallurgy J. ATTAL, R. CAPLAIN, H. COELHO-MANDES, K. ALAMI and A. SAIED Detection of interface defects in layered materials by photothermal radiometry M. HEURET, E. VAN SCHEL, M. EGEE and R. DANJOUX A low cycle fatigue wear model and its application to layered systems. A.G. TANGENA

195 203 209 217

223

233

24 1 25 1

263 27 1 28 I

289 295

305

315 323 329

vii

Session XV

Session XVI

Session XVII

Session XVIII

Session XIX

Session XX

Wear 1 The inter-relationship between coating microstructure and the tribological performance of PVD coatings S.J. BULL and D.S. RICKERBY Identification and role of phosphate coatings for tribological applications G.T.Y. WAN, R.J. SMALLEY and G. SCHWARM Protective coatings for application in seawater M.F. LIZANDIER, E. LANZA, A. SEBAOUN, A. GIROUD and P. GUIRALEDENQ Wear 2 Lubrication influences on the wear of piston-ring coatings J.C. BELL and K.M. DELARGY Wear behaviour of Cr2 0 and Al, 0, plasma sprayed coatings under lubricated and non-lubricated conditions R. VIJANDE, F.J. BELZUNCE, J.E. F E R N ~ D E Z , M.C. PEREZ and A. RINC6N Viscoelasticity Influence of viscoelastic parameters on coated bearing behaviour Y.T. SUN, B. BOU-SAID and B. FANTINO Hard coatings Morpholigical aspects of the friction of hot-filament-grown diamond thin films P.J. BLAU, C.S. W S T , L.J. HEATHERLY and R.E. CLAUSING Factors affecting the sliding performance of titanium nitride coatings F.E. KENNEDY and L. TANG The mechanism of failure of coatings in roller tests J. VIZINTIN Deformation Measurements of thin films adhesion and mechanical properties with indentation curves J.L. LOUBET, J.M. GEORGES and Ph. KAPSA Soft metallic coatings in metal forming processes P. MONTMITONNET, F. DELAMARE, E. DARQUE-CERETTI and J. MSTOWSKI Deformation and fracture of hard coatings during plastic indentation D.M. ELLIOTT and I.M. HUTCHINGS Coating evaluation Coating evaluation methods : a round robin study. H. RONKAINEN, S. VARJUS, K. HOLMBERG, K.S. FANCEY, A.R. PACE, A. MATTHEWS, B. MATTHES and E. BROSZEIT The effect of dynamic loads in tribometers - analysis and experiments H. HESHMAT Written contributions List of authors List of delegates

337

35 1 359 371

379

389

399 409 417

429 435 445

453 465 475 481 489

This Page Intentionally Left Blank

IX

INTRODUCTION The Sixteenth Leeds-Lyon Symposium on Tribology was held at the Institut National des Sciences AppliquCes de Lyon from the 5th to the 8th of September 1989. It was dedicated to the memory of the late Professor Daniel Berthe who had contributed much to earlier symposia in Lyon. As all other Leeds-Lyon Symposia, it discussed only one topic which this time was "Mechanics of Coatings". The subject was chosen because it seemed timely to bring together men of different disciplines connected with coatings to find ways of extending the industrial use of these coatings particularly where tribology was concerned. It was indeed necessary to get mechanical engineers, surface and volume physicists, theorists and experimenters, applicators and users together to measure how coatings could mean different things to different men and also to note the different criteria retained for the qualification of coatings in each speciality. It was too much to expect that a single symposium could get these specialists to agree on a given course, it was however reasonable to hope that each would take stock of that difference and in time take steps to reduce it. We hope to have met that goal. Some papers were invited and the "Call for Papers" was a great success. A Review Board was set up to examine the abstracts. Close to 60 papers were programmed which meant that triple sessions had to be held on one of the three days of the symposium. These papers were dispatched in 20 sessions which discussed theory, experimental data, hard and soft, smooth and rough coatings, solid lubricants and oxides, coating properties and coating property measurements, wear and failure mechanisms of coatings, coatings in bio-mechanics and coating evaluation. The meeting was attended by more than 150 delegates from 17 countries. This is an all time high for Lyon and of course a great encouragement to all of the organisers. We were, as always on these occasions, delighted to host a large and very active contingent from Leeds headed by Professor Dowson and Dr. Taylor. Imperial College was also very present both inside and outside of the sessions and it was very rewarding to see both familliar and new faces in such large numbers. After the opening session, on Tuesday, September 5th. delegates were taken to VilliC-Morgon where the conference banquet was held. We were priviledged in having Mrs Daniel Berthe with us. The dinner was prepared by two well known Chefs of the Lyon area, MM. Troump and Marguin and the wines were chosen by a special commission set up by the wine experts of the Laboratoire de MCcanique des Contacts. Some commotion was caused as one of the courses was rather more "Lyonnais" than expected but we hope that those who were surprised when they found out what they had eaten have since forgiven us. Water jousts were organised on Thursday evening for the delegates at Givors which is 25 kms south of Lyon. Jousters mounted, one at a time, on the pontoon of a small flat bottomed boat. Two boats come side by side and each jouster tries to "duck" his opponent by pushing him overboard with a 5 to 7 meter lance. The fight takes place in a basin which was originally part of the port of Givors on the Rhone and which was walled in relatively recently. This local form of tournament reaches back to roman times and the Givors club has been at it quite a while as it celebrated its 100th anniversary in 1986. The performance was followed by a reception given by the Lord Mayor of Givors. AU of this was accompanied by music which punctuated each ducking or lance breaking with traditional energetic tunes. Thanks to Andy Olver of Westland Helicopters, the joust spirit was carried over the next day during the Friday evening barbecue organized by the laboratory technicians. Minor changes in the

X

rules had to be introduced as delegates served as both boats and jousters and brooms were used instead of lances. The Saturday trip to beautiful Auvergne took us to Ambert, la Chaise-Dieu and le Puy and marked the end of the 16th symposium. None of this could have happened without a heavy commitment of all members of the Laboratory. To all, thanks are due for their energy, their good humour and inventiveness. We are looking forward to going to Leeds to attend the XVIIth symposium on Vehicle Tribology. Maurice GODET

xi

Professor Daniel Berthe

The 16th LeedsLyon Symposium was, dedicated to our friend and colleague Professor Daniel Berthe who died in February after a long illness. All of the members of the Laboratoire de MCcanique des Contacts de 1’INSA along with many of our friends from Leeds and elsewhere wanted to honour his memory and chose this way of doing it. It seemed fitting, as he contributed greatly to many of the earlier symposia as one of the co-editors of the Proceedings and as an organizer of the event itself when it was held in Lyon. He joined the Laboratory in 1968 and worked from the start on roughness effects in hertzian contacts and on many of the problems such as cavitation and fatigue associated with roughness. A man of great intuition and tremendous finesse, he tackled that very difficult subject in ways both orikinal and productive. Discrete, curious of all things scientific, he welcomed discussions with each one of us and helped us all in the formulation of our ideas and in the advance of our research.


SESSION I CONFERENCE THEMES Chairman :

Professor M. Godet

PAPER

(i)

On the elastic constants of thin solid lubricant films

PAPER

(ii)

Frictional properties of lubricating oxide coatings

PAPER

(iii)

Elastic and viscoelastic analysis of two multiply layered cylinders rolling over each other with coulomb friction


3

Paper I (i)

On the elastic constants of thin solid lubricant films M.N. Gardos

The literature was searched to find numerical values of elastic constants for layered hexagonal lubricants (e.g., graphite, MoS2, NbSeg, GaSe and InSe) and for selected hardcoat underlays such as TiN and Tic. The data are critically reviewed for accuracy and usefulness to a tribologist. An attempt is made to correlate the electronic and crystal structure of selected hexagonal solid lubricants with the degree of ionic-to-covalent bonding that both characterizes the crystal systems and determines the magnitude of their elastic constants. The basic intent is to provide the appropriate Young's modulus ( E ) , shear modulus ( G ) and Poisson's ratio ( u ) data to computer diagnoslicians, who need t o substitute realistic values into their iterated programs predicting the actual concentrated contact stresses associated with hardcoat/softcoat layered systems. 1

INTRODUCTION

Under concentrated contact conditions, e.g., in rolling element bearings o r gears, modifying the bearing surfaces by the addition o r hard and sofL lubricant coatings will alter the size and distribution of the contact stresses. It is well-established that under static loading, the region of maximum Hertzian stresses is below the surface o r an uncoated bcaring material. The effect of high friction/ traction and normal forces at the surface is to increase the magnitude of the maximum shear stress and raise its region of occurrence closer t o the contact surface (Pig. 1). Fedorchenko (1) showed that when an increasing number of hard inclusions are embedded in the surface of a softer matrix, and each progressively larger set carries the same normal load, the peak octahedral stress will a l s o be broughL toward the surface (Fig. 2). As the number and size of the inclusions grow, one recognizes that the upper limit is reached when a uniform, high elastic modulus hardcoat of a given thickness is formed. Superimposing a solid lubricant softcoat on top of an already hardcoated bearing surface will further alter the size and the location of the maximum (modified) HerLzian stress region. A thin coating of material more elastic than its substrate will lower the apparent elastic modulus in the contact zone and lower the maximum stress. Reversibly glassifled lubricating oils in concentrated contacts achieve the same erfect. The obvious advantages of hardcoat/oil and hardcoat/ softcoat combinations have been well-documented in the literature (1 through 6 ) . A large number of investigators brought forth models which represent, static (2 Lhrough 8 ) and dynamic-sliding (9,lO,ll) conditions. These models predict the depth, magnitude and distribution of stress fields as a function of substrate/coating(s) elastic constants and

coating thicknesses. The constants of particular interest are the Young's modulus ( E l , the Poisson's ratio ( u ) and, occasionally, the shear modulus (G). By the use of computers, the predictive models can iterate a variety of likely combinations, depending on arbitrarily selected, single and compound values of E, G, and u. However, accurate prognosis of the real contact sLresses associated with a given moving mechanical assembly, e.g., meshing steel gears coated with an 2 3 urn thick layer of reactively ion-plated TiN and further covered with 400 nm of sputtered MoS2. requires the subsLitution of accurate elastic constants to obtain an exact solution. These data become an important part of predicting the wear life of each assembly component. A search of the tribology literature for reliable values of E, G, and u for hard and soft solid lubricant films resulted in very few pieces of data. However, recent papers from basic science and optical-electronic-magnetic device coatings literature have established the basis for the estimation of elastic constants for layered hexagonal solid lubricant species such as graphite, MoS2, NbSe2, InSe and GaSe as well as for their hardcoat underlays, e.g., Tic and TiN. The present work is intended as an overview of elastic constant fundamentals and data on selected soft and hard lubricant layers. An emphasis is placed on the highly anisotropic nature of layered-hexagonal solid lubricant materials, especially those in the thin film form, where the basal planes of the crystal 13 tes are more-or-less aligned in the plane of sliding o r rolling.

A brief overview of micromechanical techniques employed to measure elastic constants i s also given. Nearly all of these measurement techniques have been used for metallic layers and hardcoats only. The application of these techniques are suggested

4

0.2

0 Y

0.1

-0.1

ROLLING DIRECTION

0.2

0.1

0 Y

-0.2

-0.3

-

-0.1

-0.2

-0.3

UNDER STATIC LOAD

0.2

0.1

0 Y

-0.1

-0.2

-0.3

OCTAHEDRAL STRESS

Fig. 1 Concentrated contact stress contours under various friction/traction conditions; shaded areas represent the region of maximum stresses. for hardcoat/softcoat combinations, where the soft lubricant layers consist of sputtered films or layers transferred from se1f- lub ricat ing compo sites .

Pig. 2 Distribution and depth of maximum subsurface stresses, as influenced by a progressively large number of hard surface inclusions from (a) to (c), under the same total load; from (1). 2

THEORY AND PHACTrCE OF ELASTIC CONSTANT MEASUREMENTS

2.1 A Brief Overview of Elasticity Fundamentals

As described in Belenkii, et al's excellent treatise (131, the relationship between the stress and strain tensors in the weak (elastic) deformation of a solid is known as Hooke's Law:

5

where dik and ulm are the synunetric, second rank stress and strain tensors, respectively. The fourth-rank tensor Ciklm is known as the elasticity tensor and its components are called the elastic moduli o r elastic constants. A completely isotropic solid has two elastic constants (E and G ) , cubic crystals have three constants (C11, C12, C44) and crystals with hexagonal synunetry typical of layered hexagonal materials such as graphite and MoS2 are described by five elastic constants.

The elastic constants for the hexagonal synunetry are: 1. 2. 3. 4* 5.

It is shown in (13) that c13

u =

-c11

f

(2) c12

where u represents the change in the dimensions of a hexagonal crystallite in the plane of its layer on application of pressure along the synunetry axis. One can also imagine u of a hexagonal crystallite as the thinning of the platelet as it is being elongated by tensile forces within the basal plane. This interesting symmetry becomes obvious when we note that u may be generally defined for a uniaxial stress state as

cxxxx = cyyyy (C11 = C22) czzzz (C33) cxxzz = cyyzz (c13 = c23) cxxyy (C12) cxzxz = cyzyz (C55 = C44)

where the following compact notation system is used: xx-1, yy-2, 22-3, yz-4, xz-5, xy-6. The same notation is applicable to cubic crystals, although the crystallographic axes do not subtend the same angle. The coordinate (xy) axes of a cube are Cartesian, while the crystallographic xy axes of a hexagonal crystal form 120° angles. The xz and yz angles are, of course, 90' in both cases. A hexagonal crystal is, therefore, characterized by Cll, C12, C13, C33 and C44:

-~ C11 and

C12 represent the binding interaction between atoms within layers, whose elastic properties in a synunetry plane are isotropic; one can best imagine these constants as those involved in idealized tensile testing of a single, hexagonal layer. They determine E and u in the synunetry (basal) plane (i.e., E l l ) . C13, along with the C33 and C44, determines interlayer binding and, to a large measure, u on application of pressure along the synunetry axis. It is difficult to measure, because the sample has to be polished at an angle to the planes of the layers: there is, therefore, a wide variation in the C13 values generated by different investigators. In many cases the value of C13 was not determined directly, but estimated from measurements and on the basis of certain assumptions. s.33 governs E in the direction perpendicular to the basal planes. This elastic constant represents the interaction between layers under compression (i.e., El). g44 represents the stresses in the basal plane which are generated as a result of shear between neighboring planes being tangentially displaced relative to each other (i.e., C44 = G). Its value can vary widely, depending on the number of basal plane defects, o r incorrect sequencing of the layers relative to each other.

where cX is the strain in the direction of the applied stress and cY is the strain in the orthogonal direction. Theoretical thermodynamic considerations dictate that in the absence of phase changes 0 < u < 0.5 (11). Since it is a positive number, the above equation indicates that an applied negative (i.e., compressive) stress results in orthogonal strains which are positive (i.e., tensile). Due to the highly anisotropic nature of hexagonal crystals, the well-known relationship connecting E with G: E G =

(4) 2(1 - u)

which is applicable to isotropic (e.g., cubic) materials only, cannot be used with layered hexagonal materials. As also discussed in (131, relationships have been established between the experimental values of the elastic constants and atomiclevel parameters of model calculations which determine the bonding-controlled interactions between atoms. The elastic properties and phonon spectra of the crystals are often calculated using model force constants governing the displacement of a given atom from its equilibrium position and the forces exerted on this atom by all other atoms of the crystal lattice. The simple assumption is frequently invoked that the interactions between atoms exist along the line connecting them and depend only on the interatomic distance. Since the interaction forces between atoms decrease quite rapidly with distance, lattice dynamics in a specific crystal structure can often (but not always) be confined to nearest neighbors. For example, the consideration of only the central forces does not apply t o graphite. It is, however, generally valid € o r a large number of layered transition metal dichalcogenides and analog compounds (13)

.

2.2 Elastic Constants for Hexagonal Crystals Table I contains a compilation of elastic constant values for layered crystals, collected by Belenkii, et a1 (13) from a large variety of literature sources. The data were obtained by

6

Table I. Elastic constants of layered crystals (in units of 1011 dynes/cm2), from (13). Rhombohedra1 Crys ta1s

Hexagonal Crystals Elastic Constant

Graphite

GaS

GaSe

InSe

TiSe2

TaSe2

NbSe2

SnSe2

12

22.9

19.4

10.3

10.7

9.1

c11

106

15.7

10.3

7.3

c12

18

3.3

2.9

2.7

4.2

____

-

-__-

c13

1.5

1.5

1.2

3.0

c33

3.7

3.6

3.4

3.6

3.9

5.4

4.2

2.8

0.8

0.9

1.2

1.4

1.9

1.8

1.8

c44

0.018-0.035

investigations of compressibility, neutron scattering, calculations of specific heat, light scattering and ultrasound propagation. Although the accuracy of certain values is open to question due to the difficulties associated with the measurement techniques, the quality of the test specimens and disagreement among investigators (see thorough discussion in Ref. 13), the following important observations can be made from the data in Table I: 1. A strong anisotropy of the elastic properties of layer crystals is indicated by the fact that Cll, C12 >> C13, C33, C44. A large difference exists between E within the basal plane (Ell) and the elastic modulus normal to it (EL)

Table 11. Selected elastic constants of graphite. Elastic Constant

c11

c33

3. The wide variation in the C44 of graphite stems from the quality of the specimens. As shown in (151, a reduction in the number of basal dislocations increases C44 significantly. The data in Table I1 indicate that not only the quality of the crystal but also the crystallite size influence C44: a smaller crystallite size appears to produce a smaller shear modulus. It is further shown in Table 11 that in spite of the fact that the moduli of graphite have been investigated the most extensively for decades, the values in Table I still

+ ++

* **

Reference

106 t- 2+ 144 t- 20ff

(16) (17)

3.9 f 0.4

(18)

-. >1.8

3.56

c44 2. The strongest elastic anisotropy is exhibited by graphite. The anisotropies of the constants of the other compounds are considerably less. As discussed later in this paper, the degree of reduction depends on the ionicity of bonding and the resultant crystal structure changes. The covalent or ionic bonding character plays an especially important role in determining the anisotropy of the elastic constants. For example, the size of C44 (i.e., G) tends to be higher in more ionic compounds, also yielding some clues as to the anticipated magnitude of the critical resolved shear stress. None of these aspects are immediately obvious from the data, as assembled and discussed in (13).

(x 1011 dynes/cm2)

(19) (20)

0.42 ? 0.2 0.405* 0.292**

Experimental data. Theoretical calculations. Canadian natural graphite. Pile graphite, with smaller crystalline size than Canadian graphite above. do not represent all the reliable data that can be found in the literature.

Conspicuously absent from Table I are the elastic constants of MoS2, a solid lubricant very important to tribologists. Those data were taken from (21). along with additional information about NbSe2 (Table 111). It is of interest to compare elastic constants calculated or measured for single crystals of graphite and MoS2 by basic researchers with data generated during quests to determine G and E of these materials for tribological applications. Martin et a1 (22) evaluated G of graphite and Nos2 powders in an epoxy resin binder. Thin beams of the respective composites were cast and the moduli determined by the vibrating reed technique. Test beams with lubricant percentages higher than 32% by volume could not be made, because the liquid epoxy used at such ratios was not sufficient to hold all the solid lubricant particles together, or to produce a

Table 111'. Elastic constants of 2H-MoS2 and 2H--NbSe2(in units of 1.011 dynes/cm2), from (17).

The best G M ~ svalues ~ were determined as:

Layered Crystal Elastic Constant

MoS2

NbSe2

*

x - direction (Gx) - 17.94 GPa 1011 dynes/cm2

=

1.79 x

y -- direction (Gy) - 31.67 GPa 1011 dynes/ cm2

=

3.17 x

z - direction (Gz)

5

1.29 x

12.94 GPa

10l1 dynes/cm2

*

**

c11

23.8

10.6/17.1*

c12

-5.4

1.4/ 7/9*

c13

2.3

3.1/-0.2*

c33

5.2(5.2)**

5.4(5.5)**

c44

1.89(1.90)**

1.95(1.98)**

Results of separate estimation methods Values in parentheses are rigid layer constants.

mixture wet enough to be cast into specimens The authors in (20) recommended that G for higher percentages of lubricant may be found by extrapolation. Although extrapolation to 100 percent lubricant content involves an error of an unknown magnitude, such curve fitting was attempted here by the use of a desktop computer in Fig. 3. Substituting 100 in place of x in the polynomials, G M ~ s- ~2.82 x lo6 psi - 19.44 GPa = 1.94 x 10l1 dynes/cm2, and Ggrapp*te 2.79 x lo6 psi 19.24 GPa - 1.92 x 10 dynes/ cm2. These data are in good agreement with C44 (MoS2) in Table 111, but off by a substantial amount of the various C44 (graphite) values in Tables 1 and 11.

30

20

10

"'

0 0

MoS2 GRAPHITE

10

20

30 40 50 60 70 80 90 100 Yo LUBRICANT BY VOLUME y = 1.8498 + 1.0863e-2x + 2.5284e-3x-2 R*2 = 0.997 y = 1.8004 + 4.4180e-2x + 2.1705e-3~"2R"2 = 0.999

Fig. 3 Shear modulus of MoS2 and graphite, as extrapolated from data in (22). In their exceptionally thorough work, Griffin and Ward (23) determined G M ~ by s ~ (a) extruding polystyrene - MoS2 powder compositions to achieve a highly oriented lay of the pigment particles by the laminar flow of the shear process, and (b) assessing the degree of orientation (and thus G) by ultrasonic pulse propagation.

If the system were comprised of perfectly aligned hexagonal crystallites in the direction of extrusion, then Gx - Gy > GZ. Since the data indicated that Gx < Gy, there appeared to be some peculiarity of MoS2 particle fracture and shear anisotropy in the extrusion direction of the xy plane and perpendicular to it. As such, it is not unreasonable to average G,, Gy and G,. The average value is 20.83 GPa = 2.08 x 1011 dynes/cm2 and it is also in good agreement with C44 in Table 111, and with G#,s2 from Martin et al's work in (20). Unfortunately, Martin and coworkers calculated EMoS2 from G M ~ s ~by, using Eq. (4). The appli cabil i ty of thjs formula to hexagonal crystall ites, even jf they were more o r less random in a cast epoxy beam, is highly questionable. As previously mentioned, it does not apply at all t o individual packets of hexagonal platelets, or an ensemble of these particles whose basal planes are generally parallel with the bearing substrate, forming a complete layer. Such alignment has been achieved f o r MoS2 by special sputtering techniques (24, 25, 26) and by run-in of either sputtered (27) or polymer-bonded (28) films. Monolithic, polycrystalline graphite compacts have also undergone basal plane alignment on their surfaces during sliding (29). If the degree of alignment can be determined by X-ray diffraction or, at the very least, by SEM photomicrography (e.g., see Fig. 4 for a schematic and Fig. 5 for the actual appearance of sputtered and run-in MoS2 films), then the best value for E must clearly lie somewhere between Ell (i.e., C11) and El (i.e., C33). Everything depends on the extent of the alignment. Judging from Fig. 5, the bending of the platelets t o a partial lay of the basal planes normal t o the applied load calls f o r some scaling to establish a realistic value for a compressive modulus. In the case of perfect alignment, El should be used. Crystal 1 i te a1 ignment-induced modulus changes are equally significant to those who use graphite fiber reinforcements in structural and self-lubricating composites. The compound moduli of these composites can be measured by convent)onal tensile, compression or flexural test methods. However, to correlate theory with practice, the modulus of a fiber or a laminating plate, as well as that of the matrix, must be known (28, 29). Therefore, any of the previously described, alignment-induced modulus changes importanE to the tribologist are equally important to the composites technologist. The data in Fig. 6 from (30) exemplify the anisotropy of moduli that exist in the various forms of graphite. The 150 x lo6 psi - 1034 GPa = 103.4 x 10l1 dynes/cm2 in Fig. 6 for a single crystal under

8

TYPE I EDGE PLANES EXPOSED

SINGLE TYPE II BASAL PLANES EXPOSED

--

LOW FRICTION

& -=z-

,,p$;FF-$Z;

'

q / p r t / ' I //// / / / l////,l,//

BURNISHED TYPE I

BULK

CRYSTAL GRAPHITE "A" " C MODULUS 150 5 1.5 (106 PSI) STRENGTH 3000 (103 PSI)

1.5

4

~

~

4

150

120

10

50

500

-r/

-

TRANSITION REGION INTERFACE

E i g . 4 Schematic r e p r e s e n t a t i o n of MoS2 f i l m s sputtered i n different c r y s t a l l i t e orientations, and t h e e f f e c t s of b u r n i s h i n g on Type I f i l m s ( c o u r t e s y of Dr. P. D . F l e i s c h a u e r , The Aerospace C o r p o r a t i o n ) .

F i g . 5 SEM photomicrograph of v a r i o u s l y runi n , Type I s p u t t e r e d MoS2 f i l m d e p i c t e d s c h e m a t i c a l l y i n F i g . 4 [ c o u r t e s y of D r . P. D . F l e i s c h a u e r , The Aerospace C o r p . , a l s o see (27) I .

b a s a l t e n s i o n i s v e r y c l o s e t o t h e experiment( E l l ) ; t h e 5 x lo6 p s i = 34.47 a l l y measured C GPa = 3 . 4 5 x loii dynes/cm2 is a l s o c l o s e t o t h e C33 ( E l ) v a l u e s i n T a b l e s I and 11. F i g . 6 a l s o p r o v i d e s c l u e s a s t o t h e modulus d i f f e r e n c e s of p r e - g r a p h i t i c carbon v e r s u s h i g h l y ordered p y r o l i t i c ( p o l y c r y s t a l l i n e ) g r a p h i t e , b o t h i n t h e random-bulk and t h e a l i g n e d - b u l k ( p l a t e o r f i b e r ) form. I t is of i n t e r e s t t o n o t e t h a t t h e i n d i c a t e d alignment of c r y s t a l l i t e s i n F i g . 6 resemble more t h e u l t r a h i g h modulus, p i t c h - b a s e d f i b e r s . I n PAN-based f i b e r s , t h e b a s a l p l a n e s of c r y s t a l l i t e s a r e a r r a n g e d around t h e p e r i p h e r y i n an "onionskin" f a s h i o n , where t h e middle is more r a d i a l l y o r d e r e d , l i k e spokes i n a wheel ( 3 3 , 3 4 ) . The e x t e n t and t y p e of a l i g n m e n t i n g r a p h i t e f i b e r s p r e p a r e d from d i f f e r e n t

F i g . 6 C r y s t a l s t r u c t u r e , e l a s t i c and s t r e n g t h p r o p e r t i e s of v a r i o u s forms of g r a p h i t e , from (32). precursors lead t o nonlinear e l a s t i c e f f e c t s . For example, t h e r e i s a d r a m a t i c i n c r e a s e i n modulus a t h i g h e r t e n s i l e s t r a i n s , due t o s t r a i n - i n d u c e d r e o r i e n t a t i o n of the b a s a l p l a n e s p a r a l l e l t o t h e d i r e c t i o n of t h e t e n s i l e f o r c e a l o n g t h e f i b e r a x i s ( 3 5 ) . The magnitude of i n c r e a s e was found l a r g e r f o r p i t c h - b a s e d f i b e r s , which have a much l a r g e r modulus and h i g h e r d e g r e e of p r e € e r r e d c r y s t a l l i t e o r i e n t a t i o n from t h e o n s e t . The t e n s i l e f o r c e - i n d u c e d a l i g n m e n t i n g r a p h i t e f i b e r s and t h e shear-induced a l i g n m e n t of s p u t t e r e d MoS2 f i l m s b r i n g up t h e q u e s t i o n of u s i n g c o r r e c t v a l u e s of u f o r l a y e r e d s o l i d l u b r i c a n t s . M a r t i n e t a1 ( 2 2 ) may have compounded t h e i r e r r o r of t r y i n g t o employ Eq. (4) f o r c o n v e r t i n g GM0s2 t o E#,s2 by assuming a U M ~ S - 0.30. If one presumes t h a t t h e o n l y u whicz has meaning t o a t r i b o l o g i s t i s t h e one d e s c r i b e d by Eq. (21, t h e n i t can b e s e e n from t h e d a t a i n T a b l e I V , t h a t M a r t i n e t a1 were o f f by a f a c t o r of two t o t h r e e . G e n e r a l l y , t h e larger the e l a s t i c anisotropy i n the c r y s t a l , t h e smaller i s t h e v a l u e of u . A l o t more Table I V . P o i s s o n ' s R a t i o f o r S e l e c t e d , Layered S o l i d L u b r i c a n t s , a s c a l c u l a t e d by E q . ( 2 ) , u s i n g d a t a from T a b l e s I , I1 and 111.

,

u

** *** I

C

GaSe

InSe

MoS2

NbSe2

0.01*

0.09

0.30

0.13

O.ll**/ 0.26***

Using a v e r a g e v a l u e s of c l o s e s t C 1 1 and C22 from T a b l e s I and 111, and C13 = 3 . 1 x 1011 dynes/cm2. Using f i r s t column of v a l u e s from T a b l e 111.

9

needs to be said about the Poisson effect in coatings comprised of these crystallites, but not without experimental evidence. The magnitude of v has a great deal to do with interfacial stresses transmitted to a coating/substrate region by a concentrated contact load. Lancaster and Wade (36), using Matthewson's analysis from (lo), showed that these stresses increase with increasing v and with reduced h/a ratio (h = film thickness; a = Hertzian half-width of contact, i.e., contact radius). In case of resin bonded solid lubricants or transfer films from polymeric self-lubricating composites, the v of the polymers is equally significant. The data in (36) and (37) indicate that the v of several polymers is both strain and strain rate dependent. At higher strains, polymers such as polypropylene, polyethylene and nylon exhibited progressively higher Poisson's ratios. At high rates of loading polymers and their composites become more incompressible, as the time of loading approaches the molecular relaxation time. A progressively increasing rate of loading increases the effective value of u to 0.5. That, in turn, leads to higher interfacial stresses. The respective elastic constants of both the pigment and the binder enter the theory and practice of determining the viscoelastic behavior of polymer layers with particulate inclusions (38). 2.3 Elastic Constants for Hard Coatings Recent reviews of modern measurement methods for the mechanical properties of thin films deal virtually with hardcoats and metallic layers only e.g., see (39). These coatings are analyzed either in a free-standing mode (where the substrate has been etched away), or still firmly attached to it. The former methods include measurement of the internal-stressinduced curling of microbeams (401, deflecting these thin beams electrostatically and by mechanical vibration (411, by deflecting with a nanoindenter (42), or simply by tensile testing of the free standing films themselves (43). With the coating still attached to the substrate, the techniques include ultramicroindentation (44, 45, 46), the use of small vibrating reeds (46, 47, 48), and Bri1louj.n scattering (49). The authors in (49) aptly state that the techniques which separate the coating from its underlay are fraught with error. The elastic properties of films may change when removed from the substrate. Therefore, the best values for TiN and Tic, deposited onto various steels, were taken from (46) and (48). In the earlier work, E T ~ Nfor reactively sputtered, stoichiometric compositions was found to be 640 GPa, with v = 0.25; E T ~ C= 460 GPa and v = 0.17. At this conference, our Swiss colleagues are reporting E T ~ Nranging from 384 to 446 GPa, depending on the type of the steel substrate (48). They also report a higher than previous E T ~ Cof 555 GPa. The literature values compared with their own data indicated the following: (a) E tends to increase with the year of measurement, (b) Ecoating < Ebulkr and (c) the magnitude of E is both substrate type and coating microstructure

dependent. These findings agree with those of Petersen and Guarnieri (41) in that 400 to 800 nm thick sputtered and chemically vapor deposited hardcoats such as Si02, Si3N4, Sic and chromium generally exhibited E different from those of the equivalent bulk materials. In most cases, the values were considerably lower than the bulk. The same thing was observed for W, Cu and A 1 thin films ( 5 0 ) . Since hard, polycrystalline coatings are deposited with one or another low index crystallographic plane more or less preferentially aligned parallel with the substrate plane (51), one would expect El (the modulus of interest in a Hertzian contact) to depend on the specific coating texture. As shown by Perry for TiN, it is indeed the case (51). E for the (110) and (111) plane of TiN is lower and that for the (100) plane is higher than the bulk value. It is due to the fact that the magnitudes of C11, C12 and C44 are different; there are also residual stresses causing plastic deformation in a polycrystal-line, textured film and the resultant alteration of the apparent moduli. For the bulk, Perry used E T ~ N= 640 GPa and V T ~ N= 0.2. 3

DISCUSSION

The anisotropic nature of the various layered crystal structures and their elastic constants is controlled by the magnitude of the atomic interaction within a layer (intralayer bonding) versus bonding between layers (interlayer bonding). It is the electronic structure of a material which determines the crystal structure. Only certain crystal structures exhibit the requisitely strong intralayer and weak interlayer bonding required for a platelet-like solid lubricant. Inasmuch as the crystal- and electronicstructure related behavior of layered transition metal dichalcogenides and the GaSe/ InSe compounds have begun to be treated with some understanding (3, 13, 52 through 571, one needs to point out here only that the magnitude of the elastic constants can serve as a guide with respect. to the usefulness of these compounds a:; solid lubricants. For example, the nature of bonding in NbSe2 is -25% more ionic than in MoS2 (52), and InSe is -15% more ionic than in GaSe (54). The data in Tables I, I11 and IV indicate that the constants of the more ionic materials (a) are less anisotropic, (b) exhibit greater interlayer attraction i.e., C44(InSe) > C44(GaSe); C44(NbSe2) > C44(MoS2); note that lower C44(G) values portend lower critical resolved shear stresses, (c) are more incompressible v(NbSe2) > v(MoS2), i.e., u(1nSe) > u(GaSe); therefore their sputtered layers under Hertzian loads would transmit more interfacial stress (which tends to enhance delamination), and (d) are probably weaker in ternis of basal plane load carrying capacity, due to the respectively lower C11 (intralayer bonding) values. On the whole, GaSe and InSe appear to be promising as solid lubricants [see (56)], complementing graphite and MoS2 for lower load, ultralow friction applications.

10

I n some c o n t r a s t w i t h t h e s e p r e d i c t i o n s i s t h e b e h a v i o r of g r a p h i t e . While t h e h i g h C 1 1 ( E l l ) v a l u e s i n d i c a t e very h i g h load- c a r r y i n g c a p a c i t y [ n o t e t h a t t h e a r i t h m e t i c a v e r a g e of t h e t h e o r e t i c a l and e x p e r i m e n t a l v a l u e s i n Table I1 i s 1250 GPa, which is t h e E of diamond], t h e u l t r a - l o w C44 ( G ) v a l u e s b e l i e t h e h i g h s h e a r s t r e n g t h of g r a p h i t e i n vacuum. I n t h e absence of any i n t e r c a l a t e d m o i s t u r e o r o t h e r i n t e r c a l a n t s , one would e x p e c t G t o b e c o n s i d e r a b l y h i g h e r . While on t h e fundamental b a s i s it makes s e n s e t h a t b a s a l p l a n e d e f e c t s (vacancies, s t e p s , kinks, stacking f a u l t s ) would reduce 71 - bonding i n t e r a c t i o n between p l a n e s and t h u s c a u s e t h e p r e v i o u s l y d i s c u s s e d r e d u c t i o n i n C44 (and t h e s h e a r s t r e n g t h ) , t h e y should be a b l e t o do s o o n l y i n t h e p r e s e n c e of some i n t e r c a l a n t . I n t h e c a s e of MoS2 and NbSe2, t h e e f f e c t s of s u l f u r o r selenium v a c a n c i e s i n t h e b a s a l p l a n e s h o u l d be e x a c t l y t h e o p p o s i t e . The p r e s e n c e of p o i n t - d e f e c t caused d a n g l i n g bonds t h e r e would i n c r e a s e i n t e r l a y e r bonding [ o r bonding t o a s u b s t r a t e , see (57)1, and t h u s i n c r e a s e C44 (G). Moisture would have t h e same e f f e c t , b u t n o t f o r t h e same r e a s o n . Hydrogen-bond-induced a t t r a c t i o n of o x i d i z e d MoS2 edge ( o r d e f e c t i v e b a s a l p l a n e ) s i t e s bonded w i t h w a t e r molecules would e q u a l l y change ( i n c r e a s e ) t h e a p p a r e n t C44 ( G ) of a water-vapor- s a t u r a t e d sample. These a r e t h e c a v e a t s one must keep i n mind when t r y i n g t o use e l a s t i c constant values a s guides f o r solid lubricant selection. A great deal depends on t h e q u a l i t y of t h e sample, a s w e l l a s t h e atmosphere and t h e t e c h n i q u e of e l a s t i c constants determination. One must be e q u a l l y c a r e f u l a b o u t t h e t e s t t e c h n i q u e used f o r h a r d c o a t s , i . e . , u s i n g t h e r i g h t t e c h n i q u e f o r t h e r i g h t specimen. A s pointed out i n ( 4 2 ) , t h e free--standing microbeam v a l u e s measure E of s i n g l e c r y s t a l f i l m s o r b a r s c u t from a b o u l e f o r a p a r t i c u l a r c r y s t a l l o g r a p h i c d i r e c t i o n , on a g i v e n h a b i t p l a n e . The n a n o i n d e n t e r , on t h e o t h e r hand, measures an a v e r a g e v a l u e . Thus, t h e two t e c h n i q u e s cannot be compared d i r e c t l y . On t e x t u r e d T i N and T i C ( o r diamond) h a r d c o a t s , where t h e p o l y c r y s t a l l i t e s a r e t u r b o s t r a t i c a l l y a l i g n e d u s u a l l y w i t h a g i v e n , low i n d e x p l a n e lying p r e f e r e n t i a l l y p a r a l l e l with t h e s u b s t r a t e , t h e two methods s h o u l d a l s o y i e l d d i f f e r e n t r e s u l t s . The number of d e f e c t s within the cubic c r y s t a l s t r u c t u r e equally i n f l u e n c e s t h e magnitude of t h e e l a s t i c c o n s t a n t s . D i s l o c a t i o n and p o i n t d e f e c t s caused by c u t t i n g , g r i n d i n g and p o l i s h i n g of a sample can i n c r e a s e t h e moduli. I n c o n t r a s t , h i g h t e m p e r a t u r e a n n e a l i n g t h e vacancy complexes, which a c t a s c e n t e r s of d i s s i p a t i o n of t h e mechanical v i b r a t i o n e n e r g y , w i l l r e d u c e t h e magnitude of t h e c o n s t a n t s ( 5 8 ) . T r i b o l o g i s t s would p r e f e r modulus measurement t e c h n i q u e s whose specimens resemble t c i b o c o n t a c t s . I n d e n t a t i o n methods, b u t w i t h o u t t h e u s e of s h a r p ( e . g . , V i c k e r s ) i n d e n t e r s , might o f f e r t h e b e s t avenue of approach. R e s e a r c h e r s from B a t t e l l e Columbus L a b o r a t o r i e s s p u t t e r e d a manganin p r e s s u r e t r a n s d u c e r on t h e bottom, c y l i n d r i c a l r o l l e r of a d u a l - d i s c r i g d e s i g n ; t h e t o p , crowned r o l l e r was c o a t e d w i t h MoS2 o r Tic of v a r i o u s t h i c k n e s s e s ( 3 ) . Upon r o l l i n g one specimen

a g a i n s t t h e o t h e r under l o a d , t h e y were a b l e t o show t h e g e n e r a l magnitude of stress changes a n d , i n p a r t i c u l a r , t h e r e d u c t i o n i n stresses a s a f u n c t i o n of s o l i d l u b r i c a n t l a y e r s . These and o t h e r , b a l l - t y p e i n d e n t a t i o n methods have a l r e a d y been shown c a p a b l e of measuring t h e e l a s t i c r e s p o n s e of t h i n polymer l a y e r s on h a r d s u b s t r a t e s (38, 59, 60). Refining both t h e a p p l i c a b l e t e s t a p p a r a t u s and t h e a s s o c i a t e d t h e o r e t i c a l c a l c u l a t i o n s a r e suggested f o r a c h i e v i n g a more d e f i n i t i v e c o r r e l a t i o n between t h e t h e o r y and p r a c t i c e of m u l t i c o a t e d , concentrated contacts. 4

CONCLUSIONS

An e x t e n s i v e l i t e r a t u r e s u r v e y was conducted t o f i n d v a l u e s of e l a s t i c moduli f o r l a y e r e d hexagonal l u b r i c a n t s and f o r s e l e c t e d h a r d c o a t u n d e r l a y s . The d a t a are c r i t i c a l l y reviewed i n terms of a c c u r a c y and u s e f u l n e s s t o a tribologist. An emphasis was p l a c e d on t h e h i g h l y a n i s o t r o p i c b e h a v i o r of l a y e r e d - h e x a g o n a l s o l i d l u b r i c a n t materials, e s p e c i a l l y t h o s e i n t h i n f i l m form, where t h e b a s a l p l a n e s of t h e c r y s t a l l i t e s a r e more-or--less a l i g n e d i n t h e p l a n e of s l i d i n g o r r o l l i n g . I t i s shown t h a t i n l i e u of e x p e r i m e n t a l v a l u e s d e r i v e d by micromechanical t e c h n i q u e s , t h e l i t e r a t u r e d a t a may be used w i t h t h e f o l l o w i n g c a v e a t s : ( a ) f o r highly aligned (run-in) coatings t h e e l a s t i c constants applicable t o single c r y s t a l s may a l s o b e a p p l i c a b l e t o t h e c o a t i n g s , ( b ) depending on t h e d e g r e e of hexagonal c r y s t a l l i t e s i z e and a l i g n m e n t i n t h e d e p o s i t e d l a y e r s ( t o b e determined e x p e r i m e n t a l l y o r a t l e a s t e s t i m a t e d ) , e i t h e r t h e EL o r compound Ell/EL v a l u e s s h o u l d b e used i n t h e stress c a l c u l a t i o n s , and ( c ) a n i n c r e a s e i n t h e i o n i c i t y of i n t r a - and i n t e r l a y e r bonding i n c r e a s e s G and u. There a r e l a r g e r c o a t i n g / s u b s t r a t e i n t e r f a c e stresses w i t h h i g h e r u , a t l e a s t i n t h e s t a t i c c o n t a c t mode. With r e s p e c t t o h a r d c o a t s , t h e i r e l a s t i c c o n s t a n t s are dependent on t h e d e p o s i t i o n and p o s t - t r e a t m e n t c o n d i t i o n s , which c o n t r o l t h e c h e m i s t r y , t e x t u r i n g and d e f e c t s of t h e l a y e r s . More o f t e n t h a n n o t t h e r e s p e c t i v e moduli are lower t h a n t h e p u b l i s h e d b u l k v a l u e s . A g r e a t d e a l of work remains i n d e v e l o p i n g improved, micromechanical i n d e n t a t i o n t e c h n i q u e s which can c o r r e l a t e c o n c e n t r a t e d c o n t a c t t h e o r y and p r a c t i c e of s o l i d l u b r i c a t e d bearing surfaces. 5

ACKNOWLEDGEMENTS

T h i s work was performed under t h e a u s p i c e s of t h e " D e t e r m i n a t i o n o f T r ibo 1o g i c a 1 Fund amen t a 1s of S o l i d L u b r i c a t e d Ceramics" program, DARPA Order No. 5177, AF'WAL C o n t r a c t No. P33615-85-C5087, w i t h B . D . McConnell a c t i n g a s t h e AFWAL P r o j e c t Engineer, References -___ 1.

I . M. Fedorchenko, "Modern T h e o r i e s of t h e Mechanism of F r i c t i o n and Wear and t h e Main Trends i n t h e Development of Composite and B e a r i n g M a t e r i a l s - A Review", Poroshkovaya

11

Metallurgiya (Soviet Powder Metallurgy and Metal Ceramics), 18(4), p. 256 (1979). 2. M. N. Gardos and C. R. Mecks, "Solid Lubricated Rolling Element Bearings Part I: Gyro Bearings and the Associated Solid Lubricants Research, Vol. I.: Summary", AFWAL-TR-83-4129, Hughes Aj rcraft Co., El Segundo, CA, Feb. 1984. 3. Ibid, "Part 1L: Turbine Bearings and the Associated Solid Lubricants Research, Vol. 1 : Summary". 4. J. F. Dill, et at, "Rolling Contact Fatigue Evaluation of Hardcoated Bearing Steels", Proc. Third. Int. Solid Lubr. Conf., ASLE SP-14, p. 230 (1984). 5. M. N. Gardos, "Physical and Chemical Stabilization of Steel Bearing Surfaces with Titanium Nitride and Titanium Carbide Hard Coatings", Proc. Industry-AcademiaGovernment Workshop, March 12-14, 1984, Vanderbilt U., Nashville, TN, Bureau of Mines, U.S. Dept. of the Interior, 1985. 6. M. N. Gardos, "The Tribooxidative Behavior of Rutile-Forming Substrates", in New Materials Approaches to Tribology: Theory and Applications. (Ed.'s L.E. Pope, et al), Mat. Res. SOC. Symp. Proc. Vol. 140, p. 325 (1989). 7.

D. Barovich, et al, "Stresscs on a Thin Strip o r Slab with Different Elastic Properties from that of the Substrate due to Elliptically Distributed Load", Int. J. Engng. Sci., 2, p. 253 (1964).

8. P. K. Gupta and J. A. Walovit, "Contact Stresses Between an Elastic Cylinder and a 1;ayered Elastic Solid", Trans. ASME, J. Lubr. Tech., Ser. F., 96, p. 250 (1974).

9. R. L. Mehan, et al, "Properties of a Compliant Ceramic Layer", J. Mat. Sci., 16, p. 1131 (1981). 10. M. J. Matthewson, "Axi-Symmetric Contact on Thin Compliant Coatings", J. Mech. Phys.

Solids, 29, p. 89 (1981). 11. Y. P. Chin and M. J. Hartnett, "A Numerical

Solution for Layered Solid Contact Problems with Application to Bearings", Trans. ASME, J. Lubr. Tech., 105, p. 585 (1983). 12 * R. Solecki and Y. Ohgushi, "Contact Stresses Between Layered Elastic Cylinders", Trans. ASME, J . Tribology, 106, p. 396 (1984). 13. G. L. Belenkii, E. Yu. Salaev, and R. A. Suleimanov, "Deformation Effects in I.ayer Crystals", Sov. Phys. Usp. 31, p. 434 (1988). 14. L. D. Landau, A. I. Akheiezer and E . M. LiCshj.tz, General. Physics-Mechanics and Molecular Physics, Pergamon Press, London, 1967.

15. E. J. Seldin and C. W. Nezbeda, "Elastic Constants and Electron-Microscope Observations of Neutron-Irradiated Compression-Annealed Pyrolitic and Single-Crystal Graphite", J. Appl. Phys., 41, pp. 3389 (1970). 16. E. S . Seldin, in Proc. 9thSennial Conf. on Carbon, Chestnut- Itill., MA, 1969 (Defense Ceram. In€o. Center, Columbus, OH), p. 59 (1969). 17. R. Nicklow, N. Wakabayashi, and I f . G. Smith, "Lattice Dynamics of Pyrolytic Graphite", Phys. Rev. B., 5 , p. 4951 (1972). 18. G. Dolling and B. N. Brockhouse, "Lattice Vibrations in Pyrolytic Graphite", Phys. Rev., 128, p. 1120 (1962). 19. C. Bownian and J. A. Krumhansl, "The Low-Temperature Specific Heat of Graphite", J . Phys. Chem. Solids, 6 , p. 367 (1958). 20. K. Komatsu, "Particle-Size Effects of the Specific Heat of Graphite at Low Temperatures", J. Phys. Chem. Solids, 6 , p. 380 (1958). 21. J. L. Feldman, "Elastic Constants of 2II--MoS2and 211-NbSeg Extracted from Measured Dispersion Curves and Linear Compressibilities", J. Phys. Chem. Solids, 37, p. 1141 (1976). 22. J . T. Martin, C. 11. Balster and F. Abdulhadj., "Measurement of Shear Modulus for Solid Lubricants: Wear Life Coefficients for MoS2 in MoS2 Resins", Lubr. Eng., 28, p. 43 (1972). 23. G. J. L. GriCfjn and D. S . Ward, "Elastic Properties of Oriented Molybdenum Disulfide-Polystyrene Composites", ASLE Proc. Second Int. Conf. on Solid Lubrication, ASLE SP-6, p. 169 (1978). 24. P. D. F'leischauer, "Effects of Crystallite Orientation on the Environmental Stability and Lubrication Properties of Sputtered MoS2 Thin Films", ASLE Trans., 27, p. 82 (1984). 25. P. D. Fleischauer and R. Bauer, "Chemical and Structural Effects on the Lubrication Properties of Sputtered MoS2 Films", STLE Tribology Trans., 31, p. 239 (1988). 26. P. A. Bertrand, "Orientation of RP-sputtered-deposited MoS2 Films", Mater. Res., 4, p. 180 (1989).

J.

27. M. R. Hilton and P. D. Pleischauer, "Structural. Studies of SputLer-depos ited MoS2 Solid Lubricant films", in New Materials Approaches to Tribolopy: Theory and Applications (Ed.'s L. E. Pope, et al), Mat. Res. SOC. Symp. Proc. Vol. 140, p. 227 (1989). 28. M. N. Gardos, "The Synergistic Effects of Graphite on the Friction and Wear of MoS2

12

Films in Air", STLE Tribology Trans., 31, p. 214 (1987). 29. Anon, "X-ray Investigation of Structural Changes in Graphite Antifriction Materials During Friction", Izv. A.N. SSSK, Mekh. Mash., 4, pp. 179-184 (1963); Risley-.Trans.-1850-(9091.9F). 30. R. M. Jones and 11. S. Morgan, "Analysis of Nonlinear Stress-Strain Behavior of Fiber-Reinforced Composite Materials", AIAA J., 15, p. 1669 (1977). 31. B. Prasad and G. Iiermann, "Response of a Laminated Beam t o a Moving Load", ATAA J., 15, p. 142 (1977). 32. W. I%. Chambers, "Low Cost, High-Performance Carbon Fibers", Mech. Eng., 97, p. 37 (1975). 33. M. N. Gardos, et al, "Solid Lubricated Turbine Bearings: Part I - Preparation of 316°C Lubricative Composites and Separators", Proc. 3rd Tnt. Conf. on Solid Lubrication, ASLIS SP-14, p. 248 (1984). 34. N. Ohmae, et al, "Atomic Configuration of Carbon Fibers Studied by Field Ion Microscopy", STLE Tribology Trans., 31, p. 481 (1988). 35. C. P. Beetz, Jr. and G. W. Budd, "Strain Modulation Measurements of Stiffening Effects in Carbon Fibers", Rev. Sci. Instrum., 54, p. 1222 (1983). 36.

.I.K.

Lancaster and D. J. Wade, "The Influence of Reversing Loads on the Performance of Self-Lubricating, Dry Bearings", Proc. 3rd Int. Conf. on Solid Lubrication, ASLIS SP-14, p. 296 (1984).

37. I. Krause, A . J . Segreto, and €1. Przirembel, "Poisson's Ratio for Viscoelastic Materials", Mat. Sci. Kng., 1, p. 239 (1966). 38. J. 11. M. van der Ljnder, P.E. Wierenga and E. P. lIonig, "Viscoelastic Behavior of Polymer Layers with Inclusions", J. Appl. Phys., 62, p. 1613 (1987). 39. D. A. Hardwick, "The Mechanical Properties of Thin Films: A Review", Thin Solid Films, 154, p. 109 (1987). 40. M. Mehregany, R. T. Howe, and S. D. Senturia, "Novel Microstructures for the In-Situ Measurement of Mechanical Properties of Thin Films", J. Appl. Phys., 62, p. 3579 (1987). 41. K. E. Petersen and C. R. Guarnieri, "Young's Modulus Measurements of Thin Films Using Micromechanics", J. Appl. Phys. 50, p. 6761 (1979). 42. T. P. Weihs, S. Hong, J. C. Bravman, and W. D. Nix, "Measuring the Strength and Stiffness of Thin Film Materials by Mechanically Deflecting Cantilever Microbeams", in Thin Films: Stresses and

Mechanical Properties. (Ed's. J. C. Bravman, et al), Mat. Res. SOC. Proc. Vol. 130, p. 87 (1989). 43. ibid, R . W. Hoffman, "Nanomechanics of Thin Films: Emphasis : Tensile Properties", p. 295. 44. Y. Tsukamoto, H. Yamaguchi, and M. Yanagisawa, "Measurements of Ultramicroindentation Hardness, Young's Modulus and Internal Stress", Thin Solid Films, 154, p. 171 (1987).

45. S. Hoshino, K. Fuji, N. Shohata, €1. Yaniaguchi, Y. Tsukamoto, and M. Yanagisawa, "Mechanical Properties of Diamondlike Carbon Films", J. Appl. Phys., 65, p. 1918 (1989). 46. Is. TGrgk, A. J. Perry, L. Chollet, and W. D. Sproul., "Young's Modulus of TiN, Tic, ZrN and IlfN", Thin Solid Films, 153, pp. 37-43 (1987). 47. G. L. Miller, M. Soni, and R. L. Fenstermacher, "A Technique f o r Investigating the Properties of Surfaces, Thin Films, and Interfaces by Means of a Mechanical Marginal Oscillator", J. Appl. Phys., 53, p. 979 (1982). 48. L. Chollet and C. Biselli, "Young's Modulus of TiN and Tic Coatings", this conference. 49. R. Bhadra, M. Grimsditch, and I. K. Schuller, "Elastic Constants of MetalInsulator Superlattices", Appl. Phys. Lett. 54, pp. 1409-1441 (1989). 50. C. T. Rosenmayer, F. R. Brotzen and R. J. Gale, "Mechanical. Testing of Thin Films", in Thin Films: Stresses and Mechanical Properties, Mat. Res. SOC. Symp. Proc. Vol. 130, pp. 77-86 (1989). 51. A. J. Perry, "The Relationship Between Residual. Stress, X-ray ELastic Constants and Lattice Parameters jn TiN Films Made by Physical Vapor Deposj.tion", Thin Solid Films, 170, pp. 63-10 (1989). 52. A . Madhukar, "Structural Classification of Layered Dichalcogenides of Group IVB, VR and VIB Transition Metals", Solid State Commun., 16, p. 383 (1975). 53. R. Takagi, "Layer-Shaped Structures and Friction Characteristics of MoS2 Family" J. Jap. SOC. Prec. Eng., p. 104 (Nov. 1980). 54. A . Nakanishi and T. Matsubara, "Note on Ionicity of Layered Compounds Gas, GaSe and InSe", J. Phys. SOC. Jap., 51, p. 1339 (1982). 55. W. E. Jamison, "Intercalated Dichalcogenide Solid Lubricants", Proc. 3rd Int. Conf. on Solid Lubrication, ASLE SP-14, p. 73 (1984). 56. M. N. Gardos, "An Analysis of the Ga/In/WSe2 Lubricant Compact", ASLE Trans., 28, p. 231 (1985).

13

57. P. D. Fleischauer, "Fundamental Aspects of the Electronic Structure, Materials Properties and Lubrication Performance of Sputtered MoS2 Films," Thin Solid Films, 154, p . 309 (1987). 58. P. A. Maksymyuk, et al, "Changes in the Elastic and Inelastic Properties of Annealed Indium Antimonide Crystals", Sov. Phys. Solid State, 30, p. 1656 (1988). 59. P. E. Wierenga and A. J. J. Franken, "Ultramicroindentation Apparatus for the Mechanical Characterization of Thin Films", J. Appl. Phys., 55, p, 4244 (1984). 60. A . Tonk, J. Sabot, and J. M. Georges,

"Microdisplacements Between Two Elastic Bodies Separated by a Thin Film of Polystyrene", paper presented at the ASME/ASLE Joint Lubr. Conf., Hartford, CN, Oct. 18-20, 1983, ASME Paper No. 83-Lub-11.


15

Paper I (ii)

Frictional properties of lubricating oxide coatings M.B. Peterson, S.J. Calabrese, S.Z. Li and X.X. Jiang

A literature search was conducted to identify the properties of surface oxide films that make them

effective in reducing friction, wear, and surface damage in sliding contacts. Based on these results it was concluded that the formation of double oxides of rhenium, molybdenum, and boron would be most effective. A number of nickel, copper, cobalt, rhenium alloys were prepared and their friction temperature properties were compared with those of the oxide films which might be produced on the surface. 1.

INTRODUCTION

In their book (1) published in 1907 Archbutt and Deeley stated that "the friction between most s o called unlubricated metallic surfaces is, therefore, not a case of true friction between pure metals but between surfaces contaminated by chemically formed films such as oxide and sulfides. In other words the surfaces are partially lubricated. Under moderate pressures such films prevent actual adhesion of metal to metal". Since that time approximately 120 papers have been written concerning the role that the oxide played in tribological processes. These reports fall into four categories: pretreatments, boundary lubrication, high temperature solid lubrication with oxides, and dry sliding. Pretreatrnents are concerned with subjects such as protecting aluminum surfaces by anodizing and the oxidation of ferrous materials to assist in metal working. In boundary lubrication, oxygen present in the lubricant acts competitively with other additives in forming surface films which prevent wear under mild operating conditions and failure under extreme pressure conditions. Such films may be metallic oxides or polymer films resulting from oxidation of the lubricant. It is also known that metal oxides react with lubricant additives to form metal soaps which are extremely effective lubricants. Metal oxides have been investigated as potential high temperature solid lubricants for temperatures above 3 5 0 ° C where many conventional solid lubricants become ineffective. However the largest number of studies have been concerned with metals in dry sliding. Here the oxide determines whether seizing or effective sliding will result. From these studies it is clear certain oxides and conditions favor "mild wear" while others favor "severe wear" (2). The question can be raised whether this accumulated knowledge can be used to develop improved alloys (or lubricants) 'Tribology Group, National Institute of Standards and Technology, Gaithersburg, MD. 2Rensselaer Polytechnic Institute, Troy, NY. 31nstitute of Metal Research, Shenyang, China

which are more effective than those currently in use. Toward this objective, the literature has been reviewed to describe the necessary attributes of an effective oxide film and then to develop and evaluate alloys which might form such oxides under tribological conditions. 2.

LITERATURE REVIEW-EFFECTIVE OXIDES

Several excellent reviews have been conducted on the subject of oxidative wear and the role of the oxide. Ludema ( 3 ) reviewed the scuffing literature with particular attention to the role of the oxide. He defines scuffing as a roughening of the surface by plastic flow and suggests that to be effective an oxide should:

(1)

enhance the adsorption of selective species from the lubricant, (2) be soft and ductile, ( 3 ) wear at a rate less than the oxidation rate, ( 4 ) not be abrasive as debris, and (5) flake off to remove stresses. Quinn ( 4 , 5 ) gives a complete review of oxidation wear which was developed for low alloy steels but should be generally applicable for materials for which the wear process is similar. Basically, after run in, plateaus which were formed during run in, oxidize at the interface temperature and grow during the sliding process. When reaching a critical thickness ( 1 ~ 3pn) this oxide film breaks up by a fatigue process to form wear debris. All aspects of the wear process are analyzed and theoretical estimates made of the wear rates. He points out that the diffusion rates of oxygen and iron determine how long it will take to reach the critical film thickness. Thus, control of diffusion rates should control wear. He also points out that stronger oxide films would be beneficial. Batchelors ( 6 ) review was primarily concerned with the factors which affect the growth of oxide films. He points out that there are a number of factors other than diffusion rates which affect the growth (therefore the wear) of oxide films. Lattj-ce misfit causes severe strains in the lattice and form unstable oxides. An oxide in the vitreous

16

state oxidizes at a lower rate than an oxide in the polycrystalline state since oxygen diffuses faster along the crystalline boundaries. Other factors of importance are the structure of the substrate, mechanical activation, liquid effects, and the mechanical and adhesive properties. Sullivan (7,8) in a comprehensive review written with great clarity describes the various oxidation/wear models. H e suggests that theories should be confined to the major mechanisms which have been defined for specific materials without trying to work out the completely general problem. He also suggests to have a more stable oxide that:

I

1

Tiwe

Tin*

I

SO-SU

__-

hn

h’ L

L

0

0

0

0

Molar volume of the oxide should be greater than the molar volume of the metal so the film is in compression on the surface. The differential thermal expansion between the metal and the oxide should be small. Both the oxide and the metal should be capable of some plastic flow to relieve the stresses in film and interface. Oxides formed by double diffusion, e . g . , Fe30,, are more stable.

Of the 120 papers published between 1929-1984 a number (25) merely noted that the oxide was important in controlling the friction and wear of metals in sliding contact. The effect would be beneficial if it reduced adhesion but harmful if it increased corrosive wear. Such effects were noted in both lubricated and dry sliding.

2.1 Models A large amount of work has been carried out to understand the process that leads to the formation and wear of oxide layers. Several independent processes have been identified which may or may not be mutually exclusive, These may be identified as sliding on a built up oxide, on an agglomerated debris layer of oxide or on a soft lubricating layer. The built up oxide layers have received the most attention. Here the oxide grows based on oxidation kinetics and is removed by some wear or failure process (9-21). Four different behaviors have been identified as shown in Figure 1. In the graph labeled FO-FW an oxide is built up on the surface of the asperity in one pass and immediately removed on succeeding passes. For convenience this is called fast oxidation-fast wear. This might apply to the early stages of wear where an insufficient amount of oxide is produced or for a metal which produces a friable oxide layer which cannot withstand the frictional stresses. A second behavior, slow oxidation-fast wear ( S O FW), mostly due to Quinn who worked with low alloy s t e e l s , shows that an oxide grows slowly as sliding proceeds until a critical film thickness is reached where the films break up and are removed as flake debris. The controlling factor is the rate of removal and the critical film thickness rather than the oxidation rate as in FO-FW. A third process might be called FO-SW. In this situation an oxide film is rapidly formed and is slowly worn away. When it is completely gone it is replaced by the original FO process. Such a

Figure 1. Dynamic models of the formation and removal of oxide films during the wear process. process has not been found for oxides but may be true for self lubricating composites or other cases where an extremely effective lubricant is used. The final model, SO-SW, refers to a process where the oxide grows slowly and wears away slowly. The resulting film thickness is the difference between the rate formation and the rate of wear. The rate of wear is a function of film thickness. If the film gets too thick the wear rate increases; if it becomes too thin, the rate of oxidation increases. In this way a stable film is maintained. This mode is thought to occur if the film failure mode is wear (abrasion) rather than fatigue or fracture. It would also seem to apply when soft lubricating oxide films are formed. It is clear that these models are not unique for a given materials combination. Changes in operating conditions and atmospheres can cause a change from one model to another. It would be expected that SO-SW would yield minimum wear if the oxidation process could be controlled so that only the amount needed was produced. To achieve this end it is necessary to identify oxide films which wear slowly. Efforts should be directed to alloys in which this model describes events since it is inherently the lowest wear situation. In 1956 Halliday and Hirst (22) conducted low amplitude fretting tests and examined the surfaces after the test. They found that the oxide films were not intact but consisted of l o o s e debris. In fact they identified periods of low friction (f = 0.05) which they attributed to rolling on oxide debris. It was thought that this condition might only apply to small amplitude slip however in 1958 Tamai (23) noted the same effect in reciprocating sliding. Furthermore Inabuchi (24,25) showed that a transition from severe wear to mild wear occurs if sufficient Fe,O, powder is added to the wear track. The powder forms a compacted agglomeration in the damage grooves and will persist for long periods of time. It is interesting to note that they found that 1 pm particles gave the best results since this is the usual thickness of wear debris. In their experiments Stott (26) in studying the friction time behavior of steels at high temperature found friction was controlled by sliding of compacted debris on compacted debris. Two

17

forms of oxide production were described: oxide formed on the surface and immediately removed (FO-FW) or metal wear debris was first produced then oxidized. This latter suggestion was first proposed by Tomlinson ( 2 7 ) and has been thought to be important since iron has often been identified as a component in wear debris. The soft lubricating film is really only a special case of the previous two. It arose from studies of the lubricating characteristics of oxides as lubricants ( 2 8 ) and studies of the sliding characteristics of metals at high temperatures ( 2 9 ) . Basically it was found that certain oxides as powders were effective lubricants and metals which formed these oxides gave the best sliding characteristics at high temperatures either self mated or in combination with ceramics ( 3 0 ) . This was not a particularly revolutionary idea since theories of boundary lubrication have been based on the formation of low shear strength films and materials in common usage (e.g., molybdenum tool steels) at high temperatures contained the ingredients to form soft oxides. Rabinowicz investigated this process in more detail ( 3 1 ) and Kruez ( 3 2 ) considered the formation of borate films in boundary lubrication. No general theory has been developed for the formation or removal of such films; however a deformation mechanism seems consistent with the fact that they are in the plastic state during the shear process. In previously discussed papers several different approaches to oxidation kinetics and film removal mechanisms have been explored. In most cases a linear or parabolic rate has been evaluated though many others have been explored. More recently dynamic kinetics have been explored where the rate can change with time or with operating conditions. However the major question is whether the oxidation process is the same under tribological conditions. Quinn finds that the diffusion coefficients are much faster but the whole question of reactions at high stresses and temperature remains unresolved. Different wear and failure mechanisms have been identified. Wear of the film can occur by abrasion, fatigue, and deformation. The ultimate failure modes may be due to these wear processes or due to fatigue fracture ( 3 3 ) or blistering of the film. The loss of adhesion or blistering is due to differential stresses between the film and the substrate ( 7 ) . This review has shown that more attention should be given to certain aspects of the sliding process. For example, Moore ( 3 4 , 3 5 ) showed that when sliding steel against copper, that copper oxide was formed and then folded into the surface with subsequent sliding. Thus the surface is a composite of metal and oxide. Rigney ( 3 6 , 3 7 ) has shown that the wear layer is a mechanically mixed layer of metal and oxide. This effect can occur by either deformation or transfer. Kerridge ( 3 8 ) showed that transfer is the first step in the wear process. Hayler ( 3 9 ) has shown with several sliding systems that two conditions exist depending upon the temperature: oxide sliding against oxide, or metal against metal. The metal on metal condition is not due to the breakdown of the oxide, but rather to the transfer of metal on the surface of the oxide. Molgaard ( 4 0 ) discusses the role of oxide transfer as part of

the wearing process. These points emphasize the general lack of information on film rheology or "what slides against what." Under certain circumstances metal may also be sliding against oxide. Several investigators have shown that under such circumstances friction can be quite low ( 4 1 - 4 3 ) . For example, Cu on Fe,O, gives 0 . 2 5 and Nickel on A1,0,, 0 . 5 5 in vacuum, Film rheology pertains to more than just defining the sliding interface. It also involves the flow mechanics of the film. Some work has begun in this area. Godet and coworkers ( 4 4 ) have addressed the problem with their so-called "third body approach." Here particle mechanics are applied to film behavior. Mazuyer ( 4 5 ) has studied thin film rheology using bubble techniques, drawing dramatic conclusions at the affect of film thickness on deformation mechanisms. Other approaches such as continuum mechanics, micromechanics, molecular dynamics, or flow mechanics have been suggested and are under investigation in the Office of Naval Research Tribology Program. Such approaches attempt to predict friction and wear based on film behavior rather than determining experimentally how friction and wear affect the film. 2.2

Variables

One of the first investigations of surface films in the U.S. was conducted by Campbell ( 4 6 ) in 1 9 3 9 . He used preformed films and determined that friction dropped significantly when the film thickness reached 0 . 3 pm. Rabinowicz (31) found that a thickness of 0.01 pm was effective in reducing friction at high temperatures. From the work of Quinn and others the maximum film thickness should be less than 3 pm to avoid failure. This suggests film values should be maintained at about 0.1 pm; however this value will depend on load and the hardness of the substrate material. Whitehead ( 4 7 ) found that the naturally occurring oxide film on copper broke down between 10 g's and 100 g's load. He also found that rougher surfaces gave a lower value. It was suggested that to prevent breakdown the oxide and the substrate should be of equal hardness. Cocks ( 4 8 , 4 9 ) found, using electrical resistance measurements that the oxide did not breakdown from normal loading but that a lateral force was needed which was less than the sliding friction force. He also noted load transitions due to frictional heating. Hirst ( 5 0 , 5 1 ) measured the load capacity of oxide films and found that films preformed by heating at high temperatures gave little surface protection. The highest load capacity was with films formed slowly at low temperatures. Lancaster ( 5 2 , 5 3 ) investigated the wear rate of 6 0 / 4 0 brass sliding against tool steel over a range of loads, velocities, and temperatures. He found that the film was protective at light loads and low speeds where sufficient time was available between passes to form the film and at high temperatures where the oxide formed a film faster than new surface was exposed. Higher temperatures were needed at higher loads and lower speed to give a protective film. This demonstrated the importance of frictional heating. Lancaster found that the mean surface temperature

18

controlled film behavior not the flash temperature. The high temperature transition occurred when the mean temperature was 300°C for brass on steel. Earls and coworkers (54-57) studied the wear behavior of steel surfaces in great detail. They found that there are a range of loads and velocities where friction and wear are unstable. In this unstable region the oxide film is suddenly removed from the pin and partially from the track. Friction and thus temperature increase; new oxide is formed, and friction and wear return to their lower values. The oxide is removed at a critical thickness which decreases with increasing load. Film failure is by cracking or blistering when adhesion is low. The behavior of the films is controlled by the mean surface temperature which is related to W1I2V (W = load, V = velocity). Atmosphere particularly moisture plays a very strong role in the wear rates (53,58-62). Increasing the concentration of reactants increases the rate of wear and the transition values. 2.3 Properties Early work (63) with oxide films suggested that oxide layers were easily broken on soft metals and that heating softens the underlying metal which aided in this disruption (64). Amorphous films were found to be more protective than crystalline films. Welch (6567) conducted extensive work on the role of frictional heating in the wear of steels. He concluded that the observed transitions were not only influenced by the formation and removal of oxide films but by structural changes and hardening caused by martenistic transformations, This hardening enhanced the protective properties of the oxide film. Bridgeman (68) measured the shear strength of a large number of inorganic compounds at various loads between high pressure anvils. From these data friction coefficients can.be derived and plotted against the hardness of the oxide. These data are shown in Figure 2 for a normal stress of 100 kg/mm2 (142,000 psi). It can be seen that friction increases almost directly with hardness (Mohs) up to a value of 0.20 to 0.25 where it then remains relatively constant. This transition occurs at a Mohs hardness of 3.5 which is equivalent to about 150 kg/mm2. At high pressures friction values are lower and the transition moves to higher hardness. Bridgeman explained these results by suggesting that shear only occurred at low hardness values and surface slip occurred with the harder oxides. It is not clear whether surface slip meant metal/oxide slip or oxide/oxide slip. Since in many cases the oxide was firmly attached to the anvils it might be assumed that oxide/oxide slip occurred; this however is not a certainty. He also noted substantial changes in composition and structure under pressure. Crystal structure changes occurred which often yielded free metal at the metal oxide interface. Peterson (28) evaluated powdered oxides as lubricants at various temperatures. Certain oxides (CuO, MOO,, COO, Cu,O) and double oxides (molybdates and tungstates) were effective lubricants at 700°C while other powdered oxides were not. Those that were effective had low melting points. This point is illustrated in

II.PM

I.H,e€!I

12. A 1 1 0 1 1 3 . CaO

2 . MOO 3 n4 .* CUlO 5 . ZnO 6. 0aO 7 . nm, 8.

9.

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TI02

IS. CrIOs 16. Fez03 11. N I O IS. Asms 19. 5r0

cdo

smo,

10. YO,

1

Figure 2.

2

3

4

5 6 7 Hardness (nohi)

I

8

9

Effect of hardness on the friction coefficient of different oxide powders used as lubricants ( 8 8 ) .

Figure 3 where friction coefficient is plotted against melting point for a series of double oxides. It can be seen that as the melting point approaches the test temperature, friction decreases to a value of about 0.15 and there after remains constant. This is essentially the Bridgeman curve where melting point is a reasonable measure of the oxide hardness. Thus these oxides are seen to be effective lubricants when their melting temperature is within 200°C of the test temperature. Metal oxides were also evaluated as metal working lubricants at high temperatures (69). Low friction was found when the oxide was soft and ductile or when a friable layer developed. CuO and ZnO were found to be effective. The ZnO behaved as a loose powder rather than a sheared film. Unfortunately the oxides which form in sliding situations are usually a very complex mixture. For example in Lancaster's work (53) the most probable film was 46 percent Fe,O,, 21.5 percent CuzO, 22.5 percent ZnO and 11 percent WO,. Other investigators using steel found various percentages of Fe,O, , Fe,O, and FeO depending upon the surface temperatures. Working with aluminum alloys of silicon and copper Razavizadeh (70,71) found that the film was composed of compacted debris whose thickness increased with load. Additions of silicon and copper to the alloy extended the mild wear region by improving the stability of 1 Copper 2 Rhenate 2 P o t d l l l m 2 Holybddte 3 copper Rhemtc 4 Sodtun Tungitdte 5 Wlybdenm Oxide 6 Cobalt Rhenati 7 P O t a i i l U m Molybdatn 8 Nickel Molybdite

9 copper TYngltate 10 Lead Molybdate I 1 Lead lungstate I2 CalcIm Halybdate 13 Calclm Tunpitate I4 Nickel lungitate 15 Tungsten Oxide

Figure 3. Effect of melting temperatures on the coefficient of friction for fifteen materials evaluated at a test temperature of 704°C (28).

19

the film, It was also concluded that iron diffuses into the surface film. Buckley ( 7 2 ) found that surface reaction films are more readily formed when the metals contain silicon. The important point to note from these and other investigations is that certain elements are beneficial in oxide films and that certain elements are found in surface films in concentrations greater than would be expected from their concentration in the sliding substrates. 2.4

(2)

Summary

A great deal of progress has been made in understanding the role of surface oxide films in tribological processes. Models have been established which account for the condition of the film and for the formation and removal of the oxide layers. Although this has been accomplished with only a few material combinations the results seem general enough to apply to other systems. Investigators have shown that oxide films will be effective under the following conditions: Thickness > .05 pm < 1 pm Soft and Ductile Wear Rate < Oxidation Rate Fail by Wear not Fatigue or Fracture Slow Oxidation - Slow Wear Model Non Abrasive Volume Oxide < Volume Metal Thermal Expansion Similar to Metal Oxide Formed by Double Diffusion Effective Debris Compaction Slip at Metal/Oxi.de Interface Forms Low Melting Point Glassy Oxide

3.

(1)

Develop alloys which form soft lubricating films. Most investigators have noted the importance of soft ductile layers in preventing the breakup of film and relieving the stresses. Lubricating films should be developed which have a long wear life and low friction. Anticipated problems involve forming

RESEARCH PROGRAM

Based upon the previous conclusions it was decided to investigate approach 1; that is, to try to develop alloys whose naturally occurring oxides would be low shear strength solid lubricants. Friction tests were first run on a variety of oxides which might be formed at high temperature. Alloys were then made containing elements which might form these oxides. Comparisons were made between the frictiontemperature behavior of the oxides and the alloys. The results are described in the following paragraphs and in references 73 and 74.

3.1

However many important questions remain. These have more to do with the film itself. What determines the composition of the film and why are certain elements concentrated there? What are the properties of such films and what properties are required for minimum wear and maximum load capacity? New analytical techniques are available such as the microindenters and the force microscopes which can determine the film properties, Another unresolved question is the deformation mechanism of the film. Does slip occur at the metal/oxide interface; at some oxide/oxide interface; or is the whole film experiencing shear or flow? Can continuum mechanics be applied to oxide films s o that friction, wear, film thickness, and load capacity can be predicted. Will it be necessary to experimentally determine the behavior of every important combination? However the most important question to be answered is whether there is sufficient information available after 8 2 years so that better wear resistant alloys can be defined. Two different approaches seem possible based on the results of the literature search:

such oxides to the exclusion of others in sufficient quantities to be effective in a practical alloy system. A second approach involves improving the wear resistant properties of the generated oxide film. Previous research indicates that removal processes control tribological behavior therefore a more wear resistant, failure resistant film is needed. Failure should be by wear (SO-SW) not when a critical film thickness is reached. What is needed is a hard coherent layer with no distinct interface between the oxide layer and the base metal. Certain multivalent elements such as tantalum, niobium, silicon, and chromium appear to have this capability but much additional work must be carried out.

Friction Apparatus

A schematic diagram of the reciprocating test apparatus is shown in Figure 4 . It is used in two configurations. For the lubricant tests a hardened tool steel pin (T-15) slides back and forth on a T-15 tool steel flat (Figure 5). The tool steel flat has surface grooves to contain the oxide powder. For the alloy tests the configuration consisted of an A1,0, ball sliding back and forth on the alloy plate. The A1,0, ball was used s o that the oxide film would not be modified by iron oxides. The ball is mounted in a special holder and is affixed to the arm which moves back and forth with an air cylinder. A strain gage mounted between the cylinder and the arm allow the friction force to be measured. The

Figure 4 .

Schematic diagram of wear apparatus.

20

Figure 5. Diagram of test specimens for evaluating friction properties of oxide powders. flat alloy specimen is mounted on a heated table with the furnace surrounding both specimens. The load in the experiments is 142 N. The pin moves back and forth in a single track 2.5 cm in length at a rate of 2.5 cm/sec. 3.2 Materials The oxides were obtained from commercial sources or prepared using appropriate chemical synthesis techniques. Small ingots of nickel containing various amounts of rhenium and copper were prepared by mixing the powders and melting them in an inconsumable electrode arc furnace. In order to obtain a high purity level sample all powders were first heated to high temperatures for one hour in a vacuum furnace to expel the dissolved gases. Because of the large difference in melting point of the metals electromagnetic stirring was used. The alloys were remelted several times to assure a uniform distribution. The compositions of the alloys are shown in Table 1. Typical microstructures of the nickel base copper/rhenium alloys are shown in Figure 6 and x-ray maps of a typical alloy are shown in Figure 7. A l l of the alloys had the dendritic structure characteristic of cast materials, Nil (5 Cu, 5 Re) was somewhat different in that clear grain boundaries were visible. Table 1 Alloy Compositions Atomic Percent Soecimen Number Ni-1 Ni-2 Ni-3 Ni-4 Ni-5 Ni-Re

Ni -

cu

Re

90 85 80

5 7.5 10 12.5 15

5

75 70

Ni-Cu

92.5 92.5

Cu-Re

0

0

7.5 92.5

7.5 10 12.5 15 7.5 0

7.5

Figure 6. Microstructure of Ni-Cu-Re alloys.

Figure 7. Image of absorbed electron and x-ray map. (a) Image of absorbed electron, (b) Ni K,, (c) Cu K,, and (d) Re La. X-ray diffraction showed that the alloys consisted of two solid solution phases, Ni(CuRe) and Re(NiCu). The amount of Re(NiCu) increased with rhenium content. Two regions can be observed in Figure 6, a bright region and a dark region. The bright region corresponds to Re(NiCu) which is rhenium rich; the dark region corresponds to Ni(CuRe). The distribution of nickel, copper and rhenium can be seen from the absorbed electron image and the x-ray maps. The compositions of the bright and dark regions for Ni-2 were determined to be as follows:

Ni cu Re

BriFht

Dark

74.4 3.0 23.7

88.2 6.8 5.1

There is a small difference in hardness between the two phases. The bright region has a Vickers hardness of 190-210 kg/mm2 and the dark region 160-180 kg/mm. 3.3

Friction-Temperature Behavior (Oxides)

As a first step in the program a survey jras made to determine what elements could be included in high temperature alloys and what oxides they produced. Relevant oxide data for these elements are shown in Table 2. Friction tests were run at several different temperatures using the appropriate oxides. These data are shown in Table 3. Very few of the friction coefficients were similar to the unlubricated condition indicating that all

21

Table 2 Oxide Reference Data Nohs

w

iwulLwa-

Fe

1641 1831 1835 2230 2078 1168 296 1200 130 795 1473 670 1977 460 2573 1229 1336 1855 2047 450 1460 2377

Ni CO

Re

0s HO

w V

cr CU

Ti A1

B Nb

5 5.5 6 5 (5.5) (4) (1)

- -y

.70

2 .LO r

layer Lattice

8

.50

6

.40

u

(4) 2 1.5 5 (3) 8.5

I

.90 .80

Poison Layer Lattice (Glass) Toxic (Glass) Toxic

Y

,Y

.30 .20

%

-

n

0 A

0

. .

0

.I0

8.5 4 3.4 5.5 9

100

2w

300

400

500

600

loo

Temperature OC

Glass Former

Figure 8, Effect of temperature on the coefficient of friction for the various double oxides.

(4.5) (6.5)

Table 3 Sliding Friction Coefficients for Single Oxides T15 T o o l Steel vs Sand Blasted Stainless Steel 2Q!t%

-

2lcc

2w c .

Unlubrricated

.78*

PbO

.19*+

.lo

.60 .10

0203

.64

.51

.18

cro, Re207 ReOz cu, 0 cuo coo

.14 .35

.23

V205

TiO,

.68

A1203

.77 .41 .70

woo,

(.:e,o, '3

cr20,

NiO

.75

.64

.30 .60 .46 .51 .41 .60 .46 .53

HOO,

.46+*

.14 .50 .30 .69 .60 .52

-

.80

.27 .48 .22

a4

-

0.3

-

0.a

-

.18

.38 .56 .40 .42 .32

I 0

.64 .69

-No data taken. +Initial frictlon coefficient. **Friction coefficient after 5 minutes

oxides have some effect. Unfortunately none of these oxides were particularly effective in the low temperature range so efforts were concentrated on the double oxides. Basically this approach was used as a technique to lower the melting point of oxides and therefore lower the friction. An extensive literature search was conducted to isolate low melting point double oxides with particular attention to the rhenates, molybdates, tungstates, vanadates, and borates. Friction tests were run on the most appropriate compounds to determine their friction-temperature characteristics. The results for the four most effective compounds are shown in Figure 8. Since two of the most effective compounds were rhenates, they were selected for more detailed examination. Since nickel or cobalt base materials would probably be used at temperatures above 600°C with additions of copper and rhenium to form copper rhenate, the friction characteristics of all possible rhenates was explored, These results are shown in Figure 9. It is seen that there is a general lowering of friction coefficient with increasing temperature. Furthermore the compounds with the lower melting points gave the lowest friction,

200

400

600

600

lEMPER*NRE (C)

Figure 9. Effect of temperature on the coefficient of friction for four different rhenates. The friction temperature curve for copper rhenate is shown in more detail in Figure 10. Friction decreases rapidly in the 26-100°C temperature range. Friction is unstable in the 150-250°C range then decreases gradually above 350°C. When dried powder is used, the unstable region (150-250°C) is avoided. Thus it was concluded that the drying of the copper rhenate disrupts the wet lubricant film causing intermittent metallic contact. Since the increasing temperature behavior is essentially the same as the decreasing temperature behavior it is concluded that no reactions take place between the copper rhenate and the steel surface and no changes take place in the copper rhenate. 3.4

Frictional Behavior - Ni-Cu-Re Alloys

The first experiments were conducted with a Cu 7.5 Re alloy. This is a two phase alloy of copper and rhenium since the metals are mutually insoluble. Its coefficient of friction as a function of temperature is shown in Figure 11. A value of about 0.20 is obtained from roo111teinpernture to 500°C where friction decreases. Ai.. incrinse in friction is found at approximately 330°C. Above 200°C the

22

C4 ReM)Z

T 07 -

I

O8

0

0 INCREASING t GECREASING

-

06

0

UICRUSINC

A GECREASINO 05-

X

0 4

-

OJ

-

DRIED

+X )*

0

0

02-

b

0 x

x

x

O ' l

I 0

200

600

400

0

800

2W

TEYPER*TURE (C)

Figure 1 0 .

0.0

-

0.7

-

Figure 1 2 .

n cu~mi)o +

CuRsUV

0 C"(R.O4)?

0.6 0.5

-

0.4

-

0,3

- -+

0.2 0.1

-t

-

-

I

0 1

0

2m

400

600

800

TWPER*NIIE (C)

Figure 11.

800

600

PUPER*TWE (C)

Effect of temperature on the coefficient of friction for copper rhenate.

-

400

Comparison of the friction properties of a Cu-Re alloy with the friction properties of a number of oxide powders.

results are very similar to the copper rhenates giving almost identical values. There is no similarity between the friction for the alloy and that for the single oxides. Thus it is assumed that copper rhenates are formed on the surface of the alloy and these oxides control the frictional behavior. A different effect was found to be responsible for the low friction at room temperature. This is illustrated in Figure 1 2 where Re,O, is used to lubricate copper. Both the rhenium oxide and the rhenium oxide in water gave low friction at low temperatures, Surface analysis showed that hydrated copper rhenates were formed on the surface. This is confirmed in the friction experiments where upon heating friction rises above 100°C to the value of the copper rhenate. Thus it is suggested that in sliding on the Cu 7 . 5 Re alloy at low temperatures Re,O, is formed. Being hydroscopic it picks up water and reacts with the copper to form hydrated copper rhenate. This accounts for the low friction at lower temperature. A comparison was also made between the frictional behavior of Ni-Cu-Re alloys and their potential oxides. These results are shown in Figure 1 3 . The nickel alloys with additions of various amounts of copper and

Effect of temperature on the coefficient of friction for A1,0, sliding against copper with various lubricants.

rhenium ( s e e Table 1) gave friction values which were intermediate between those of Ni(ReO,), and Cu(ReO,),. The values were also higher than that for the Cu-Re alloy. Basically the addition of nickel in large amounts to the Cu-Re alloy caused an increase in friction either because some Ni(Re0,) was formed or because less Cu(ReO,), was formed. Overall, however, it appears from Figure 1 3 that the formation of Cu(ReO,), was favored. A considerable amount of time was spent in the analysis of the films formed during the friction testing. These results are reported in reference 7 4 . In general it was found that the composition of the oxide varied considerably in depth. At 800 C the surface of the wear track consisted of nickel and copper oxide. Between this external oxide layer and the alloy surface rhenium oxides were found. The alloy surface was rhenium rich with the maximum concentration ( 5 2 Re, 52 Ni, 6 Cu) occurring 9 pm below the surface. No copper rhenates were found in the wear track or the debris. In separate static experiments with the alloy it was confirmed that the rhenates were formed and quickly evaporated from the surface leaving the other oxides. Thus the rhenates may only be on the surface for a short time at the higher temperatures.

0 Ni I

0.7

-

+

-

a HI J

*

0.6

Ni2

Hi.

I 0

200

400

600

(I00

lDGJ

TEYPER*WRE (C)

Figure 13.

Comparison of the friction of A1,0, sliding against Ni-Cu-Re alloys and two potential naturally occurring oxides,

23

3.5

Frictional Behavior Ni 7 . 5 Re Alloy The friction-temperature behavior for Ni

7 . 5 Re alloy is compared with that for powdered Ni(ReO,), in Figure 1 4 . The results are

similar and lubricating temperature Re produced 0.B

it is concluded that Ni(ReO,), is the alloy over the whole range, Neither NiO, Re20,, Ni, or such values.

,

1

0.I

a :

zoo

0

4 M

600

800

l E Y P D U N R E (C)

Figure 1 4 .

3.6

Comparison of the friction behavior of a Ni 7 . 5 Re alloy with Ni(ReO,), powder.

Summary

The results show that alloys can be devised with low friction over a broad temperature range by adding elements which form lubricating oxides. The concept is not universal and considerably more work will be necessary to determine what alloys will behave in this manner and which will not. At this stage of the investigation it is not clear that practical alloys will result since questions of strength, oxidation, resistance, and wear rates remain. 4.

ACKNOWLEDGEMENT

This work was performed for the Material Division of the Office of Naval Research under Contract No. 88-F-0011 and for the National Science Program, China Program under Grant No. INT-8617231 to Rensselaer Polytechnic Institute, Troy, NY. 5.

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LUDEMA, K.C., "A Review of Scuffing and Running In of Lubricated Surfaces," Wear, 1984,

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QUINN, T.F.J., "Review of Oxidational Wear, I , 11," Trib International, 1983,

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BATCHELOR, A.W., SLACHOWIAK, G.W. and CAMERON, A., "The Relationship Between Oxide Films and the Wear of Steels," Wear, 1 9 8 6 , 113,203. SULLIVAN, J.L., "The Role of Oxides in the Protection of Tribological Surfaces I , " Proc. I. Mech. E., Tribology Friction Lubrication and Wear Fifty Year on I Mech E, 1987, 1987-5, 293. SULLIVAN, J.L., "The Role of Oxides in the Protection of Tribological Surfaces 11," Proceeding 1987 Conference, Tribology Lubrication Wear Fifty Years on I. Mech. E., 1987, 87-5. YOSHIMOTO, G. and TSUKIZOE, T., "On the Mechanism of Wear Between Metal Surfaces," Wear, 1 9 5 7 , 1, 472. QUINN, T.F.J., "The Role o f Oxidation in the Mild Wear of Steel," British JAP, 1 9 6 2 , l3, 33. EARLS, S.W.E. and POWELL, D.G., "Variations in Friction and Wear Between Unlubricated Steel Surfaces," Proc. I. Mech. E., 1966, 181, (Part 3 0 ) , 16. QUINN, T.F.J., "Effect of Hot Spot Temperatures on the Unlubricated Wear of Steel," ASLE Trans., 1 9 6 7 , lo, (No. 2 ) , 158.

TAO, F.F., "The Role of Diffusion in Corrosive Wear," ASLE Trans., 1968, ll, 121.

TAO, F.F., "A Study of Oxidative Phenomena in Corrosive Wear," ASLE Trans., 1 9 6 9 , 2 , 9 7 . QUINN, T.F.J . , "Oxidational Wear," Wear, 1 9 7 1 , l8, 413. QUINN, T.F.J., BAIG, A.R., HOGARTH, C.A. and MULLER, H . , "Transitions in the Friction Coefficient, the Wear Rates and Composition of the Wear Debris Produced in the Unlubricated Sliding of Chrome Steels," ASLE Trans., 1973, 16, (No. 4 ) , 239.

MOLGAARD, J. and SRIVASTAVA, V.K., "The Activation Energy of Oxidational Wear," Wear, 1 9 7 7 , 41,(No. 2 ) , 263. QUINN, T.F.J., "The Division of Heat and Surface Temperatures at the Sliding S t e e l Interfaces and Their Relation to Oxidative Wear," ASLE Trans., 1978, 2 l , (No. l ) , 78. SULLIVAN, J.L. and QUINN, T.F.J., "Developments in the Oxidational Theory of Mild Wear," Trib. International, 1 9 8 0 , 13, 153. QUINN, T.F.J., ROWSON, D.M. and SULLIVAN, J.L., "Application of Oxidational Theory of Mild Wear to the Sliding Wear of Low Alloy Steel,''Wear, 1 9 8 0 , 65, (No. l), 1. SULLIVAN, J.L. and HODGSAN, S.G., "A Study of Mild Oxidative Wear for Condition of Low Load Speed," Wear, 1988,

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HALLIDAY, J.S. and HIRST, W . , "Fretting of Steel," Proc. Roy. SOC., 1 9 5 6 , m, 411.

TAMAI, Y., "On Contact Resistance Between Surface Oxidized Metals in Repeated Sliding," Wear, 1958, 1,377. IWABUCHI, A., HORI, K. and KUBOSAWA, H . , "The Effect of Oxide Particles Supplied at the 1nt.erEacebefore Sliding on the Severe/Mild Wear Transition," Wear, 1988, 1 2 8 , (No. 2 ) , 123.

24

IWABUCHI, A., HORI, K. and KUDO, H., "The Effects of Temperature, Preoxidation and Presliding on the Transition from Severe to Mild Wear," Proc. 1987 International Wear Conference, p. 2 1 1 , ASME. STOTT, F.H., GLASSCOTT, J . and WOOG, G.C., "Factors Affecting the Progressive Development of Wear Protective Oxides on Iron Base Alloys during Sliding at Elevated Temperatures," Wear, 1 9 8 4 , 97, (No. l ) , 9 3 . TOMILINSON, G.A., "The Rusting of Steel Surfaces in Contact," Proc. Roy. SOC., 1927,

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835.

HIRST, W. and LANCASTER, J.K., "Influence of Oxide Films and Lubricant Films on the Friction and Surface Damage of Metals," Proc. Roy. SOC., 1 9 5 4 , m, (No. 1 1 5 4 ) , 324.

HIRST, W. and LANCASTER, J.K., "Surface Film Formation and Metallic Wear," JAP, 1 9 5 6 , 21, (No. 9 ) , 1 0 5 7 . LANCASTER, J.K., "The Influence of Temperature on Metallic Wear," Proc. Roy. (No. 1 , 4 5 5 ) , 1 1 2 . SOC., 1 9 5 7 , LANCASTER, J.K., "The Formation of Surface Films at the Transition Between Mild and Severe Wear," Proc. Roy. SOC.,

m,

lo, 4 0 0 .

KRUEZ, K.L., "EP Films from Borate Lubricants," ASLE Trans., 1 9 6 7 , lo, 6 7 . OSIAS, J.R. and TRIPP, J.H., "Mechanical Disruption of Surface Films on Metals," Wear, 1 9 6 6 , 9 , (No. 5 ) , 3 8 8 . MOORE, A.W.J. and TEGART, W.J.McG., "Rupture of Oxide Films During Repeated Sliding," Aust. Jour. of Scientific Research, 1 9 5 1 , 4 , 1 8 1 . MOORE, A.W.J. and TEGART, W.J.McG., "Effect of Included Oxide Films on the Structure of Beilby Layer," Proc. Roy 458. Soc., 1 9 5 2 , RIGNEY, D.A., CHEN, L.H., NAYLOR, M.G.S. and ROSENFIELD, A.R., "Wear Processes in Sliding Systems," Wear, 1 9 8 4 , 100, 1 9 5 . CHEN, L.H. and RIGNEY, D.A., "Transfer During Unlubricated Sliding Wear of Selected Metal Systems," Wear, 1 9 8 8 , 105,

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47. (38)

KERRIOGE, M . , "Metal Transfer and the Wear Process," Proc. Phy. Soc., 1 9 5 5 , (Part 7 ) , 4 0 0 . HAYLER, M.G. and EARLS, W.E., "An Interpretation of the Unlubricated Sliding Process Between N75 and ENlA," Wear, 1 9 7 1 , U, 3 9 3 . MOLGAARD, J.M., "A Discussion of Oxidation, Oxide Thickness and Oxide Transfer in Wear," Wear, 1 9 7 6 , 40, (No.

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MACHLIN, E.S. and YANKEE, W.R., "Friction of Clean Metals and Oxides with Special Reference to Titanium," JAP, 1 9 5 4 , 25, (No. 5 ) , 5 7 6 . COFFIN, L.F., "A Study of Sliding Metals with Particular Reference to Atmosphere," Lube Eng., 1 9 5 6 , l2, (No. l ) , 50. COFFIN, L.F., "A Fundamental Study of Synthetic Sapphire as a Bearing Materials," ASLE Trans., 1 9 5 9 , 1,108. GODET, M., PLAY, D. and BERTHE, D., "An Attempt to Provide a Unified Treatment of Tribology through Load Carrying Capacity, Transport and Continuum Mechanics," JOLT, 1 9 8 0 , 192, (No. 2 ) , 1 5 3 .

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COCKS, M., "Role of Atmospheric Oxidation in High Speed Sliding," JAP, 1 9 5 1 , 8 ,

PETERSON, M.B., MURRAY, S.F. and FLOREK, J.J., "Consideration of Lubricants for Temperature Above 1000," ASLE Trans., 1 9 6 0 , 2, (No. 2 ) , 2 2 5 . PETERSON, M.B. LEE, R.E. and FLOREK, J.J., "Sliding Characteristics of Metals at High Temperatures," ASLE Trans., 1 9 6 0 , 3 , (No. l ) , 101. PETERSON, M.B. and LEE, R.E., "Sliding Characteristics of the Metal Ceramic Couple," Wear, 1 9 6 4 , 7 , 3 3 4 . RABINOWICZ, E., "Lubrication of Metal Surfaces by Oxide Films," ASLE Trans., (32)

MAZWER, D . , GEORGES, J.M. and CAMBOU, B., "Shear Behavior of an Amorphous Film with Bubble Soap Raft Model," J . Phys. France, 1 9 8 9 , 49, 1 0 5 7 . CAMPBELL, W.E. , "Variables Influencing the Coefficient of Static Friction Between Clean and Lubricated Metals," Trans. ASME, 1 9 3 9 , 61,6 3 3 . WHITEHEAD, J.R., "Surface Deformation and Friction of Metals at Light Loads," Proc. Roy. SOC., 1 9 5 0 , m, 1 0 9 . COCKS, M., "Surface Oxide Films in Intermetallic Contacts," Nature, 1 9 5 2 ,

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EARLS, S.W.E. and POWELL, D.G., "Surface Temperature and its Relation to Periodic Changes in Sliding Conditions Between Unlubricated Steel Surfaces,'I ASLE Trans., 1 9 6 8 , 11, (No. 2 ) , 1 0 9 . POWELL, D.G. and EARLS, S.W.E., "Wear of Unlubricated Steel Surfaces in Sliding Contact," ASLE Trans., 1 9 6 8 , ll, (No. 2 ) , 101. POWELL, D.G. and EARLS, S.W.E., "Friction and Wear Results on a Pin-Disk Machined Applied to a Ring Traveler Problems," Proc. Tribology Convention, I. Mech. E., 1 9 6 8 , 182, (Part 3N). TENWICK, N. and EARLS, S.W.E., "A Simplified Theory for Oxidative Wear of Steels," Wear, 1 9 7 1 , l8, 3 8 1 . DANIELS, R.O. and WEST, A.C., "Influence of Moisture on the Friction and Surface Damage of Clean Metals," Lube Eng., ll, 1 9 5 5 , (No. 4 ) , 2 6 1 . ALLEN, G.P. BUCKLEY, D.H. and JOHNSON, R.L., "Friction and Wear with Reactive Gases at Temperatures to 1 2 0 0 , " NACH TN 4316, 1958.

CORNELIUS, D.F. and ROBERTS, W.H., "Friction and Wear of Metals in Gases up to 6 0 0 C," Trans. ASLE, 1 9 6 1 , 4 , (No. 4 ) , 20.

BJERK, R.O., "Oxygen - An Extreme Pressure Agent," ASLE Trans., 1 9 7 3 , lf5, (No. 2 ) , 9 7 . BUCKLEY, D.H., "Oxygen and Sulfur Interactions with Clean Iron Surfaces," ASLE Trans. 1 9 7 4 , l7, (No. 3 ) , 2 0 6 . BOWDEN, F.P. and YOUNG, J.E., "Friction and Adhesion of Clean Metals," Nature, 1949,

164,1 0 8 9 .

FINCH, G.I. and SPURR, R.T., "Surface Changes Due to Sliding," Proc. Roy. SOC., 1952,

m, 462.

25

WELSH, N.C., "Frictional Heating and its Influence on the Wear Rate of Steel," JAP, 1975, 2 ,(No. 9 ) , 960. WELSH, N.C., "Wear of Dry Steels I General Patterns," Phil. Trans. Roy. SOC., 1964, m, 30. WELSH, N.C., "Wear o f Dry Steels I1 Interpretation and Special Findings," Phil. Trans. Roy. SOC., 1964, 51. BRIDGEMAN, P.W., "Shearing Phenomena at High Pressures," Proc. Amer. Acad. Arts and Sciences, 1 9 3 6 , 71, 387. HENSLEY, C.F., MALE, A.T. and ROWE, C.W., "Friction Properties of Metal Oxide at High Temperatures,"Wear, 1968, ll, (No.

a,

3 ) 233.

RAZAVIZADEH, K. and EYRE, T.S., "Oxidative Wear of Aluminum Alloys. I," Wear, 1982, 79, (No. 3 ) , 325. RAZAVIZADEH, K. and EYRE, T.S., "Oxidative Wear of Aluminum Alloys. 11," Wear, 1983, 82, No. 3 ) , 261. BUCKLEY, D.F. and JOHNSON, R.L., "The Influence of Silicon Additives on the Friction and Wear o f Nickel Alloys at Temperatures to 1 0 0 0 , " ASLE Trans., 1 9 6 0 , 3 , (No. l), 9 3 . (73) PETERSON, M.B., CALABRESE, S . J . and STUPP, B., "Lubrication with Naturally Occurring Double Oxide Films," NTIS ADA 124248 1982, U.S. Department of Commerce. ( 7 4 ) PETERSON, M.B. CALABRESE, S.J., LI, S.Z. and JANG, X.X., "Lubrication of Alloys with Naturally Occurring Oxide Films," Final Report, NSF Grant INT-8617231, in process of publication.


21

Paper I (iii)

Elastic and viscoelastic analysis of two multiply layered cylinders rolling over each other with coulomb friction J.J. Kalker

The problem treated in this paper is of interest for the analysis of coatings that consist of one or more elastic or viscoelastic layers bonded together and to a substrate. Each coating-cum-substrate ("cylinder") is modeled as a twodimensional elastic or viscoelastic half-space consisting of layers with arbitrary thickness whose material constants differ. The cylinders are in rolling contact; friction is modeled by Coulomb's law; partial slip in the contact area is allowed. The analysis is linear. The problem is attacked by an influence function method (Green's functions). The influence functions are the displacement-stress field in the half-space due to a normal and a shearing standard loading moving over the (visco)elastic half-space with rolling velocity. They are determined by means of a complex Fourier transform, which is inverted by a method that warrants a prescribed accuracy. The two influence functions are each convoluted by a weight function. The weight functions are found with the aid of algorithms which have proved their utility in Kalker's programs CONTACT and LAAGROL, and which have been established rigorously by Kalker (1988) in the elastic case. Apart from frictionless and fully sliding contact, loadings due to partial slip in the contact may be determined; the displacement-stress field both on and inside the half-space may be computed. Up to now, an implementation has been made in which the cylinders consist of a single elastic layer bonded to a rigid base, and where only the surface load and displacement distributions are calculated (LAAGROL). The determination of the surface elastic field due to finite creepage resulting in partial slip in the contact area is the main thrust of this program, The method presented is akin to that of Bentall-Johnson ( 1 968), but automated, modernised, and extended.

1 INTRODUCTION

Consider two infinite rigid cylinders with parallel axes which are covered with a number of homogeneous, isotropic, linearly elastic or viscoelastic layers that are completely bonded to each other, and to the cylinder they cover. They are pressed together and subsequently rolled over each other, until a steady state sets in. The circumferential velocities of the cylinder-cum-layers systems may differ, so that partial or complete slip occurs in the interface. Friction is present in the interface; it is assumed to behave according to Coulomb's law with a constant friction coefficient. It is required to find the displacement and the stress in the layers with respect to the Eulerian coordinate system that is attached to the axes of both cylinders and which is, consequently, fixed to the contact area. In particular, one is interested in the displacements and loads present in the contact area. The analysis is linear, and twodimensional. For the calculation of the (visco)elastic field the cylinders are approximated by layered (visco)elastic half-spaces in contact. The surface load is approximated by a function which is constant in adjoining, equally long intervals, with the aid of algorithms that have proved their utility before in the programs CONTACT and LAAGROL, and that have been established rigorously by Kalker (1988) in the elastic case. In order to use these algorithms the (visco)elastic field due to a typical normal surface load, and that due to a typical shearing surface load are required. To find these fields, the displacements and stresses are expressed in Airy's stress function which obeys a twodimensional bipotential PDE. This equation is attacked by applying a complex Fourier transform in the tangential direction, and by analytically solving the resulting fourth order ODE in

the normal coordinate. The solution, a Fourier transform, is inverted numerically by a method which guarantees a prescribed accuracy. The method presented is akin to that of Bentall and Johnson ( 1 968), but extended, automated, and modernised. PART I 1

- THEORY

ELASTICITY THEORY

The cylinders are numbered 1 and 2, see Fig. I . We introduce a Cartesian coordinate system with the plane z = 0 in the mutual tangent plane of the cylinders, the y-axis in the axial direction, and the x-axis in the tangential direction; the z-axis points into body 1. We denote the normal stresses ux, uy, uz, and the shear stresses as rxy, ryz, rzx. All quantities (displacements, stresses, strains) can be provided with a subscript a = 1,2, signifying cylinder a. The displacements are u(u,v,w); the linearised Figure I . Two strain ex, ey, e,, exy, e z, ezx. We cyliriders i r i contact. assume a twodimenslonay situation, in which the dependence on y of all quantities disappears, and in which the y-component of the displacement v = 0 (plane strain),

a

-=o,v=o dY Hooke's law reads:

28 1 e = - u - (u x E x E y 1

ey =

uy -

(ux

+ uz)

E: elasticity modulus

+u

u : Poisson’s ratio

e = - 1u - ” ( u + u ) z E z E x y I +v --l + u e =---E ‘yz’ xy E ‘xy’ e y z l + u e =-

-

(2)

I - u E

+w=-

2

+ v)

v(l Hl,xxx -

E

Hl,xzz

+

’(’)

while the strains read: in which f(z) and g(x) are arbitrary functions of z and x. We can absorb these in H: H(x,z) := H I ( x , z ) + k(z)

The equations of equilibrium, if we omit inertia effects and body forces, are

I-v Then 2

2

E

7 YZ

0, e

=o,

XY

=

H,xxx-

0, e y z = 0, rxy = 0, 1 - VL

u =v(u + u )

Y

x

I

+ v)

v(l

E

H,xzz’

If we substitute this into (Sc), then we get the following differential equation for H :

From ( I ) , ( 2 ) , and (3) we see that =

v(l+y)H. E ,xxz’

H , ~ z z-

w=- I - v

Y

E

=2 f@),

I - u E e,xxx(x) = 2 dx).

u=-----1 - v E

(v = 0) e

+ 4 ~ ) ,k ,222 (z)

z

+ v)

u(l

H , ~ z z z-

E

(5)

so that

+-

E

H,xxzz

1 - v E

--

+

v(l H,xxxx -

+ v) E

H,xxzz=

+ u)

2(1

E

e.. = 0

H,xxzz

or H,zzzz

+

2H,xxzz

H,xxxx

+

=

0.

H is called A i r y ’ s stress function. Summarizing: The equations of equilibrium are u

x,x

u=- I - v E

=o zx,z

+r

7zx,x

+ uz,z

u = H

x

They can be solved by setting

v(l H , ~ z z-

w=- 1 - v E

I

=o.

2

+ v) E

2

v(l H,xxx -

H,xxz

+ v) E

H,xzz

CJ=H 7 ,zzzx’ z ,xxz’ xz

= -

u =v(u + a )

rxZ= -F,xz,

uX = F ,zz’

uz = F,xx

(8)

x

Y

H,Zzzz in which F is an arbitrary, 3x differentiable function x and z. We have, according to (3), ( 6 ) , (8)

( 1 1)

H,xxzz’ (C)

z

2H,Xxzz

(b)

+

H,xxxx

=

0.

( 4 J

We note that ( 1 1) holds for any twodimensional, homogeneous isotropic elastic body. When we consider a layered medium with each layer homogeneous and isotropic, ( 1 1) holds for each layer separately. 1.1

(9a), (9b) can be satisfied by assuming that

+

(a)

A fundamental boundary value problem

We assume that both layer and cylinder can be taken as plane as f a r as elasticity calculations are concerned. For the boundary values we retain the real geometry. The situation is shown in Fig. 2. The layers consist of several sublayers; the interface between sublayer i and sublayer i + 1 has the equation

29 z = ( - 1 ) a- 1 Dai, a = 1,2; i = 0 ,...,m

. Dai E 7R, (12a)

2

CONTACT FORMATION

Q1'

a i .' number of sublayers of layer a. DaO = 0 < Dal < Da2 ... < Dam def - Da.

m

( 1 2b) ( 1 2C)

Consider two cylinders, see Fig. 5. The boundaries between rubber and steel are not shown.

a

(a 1

The situation is shown in Fig. 2. The sublayers are completely bonded together, so that we have that u, w, uz, rxz are continuous across the inter(13a) face of two sublayers.

Figure 2 . T h e layers and the cylinders.

2

The subscript a is omitted as long as this causes no confusion. The layers are rigidly bonded to the cylinder. So

u (x, (-1)"-l

Da) = w (x, ( - 1 f - I

D ) = 0. a

+o

1

contact

d=O

(13b)

undeformed surface

Moreover, it lies at hand to suppose that u, w, ux, uz, rxz -+ 0, far from the contact area. Therefore, we assume

H

-+

Ix I

0 with all derivatives if

-+

03.

Finally, we assume that at the surface z = 0 u (x,O) def - u(x) = prescribed rx z(x , O ) def - r(x) = prescribed.

u ndeformed surface

X

(14)

(15)

We shall use solutions of this type to construct the more complicated solutions we need. In particular, we consider the case when u(x) and r ( x ) are piecewise constant, see Fig. 3. These traction distributions can be considered as built from elements, see Fig. 4. We are interested in the influence numbers, i.e. the displacements in y due to the element with height 1, width a, and centre x. The traction distribution, hence the displacement, is determined by the numbers ui, ri, heights of the i-th element.

Figure 5. T h e cylinders touch in Fig. 5a. T h e layers are not shown. T h e y approach each other over a certain distance in Fig. 5b. I n Fig. 5c a deformation occurs, which cancels the penetration in Fig. 56. I n Fig. 5d the construction o f the deformed distance i s shown. In Fig. 5a the cylinders touch; their vertical distance at the position x is h '(x). h '(x) is given by h'(x)=- 1

( - +1 F )

1

x 2,

Rl 2 R : radius of cylinder a.

a

Subsequently the cylinders are pressed together, causing their centres to approach each other over a distance p. If we omit the elastic deformation, their distance is now h(x) = h'(x) - p =

Figure 3. Piecewise constant traction.

a,

( l +-)2R2 1 2Rl

- w,(x) + w,(x) t 0 as the bodies cannot overlap d(x) = 0: contact. X t V *

Figure 4 . A n element.

(17)

NOW the bodies overlap, see Fig. 5b; this is cancelled by the elastic deformation shown in Fig. 5d, and the bodies look as shown in Fig. 5c. It holds that the distance after deformation is d(x), and from Fig. 5d we can tell d(x) = h(x)

x

x 2 - p.

1

We assume that the bodies cannot exert tractive forces on each other, or u(x) 5 0; and that tractions can occur in the contact only, or u(x)d(x) = 0, while the normal force is

30

continuous, in the sense that q ( x ) = q ( x ) = u(x). Summarizing, we obtain

has never failed so far. T h i s , added to the f a c t that the second alternative allows e a s y generalisation to the threedimensional case (Kalker. 1 9 8 8 ) leads us to adopt the second alternative. If instead of p the total force Qz =

s-oo (u(x)) dx is given,

we use the discretised version Q

-

=

00

=

We assume an element with length a; and we want to know the traction/displacement in the interval (-fna,f(n+ 1)a) of the x-axis. This is called the potential contact; n can be chosen freely as long as the entire contact area is within the potential contact. We cover this interval with the elements of Figs. 3, 4. These elements are numbered i = 1, n and they are determined by the tractions in their centres, ui, n - 1 and rai. Their centres are in xi = ( i - 7) a. wai is also sampled in these points; it holds the following connection between wai and the tractions uj and the tractions raj, the latter of which we consider given. Then we want to solve the following problem. Find all uj:

7

a ui as an auxiliary

I

condition. The approach p will be considered as Lagrange multiplier (an unknown) of this auxiliary condition, and if we define

w (x.) - w (x.) = C ( A . . U . + B . . 7.) 1 1 2 1 j 11 J '1 1 ( A . . , B . . : influence numbers) U 11 then the tableau is:

-1a u.J

'

= N

j

u. < 0; d . = d(x.) >_ 0; u.d. = 0;

J-

J

J

J J

r . given. J

(20)

with h

The following algorithm solves the so-called complementarity system (20), if approach p is given:

Algorithm N , Kalker (1983, 1988) For all i within the potential contact Step 0. Suppose ui = 0, 1 5 i 5 2n + 1 ; we assume ri given. Step 1. If d i 5 0, then i is placed in index set (= set of indices) K . If di > 0, then i is placed in index set B ( K : contact, B: surface of the half-space outside contact ("exterior")). Step 2. We set di = 0 if i is in K ; we set ui = 0 if i is in B. These are 2n + 1 linear equations for the 2n + 1 unknowns ui; Solve them. Step 3. If i lies in K and the just-found ui 5 0, i will remain in K. If i lies in K and the just-found ui > 0, one such i will go to B. If i lies in B, i will remain in B. Step 4. If K is changed in step 3, then go to step 2. Step 5. Now ui 5 0 in K ; ui = 0 in B , di = 0 in K . We verify whether di t 0 in B. If i is in B and di < 0, one such i will go to K ; otherwise K and B remain unchanged. Step 6. If K is changed in step 5 , then go to step 2. Step 7 . Now ui 5 0 in K , ui = 0 in B, di = 0 in K , di ? 0 in B: We are ready. Remark. This algorithm can be proved rigorously to converge towards the unique solution of (20) in a finite number of steps, see Kalker (1983, 1988). The number of iterations, though finite, may be large; actually it will be of the order of 4n, n: the number of elements in the contact area. Two methods may be used to accelerate the process: 1. Only one element of K goes to B, and vice versa. Hence the system of linear equations of step 2 changes only little, so little that the solution may be updated by a simple update formula which requires only O(n2) elementary operations. 2. Alternatively one may modify K and B in step 3 by allowing all i to go to B for which the just-found ui > 0; and by allowing all i to go to K in step 5 for which di < 0. The first alternative is attractive in that the proof of the algorithm remains unchanged. The second alternative is simpler, but our proof of the algorithm breaks down. Yet the algorithm is so robust that even with the modification it

. = h'(x.) - 1 Bi j rj

tl

'

j

The algorithm runs as above, with p as an extra variable that can take any value. 3

FRICTION

Let Vv be the slip of body 2 over body 1 when 1 and 2 are considered rigid. In the time interval (T - t, T) the relative displacement will be Vu t. As a result of the elastic deformation of the layers on the cylinders, the particle that was in x at the time T has undergone a tangential displacement of u(x) with respect to the cylinder. At the time T - t the particle was in x + Vt, see Fig. 6. The tangential displacement of the particle with respect to the cylinder at the time T - t is u(x + Vt). The net tangential displacement of the particle with respect to the cylinder in the time interval (T - t, T) will be u(x) - u(x + Vt). Therefore the total tangential displacement of the cylinder (2) with respect to (1) is: v,(x) = v u t

+ (u,(x + Vt) - u2(x + Vt)) + - ( u p ) - u2(x)).

(22)

If we choose Vt = a, where a is the width of an element, then we get v. = av

+ ui+l

- u.; Vt = a

(23)

(u = u1 - uz).

Rolling velocity Particle velocity 4

-0 0:same particle

! x+Vt

I I

X

x+vt

Figure 6 . T h e movement of a particle through the contact plane.

31

With the aid of the influence numbers vj is expressed linearly in the oi and the ri. Concerning the forces we observe that the stress is continuous across the interface of the bodies. so that

r 1(x) = r2(x),

I

5 -fo.

1

< 0).

If the slip at element i, vi # 0 then we have in K . ri = foi sign (vi)

(25)

t!

v(v + 1) u=- 1 - V L E H , ~ z zE H,xxz w = - 1 - vL.

E

I I

F1,zzzz

I

Renzark. When in step 3 only one i with I r i I > -fui is allowed to pass from the area of adhesion A to the area of slip S, and when in step 5 only oiie i for which ~i and vi have the same sign is allowed from S to A , the algorithm F can be proved rigorously, in the same manner as N. Then, as in N (see the Remark after it) there are the same two alternatives by which F may be accelerated. We have adopted the second alternative, which has actually been given in our presentation of F. As in N, no failures have been observed. 3.1

+

V(Y

H,xxx-

2H,xxzz

+

+

1) :I

E

,xzz

H,xxxx = 0, 1x1

H-Oif u = H

z

,xxxz’ xz

=

(26~)

-00

given at z

= -

7

(u,w) = (0,O) if z

H,xxzz’ ff-1 (-1)

=

0

(26d) (27)

Dff.

Appendix E , ( E l 5a) specialises v to be constant, and E to

I

I

App. E (E 14)

with E(r) as in App. E (E15). The superscript f indicates a complex Fourier transform with respect to time and parameter r see A p. E (E7, sqq). It is shown in Appendix A that ef.,’ uf., u f f o r m a purely elastic field for any value of 11 1J 1 the parameter r. Hence we may introduce the A i r y stress function H as in ( 1 1 ) (we omit the parameter and the superscript f):

The problem is now solved by the following algorithm. Algorilhm F IKalker (1983, 1988)) Step 0. Initiate with ‘ri.=, 0. We work only within the contact area K , 1 in K, ui is given. Step I . If r i > - f q (q < O!), then i is placed in S (index set: area of slip). If I r i I 5 - f q , then i is placed in A (index set: area of adhesion). Step 2. If i is in S, r i is set equal to - f q sign (ri) which means that I ri I is reduced to - f q , while r i retains its sign. If i is in A then vi is set equal to 0. These are linear equations. Solve them. Step 3. If i is in A , as well as the just-found I r i > - f q , then i is placed in the area of slip. No further mutations; the area of adhesion can only decrease. Step 4. If A is changed in step 3, then go to step 2. Step 5 . Now it holds in A : I r i 5 -fui and vi = 0, and in S: 1 r i I = -mi. If i is in S and r i and vi have the wrong sign with respect to each other, see (25), then i is placed in the area of adhesion A , see (25). Step 6. If S is changed in step 5 , then go to step 2. Step 7. Now it holds in A : I r i 5 - f q , and vi = 0: area of adhesion, and in S: r i = fui vi/ I vi I : area of slip. We are ready.

v f uf - IJ E(r) ‘hk‘ij

f e..(x ,r) = 1J

.(

1

ELASTICITY A N D VISCOELASTICITY

In Appendix E it is shown that for a certain class of viscoelastic materials

(24)

u 1(x) = u2 (x).

We assume that the friction can be described by the law of Coulomb-d‘Amontons, with a friction coefficient f . Discretised, this reads: 17.

4

E(r) = (1

- jqr)/(K

App. E (E I5a)

- jqQr)

with K , Q, q viscoelastic constants which are interpreted in App. E , (E15). When K = Q, one regains elasticity with E = I/K. Consequently, (26a,b) become f

( 1 - jqr) u = ( K

- jqQr)((l - v

f

2

f

) H,Zzz -

2

f ( 1 - j q r ) w = (K - jqQr)((l - v ) H,xxx

f

41 + Y ) H,xxz)

-

(28a) f 4 1 + v) H,xzz). (28b)

We transform back, cf. App. A , (A16): ( I + q d/dt) uf = ( K + q Q d/dt)((l

(1

+ 9 d/dt)

f w = (K

41

- v 2 ) H,Zzz +

+ v) H,xxz)

+ qQ d/dt)(( 1 - Y 2 ) H , x x x + - 4 1 + v ) H,xzz).

(294

(29b)

In steady state rolling in the positive x-direction with velocity V > 0, d/dt = -Va/ax, hence

The Panagiotopoulos process

Because the algorithm F, assuming a certain ui, will change the ~i with respect to their original values, the algorithm N, which uses these values as data, will change the oi as well, thus causing a discrepancy. We solve this by repeating the algorithms N and F: N F N F N F ... until a convergence of ui and r i occurs. This process is called the Panagiotopoulos (1975) process. If it is performed once: N F , it is called the John~ou process (Bentall-Johnson (1967)). There is no guarantee that the Panagiotopoulos process converges, and if it converges, whether the solution found makes sense. I n my examples, treated by the LAAGROL program, no complication occurred, and a most convincing convergence was reached after 4 x NF.

We introduce a complex Fourier Fansform with respect to x, with k as parameter and a hat ( ) as transform indicator. The complex Fourier transform is described in App. E , sec. E4. We obtain in a multilayer

32

i

1 - jq.Vk 1, ...,mff' mff : number of layers; E.I = K . - jq.Q.k

=

Ei

1

&(k,z)

+ v.

A

u =jk

=

jk 3 (1 - v.)

1

A + jkv.;

3

H

(33)

2"

xz =

,z'

(32)

+ (1 + kz) Bi) ekz + + (-Ci + (1 - kz) G i ) e-kz]

Gzi(k,z) = jk [(A.

1

,zz

1

3"

I

3xz1.(k,z) = k [(Ai + (2 + kz) Bi) ekz + + (Ci + (kz -

(34)

H,Zz

(41c)

2 ) Gi) e-kz]

+ (3 + kz) B.) ekz + + (-Ci + ( 3 - kz) Gi) e-kz],

(414

cxi(k,z) = -jk [(A.

with A

2"

H,Zzzz - 2k H ,zz

+ k 4"H = 0.

(35)

We confine ourselves to body 1 ; the layer of body 2 is treated similarly. We solxe the differential equations (35); they are ODE in z, for H. We find in layer Li

I

(36)

+ zBi(k)) e kz + (Ci(k) + zGi(k)) e-kz,

integration constants depending on k. A., B., C.,1 G.: 1 1 1 Consequently, the tra;sformed the transformed layer Li,

(37)

field quantities become, in

A

i = 1 ,..., m

L. = ((k,z) I D i- 1 5 z 5 Di),

+ v.1

1 =

[(k 3(Ai

+ zBi) + (3 -

(38)

2vi) k2Bi) ekz

(42) constitute 4m linear equations; for the 4m integration constants Ai, Bi, Ci, Gi, i = 1,...,m. The coefficients of these equations and the integration constants are functions of the transform parameter k. Let Ai

=

T T (Ai,Bi.Ci.Gi) , Oi = (O,O,O,O) , i = 1,..., m.(43)

~

+ (-k 3(Ci + zGi) + ( 3 j(1 + v.) 1 3 [(k (Ai

~

+

E; (k 3(Ci '

+ zGi

Gzi(k,z) = jk [(k 3(Ai

2vi) k2Gi) e-kz]

+ zBi) +

Then the boundary conditions (42) become, in symbolic form (39a)

2v.k2B.) ekz + 1

1

- 2vik 2G . ) e-kz]

(39b)

+ zBi) + k 2 Bi) ekz +

+ (-k 3(Ci + zGi) +

k2Gi) e-kz]

(39c)

.(k,z) = k [(k 3 (Ai + zBi) + 2k 2 Bi) ekz + xz1 + (k 3(Ci + zGi) - 2k2Gi) e-kz]

3 2 kz [(k (A. + zB.) + 3k Bi) e + 1 1 + (-k 3(Ci + zGi) + 3k 2 Gi) e-kz], (k,z) E

5XI.(k,z) = -jk

(394

ti.(39e)

We write

where N is a 4m x 4m complex matrix function of k which is regular and continuous everywhere. Define S(k) as the first column of N - l , and T(k) as the second column of N - I . Then we have, i f S and T are partitioned :

[A"] Am

=

[

s']

1 + v.

j(l &.(k,z) =

+ (3 - 2vi + kz) Bi) ekz + + (-Ci + (3 - 2ui - kz) Gi) e-kz]

+ v.) E:

[(Ai

(41a)

2vi) Gi) e-kzl

T']

$/k

m '

S.,T. are complex 4-vectors. 1

1

u (x)=I(x)=o

1x1 > a

= I I(k) = (sin (ka))/k

1x1 < a

0

A

+ (2vi + kz) Bi) e kz +

' + (Ci + (kz -

[

(45)

We are interested in the response of the layered medium to the normal surface load

[(Ai

E.

$/k+

m '

and omit the primes again. In terms of the new definition (40) of Ai, Bi, Ci, G i we obtain $.(k,z) =

(42b)

&i(k,Di) = Gz,i+l(k,Di); qxzi(k,Di) = $Xz,i+l(k.Di), i = 1 ,...,m- 1. (42c) Continuity of u, w, uz, T~~ on the inner boundaries, between the constituent layers.

+

Ei

&.(k,z) =

(42a)

Surface loads prescribed. G;(k,Di) = ;i+i(k,Di); &i(k,Di) = Qi+l(k,Di);

C.

that

;.(k,z)

= 6,(k,D) = 0, D = Dm. a. ;,(k,D) Perfect adhesion between the layer system and the rigid substrate. b. sz;zl(k,O) *f- $(k) = prescribed,

h7Xzl(k,0) e-f ?(k) = prescribed.

D o = O , Dm = D

fI(k,z) = (Ai(k)

ti.(41c)

We consider the boundary conditions:

i = 1 ,..., m,

L i = ((x,z) D i - l 5 z 5 Di),

(k,z) E

(4 1b)

and also to the tangential surface load

33

(x) = I(x). 0

(46b)

7

We will approximate the true surface stress distribution by the following piecewise constant one: n u(x)

C

=

uh I(x - 2ha)

A

So we have obtained the elements of F; they are complex. However, F itself is real, so that A

h=-n n

F(k) =

1

T(X)=

Si, Ti: see (42), (44), (45); they are complex 4-vectors, functions of k and ~ ( 5 2 ~ )

r h I(x - 2ha)

(47)

+j

h=-n where (%,Th) are constants to be determined by the algorithms N and F, and the Panagiotopoulos process. The calculation consists accordingly of two parts: 1. We must know the elastic field Fn x,z) (un(x,z), due to the wn(x,z), U;(X,Z), 7iz(x,z), u:(x,z))

cr=

0

7(x) = 0

(484

-00

1

F(x) sin (kx) dx

J'

J'

00

C

F(x,z) =

- 2ha,

(u Fn(x

h=-n

h

z)

+ rhFt (x

- 2ha,

2)).

(49)

For the determination of (Uh,Th) we need, apart from the surface load, the surface displacement: n ul(x,O) = u(x) def -

C

{uhun(x - 2ha) + h=-n + rhu t (x - 21ia))

(5Oa)

n

w(x) def - w (x,O) = -

4.1

1

C h=-n

(uhwn(x - 2ha) + + rhw t (x - 2ha)). (50b)

The Fourier transform of the influence functions

We t r y s f o r m uo(x) and ro(x); we denote the result by $o(k), ro(k), and we drop the subscript zero. For a purely normal or a purely tangential load we have An

An

At

At

u (k) = (sin ka)/k,

r (k) = 0 r (k)

u (t) = 0,

(51a)

= (sin ka)/k.

(51b)

Usually, our considerations hold for a purely normal and for a purely tangential load, and then we will drop the superscripts "n" or "t". Occasionally, however, it is essential to distinguish between the two types of loading, and then we will use the superscripts. A We recall that the connection between the elastic field F and the integration constants Ai was given in (41). In symbolic form we have

k = M.A. = M.. (S. $/k 1

1

I

1

+ T. $/k)

= Sy$/k

+ T:

$/k,

(52a)

with Mi a complex 5 x 4 matrix depending on k and z, defined by (41); (52b)

F(x) cos (kx) d x :

even in k. (53a)

F(x) sin (kx) dx:

odd in k. (53b)

-00 00

-00

=

is J'r",

-

s

l o o

n

F(x) cos (kx) dx + -00

On the other hand,

(48b)

We call Fn and F t the normal and tangential irzfluerzce furicfioizs of the problem. 2. Once we have the influence functions, we determine the weight factors (Uh,Th) by the algorithms N and F, and the Panagiotopoulos process. Then the resulting field is

s

00

-00

Re &k)) =

F(x) r(x) = I(x).

.

elkx F(x) dx =

so that

and the similarly defined elastic field Ft(x,t) = (ut(x,z) ,...,...,...,...)T due to the surface load u(x) = 0,

0

Im (k(k)) =

surface load u(x) = I(x),

s

2s =-

+

2s

-00

J'OO

-00

k(k) e-jkx dk = Re (k(k)) e-jkx d k

+

Im &(k)) e-jkx dk

so that, since F(x) is real, F(x)

iJ'y + 1J'y =

Re (k(k)) cos kx dk

+

Im ($(k)) sin (kx) dk

(54)

whicli are real integrals, one a cosine, one a sine transform. We will show in Appendix C how these integrals can be calculated numerically, fast, and with a prescribed accuracy. When we consider elasticity rather than viscoelasticity, K = Q, and some gain in calculation speed can be obtained by keeping track of the real and imaginary quantities. Then (52) can be formulated in Frms of purely real and purely imaginary components of F, while there is hardly any need of complex arithmetic. Either one or the other integral appears alone in (54). This yields a reduction in calculating speed of roughly a factor 4, which is due to the circumstance that a complex multiplication results in 4 real products instead of in I . On the other hand, the algorithms N and F are equally fast in viscoelasticity as in elasticity, so that once the influence functions are known, the viscoelastic and elastic calculations are equally fast. 5 CONCLUSION A fast method has been presented for the calculation of the elastic field on- and inside a viscoelastic or elastic multilayered cylinder. It is found that the calculation times for a viscoelastic multilayer differs not too much from its elastic counterpart. Details of the calculation are given in the Appendices of this paper, as well as a dimensional analysis.

34

REFERENCES

APPENDICES, see:

BENTALL, R.H. and JOHNSON, K.L. 'Slip in the rolling contact of two dissimilar elastic rollers', Int. J. Mech. Sci. 1967, 9, 389-404. BENTALL, R.H. and JOHNSON, K.L. 'An elastic strip in rolling contact', Int. J. Mech. Sci. 1968, 10, 637-663. KALKER, J.J. 'Two algorithms for the contact problem in elastostatics', In: Contact mechanics and wear of wheel-rail systems, Eds. Kalousek, Dukkipati, Gladwell, 1983, Univ. of Waterloo Press, 10 1 - 120. K A L K E R , J.J. 'Contact mechanical algorithms', Comm. Appl. Num. Meth. 1988, 4, 25-32.

KALICER, J.J. 'Elastic and viscoelastic analysis of two multiply layered cylinders rolling over each other with Coulomb friction', 1988, Complete report, available from author.

SESSION II THEORY Chairman:

Professor D. Dowson

PAPER II (i)

Analysis of damage mechanism using the energy release rate

PAPER II (ii)

Integrity of wear coating subjected to high-speed asperity excitation

PAPER II (iii)

Coating design methodology


31

Paper II (i)

Analysis of damage mechanism using the energy release rate P. Destuynder and T. Nevers

The elastic energy stored in a structure is a function of the various parameters which are defining the structure. Its derivative with respect to damage parameters is the energy release rate. It is the thermodynamic force connected to the evolution of this damage. Using domain derivative this quantity can be derived from the expresssion of the elastic energy for several structural models for static and dynamic problem as well. Obviously the relation between the energy release rate and the damage evolution requires a constitutive relationship. And only the experiments can furnish such an information. An example occuring in the delamination of composite plate is given in this paper.

x3

1 . GENERAL CONSIDERATIONS Let us consider a plate made of coniposite materials as shown on figure 1. We assume that there exists a delamination crack between two layers of fibers differently oriented. The mechanical behavior of the whole plate submitted to in-plane or transverse loadings can be represented through an assembly of three thin plates (see figure 2). The connection at the crack tip ensures that the displacement fields are continuous. In the framework of thin plate theory (Kirchhoff-Love theory) this implies the continuity of displacements and rotations at the crack tip. One could object that such a model does not represent accurately what really happens in the vicinity of the crack tip. This is true. But as far as quantities connected to the energy are concerned the model described above is consistent. More precisely one can prove that it permits to represent the energy release rate. This problem has been extensively studied in publications. Let us mention The experimental approach of OBrien T.K. [ 11 and the numerical formulation due to Raju I. and Crews J. [2]. With another respect a structural approximation of such problems has been suggested by Chai' I. Babcok C.D. [3] for instance.

2 . THE PLATE MODEL The medium surface of the plate is denoted by w and is referred to the system of axes x,

plan mayrn d i fl t

\

/

I

plan mown d t f l

Figure 1

firrurr

-

rE

Figure 2

(for cx = 1 or 2). The coordinate x3 describes the thickness of the plate. The displacement fields are denoted by u, for the in-plane components and by u3 for the deflection. Both are functions of the coordinates x,. They describe the kinematics in the different parts of the plate as follows. The resulting stiffness tensors of each plate are Rm,pkF (membrane effect) and Rb,pkF is the bending modulus tensor. In each plate the membrane stress is nap and the bending moment is map. The constitutive relations are :

I:

38

on w, (corresponding to the safe part of the plate)

Then the Principle of Virtual Work leads to the following variational relationships for any kinematically admissible displacement fields (v3,va) satisfying the continuity requirements given at (1) :

On wd (corresponding to the delaminated area)

where the exponent stands for the upper or lower par of the delaminated area of the plate and Rckapkp is the coupling stiffness tensor due to the fact that the portions of the plate corresponding to the delaminated area are no more equilibrated (i.e. non symmetrical). They are deduced from the reduced stiffness tensor +_

With another respect the transverse shear stress can be obtained from the three dimensional equilibrium equations. As a matter of fact from :

Rapkp by :

one deduces

Jz

Jz rz

where 5' = (z+~)/2 and 6- = (z-E)/~ denote the medium surface of each sub-plate corresponding to the delaminated area (see figure 1).

on both the delaminated and the safe part of the plate. This formulae is certainly not very accurate particularly if it is used in a numerical scheme (because it involves third order derivatives of the deflection u3 with respect to the coordinates xa). This remark suggests to define a finite element scheme where the transverse shear will be chosen as an unknown. For more details we refer to Destuynder Ph. and Nevers Th. [4]. The continuity requirements which have been prescribed on the displacements at the connection between the delaminated area and the safe part of the plate permit to deduce from the Principle of Virtual Work, the stress continuity relations which have to be satisfied at the crack tip. First of all the continuity of the displacement va implies:

Then from the continuity of the rotations along the crack tip one deduces :

39

elastic problem set over QEq is denoted by (crq,uq) and the corresponding energy is : and finally the continuity of v3 leads to :

where the derivative with respect to the coordinates "i" has the meaning of a derivative with respect to the coordinates : It is worth to notice that these relations do not imply the stress continuity at the crack tip. This is due to a classical boundary layer phenomenon along yf wich certainly involves stress singularities that can not be reproduced only with the plate model. A complementary local analysis would be necessary. But in the sequel we are interested by an energy balance criterion which will traduce the amount of elastic energy that the structure is able to spend in the evolution of the crack tip, (i.e. the delamination).

x'i = xi + T-, ei(xI,x2).

The derivative of Jrl with respect to the crack tip in the direction 8 is then defined by (Gateau derivative) :

The computation of G (the energy release rate), can be done analytically. Furthermore if one notices that the partial derivative of J11 with

3 . COMPUTATION OF ENERGY RELEASE RATE

THE

First of all let us come back to the three dimensional elastic energy. The energy release rate is defined as the derivative of this quantity with respect to the crack tip position. In order to obtain an analytical expression let us introduce the following notations. Let 8 = (8,) being a vector field defined over RE, which is the open set occupied by the whole plate. The following properties are assumed : i) the restriction of 8 to the crack tip represents a virtual movement of it : ii) the support of 8 is an arbitrary small neighborhood of the crack tip ; iii) the vector 0 is everywhere parallel to the delaminated area (i.e. to the medium surface w). In other words one has

e3 = 0 ;

respect to uq is null (stationarity of the elastic energy at the solution), it is sufficient to compute the partial derivative of Jq with respect to q. In the reference [5] we obtained :

as a matter of fact the above integrals are limited to a neighborhood of the crack tip Tf because the support of 8 is included in such a neighborhood. Using integrations by parts (Stokes formulae) one can prove that G only depends on the value of the normal component of 8 along the crack tip. But it is more convenient to work with the expression (8) in the sequel. Let us split the second term as follows.

iv) the components 0, are independent on x3. For each value of a (small) parameter

c =,-'J;

oijai uj a, 8, c

denoted by q, one associates the open set QEq similar to REbut such that :

M E RE , F'l(M)=M+qB(M)E R" and the crack length on Rm is l+q (8 being unitary at the crack tip). The solution of the

In order to derive from this expression a numerical approximation of G, one could

40

suggest to substitute in (9) the plate approximation for the stresses and the displacements u. Unfortunately this would lead to a wrong expression. This strange phenomenon is due to the transverse shear. The next section is devoted to the derivation of a correct expression for G using only information coming from the plate solution. Mathematical justifications are detailed in the reference [6].

4 . APPROXIMATION OF THE ENERGY RELEASE RATE USING A PLATE THEORY The Kirchhoff-Love model that has been described in the preceding chapter rests on several physical hypothesis : i) The transverse shear energy is negligible compared with the in-plane stress energy. ii) The in-plane stresses are well approximated by the plate solution. iii) The displacement fields and their first order derivatives are well approximated by the plate solution. First of all the Principle of Virtual Work enables us to write :

then the constitutive relationship leads to (Sa3p3 being the shear component of the compliance tensor) :

which gives by eliminating u3 :

and then from (9) :

Introducing this relation in the expression of G one obtains :

,

As a matter of fact it is possible to introduce now simplification due to plate theory. From the properties formulated above one can neglect the energy due to the transverse shear stress. Hence we suggest the following formula where the different fields (in-plane stresses and displacements) are those of the plate model :

r

This expression of G involves three contributions corresponding on the one hand to the upper and lower part of the delaminated area and on the other hand, to the safe part of the plate.The practical contribution of each term is limited to a neighborhood of the crack tip. It can be chosen arbitrarily small because the expression of G only depends on the value of 8 on the crack tip line. Hence the support of 8 will be limited in the numerical computation to a crown of finite elements surrounding the crack tip. There exists several other ways to derive an expression of the energy release rate from a plate model. Let us mention two of them but which would lead to a wrong formulation. The first one consists in deriving the plate energy with respect to the crack tip. One would only obtain the two first terms in the expression of G given at (12). As a matter of fact this paradox comes from the fact that it is not possible to invert the derivation of the three dimensional energy and the simplification due to the plate approximation. The difficulty arises in the approximation of the transverse energy term. It is null for a plate model but not its derivative

41

with respect to the crack tip. Another possibility would be to introduce the plate approximation of the transverse shear stress in (9). Unfortunately this does not work ! The mechanical explanation is not straightforward. It is due to the fact that near a edge or a geometrical singularity, the Kirchhoff-Love hypothesis is no more correct. Hence only partial informations are reliable. In our case the in-plane stress is correct but not the transverse shear. It is the basic reason which permits to prove mathematically that the right expression for G is the one given at (12), see [6] for details.

6.A FIRST COMPARISON BETWEEN COMPUTATION AND EXPERIMENT (collaboration with ACrospatiale)

B

The requirements for a nice finite element scheme are very restrictive and most of the known methods have important drawbacks when composite materials are concerned. In this analysis we used the QUAD 4 element [7] or a triangular element (second degree) based on Mindlin theory. A special reduced integration technique is necessary for the transverse shear energy term. But we are aware that improved plate element have to be used. The numerical solution is performed using a diagonally preconditioned conjugate gradient algorithm. The meshes used are represented on figure 2. The computation of the energy release rate is done with a vector field 0 the support of which is limited to the first strip of finite element mounding the crack tip on each side (see figure 2). Because of the good numerical stability of the expression of the energy release rate, it is not necessary to extend very much the area on which this computation is done (i.e. the support od 0). As a matter of fact 6 is successively chosen being equal to 1 (alternatively in direction x and y) at the degree of freedom linked to the points on the crack tip and zero at the other. Because G is a linear form on 6 one thus obtains the value of the energy release rate as a vector field distributed along the crack tip the components of which have the physical meaning of an energy available at each point for creating a new delaminated area. This area corresponds to the one described bu the field 0. Hence in order to keep a physical meaning for the energy release, it has been normalized by the area created by 0 in the numerical examples.

w

I

41 6 r n n

-

x-

xa -

Y

180 mm

35 mm 00

5 . NUMERICAL APPROXIMATION OF THE ENERGY RELEASE RATE

Orientation o f fibers

,loading

x 35 mm

\

Delamination

oriented f i b e r s specimen

Figure 3

A specimen made of stacke'd carbon fibers oriented in the same direction is considered (see figure 3). The computation of the enery release rate has been performed for several crack lengths and compared with experimental results performed at the ACrospatiale. The global value of the energy release rate seems to be in agreement with the experiment. A first conclusion was that the energy rate is not an intrinsic quantity for delamination. But after a careful examination of the crack tip geometry we discovered that the evolution of the crack led to a curved line and that the evolution the middle point of one unit length did not correspond to the same area created (see figure 4). Then a normalization of G with respect to the area created permitted to suggest that there exists an intrinsic critical value for G. Furthermore the experimental results obtained by Lang at ACrospatiale corroborate this result. More precisely the numerical curve drawn on figure 4 was also obtained experimentally (with the maximum).

7.COMPARISON FOR A MULTILAYERED PLATE WITH A HOLE (traction test) (collabortion with Dassault) Two different kinds of specimen have been considered. The first one has 8 layers of carbon fibers andthe second one has 32 layers. The finite element mesh which has been used is shown on figure 5.

The 8 layers specimen Three different cases stacking sequences

42

interface corresponding to the maximum value of G. May be this is just a particular case.

have been considered : /0/45/-45/90/,,

Figure 6

1451-45/o/90/s and /45/O-45/90/s (s stands for symmetrical).

D i s t r i b u t i o n o f G a l o n g the crack l i p at [ h e i n i e r f a c e w h e r e il F i r s t stack. sequ.

S e c o n d stack. sequ.

IS

marinlum

Thlrd s l a c k . sequ.

L The 32 layers specimen

0.

F i g u r e 5 F i n i t e e l e m e n t m e s h u s e d : 1 is t h e s a f e part. 2 c o r r e s p o n d to the d e l a m i n a t e d a r e a . T h e c r a c k l i p i s a1 l h e c o n n e c l i o n .

For each one the delamination has been located at the four possible interfaces. The eight results (energy rate are represented on figure 7). For each one the maximum of G is indicated. In any acse it is obtained at point A on figure 5. In order to give an idea of its distribution along the boundary it is drawn for three cases on figure 6. With another respect one has to point out that the value of G is not really meaningful in the analysis of delamination. This quantity has to be refered to the angle between the fibers of the surrounding layers. But it worth to compare with experimental results obtained on a specimen. In the three cases one can observe that a large delamination appears at the interface corresponding to the largest value of G. Furthermore small stable cracks start from almost each interface. The deepest delamination is obtained with the second stacking sequence which is the one which led to the largest value of G. The micrographies (performed by AMD-BA) of the specimen along the cutting line shown on figure 5 point out that the delamination is effectively located at the

Here again three different stacking sequences have been studied. For each one a small delamination area has been located at the interface between two layers. Several interfaces have been examined. Furthermore it has been observed on experimental tests that a delamination starts from the lateral edge just before the collapse of the specimen. Hence a computation including both a lateral and a hole delamination has been performed. The results are summarized on figures 8 and 9. Micrographies (AMD-BA) show that here again the delamination is the most important where G is the largest. Whether it is a mechanical result or a chance is still to be discussed. This work was partially supported by STCANDCN, ACrospatiale and DRET. The authors thank M. Lelan (DCN), Lang (ACros.) and Petiau (AMD-BA) for their suggestions.

8 . REFERENCES [ I ] O'Brien T.K. Mixed mode chain energy

release rate effects on edge delamination of composites, NASA Tech. memo. 84592 (1979).

[2] Raju I. Crews J. Interlaminate stress singularities at the free edge composites laminates. Comp. Struc. Vol. 14, no 1, p. 21-28 (1981). [3] Chai' H. Babcok C.D. Two dimensional modeling of compressive failure in delaminated laminates. Journal of Composite Materials, Vol. 19, p. 67-98 (1987).

43

[4] Destuynder Ph. Nevers Th. A newfinite element scheme f o r bending plates, Comp. Meth. Appl. Mechs. Eng., 68, p. 127-139 (1988). [5] Destuynder Ph. Djaoua M. Sur une in'erprttation de l'inttgrale de Rice en mtcanique de la rupture fragile, Math. Meth. in Appl. Sciences, Vol. 3 (1981).

[6] Destuynder Ph. Nevers Th. Un modZle de

calcul de forces de dtlaminage dans les plaques minces multicouches, Journal de MCcanique ThCorique et AppliquCe, Vol. 6, no 2, p. 179-207 (1987). [7] Mac Neal R.H. A simple quadrilateral shell element, Int. J. Solids and Structures, 8, p. 175-184 (1978).

Figure 7 s t a c k i n g s e q u e n c e /0/45/-45/90/s

1451-4 5101901, interface Gmax

stacking sequence interface

Gmax

.16 J m - l

9Ol90

.227 Jm-

0190

.224 Jm-

451-45

.25 J m - l -1 . I 8 Jm

4510

.14 J m - l

90190 w-45190

-4510 451-45

.352 Jm-I .336 Jm-

s t a c k i n g s e q u e n c e /45/0/-45/90/, Gmax in t e r r a c e 90190 -45190 01-45 4510

.192 Jm-l .205 Jm-l .194 Jm-l .329 Jm-l

Figure 8 Stacking sequence /0/45/0/-45/0/90/0/45/0/-45/0/45/0/90/0/45Is

( r a n d om s e q u e n c e ) interface /45/0/ (-4 from the medium surface)

G m a x = .0076 Jlm

i n t e r f a c e /0/-45/ ( - 1 5 from the medium surface)

G m a x = .0102 J/m

Stacking sequence /0/0/45/-45/0/0/90/90/0/0/45/-45/0/0/45/4 U S

44

(repeated sequence) interface /-45/01 (-4 from the medium surface)

G m a x = .0077 J/m

interface / 9 0 / 0 / ( - 8 from the medium surface)

G m a x = .0089 J/m

Stacking sequence /0/0/0/0/45/45/-45/-45/0/0/0/0/45/45/90/90/s

(stummering sequence) i n t e r f a c e /O/-451 ( - 4 f r o m t h e m e d i u m s u r f a c e )

G m a x = .0073 J/m

i n t e r f a c e / 4 5 / 9 0 / ( - 2 from t h e m e d i u m s u r f a c e )

G m a x = ,0073 J/m

i n t e r f a c e / 4 5 / 0 ( - 4 from t h e medium surface;

G m a x = .0071 J/m

t h e d e l a m i n a t i o n is b o t h on t h e h o l e a n d the lateral b o u n d a r y )

(on t h e h o l e )

i n t e r f a c e /45/90 ( - 2 from t h e medium surface: t h e d e l a m i n a t i o n i s both o n t h e h o l e a n d the lateral b o u n d a r y )

G m a x = .0067 J/m (on t h e h o l e )

F i g u r e 9 I n t e r f a c e / 9 0 / 0 / (-8 f r o m t h e medium s u r f a c e w h e r e G i s m a x i m u m in t h e f i r s t s t a c k i n g s e q u e n c e )

45

Paper II (ii)

Integrity of wear coating subjected to high-speed asperity excitation F.D. Ju and J.-C. Liu

When hard coatings are designed to protect substrates against the frictional excitation of asperities, it is important to consider parameters that would affect the integrity of the coating. Thermomechanical cracking and coating delamination are the major failures of hard coating. In analytical modeling, it is important to know the limitation of the model and the validity of the conclusions drawn from the analysis. The paper addresses the postulation of a two-dimensional model, which is used for the mathematical simplicity to study the effects of various parameters. For high speed asperity excitation, thermal stress dominates the analytical criteria. The paper considers the ef-fect of coating thickness and its critical value. Material parameters are grouped into those Of mechanical properties and those of thermal properties. The differences of those properties between the coating and the substrate directly affect the integrity of the coating. Irregularities, especial1Y in the neighborhood of the coating/substrate interface, are introduced to study their damaging effects to the coating integrity. The paper also addresses the significance of some unavoidable randomness in coating and the resulting effect on the coating integrity. 1. m O D U C T ION

The present paper addresses the integrity of a coated medium, which is subjected to the frictional excitation of a high-speed asperity. Break-down of the coating integrity occurs principally in the form of cracking of the coating o r delamination of the coating from the substrate. With Coulomb friction predominates in asperity excitation, the stress state in the coated medium and particularly in the neighborhood of the coating/substrate interface is governed by the thermo-mechanical field. The thermal field results from the dissipative frictional power, which manifests as thermal load traversing over the wear surface of the coated medium. The thermal component of the stress state dominates with increase of the asperity speed. These high thermal stresses will then initiate fracture in the coated material, inasmuch as the coating is introduced as a surface modification to improve the surface wear property of the contacting bodies. The integrity of the coating relies first on the choice of the coating material, which would reduce friction as well as resist thermal cracking. The integrity of the coating also depends on the interaction between the coating and its substrate, which it is designed to protect. The design of an effective coating is, therefore, depending on the property of the coating, its geometry, and its property matching, o r mismatching, with the substrate. For the purpose of a fundamental understanding of the parametric effects which can best adapt to later application to design, the study adopted an analytical formulation. The mathematical model is represented by differential equations, which govern the thermo-mechanical field of the coated medium and the substrate. The dynamic boundary conditions are described by the boundary values of the field. From the analyti--

cal formulation, mechanical and thermal properties that affect in a dominant way the thermomechanical field can be identified. The effect of the coating thickness and their irregularities can be quantified. In the analyses, emphasis has been placed on the coating being a hard deposition over the substrate. The mathematical model is thus simplified to allow the use of thermoelastic formulation. F o r hard coatings, it is postulated that failures will initiate by thermo-mechanical cracking. The crack may occur with cohesive failure. The criterion is the maximum tensile stress to reach a limit. Shear crack may exist in the coating/substrate interface. The limiting shearing stress will then be the cause of coating delamination. The paper will first address the coating as a single material in its response to the asperity excitation. The purpose is to identify those important characteristics of the coating material. The deterministic effect of coating thickness will be established, especially when the coating is thin, in the neighborhood of from 20 to 100 p . The interfacial relationship between the coating and the substrate will be studied in detail for both the mechanical p r o perties and the thermal properties of both mat.erials. The interfacial irregularities, defects and random thickness, will then be discussed. 2. -TICAL

FORMUUW

The traversing asperity imposes a moving traction over the surface as well as a moving heat source caused by the rate of frictional work. The stress field caused by the traction, normal and frictional, is the mechanical portion of the response, while that of the heat source is the thermal portion of the response. In numerical computations, the size of the asperities are of the order of 1 mm. The total thickness of the medium including both the coating layer

46

and the substrate is at least an order of magnitude larger than the asperity size. Mathematically, the material is represented by a half space with the asperity traversing over the surface boundary at a uniform speed (V) as shown in Fig. 1.

provided that the geometry is uniform in the traversing direction and the solutions are of steady-state. Equations in (1, 2) become x (?..TI B JJ

ValTB ,

=

(3)

where v B is the Poisson's ratio, M=V/C2

(=

1/2) , i s tho Mach number of shear in

2

[V p,,/p,,]

pI1pB/pBp,,. The stress field { u . . } is computed from the solved displa--

Region 1 1 , and G

=

1J

cement

field

(ui) through

the

thermoelastic

Hookian law given by:

where Fig. 1

2 - D model of moving asperity over coated medium

The asperity is characterized by the contact pressure p(x ) , distributed over a contact 1

width of 2a. The coefficient of friction pf is postulated at the steady state value corresponding to that of the surface temperature. For hard coating surface, Blau [ l ] and Ruff and Blau [ 2 ] , demonstrated that the surface yield, due to the asperity excitation, are sub-granular. The plastic deformation and surface shear for hard wear material are restricted to a very thin surface layer of 4-7 microns. If the depth at which cracks initiate is of an order larger than that of the plastic zone, the thermo-elastic theories for crack initiation may apply. The governing differential equations are the Fourier equation and the thermo-elastic Navier's equation, respectively expressed in the material coordinates (fixed to the coated medium):

Jij

i s the Kronecker delta.

On the surface boundary, the rate of friction work done by the asperity's traversing over the wear surface manifests as heat input. The asperity excitation also exerts a pressure and friction force on the boundary. Hence at x = 2 0,

where k is the thermal conductivity, x

used. Both governing equations ( 1 . 2 ) require explicit time-dependent solutions. The analytical complexity may be alleviated by using the convective coordinates (fixed to the asperity),

is the

1

the contact zone and zero elsewhere on the sur-face boundary. The temperature and the stress field satisfy the regularity condition at irifinity. At the coating/substrate interface, the continuity conditions hold for temperature, heat flux, traction, and displacement, that is. at x 2 = H. TI

where (1, p ) are the Lame's elastic coefficients, Uiis the displacement field. T is the temperature field, p is the mass density, LY is the coefficient of thermal expansion, x is the thermal diffusivity, i and j index the coordinates and /? indexes I and I1 for the coating layer and the substrate respectively, and where a dot over a variable denotes a time derivative. The indicia1 summation convention and Schouten's partial derivative notation, di = d/bxi, are

1

coordinate in the traversing direction of the asperity, and p(x ) is the asperity pressure in

=

TI', I u2j

=

I

11

kIJ2T = kIId2T , I1 I I1 UZj, uj = uj .

(9-a) (9-b1

For the steady state solution of the homogeneous wear medium, Equations ( 3 , 4 ) are solved with the boundary and continuity conditions using the method of Fourier transform. The method facilitates the parametric study of the properties. When irregularities occur in the medium, homogeneity condition in the traversing direction of the asperity no longer holds. The condition for transformation to equations in ( 3 , 4) cannot be justified. The more complex equations in ( 1 , 2), which are defined in the material

47

coordinates, must be used. With the explicit. time variable, finite difference method is applied for the solution of specific materials and specific geometries.

3 . 89PERIT'f-EXCITATION OVER A HARD WEAR MEDIUM

From the governing equations, the boundary conditions and the continuity conditions (I 9 ) , it is noticed that the thermo-mechanical u . } i s influenced by the asperity state ( a . ij'

1

parameters (a, t , P , V) and the material parame-ters ( A , p , p , a , k , 6 , p,). The coefficient of Coulomb friction p f affects as a material parameter on the wear surface only. The asperity parameter (1) is the aspect ratio of the asperity contact area, the length perpendicular to the traverse direction to the width in the traverse direction. The three dimensional characteristics of the moving asperity was solved by Huang and Ju [3].

0.5

3

.

012

0:ll

0:G

'

1'2

O!C

'

1'A

'

1%

& = Xl/A

Fig. 2

Stress fields for varying contact area and load distribution

(mctangular.

uniform pressure)

1.5-

------0

Stress field corresponding to varying 0.2

0.4

0.6

'0.8

L

Pig. 3

1.0

1.2

1.4

1.6

a two-dimension solution (t = m ) . Two dimensional modeling is therefore useful f o r the determination of the characteristics of the wear coating, but not in the actual evaluation of the stress state. The asperity velocity (V) influences the thermo-mechanical field in both the heat input, Equation ( 6 ) , and the convective terms in Equations (3, 4). The latter, occur-ring in the differential equation, can be combined with the material parameters, forming the Peclet Number ( R = Va/rt) in Equation ( 3 ) and the Mach Number (M = V/C) in Equation ( 4 ) . The former, being the surface rubbing speed, directly determines the rate of heat input. It is conceivable that at low rubbing speed the mechanical portion of the stress dominates. The static case of V = 0 is indeed the limiting case. At high speed, however, the thermal stress prevails. Huang and Ju [3] demonstrated that at. a rubbing speed of 1 5 m/s the thermal stress is more than six time that o f the mechanical portion of the stress. It was noted that the maximum values of the thermal and the mechanical components o f the stress do not occur at the same location nor do they have the same principal directions. Hence, the estimate of tho wear characteristics, due to high speed asperity excitation, shall be based on the thermal stress state. I n the material parameters. the mass density occurs in the inertial term in Equations ( 2 , 4). However, since the asperity traversing speed is much below the Rayleigh wave speed, its effect there is essentially perturbational. In Equations ( 1 , 3 1 , the mass density is combined with the specific heat (c) as the thermal capacity (pc), contributing to the thermal diffusivity ( 6 ) of the material. The thermal conductivity ( k ) , because of its presence in the boundary condition, Equation ( 6 ) . and the continuity condition, Equation ( 9 ) , is an independent parameter. The material parameters are therefore grouped as the mechanical constitutive coefficient [ A , p , o r I / , El and the thermal parameter [ a , k , x]. The coefficient of expansion is the principal excitation in Navier's equations ( 2 , 4 ) . The mechanical property is dominated by a single parameter [ a E / ( l - v ) ] . The thermal properties are grouped in dual parameters, [ k , n ] o r [k, pc]. Using the latter, Ju and Huang [3] concluded that, for materials of comparable thermal conductivity, materials of high thermal capacjty are definitely preferred for the resulting lower temperature field. However, for materials of comparable thcrmal capacity, those of high thermal conductivity yield lower thermal stress state. Moreover, because of its correspondingly lower Peclet number, a relative larger critical depth qcr is the dimensionless

x p

aspect ratio The asperity parameters involve those excitation-related (V, P) and those contact area configuration-related (a, t). Larger half-width (a) leads to longer period of heat input. The thermo-mechanical field does not depend on the shape of contact area, Fig. 2 [3]. Yet its aspect ratio affects the temperature and the thermal stress states, Fig 3 [3]. It is noticed that at the critical depth, at which the maximum value of principal thermal stress in tension occurs, a square o r a circular contact area (t = 1) could result in almost six times the value of

depth at which the maximum principal thermal stress occurs, where pl is the depth coordinate x2 modulated by the asperity half width (a). Ju and Liu [4] found that the critical depth depends predominantly on the Peclet Number. I n their study, the critical depth was computed directly by maximizing the thermal tensile stress with respect to positions under the asperity inside the material. The relationship between critical depth and the Peclet Number for all materials in the two dimensional formulation may be simplified to satisfy the exponential form R(qcr ) 2 ' 2 7 5

=

20.4368.

(10)

48

The relation is depicted in Fig. 4. The square symbols in the figure represent actual materials; they are Aluminum (Al). Silicon Carbon (Sic), Aluminum Oxide (A1203), Stellite 111 (St), and Zirconium (Zr) with the same asperity speed of 15 m/s, and the same asperity width of 0.254 mm. The traversing speed has been varied for Aluminum Oxide and Stellite 111. They all result in the same curve. Invariably, the critical depth is located at the cold side in the neighborhood where the large temperature gradient occurs. Because oP the combined effect maximum tensile stress and a discontinuity in material property, the critical depth shall characterize the materiaJ chosen for the coating when the thickness of coating becomes critical.

for the coating is at qcr = 0.16.

Invariably,

the worst case occurs in the neighborhood of the critical depth. Figs. 5 and 6 show the principal stresses in the coating and the substrate respectively Por various variances of mechanical parameter. For the variance of one, the coating and the substrate are of the same material. For variances larger than one, the substrate is of softer material; while less than one denotes For thick coatings (7 > stiffer substrate. 0 . 1 6 ) , the maximum stress in the coating occurs at the critical depth. The figures demonstrate that softer substrate provides less support for the coating. The thermal stress is thus higher. Stiffer substrate reduces the stress in the coating but takes on more stress especially for very thin coatings. Figs. 7 and 8 show the effect of the thermal conductivity variance. For less conductive substrate (flk = lo), the thermal stress is higher in the coating, especially at the coating/aubstrate interface for thin coatings. When the substrate is more conductive (the variance is 0 . 5 1 , more heat is readily transferred to the substrate. The thermal stress is correspondingly reduced. Fig. 9 illustrates a combined curve for maximum principal thermal stresses in the coating and in the substrate due to variance in thermal capacity. In both cases, the stresses are evaluated at the critical depth.

Peclet Number = Va/rc

Fig. 4

Critical depth vs. Peclet number in 2diaensional case

IN

4. ECT

A C

v

I t was pointed out by Ju and Chen [ 5 ] , that the phenomenon of thermo-mechanical cracking will be the same as a single material of the coating if the coating thickness is of the same order of magnitude as the asperity width. The interaction between coating and the substrate becomes significant only for coating thickness being of order of magnitude smaller than the asperity width. Ju and Liu [6] studied the effect of coating thickness in the neighborhood of the critical depth for various property differences between the coating and the substrate. In Fig. 5 through Fig. 9 , the principal stresses in both the coating and the substrate are shown for the parametric variances of [bE/(l-+)], as the dominant mechanical property, and the thermal parameters [k] and [pc]. The variances are designated as:

nM

= [UE/( 1 -Y ) 1 I/[UE/ ( 1-V) 1 I I ,

npc =

[pc1,/[pc1,,.

1 t Fig. 5

u1.i-

H/a

I

Maximum principal thermal stresses in coating layer versus coating thickness for different mechanical mismatches (surface material properties are constant)

I

(11)

(13) I a

For all those variances, since the interest was essentially in the effect of parametric matching (or mismatching) between the coating and the substrate, the numerical values of the coating is set for the Stellite I 1 1 with the Peclet Number R=1400. The corresponding critical depth

a. n

.ie

.m

1.20

1. 68

Wa

2.00

2.40

2.00

3.28

w1.c- I

Fig. 6 Maximum principal thermal stresses in Substrate versus coating thickness for different mechanical mismatches (surface material properties are constant)

49

R.

1

//---?--?->-

0.s

.-

.I8 '

II

1. 1400

----

himum stress atd interface

@.an

.b

.ie

1.b

c I

.

k

rIk

=I

Uaxina stress near 'ler (depth of max. principa ttwml stress)

1.60

2.10

2.08

2.80

Fig. 7

3.20

m1.c-

Wa

single material, 1 = 1.0, the principal angle k is small at locations closer to the wear sur-face. As a result, the shearing stress is correspondingly small. Significantly, the interfacial shearing stress reaches a maximum in the neighborhood of the critical depth of the coating. The existence of the interfacial shearing stress could cause interfacial shear cracks that would lead to coating delamination. The interfacial shearing stress can be controlled by proper selection of coatings to match the substrate.

I

-

I

Maximum principal thermal stresses in coating layer versus coating thickness for different mismatches in thermal conductivity (surface material properties are constant)

,

f j

1.00

..

.90

..

/ . . -

.-

.28

.-

.I0

--

'

0 . 0

near .ie

I

.is

)

~

1.i~

I.KB

2.09

Fig. 8

2.40

2.80

3.20

I1.E- I

Wa

Maximum principal thermal stresses in substrate versus coating thickness for different mismatches in thermal condutivity (surface material properties are constant)

.90

..

.I0

..

.. .61 .a' *\ .I0 .. .7B

is i n the substrate for thin coatings .I0

.-

4 Wa

Fig. 9

----

0.s

I

m1.t- I

Maximum principal thermal stresses versus coating thickness for different mismatches of thermal capacity (surface material properties are constant)

To study the criterion f o r coating delamination, Ju and Liu [6] also showed the effect of the shearing stress at the coating/ substrate interface, Fig. 10. The existence of the interfacial shearing stress results when the principal direction is not parallel to the wear surface. Theoretically, when the principal angle is zero, the interfacial shearing stress vanishes. Fig. 10 uses the variance in thermal conductivity without loss of generality. For a

Interface shear stress ( a

t7

) versus

coating thickness f o r different mismatches in thermal conductivity (surface material properties are constant)

h i m stress at interface

Haximum stress

1.0

Wa

Fig. 10 .4n

'.I"-'1 %

u1.t-

..-.__ >

.88

Ilk=-

5.

S

In the mathematical idealization, the coating is postulated to be of a known uniform thickness and to be smoothly and coherently bonded to tlie substrate. Such idealization, however feasible, would be too expensive to fabricate; o r variation would eventually occur through wear. Inclusions do exist in the neighborhood of' the interface. The thickness of the coating may vary either through manufacturing tolerance o r through wear. Chen and Ju [7 - 101 considered the effects of a small void cavity at the coating/substrate interface, and also an interfacial crack to simulate weak bonds. I,iu end Ju [ l l ] studied the effect of random coating Khickness on the temperature field. In both )areas of studies, emphasis is placed on the effect of coating irregularities to estimate the integrity of the coating. In the problem of cavity, o r void inclu-. sion, the homogeneity condition in the traversing direction of the asperity no longer hold in the vicinity of tlie cavity, Fig. 11. Hence, the governing differential equations, given in ( 1 , 2), must be used. Regularity conditions are still to be satisfied at infinity. The boundary The continuity conditions (6, 7, 8) remain. conditions ( 9 ) hold at interface, except at cavity. Heat transfer at cavity is negligible in comparison to that of the connected region. Small contact is ignored, allowing a tractionfree condition at the cavity boundary. Because of the complexity of tlie geometry and the boundary conditions, the finite difference method was employed to solve the problem. The finite difference equation and the energy balance method applied on the surface boundary and the cavity boundaries for the temperature field are dis-

50

V

Fig. 11

The effect of interfacial cracks involves the solution for the fracture toughness of cracks at the interface of dissimilar materials. The trend can be drawn by studying the highspeed frictional heating effect on the stress intensity factors of a near-surface line crack, Fig. 13. Ju and Chen [ l o ] concluded that the phenomenon of ligament heating also exists as in the case for the near surface cavity. The thermal state leads to the presence of a critical ligament thickness. The stress intensity factors increase with the material stiffness and the coefficient of thermal expansion, but decrease with the increase of the thermal conductivity. numerical results are not presented since the solution to a near-surface line crack will only give a qualitative understanding to the real effect of an interfacial crack.

AS PE R I TY

Two-dimensional model of a coated wear surface with a cavity

cussed by Chen and Ju [ 7 ] . It was found that, for near surface cavities, the ligament region between the cavity and the wear surface will reach much higher temperature than its surrounding regions. The high temperature field in the ligament region thus alters the temperature distribution in the vicinity of the cavity. As a consequence, the location where the principal tensile stress reaches a maximum changes. Chen and Ju [ 8 , 91 demonstrated that, if there is a cavity type defect in the vicinity of the wear surface, the critical depth will be reduced near the trailing end of the cavity. The relation-ship can be expressed as: R(Lcr)1’83

=

17.53,

where Lcr is the critical ligament thickness, which is defined by the distance between the wear surface and the cavity, dimensionally modulated by the half-width of the asperity. If o r weak bonds are unavoidable in the cavities process of surface modification, the designer has another critical thickness to consider for the coating. The location of the cavity also affects the principal angle of thermal stress in the vicinity of the cavity, Pig. 12. In the neighborhood of the critical ligament thickness, designated in the figure as L = 0 . 9 4 , the high value of principal tensile stress combined with a large principal angle definitely point to a cause for coating delamination.

Fig. 13 Two-dimensional model with line crack In the problem of the temperature field in a coated medium with random coating thickness, the thickness H is first considered to be only a function of the sample variable II. The thickness remains uniform in each sample. The variable II ranges over a probability space fi composed of all the specimens. The probability density D ( & ) in fi is assumed to be measurable. Hence, all of the statistical quantities (such as expected value, standard deviation, etc.) are well-defined. The governing differential equation, given in Equation ( 3 ) is used. Regularity conditions are still to be satisfied at infinity. The boundary condition ( 6 ) and continuity conditions (9-a) remain. The interface is defined by x = Ho + c’f(a), o r in dimensionless 2 quantities, 7 ( = x /a) = d + cf((Y), where Ho is 2 the mean coating thickness, and the term c ’ f ( L y ) account for the random fluctuation of the coating thickness. For numerical computations, a cyclic function is chosen to be the random variation on the coating thickness; i.e.,

-

f(a)

=

sin(cup).

(15)

The Gaussian distribut.ion is the corresponding probability density function of the process;

w

;3 . 0 0 2.50

2.80

427 b

1.50

I .OO

.50

+ -1.00 -.58 -1.58

t

I

I

. x1.c- I

Fig. 12 Principal angle of thermal stress vs. 1 igament thickness

‘

2b“

where b is the standard deviation of a random variable with Gaussian distribution, and h = 2 and p = 0 . 2 are used. The corresponding coefficient of the variation of coating thickness is computed to be 0.1%. Fig. 14 arid 15 show the mean temperature and its standard deviation with respect to pl (the depth direction for mean coating thickness do = 0.03. The effect of the random coating thickness on the temperature response can be observed by a hump change of mean temperature

51

and a relative maximum of standard deviation at v = d .

S t a n d a r d Deviation (at the interface) Legend

Mean Temperature 0.060 n

CN

0.050

U

w

h

\-,.L-

0.040

(with coating thickness d0=0.03) Legend - nk=io o

__ __

nk= 2 o nk= o s nk= 0 . 1

O.O3OI 0.020

-

I l k = 10.0

__

nk =

__

ll k = 0.5

nk=

5.0

0.1

---z

00"'~

----+

0.000 0 000

0 030

0060

0 090

0 120

0 150

do

Fig. 17 Standard Deviation at the coating/ substrate interface as a function of mean coating thickness d f o r thermal Fig. 14

Mean temperature as a function of 7 with coating thickness do = 0.03 for thermal conductivity impedance

Fig. 18 and 19 demonstrate the effect of "frequency" (p). Fig. 18 shows that p has very little effect on the mean response. However, F i g . 19 demonstrate the magnitude of standard deviation increases as p increases up to p = 2 , and thereafter becomes constant. The reason is when p gets larger and larger, the randomness tends to become uniform distribution. The coefficient of variation of the temperature can reach as high as 22% when the mean coating thickness d is about 0.05.

S t a n d a r d Deviation (with coating thickness d0=0.03) Legend

0.007

nk = i o . o

-

-- nk = 2.0

__

0.004

ll k = 0.5

nk = 0.1

0.003

0.001

0.000 0.000

conductivity impedance

Mean Temperature

i

(with coating thickness d 0 = 0 . 0 5 )

I

0.050

0.100

0.150

0.200

'I

Fig. 15 Standard deviation as a function of 7 with coating thickness d = 0.03 for

-n - 10.0 _ _ _-c. ___-------- -----

U0.015

W

-nb=

thermal conductivity impedance O.O1 O

Fig. 16 and 17 plot the mean temperature and its standard deviation at the coating/substrate interface with respect to the mean coating thickness d . The coefficient of variation for

0.0°5

i

t

0.5

rrrk=

a. 1

/

0.000

t

0 000

temperature at the interface can reach 18% for thin coatings with a thickness randomness of only about 0.1%. This indicates the occurrence of a large deviation of the temperature from its mean value as a result of the small randomness of the coating thickness. Therefore, the amount of deviat.ion from expected values is by no means negligible.

2.0

/-TIk=

1.000

2 000

3 000

5 000

4 000

P

Fig. 18 Mean temperature as a function of the frequency p with coating thickness d 0.05 for

=

thermal conductivity impedance

S t a n d a r d Deviation (with coating thickness d 0 = 0 . 0 5 )

Mean T e r n p e r a t u r e

4.5a-3 T I

(at the interface) Legend ~ 0 . 1 2 0

0.080

-

n

--

I1 = 5 . 0

= 10.0

nk=

_.

nk =

-----L-L 1.50-3

0.5

1 . 0 0 - 3 1 , , ~ ~ / ~ *

0.5.-3 0.000 0.000

o 000

o 030

o 060

o

ago

a 120

do

a

150

Fig. 16 Mean temperature at the coating/substrate interface as a function of mean coating thickness d for thermal canductivity impedance

0.1

01

0 040

0 000

---..--_-

-Ilk=

Fig. 19

+--

I

1.000

2.000

3.000

4.000

5.000

P

Standard deviation as a function of the frequency p with coating thickness do = 0.05 for thermal conductivity impedance

52

Liu and .Ju [ll] concluded that the standard deviation of the temperature field depends upon ( 1 ) the thermal conductivity, (2) the mean coating thickness, (3) the random fluctuation function f(a). In the numerical example, a large standard deviation of temperature for thin coating can be observed. As a consequence. the coating bonding strength, which is selected on the basis of the mean value estimation of temperature, may prove to be unreliable because of the large probability of higher temperature field there. It is expected that the temperature gradient in the neighborhood of thin coating interface has also a significant amount of deviation, which must be considered carefully in the related thermal failure analysis. 6.

REFERENCES (1) Blau, P.J.. "The Role of Metallurgical Structure in the Integrity of Sliding Solid Contacts," S o l i d Contact a n d L u b r i c a t i o n , ASME AMD, 39, 1980, pp 135-191.

(2) Huff, A.W., and P.J. Blau, "Studies of Microscopic Aspects of Wear Processes in Metals," National Bureau of Standard, NBSIR 80-2085, June 1980. (3) Huang, J.H., F.D. Ju, "The Asperity and Material Parameters in Thermo-mechanical Cracking due to Moving Friction Loads," l y e

of New Technology to I m p r o v e l e c h a n i c a l Readiness, Reliability and laintainability, Ed. T.R. Shives, Cambridge Univ Press, 1987, pp. 205-214.

CONCLUSION:

In the design of hard coating to provide a wear surface for the substrate against highspeed frictional load, the integrity of the coating depends much on the coating thickness and the parametric matching with the substrate. For thick coatings, order of 1 mm, the effect of the substrate on the coating integrity is negligible. Therefore, critical considerations for the appropriate thickness and the interaction of coating and substrate must be given to coating thickness less than 100 microns.

It was found that the principal thermal stress attains a maximum tensile value at a distance from the wear surface, called the critical depth. Discontinuity in material property further aggravates the stress state. For better integrity of the coating, its thickness should avoid to be located in the neighborhood of the critical depth of the coating material. The critical depth is exponentially related to the traversing speed of the asperity and the single material property, the thermal diffusivity. Moreover, if the coating process cannot avoid weak bond that interfacial cavity o r crack would develop through use, the coating thickness has another critical thickness to consider. The second thickness that may lead to premature delamination is the critical ligament thickness, which is also controlled by the same parameters as for the critical depth. The relative stiffness between the coating and the substrate is essential governed by the support that the substrate provides for the coating. The softer the substrate is, the more stress must the coating be subject to the frictional loading. The thermal conductivity o f the substrate also is influential in the design for coating integrity. The stress level is lower in the coating, when the substrate is more conduc-tive. Interfacial shearing stress as a criterion for coating delamination is determined by the parameter matching and the coating thickness. The shearing stress rises rapidly as the coating increases in thickness towards the critical depth of the coating material, o r when there is an interfacial void. 7 . ACKNOWLEDGEMENT

The paper is part of the work performed under the ONR grant No. ONR-N00014-89-53325. Dr. Marshall Peterson is the program manager.

(4) Ju, F.D. and J.C. Liu, "Effect of Peclet Number in Thermo-Mechanical Cracking due to High-speed Friction Load," J o u r of T r i b o l o g y , 110, No.2, April 1988, pp. 217-221. (5) Ju, F.D. and T.Y. Chen, "Thermo-mechanical

Cracking in Layered Media," J o u r of T r i b o l o g g , 106,No.4, October 1984. pp. 513-518. (6)

Ju, F.D. and J.C. Liu, "Parameters Affecting Thermo-mechanical Cracking in Coated Media due to High-speed Friction Load," J o u r of I r i b o l o g y , 110, ~ 0 . 2 , April 1988, pp.222-227.

(7) Chen, T . Y . and F.D. Ju, "Cavity Effect in a Coated Medium due to Dry Friction of a Moving Asperity (A Temperature Field Solution)." ASLE T r a n s a c t i o n , 3 ,No.4, October 1987, pp. 437-435. (8) Chen, T.Y. and F.D. Ju, "Thermo-mechanical Cracking in the Vicinity of a Near-Surface Void due to High-speed Friction Load," J o u r of T r i b o Z o g y , 110,No.2, April 1988, pp. 306-312. ( 9 ) Chen, T.Y. and F.D. Ju. "Friction-Induced

Thermo-mechanical Cracking in Coated Medium with a Near Surface Cavity," J O U F of T r i b o l o g y , 111,No.2, April 1989, pp.270-277. (10) Chen, T.Y. and F.D. Ju, "High-speed

Frictional Heating Effect on the Stress Intensity Factors of a Near-Surface Line Crack," A d v a n c e s in F r a c t u r e R e s e a r c h , Ed. K. Salama et al, 3 . Pergamon Press, March 1989, pp. 2331-2338. (11) Liu, J.C. and F.D. Ju, "Asperity Excited Thermo-Mechanical Field in Media with Uniformly Random Coating Thickness," Jour of I r i b o l o g y , Lu,No.1. Jan 1989, pp. 129-135.

53

Paper II (iii)

Coating design methodology M. Godet, Y. Berthier, J.-M. Leroy, L. Flamand and L. Vincent

Many coatings have been developed in recent years but their use in machinery is hampered by the lack of design methods for coated elements. While it is quite clear that the limitations in design methods of homogeneous elements used in rubbing contacts, and which relate essentially to the surface as opposed to the bulk aspects of the problem, apply also to coated elements, it is possible to develop methods which will help choose coating/substrate combinations that can withstand the mechanical and thermal loads applied to the contact by the mechanism under study. This paper discusses these methods and suggests that if they were applied to the rubbing elements or first-bodies, they could identify non compatible combinations under the working conditions envisaged and thus eliminate a large part of the trial and error process which is current today in the choice of coatings. Mechanical and thermal characteristics, thin layer solid mechanics theories along with a general pluridisciplinary approach are needed if these methods are to be developed.

INTRODUCTION

1

A formidable effort has been invested by material scientists in the development of new coatings and new coating methods for tribology. This effort has not been rewarded as only few of these new products or techniques have reached the application stage. Several reasons explain that failure:

-

-

the multiplicity of coatings and of coating methods the lack of intrinsic tribological characteristics the lack of design methods for coated machine elements.

This paper is general as it attempts to see what can be done to extend the use of coatings in engineering applications where tribology is concerned. It is however particular as it is limited to bulk or first-body considerations and illustrates the change in bulk material stress level induced by coatings as well as in the stresses in the coatings themselves. Rather than list hundreds of papers in the bibliography and be certain that half would be left out, it was chosen not to include a general bibliography. Only the source papers of the figures are given.

2

DESIGN METHODOLOGY IN TRIBOLOGY

An engineer knows how to design beams and even much more complicated structures. He is however at a loss when it comes to designing mechanisms with rubbing parts which do not belong to the current engineering practice. The job is often passed on to the material expert who is asked to find an empirical solution to the problem. The premice is that the rubbing elements themselves are able to withstand the loads transmitted normally to the contact but that something must be done to the surfaces to accommodate or control the tangential components. The purpose of this paper is to show that that premice is not founded when coated elements are used. Applications in which tribology is involved include all mechanisms which taken in a broad sense include gears, bearings, seals, clutches, brakes, etc. along with quasi static liaisons such as blade roots, cables, bolts, bearing housings, gaskets

...

Mechanisms transmit loads from one machine component to an other, under given conditions of speed, temperature and for a given environment. Figure 1 illustrates how a mechanism reduced to its external actions and environment imposes its working conditions to the rubbing surfaces known here as first-bodies. The shape of these first-bodies, differs

54

e

7 / / / /

/ / / /

200

/ / / / / / / I / / / / / / / /

1st body

2.3. From third-bodies 100

0

c

a

c

0°C

I

Fig. 1 : Mechanisms, first and third-bodies

from one application to another. Firstbodies only function properly if they are at least partly separated by an efficient third-body such as an oil film, solid lubricant etc.. The design process thus includes three steps, which concern respectively each element of the triplet: mechanism, first and third-bodies.

Identification of the load-carrying mechanisms capable of separating the two first-bodies under the conditions defined. Surface and material scientists must work along with mechanical engineers on this subject. In conclusion, from his understanding of the running conditions existing in dif-. ferent mechanisms, the designer must solve successively the problems posed by the first and then by the third-bodies. There is no point in tackling the third element of the triplet if the first two are not totally dealt with. He knows how to tackle homogeneous first-bodies and some third-bodies. Let us see what information he has to design layered or coated first-bodies. For clarity, the argumentation will often be oversimplified.

The following information is given by the material scientist with each coating:

-

Let us identify what information should be collected from each element of that triplet to advance in 'the design of coated machine elements.

2.1

_From mechanisms

Identification of the mechanism running conditions. This can be done either theoretically or experimentally. Gear loads, for instance, can be calculated, but relative displacements between cable strands must be measured during an expertise. This is performed by mechanical engineers who are at home with most classical mechanisms. 2.2. From first-bodies

Identification of:

. .

mechanical and thermal first-body properties and of operating limits for both temperaturte and stress. These values must be determined by material scientists. the stress aid temperature fields imposed by the mechanism running conditipns on the machine elements or first bodies. This is done by mechanical engineers.

COATINGS, THE MATERIAL APPROACH

3

-

deposition method (CVD, PVD..), composition, thickness, hardness (both indentation and scratch), indication on coating to substrate adhesion, applications where the coating did well , friction and wear data produced on a pin and disc machine.

All of these parameters are required by the coating expert to identify, qualify and monitor his product in a material sense. Note that none of these refer to the actual conditions that the rubbing surfaces are likely to encounter in a real application. 4

COATINGS, VIEW

THE DESIGNER'S

POINT OF

Unfortunately, out of these indications, only the thickness can be fully taken into account by the designer. There is no direct explicit relation between deposition method, coating composition, hardness and coating strength expressed in terms of stress. Indications on adhesion is impossible to transpose in mechanical terms and the emphasis on that characteristic is quite different when viewed by mechanical engineers and material scientists. That very important point will be taken up below. Earlier industrial applications produce valuable indications but the information is relative and the working conditions are very rarely clearly defined. Pin and disc results are totally useless as friction and wear are not intrinsic material propert ies

.

55

The following information is needed in design:

-

temperature distribution stress distribution

Assuming that as discussed in 51, all the relevant information (heat fluxes, external temperature distribution, load and external displacement distribution and their variation with space and time) has been extracted from an analysis of the mechanism, the designer must be able, as a very first pass, to calculate (or at least estimate) the stress and temperature distribution at all critical points in the first-bodies. To do this, he requires the: Young's modulus, Poisson's ratio, coefficient of thermal expansion, thermal conductivity, density, specific heat,

-

-

of both coating and substrate materials. He also needs:

-

the temperature and stress limits for both materials to evaluate the severity of the temperature and stress fields determined above, the coating thickness mentioned above, information on residual stresses to assess the overall stress level exhibited by the working coated first-body,

and last but not least the designer must be able to call upon efficient theories to determine these temperature and stress fields for conditions representative of those found in pratice. It is immediately apparent that most of the qualifying data produced by the coating expert and which is of fundamental importance to him is quite useless to the designer. It is therefore the designer's job to convince the expert that the data furnished is quite insufficient to promote his product. FIRST-BODY DESIGN

mentioned above, friction and wear are not intrinsic material properties. In a similar way, bulk properties of coated first-bodies do not follow simply from the bulk properties of substrate and coating. While this seems to be generally accepted, its consequences in Tribology have not been fully worked out. Indeed, a good coating/substrate combination can provide both good and bad first-body behaviour depending on contact conditions. However, unlike friction and wear, theory can be of some As

The examples presented are representative, they were not chosen to illustrate any particular point but were picked among cases involving common materials, a steel substrate and a TiN coating for example, working under realistic contact conditions. For simplicity, only normally loaded static contacts are considered here. A detailed presentation of the thermoelastic theory developed and of its results results are given in references 1-3. Coatinqs can weaken substrates

-

5

help in explaining layered or coated first-body action, and point out to some rather unexpected and not always beneficial consequences.

The hertzian contact formed between a rigid cylinder and a coated elastic substrate is presented. The ratio of the coating to the substrate modulus Ec/Es varies between 0.5 and 3 . In figure 2, the ordinate gives the maximum von Mises avM stress in the substrate normalised to the hertzian pressure po and the abcissa gives the coating thickness ec normalised to the half hertzian width ao. The point of maximum von Mises stress is always located at the center of the contact but its depth can vary from the interface into the substrate bulk. For coatings, for which 0 . 5 < ec/ao 1.5, protect<substrates. This is not surprising as the highly stressed zones are then located in the coating. An extensive parametric study has shown that there is no thickness which can optimize simultaneously interface shear and von Mises stress.

56

Small temDerature rises stresses in thin coatinqs

.a

e -

.6

.4

.2

0.01

0.05

0.1

0.5

4

ec 1% Fig. 2 : Variation of the maximum normalised (with respect to the uncoated hertzian pressure p o ) von Mises substrate coating

(S, M )

stress thickness

(e,)

with

o f Ihe uncoated substrate (a,) to substrate

coating (E,)

the

ratio

of

to the half width (a,)

(E,)

induce hiqh

It is necessary to distinguish between mechanical (load) and thermal (temperature) effects which are both present in contacts but which can have distinct consequences, Figure 3 shows that high surface stresses (axx=200 MPa) are generated in thin ( 5 ~ 1 0 - ~ mWC ) coatings deposited on a steel substrate and which are subjected to modest temperature rises (70°C). The dilatation coefficients of WC ant steel are respectively 5 and 12x10("C)-' and their elastic moduli are 550 and 210 GPa. pere an elliptical heat flux of 0.5 W/mm maximum was applied to the two-dimensional coated medium. Clearly such temperature rises are common in tribology, and much higher stresses can be expected under normal operating conditions if coating and substrate properties are mismatched as they are in this case. Note that the internal stress drops slightly with coating thickness and also that the stresses in the substrate are scarecely altered by the coating presence.

for different ratios of

coatinq stiffness effects on contact pressure distribution

moduli.

Figure 4 gives the pressure distribution calculated when a rough steel (E = 245 GPa) cylinder is pressed on a smooth steel substrate which is covered: elliptical heat llux q

5

lo6

W i d

- with a stiff (E

= 490 GPa) 5 ~ 1 0 - ~ m thick coating of the TiN type, covered wi h a flexible (E = 0 , 8 GPa) 5xIO-'m thick coating of the elastomeric type.

-

I 5 Ilm

I

The protection afforded by the flexible coating is clear.

t 2 ~ = 5 m m i

Sic

-6 -1 E = 420 GPa V = .16 a = 5.10 ("C) 5 2 k = 100 W/(m."C) D z 3 . 6 1 0 m is

E = 200 GPa

S t e e l k = 46 W/(m."C)

Tmax = 70

coating thickness : 1.25 pn

v = .3 a = 12.10 ("C)

D = 1.3 10'

m2/s

'C

coated surface

,/

A . c XIL

4

-4

contact abcissa

\

uncoated surface

-100

Fig. 3 : Surface stress (ax ) dislribution generated in heated coated and uncoated media. Maximum surface temperature is 70 "C in both cases

0

500

1000

contact abcissa

Fig. 4 : Surface load distributions for rough substrates coated with stiff and compliant coatings

57

6

DISCUSSION OF THEORETICAL RESULTS

The examples given above are enlightening as they show that coated machine elements present stress and temperature fields which depend on the mechanical and thermal properties of the coating and of the substrate and on the mechanical and thermal loads imposed. They also show that these stress and temperature fields can be calculated. Coatings are therefore not intrinsically good or bad in tribology and their analysis must therefore be included in the design of coated machine elements. The analysis is however not easy to perform essentially because there is very little data on the thermal and mechanical properties of coatings. This is a very serious limitation in the design of coatings. This point will be taken up later. The parametric study conducted is also of interest for at least two reasons:

-

-

it shows that it is impossible to predict the results expected when a p a r t i c u l a r coating/substrate combination is used in a given contact. Even an educated intuition is incapable of taking into account the effects of changing stiffnesses, conductivities and dilatations. Each case must be worked out separately. it gives a different weight to some of the phenomena which are often considered to be basic in coating practice. Two examples, coating to substrate adhesion and coating thermal effects are discussed below.

interface adhesion Calculations show for instance that unless the coefficient of friction is very high , beyond 0.3 for instance , the s h e a r stresses developed at t h e coating/substrate interface are low particularly for thin coatings. On the other hand the tensile and compressive stresses developed in the coating can be very high. This suggests that, unless great care is given to the matching of thermal and mechanical properties of coating and substrate, coatings are more likely to fail through tension and compression than through interface shear. Could it be that the coating delamination observed on occasion is caused initially by tension and compression and not by interface shear and that delamination follows the initial damage. If this were to be the case the emphasis on adhesive coating/substrate conditions could be reassessed and a broader view which would include tensile and compressive aspects preferred.

thermal effects It is common to consider that thin coatings isolate substrates. This must be qualified. Under static eo ditions, and for thin coatings ( 0 . The curve f o r t h i s case of F,/fW' = 0.57 i s nearly l i n e a r f o r S > 1 (wind-up) o r S < 2 (unwind); t h a t is, under steady s t a t e conditions, t h e increase in microslippage with t r a v e r s e i s constant. For low values of S o r a t points where t h e t r a v e r s e i s reversed, some n o n l i n e a r i t i e s occur because t h e slippage r a t e i s nonuniform. To b e t t e r understand t h e s e n o n l i n e a r i t i e s , i t i s helpful t o compare t h e shear s t r e s s p r e d i c t i o n s , which a r e a l s o shown in Figure 3. Figure 3B shows t h e shear s t r e s s a f t e r t h e cylinders have t r a v e r s e d one half width of In contact b , on t h e d e f l e c t i o n curve. advancing from Figure 3A t o 3E, a l l o f t h e shear

115

s t r e s s r e g i o n s l i m i t e d by f r i c t i o n r e p r e s e n t non-recoverable l o s s e s and must be made up by additional tangential deflections. F i g u r e 3C shows a steady s t a t e c o n d i t i o n a t S = 3.0. Again t h e r e a r e non-recoverable l o s s e s , although here t h e l o s s r a t e w i l l be c o n s t a n t . F i g u r e 3D shows t h e shear s t r e s s c u r v e a t S = 2 . 5 on t h e rewind and F i g u r e 3E shows t h e steady s t a t e rewind curve, i l l u s t r a t i n g t h a t t h e rewind c o n d i t i o n i s j u s t t h e m i r r o r image o f t h e forward t r a v e r s e . The i n f l u e n c e o f t h e t r a c t i o n parameter was explored u s i n g ATCON and t h e r e s u l t s a r e presented i n F i g u r e 4 . Case 1 r e p r e s e n t s predictions f o r a c y l i n d e r w i t h a h a l f width o f 0.01 i n c h , a f r i c t i o n c o e f f i c i e n t o f 0 . 3 , and an i n i t i a l "wind-up" o f 1 . 9 pm (75 p i n . ) . F o r Case 2 t h e "wind-up" i s reduced t o 0.95 pm (37.5 p i n . ) , which r e s u l t s i n a r e d u c t i o n i n t h e t r a c t i o n parameter t o 0.29. I n Case 3 t h e f r i c t i o n c o e f f i c i e n t i s i n c r e a s e d and t h e h a l f w i d t h i s decreased so, a g a i n , t h e t r a c t i o n parameter i s 0.57. As was a n t i c i p a t e d from Kal k e r ' s work, the scaling parameters c h a r a c t e r i z e t h e t r a c t i o n equations. Several combinations o f values o f b , f , and i n i t i a l "wind-up" produced t h e same v a l u e o f F,/fWi and e s s e n t i a l l y t h e same values o f f o r a given distance traversed.

Half Width, inch

Friction, f

025 001 025 001 025 001 018 000707

03 03 015 03

Case F,/fW' _ _ _mm 0 0

0 A

I

2 3 4

I

OL

05

057 029 057 057

I

10

I

15

1.2pm. d i a . C l e a n e d f l o a t g l a s s m i c r o s c o p e s l i d e s were immersed i n t h e d i l u t e d e m u l s i o n s and withdrawn, t h e excess s o l u t i o n being allowed t o d r a i n away. The c o a t e d s l i d e s were t h e n d r i e d a t 40C f o r one h o u r f o l l o w e d by a f u r t h e r h o u r u n d e r vacuum. T h i s p r o c e d u r e p r o d u c e d u n i f o r m f i l m s of a b o u t 4 p m . t h i c k n e s s a s m e a s u r e d by a l a s e r profilometer. 2 . 2 Thick F i l m P r e D a r a t i o n . T h i c k f i l m s were c a s t u s i n g u n d i l u t e d e m u l s i o n s a n d t h e s e were c o n t a i n e d b y a s i l i c o n e rubber b a r r i e r around t h e edges of t h e f l o a t g l a s s s l i d e s . These f i l m s were d r i e d i n a s i m i l a r manner t o t h e t h i n f i l m s . T h e r e was some n o n - u n i f o r m i t y i n t h e i r t h i c k n e s s but t h e average value a s m e a s u r e d by m i c r o m e t e r was 500pm. A t t e m p t s t o p r o d u c e t h i c k e r f i l m s were unsuccessful. 2 . 3 Thin Film F r i c t i o n Measurements. I n o r d e r t o d e t e r m i n e an i n t e r f a c i a l component v a l u e o f t h e c o e f f i c i e n t o f f r i c t i o n , t h e t h i n f i l m s p r e p a r e d were sheared by a flamed g l a s s hemispherical i n d e n t o r o f r a d i u s 4.93mm. u n d e r a n a p p l i e d l o a d s i n t h e r a n g e 0 . 0 1 - 0.5N. The m e a s u r e m e n t s were c a r r i e d o u t a t ambient t e m p e r a t u r e w i t h a s l i d i n g s p e e d o f O . l S m m / s e c . The e q u i p m e n t u s e d f o r t h e s e measurements h a s been d e s r i b e d i n d e t a i l elsewhere (6) . 2 . 4 Thick F i l m S c r a t c h i n s ExDeriments.

Low l o a d s c r a t c h i n g e x p e r i m e n t s were carried o u t f o r t h e t h i c k f i l m specimens u s i n g t h e same a p p a r a t u s d e s c r i b e d i n Section 2.3, with t h e exception t h a t t h e s p h e r e u s e d t h e r e was r e p l a c e d w i t h a

3 . 1 T h i n F i l m A d h e s i o n Component Experiments. No s i g i f i c a n t t r e n d s were o b s e r v e d f o r the i n t e r f a c i a l f r i c t i o n data obtained f r o m t h e low l o a d s l i d i n g s p h e r e experiments f o r t h e various films s t u d i e d ; t h e c o e f f i c i e n t s of f r i c t i o n w e r e a l l within t h e range 0.38 & 0 . 0 7 a t t h e n o r m a l l o a d o f 0 . 0 1 N . However t h e r e were r e l a t i v e l y l a r g e v a r i a t i o n s i n t h e d a t a w h i c h was t h o u g h t t o a r i s e f r o m d i f f i c u l t i e s i n obtaining reproducible evenly t h i n films. A t t h e dilution f i n a l l y u s e d t h e r e w a s no d e t e c t a b l e s l i d i n g damage p r o d u c e d a s j u d g e d f r o m s c a n n i n g e l e c t r o n m i c r o s c o p e (SEM) examination of t h e f i l m s . P r e l i m i n a r y work u s i n g f i l m s d e r i v e d from 1 0 f o l d d i l u t i o n of t h e o r i g i n a l s o l u t i o n r e s u l t e d i n some e v i d e n c e o f t e a r i n g ; f i l m s c a s t from 100 f o l d d i l u t i o n s g a v e t r a c k s t h a t were c l e a r l y v i s b l e b u t t h i s deformation appeared t o be s o l e l y due t o ploughing p r o c e s s e s . P r e v i o u s work h a s e s t a b l i s h e d t h a t f i l m s s h o u l d be l e s s t h a n a b o u t 200nm f o r t h e f r i c t i o n t o be i n d e p e n d e n t o f t h e t h i c k n e s s ( 6 ) . T h i s a r i s e s from t h e "penumbral e f f e c t " i n which m a t e r i a l outside t h e Hertzian contact area is u n d e r s u f f i c i e n t p r e s s u r e , due t o t h e g e o m e t r y o f t h e s p h e r e , t h a t it makes a significant contribution t o the frictional traction. 3 . 2 Low Load T h i c k F i l m E x D e r i m e n t s . The f r i c t i o n t r a c e s f o r t h e s c r a t c h i n g e x p e r i m e n t s on t h i c k f i l m s a t t h e l o w e r n o r m a l l o a d o f 0.01N showed no o b v i o u s e v i d e n c e o f s t i c k - s l i p b e h a v i o u r . I t was f o u n d t h a t t h e r e were two d i s t i n c t t r e n d s i n t h e v a r i a t i o n of t h e f r i c t i o n c o e f f i c i e n t (p) w i t h t a n 0 ' d e p e n d i n g on t h e r e l a t i v e proportion of t h e rubbery and g l a s s y b l o c k s i n t h e copolymer. A t y p i c a l s e t o f d a t a a r e shown i n F i g u r e 3 f o r o n e of t h e more g l a s s y p o l y m e r s . I n g e n e r a l f o r t h i s g r o u p o f p o l y m e r s , 1.1 i n c r e a s e d g r a d u a l l y from a v a l u e o f a b o u t 0 . 5 f o r t h e b l u n t e s t cone t o about u n i t y f o r t h e s h a r p e s t . However f o r t h e more

143

r u b b e r y polymers ( t y p i c a l r e s u l t s shown i n F i g u r e 4 ) t h e f r i c t i o n was much g r e a t e r with values of about 1 . 5 f o r t h e b l u n t e r c o n e s and i n c r e a s i n g t o h i g h e r v a l u e s of u p t o c a . 4 i n some c a s e s f o r t h e sharper cones. The damage p a t t e r n s r e s u l t i n g from t h e s e e x p e r i m e n t s were examined u s i n g an SEM and were s i m i l a r i n c h a r a c t e r t o t h o s e found a t h i g h e r normal l o a d ( s e e l a t e r ) , b u t were s m a l l e r i n s c a l e . T h e f r i c t i o n t r a c e s were c o n t i n u o u s i n a l l c a s e s even though i n some i n s t a n c e s t h e s h a r p e r c o n e s c l e a r l y produced t h e c l a s s i c " a r r o w head" t e a r s ( F i g u r e 5 a ) . For t h e b l u n t e r c o n e s , t h e t e a r i n g damage was c o n s i d e r a b l y l e s s s e v e r e w i t h some e v i d e n c e of e l a s t i c - p l a s t i c p l o u g h i n g j u d g i n g by t h e p a r t i a l r e c o v e r y of t h e g r o o v e s ( F i g u r e 5 b ) . The r e c o v e r y was g r e a t e r f o r t h e more r u b b e r y p o l y m e r s . 3 . 3 H i g h e r Load Thick F i l m E x p e r i m e n t s . A t t h e h i g h e r normal l o a d of 1N t h e r e was

a g r o s s s t i c k - s l i p r e s p o n s e and i t was a l s o possible t o discern a greater g r a d a t i o n i n t h e b e h a v i o u r of t h e polymers from t h e s e e x p e r i m e n t s . F o r t h e most r u b b e r y p o l y m e r s , t h e s t i c k p h a s e s o f t h e f r i c t i o n t r a c e s t e n d e d t o be rounded and t h e d i s t a n c e between p e a k s was g r e a t e s t w i t h a v a l u e i n t h e r a n g e 18mm; f o r c o n v e n i e n c e t h i s c o m p a r a t i v e measure o f d i s t a n c e r e f e r r e d t o h e r e was t h a t r e c o r d e d on t h e c h a r t t r a c e a t a constant speed. This w i l l correspond t o a much s m a l l e r d i s p l a c e m e n t o f t h e cone on t h e t h i c k f i l m . The mean peak v a l u e of p was a l s o t h e g r e a t e s t f o r t h i s g r o u p a t a b o u t 0 . 9 . The d e f o r m a t i o n s p r o d u c e d by t h e cone were o f t h e c h a r a c t e r i s t i c a r r o w head t y p e but q u i t e e l o n g a t e d a s though c o n s i d e r a b l e e l a s t i c r e c o v e r y had t a k e n place (Figure 6 a ) . The polymers w i t h i n t e r m e d i a t e rubbery g l a s s p r o p e r t i e s exhibited s h a r p e r and h i g h e r f r e q u e n c y s t i c k - s l i p b e h a v i o u r , where t h e mean d i s t a n c e between p e a k s on t h e c h a r t p a p e r was a b o u t 4 m m . The mean peak v a l u e o f p was n e a r l y a s g r e a t a s i n t h e p r e v i o u s group a t a b o u t 0.85. The d e f o r m a t i o n p a t t e r n was a l s o o f t h e a r r o w head t y p e b u t l e s s elongated indicating l e s s e l a s t i c recovery (Figure 6 b ) . In a d d i t i o n , t h e t e a r s were more e r r a t i c b o t h i n s i z e and s p a c i n g ; t h e y were o f t e n s u p e r i m p o s e d . The most g l a s s y group of polymers c a u s e d a v e r y uneven ' s t i c k - s l i p ' of s m a l l e r a m p l i t u d e and h i g h e r f r e q u e n c y . The s p a c i n g was i n t h e r a n g e 3.0-3.4mm. and t h e mean peak v a l u e of p was a b o u t 0 . 5 5 . The t e a r s were much s q u a t t e r and more rounded; i n some c a s e s t h e t e a r s a p p e a r e d t o merge i n t o one c o n t i n u o u s deformation zones of varying width (Figure 6 c ) .

4.ANALYSIS OF RESULTS. S c r a t c h i n g may be c h a r a c t e r i s e d by measuring t h e c o e f f i c i e n t of f r i c t i o n a s a f u n c t i o n of t h e cone a n g l e ; a c t u a l l y t h e p a r a m e t e r u s e d i s t a n @ I , where @ I i s t h e a t t a c k a n g l e which i s shown i n

1

0

Tan 0' 2

Figure 3. F r i c t i o n c o e f f i c i e n t a s a f u n c t i o n of t a n @ ' f o r one of t h e h a r d e r polymers.(

@ I =

cone a t t a c k a n g l e )

i P

zw

c

Ecr,

cr,

w

0 U

z

2z

E 0 Figure 4 . F r i c t i o n c o e f f i c i e n t a s a f u n c t i o n of t a n 0 ' f o r o n e of t h e s o f t e r polymers.

(

@ I =

cone a t t a c k a n g l e ) .

F i g u r e 1 . T h i s e n a b l e s t h e t y p e of m a t e r i a l r e s p o n s e t o b e c h a r a c t e r i s e d and c e r t a i n o t h e r parameters such a s t h e c r ; . t i c a l c u t t i n g a n g l e which c o r r e s p o n d s t o t h e t r a n s i t i o n from d u c t i l e p l o u g h i n g t o c h i p formation t o be a s s e s s e d . 4 . 1 how J,oad S c r a t c h i n a E x D e r i m e n t s .

The c u r r e n t d a t a do n o t , on f i r s t c o n s i d e r a t i o n , seem t o c o r r e s p o n d t o t h e t r e n d s d i s c u s s e d above a n d , i n p a r t i c u l a r , t o t h e work c a r r i e d o u t on P T F E . I n t h e c a s e of PTFE, t h e i n t e r f a c i a l f r i c t i o n a l work i s s m a l l compared w i t h t h e t o t a l d e f o r m a t i o n work, and was t h e r e f o r e n e g l e c t e d . F o r t h e s y s t e m s h e r e , t h i s component of f r i c t i o n i s r e l a t i v e l y h i g h and h a s t o be i n c l u d e d . Thus i n o r d e r t o d e t e r m i n e t h e i n t r i n s i c v a r i a t i o n of p w i t h t a n 0 ' f o r t h e d e f o r m a t i o n modes o n l y , t h e i n t e r f a c i a l c o e f f i c i e n t of f r i c t i o n must b e s u b t r a c t e d from t h e o b s e r v e d v a l u e s .

144

Figure 5a. SEM photomicrograph of lower load thick film experiments. Demostrating "arrow head" tears.

Figure 5b. SEM photomicrograph of lower load thick film experiments. Demostrating partial recovery in grooves.

Figure 6a. SEM photomicrograph of harder thick film specimen after high load experiment.

Figure 6b. SEM photomicrograph of intermediate thick film specimen after high load experiment.

I45

0

1

Tan 0' 2

F i g u r e 8 . The d a t a f o r F i g u r e 4 w i t h t h e i n t e r f a c i a l f r i c t i o n s u b t r a c t e d from t h e measured v a l u e s . ( l i n e h a s g r a d i e n t 2/n)

F i g u r e 6c. SEM p h o t o m i c r o g r a p h of s o f t e r t h i c k f i l m specimen a f t e r h i g h l o a d experiment,

T h i s h a s been done assuming s i m p l e a d d i t i v i t y f o r t h e d a t a shown i n F i g u r e s 3 a n d 4 ; t h e r e s u l t i n g p l o t s a r e shown i n F i g u r e s 8 and 9 r e s p e c t i v e l y . H a r d e r P o l v m e r s : The d a t a i n F i g u r e 8 r e p r e s e n t s t h e harder polymers and i s p e r h a p s more s t r a i g h t f o r w a r d t o i n t e r p r e t . The c o e f f i c i e n t o f f r i c t i o n i n scratching experiments f o r simple glassy p o l y m e r s s u c h a s v i r g i n PTFE c a n b e a s c r i b e d t o t h e sum o f t h e h y s t e r e s i s

1.0 1

g 0.8 il

t?

iiIS w

0.6

0 U

gz

0.4 0.2

o.n . ... 0

F i g u r e 7 . The d a t a f o r F i g u r e 3 w i t h t h e i n t e r f a c i a l f r i c t i o n s u b t r a c t e d from t h e measured v a l u e s . ( l i n e h a s g r a d i e n t 2/n)

losses and v i s c o e l a s t i c - p l a s t i c d e f o r m a t i o n . Thus a c c o r d i n g t o e q u a t i o n s (1) a n d ( 3 ) t h e g r a d i e n t o f t h e d a t a i n F i g u r e 8 s h o u l d be 2 / n . T h i s l i n e i s shown a n d it c a n b e s e e n t h a t t h e d a t a a t low a t t a c k a n g l e s i s somewhat l e s s t h a n e x p e c t e d on t h i s b a s i s . A t t h e h i g h e r a t t a c k a n g l e s t h e r e i s a marked d i v e r g e n c e from t h e l i n e s i n c e p i s no l o n g e r s e n s i t i v e t o t h e a t t a c k a n g l e . The l a t t e r behaviour i s very similar t o t h a t o b s e r v e d when t h e r e i s c h i p f o r m i n g t a k i n g p l a c e , o n l y i n t h i s case t e a r i n g (an analogous p r o c e s s ) i n t e r v e n e s i n t h e p l o u g h i n g p r o c e s s . Thus it seems f o r t h e h a r d e r polymers t h a t t e a r i n g r e p r e s e n t s a n e n e r g e t i c a l l y more f a v o u a b l e p a t h f o r accommodating s l i d i n g t h a n d o e s p l a s t i c ploughing. I t was commonly o b s e r v e d f o r t h e s e harder polymers t h a t t h e c o e f f i c i e n t of f r i c t i o n a t t h e h i g h e r a t t a c k a n g l e s , was e v e n l e s s t h a n e x p e c t e d on t h e b a s i s o f h y s t e r e s i s l o s s e s ( e q u a t i o n 1) which i s t h e m a j o r component o f t h e t e a r i n g e n e r g y . However, t h e model f o r h y s t e r e s i s was b a s e d on s l i d i n g o v e r a v i s c o e l a s t i c h a l f - s p a c e . For t h e s h a r p e r c o n e s , t h e p e n e t r a t i o n w i l l be g r e a t e r and hence sub-surface deformation i n these coatings i s u n l i k e l y t o be a c o n t r i b u t o r y f a c t o r . The m a j o r h y s t e r e s i s l o s s e s w i l l a r i s e f r o m d e f o r m a t i o n a t t h e c r a c k t i p s of t h e t e a r s . This w i l l be a f u n c t i o n of t h e l e n g t h of t h e c r a c k s a n d n o t n e c e s s a r i l y t h e cone a n g l e , I n summary, f o r t h e s e h a r d e r polymers only t h e d a t a a t t h e lower c u t t i n g angles tended t o t h e expected r e s u l t i s t h e c o n s e q u e n c e o f two f a c t o r s . F i r s t l y , penetration of t h e t h i c k f i l m w i l l be markedly less f o r t h e b l u n t e r cones and hence t h e s l i d i n g c o n d i t i o n s w i l l c o r r e s p o n d more c l o s e l y t o t h e c o n d i t i o n s assumed i n t h e d e r i v a t i o n o f ( e q u a t i o n 1) . S e c o n d l y , SEM e x a m i n a t i o n showed t h a t t h e r e was c o n s i d e r a b l y l e s s t e a r i n g f o r these cones; t h a t i s p l o u g h i n g seemed t o be t h e d o m i n a n t damage p r o c e s s .

146

S o f t e r P o l y m e r s : Moving o n t o a c o n s i d e r a t i o n o f t h e more r u b b e r y p o l y m e r s , F i g u r e 7 c l e a r l y shows t h e much g r e a t e r c o e f f i c i e n t s of f r i c t i o n f o r t h e s e p o l y m e r s , which i s p a r t l y t h e r e s u l t of t h e i r g r e a t e r f r a c t u r e t o u g h n e s s . T h i s i s t h e r e s u l t of g r e a t e r h y s t e r e s i s l o s s e s a t t h e crack t i p s of t h e t e a r s . However, a n o t h e r s i g n i f i c a n t contributory factor i s t h a t generally t h e t e a r i n g was o b s e r v e d t o be n o t continuous, with t h e r e s u l t t h a t t h e c o n e s would have t o s l i d e o u t o f t h e d e p r e s s i o n once t e a r i n g was a r r e s t e d . This i s equivalent t o introducing a Coulombic t y p e i n t e r a c t i o n i n t o t h e c o n t a c t which c a n g r e a t l y i n c r e a s e s l i d i n g f r i c t i o n between two b o d i e s ( l 2 ) . The c r a c k a r r e s t a r i s e s from t h e way i n which t h e c r o s s - s e c t i o n a l a r e a of t h e t e a r increases with t h e s l i d i n g d i s t a n c e a s t h e cone g r a d u a l l y i n d e n t s f u r t h e r i n t o t h e coating. Since t h e crack resistance is proportional t o the crosss e c t i o n a l a r e a of t h e c r a c k , t h e t e a r i n g e n e r g y e v e n t u a l l y becomes g r e a t e r t h a n t h a t r e q u i r e d f o r Coulombic f a i l u r e . To a f i r s t o r d e r , t h i s i s only a f u n c t i o n of t h e cone a n g l e and n o t t h e p e n e t r a t i o n d e p t h a s t h e a d h e s i o n component o f f r i c t i o n h a s a l r e a d y been s u b t r a c t e d from t h e d a t a . For t h e b l u n t e r c o n e s , t h e d e f o r m a t i o n t r a c k s were r e l a t i v e l y continuous so t h a t t h e c o e f f i c i e n t of f r i c t i o n values represent t h e almost continuous t e a r i n g of t h e polymers, w i t h no a d d i t i o n a l Coulombic c o n t r i b u t i o n . 4 . 2 P i a h e r Load E x p e r i m e n t s ,

The d a t a from t h e h i g h e r normal l o a d t h i c k f i l m measurements s i m p l y p r o v i d e s a d d i t i o n a l e v i d e n c e o f t h e above p h y s i c a l i n t e r p r e t a t i o n s of t h e low normal l o a d t h i c k f i l m d a t a . There was a l a r g e difference i n t h e p values f o r t h e harder and s o f t e r p o l y m e r s . T h i s d i f f e r e n c e , w i t h t h e h a r d e r g l a s s i e r polymers being a b o u t a f a c t o r of two l e s s t h a t t h e s o f t e r p o l y m e r s , i s e x a c t l y what would be e x p e c t e d on t h e b a s i s of t h e c r a c k r e s i s t a n c e a r g u m e n t s p r e s e n t e d above and corresponds t o t h e observed d i f f e r e n c e a t t h e low normal l o a d . A major a d v a n t a g e o f c a r r y i n g o u t s c r a t c h i n g a t a h i g h e r normal l o a d i s t h a t it i s p o s s i b l e t o e s t i m a t e t h e t e a r i n g e n e r g y of t h e c o a t i n g . The c a l c u l a t i o n of t h e c r a c k r e s i s t a n c e would i n v o l v e d i v i d i n g t h e t e a r i n g work by t h e c r o s s - s e c t i o n a l a r e a of t h e t e a r s . The t e a r i n g work i s p r o p o r t i o n a l t o t h e a r e a u n d e r a s t i c k p h a s e a s shown i n F i g u r e 9 , a s mentioned p r e v i o u s l y t h i s c o u l d be converted i n t o t h e a b s o l u t e value of t h e t e a r i n g work from a knowledge o f t h e c o m p l i a n c e o f t h e f o r c e t r a n s d u c e r . Crude e s t i m a t e s of t h e c r a c k s u r f a c e c o u l d b e o b t a i n e d from e l e c t r o n m i c r o s c o p y . However, t h i s would p r o b a b l y r e s u l t i n an o v e r e s t i m a t e of t h e c r a c k r e s i s t a n c e s i n c e t h e f r a c t u r e process w i l l occur i n t h e s l i p p h a s e and c o r r e s p o n d s t o u n s t a b l e f r a c t u r e . The problem i s t h e n t h a t t h e energy s t o r e d i n t h e s t i c k phase i s i n e x c e s s of t h a t r e q u i r e d t o

Elastic Energy

A Figure 9.Schematic s t i c k - s l i p t r a c e f o r an e l a s t o m e r i c body, where t h e s h a d e d a r e a under t h e s t i c k phases i s proportional t o t h e t e a r i n g angle.

p r o p a g a t e c r a c k s and i s d i s s i p a t e d a s k i n e t i c energy. These c a l c u l a t i o n s were n o t c a r r i e d o u t h e r e b u t i n t e g r a t i o n of t h e discontinuous p a r t s of t h e c h a r t o u t p u t s i n d i c a t e d t h a t t h e f r a c t u r e energy o € t h e s o f t e r p o l y m e r s was a b o u t a f a c t o r o f two g r e a t e r t h a n t h e medium h a r d n e s s p o l y m e r s and a b o u t a f a c t o r o f t h r e e g r e a t e r t h a n t h e h a r d e s t polymers. This t r e n d i s e v i d e n t from t h e d e c r e a s e i n magnitude of t h e s t i c k d i s t a n c e a n d a m p l i t u d e of t h e s t i c k p h a s e w i t h i n c r e a s i n g h a r d n e s s . The g r e a t e r compliance and f r a c t u r e toughness of t h e s o f t e r p o l y m e r s a l l o w s g r e a t e r s t r a i n s t o b e s t o r e d p r i o r t o Coulombic f a i l u r e when t h e s l i p p h a s e commences. For t h e h a r d e r p o l y m e r s , t h e s l i p p h a s e i s i n i t i a t e d by f u r t h e r t e a r i n g which produces t h e o v e r l a p p i n g arrow head tears. 4 . 3 A b r a s i v e Wea r , The aim o f t h i s s t u d y was t o d e t e r m i n e t h e damage o r wear r e s i s t a n c e of r e p r e s e n t a t i v e o r g a n i c c o a t i n g s . One o f t h e more common damage r e g i m e s i s a b r a s i v e w e a r . The r a t e of a b r a s i v e wear of p o l y m e r s u s u a l l y c o r r e l a t e s q u i t e w e l l with t h e i n v e r s e of t h e i r f r a c t u r e toughness (13) . For t h e presenc system, t h i s would imply t h a t t h e a b r a s i v e wear would i n c r e a s e w i t h t h e h a r d n e s s of t h e p o l y m e r s and c o n s e q u e n t l y w i t h a r e d u c i n g c o e f f i c i e n t of f r i c t i o n . A s i m i l a r dependence was found f o r t h e PTFE s y s t e m s s t u d i e d by B r i s c o e e t a l ( 3 ) . T h i s was i n t e r p r e t e d i n t e r m s o f damage e f f i c i e n c y . In t h e c u r r e n t context, t h e Coulombic f r i c t i o n a l component of t h e s o f t e r p o l y m e r s can b e r e g a r d e d a s n o t c o n t r i b u t i n g t o t h e damage work.

147

5.CONCLUSIONS. Coatings w i t h a spectrum o f materials b e h a v i o u r c a n be o b t a i n e d b y u s i n g copolymers comprising of rubbery and g l a s s y b l o c k s , T h e damage t o l e r a n c e o f s u c h c o a t i n g s i n terms o f t h e i r r e s p o n s e t o i s o l a t e d s l i d i n g p o i n t c o n t a c t s has b e e n a s s e s s e d . T h e n a t u r e of t h e damage is analogous t o that observed for bulk elastomer s p e c i m e n s which d e p e n d s o n their hardness. A t l o w normal loads, continuous s l i d i n g contact occurs with cones and an a n a l y s i s c a n be made of t h e way i n w h i c h t h e n o n - a d h e s i v e component o f t h e c o e f f i c i e n t o f f r i c t i o n (p) v a r i e s w i t h the tangent of the attack angle (tan 0 ' ) . The r e s u l t s c l e a r l y d i s c r i m i n a t e between soft r u b b e r y polymers w i t h a h i g h f r a c t u r e toughness and harder glassier p o l y m e r s w i t h a lower f r a c t u r e t o u g h n e s s . For s l i d i n g w i t h cones a t higher normal loads, s t i c k - s l i p b e h a v i o u r i s observed. The a m p l i t u d e o f t h e s t i c k p h a s e s decreases w i t h i n c r e a s i n g h a r d n e s s of t h e p o l y m e r s d u e t o t h e r e d u c t i o n i n the f r a c t u r e toughness. I n addition, t h e d u r a t i o n of t h e s t i c k p h a s e s decreases with harness because of the reduction i n t h e c o m p l i a n c e . The f r i c t i o n a l work a s s o c i a t e d w i t h t h e s t i c k phases c a n be u s e d t o estimate t h e t e a r i n g e n e r g y , On t h e b a s i s o f t h e s e s t u d i e s w e a r e a b l e t o c o n c l u d e t h a t the three b r o a d i n v e s t i g a t i v e methods p r o v i d e a m e a n s of estimating the durability of organic f i l m s , particularly their sensitivity to f r a c t u r e damage. T h e s u b j e c t i v e SEM assessment is g e n e r a l l y c o n s i s t e n t w i t h t h e i n t e r p r e t a t i o n of b o t h t h e s t r a i n ( t a n 0 ' ) a n d load d e p e n d e n c e o f t h e f r i c t i o n and t h e e x t e n t o f t h e measured stick-slip contribution to the frictional force. References

(1) B E N J A M I N , P . a n d WEAVER, C . ' M e a s u r e m e n t of A d h e s i o n of T h i n F i l m s ' . P r o c . Roy. SOC. Lond., 1960, 163. (2) BRISCOE, B . J . , LAKCASTER, J . K . a n d EVANS, P . D . ' D u c t i l e t o B r i t t l e Transitions i n the Single Point C o n t a c t D e f o r m a t i o n a n d A b r a s i o n of y - i r r a d i a t e d PTFE i n P o i n t C o n t a c t s ' . P r o c . 1 2 t h Leeds-Lyon T r i b o l o g y Symp. ,p p 3 9 - 4 6 , B u t t e r w o r t h s , Guildford, (1985). ( 3 ) BRISCOE, B . J . , EVANS, P . D . a n d LANCASTER, J . K . ' S i n g l e P o i n t D e f o r m a t i o n a n d A b r a s i o n of y - i r r a d -iated PTFE'. J Phys. D : Appl. Phys., 2Q, 1 9 8 7 , 3 4 6 . ( 4 ) GREENWOOD, J . A . a n d TABOR, D . ' T h e F r i c t i o n o f Hard S l i d e r s o n L u b r i c a t e d R u b b e r : T h e I m p o r t a n c e of Deformation Losses'. P r o c . Phys. S O C . , 71,1 9 5 8 , 9 8 9 . ( 5 ) SCHALLAMACH, D . ' A b r a s i o n of R u b b e r b y a Needle' . J . P o l y m . S c i . , 9, 1952, 385.

m,

( 6 ) SCRUTON, B . P h . D T h e s i s , T r i n i t y C o l l e g e , Cambridge, ( 7 ) BRISCOE, B . J . a n d TABOR, D . ACS P r e p r . , 21, 1 9 7 6 , 1 0 . ( 8 ) BOWDEN, F . P a n d TABOR, D . ' T h e Friction and Lubrication of Solids', Clarendon P r e s s , Oxford, ( 1 9 5 0 ) . ( 9 ) LAMY, B . ' E f f e c t of B r i t t l e n e s s I n d e x and S l i d i n g S p e e d o n t h e M o r p h o l o g y of S u r f a c e S c r a t c h i n g i n A b r a s i v e o r Erosive Processes'. Tribology I n t l . , 17, 1 9 8 4 , 3 5 . (lO)BETHUNE, B . J . ' T h e S u r f a c e C r a c k i n g of G l a s s y P o l y m e r s u n d e r a S l i d i n g S p h e r i c a l I n d e n t o r ' . Mat. S c i . , 11, 1976, 199. ( l l ) T R E N T , E M . i n 'Metal C u t t i n g ' , 2 n d . Edition. Butterworths, Guildford, (1984). ADAMS, M . J . , BRISCOE, B . J a n d WEE, T K . 'The D i f f e r e n t i a l F r i c t i o n E f f e c t of K e r a t i n F i b r e s ' . T o be p u b l i s h e d i n J Phys. D . : Appl. Phys. 1969, LANCASTER, J . K . Wear, 2 2 3 - 2 3 9 , ' A b r a s i v e Wear of P o l y m e r s ' .

.

2,


SESSION VI ROUGH COATED SURFACES Chairman:

Professor K. Ludema

PAPER VI (i)

Effect of surface coatings in a rough normally loaded contact

PAPER VI (ii)

Elastic behaviour of coated rough surfaces


Paper VI (i)

Effect of surface coatings in a rough normally loaded contact Ph. Sainsot, J.M. Leroy and B. Villechaise

2D simulation of a rough elastic cylinder normally loaded on a plane coated elastic medium is presented. The effect of soft and hard coatings on the rough contact pressures and on Von Mises stresses associated is shown. The hertzian contact pressure field is significantly altered by the surface roughness. The presence of a soft coating greatly reduces these perturbations and Von Mises stresses under the surface. Hard coatings also reduce these stresses, but in a less order, and for thicknesses less than 10 pm the maximum Von Mises stress is located at the coating/substrate interface. A

INTRODUCTION

1

computer simulation of the dry rough contact between two homogoneous elastic bodies [ l ] has been developed in the last few years.

A

The simulation shows that surface microgeometry greatly disturbs the classical hertzian pressure pattern [2,3] and Von Mises stresses under the surface, and that the deflection of the asperities generates high stresses, close to the surface [4]. important effects wich are superposed in a rough contact have been identified :

TWO

- a global effect, related to the contact macrogeometry and to the normal load, it’s the classical hertzian effect , - a local effect which is related to the contact microgeometry and thus to the loads carried by the asperities. Further a compliant surface coating has been shown to decrease the local effects

Fig. 1

-

Microgeometry of the cylinder

The layered body consists of two layers of linearly elastic materials of finite thicknesses, bonded together (fig.2). The first layer is the coating, its thickness is very small compared to the contact width. The second one is the substrate, though this method concern finite thicknesses, its dimensions are such that it can be taken as semiinfinite. The coating thickness studied varies between 1.25 pm (ec/a = 8.5 , and 20 pm (ec/a = 135.

[51.

This paper analyses the effects on the pressure distribution and on the Von Mises stresses of soft and hard coatings of variable thicknesses. 2

MODEL

The simulation is limited to the case of a dry frictionless contact, between a real rough elastic cylinder and a smooth layered elastic body. The cylinder microgeometry is determined by stylus profilometry and is presented in figure 1. This microgeometry is discretized using a micron step.

Fig. 2

-

Model and notation

152

The followinu assumDtions are made

-

small and plain-strain elasticity theory - layers are perfectly bonded together - normal (frictionless) contact

!li

.......,La..,...

__.__ .....

w __

I

__L

I

I .............. ......... .......' ...

I

A hertzian case is studied

The uncoated case with smooth surfaces is the hertzian case. The maximum pressure (P ) , and the half contact width (a) are qaken as reference. pH = 2.2 GPa a = .15 mm

Younu's moduli cylinder : E substrate : E, coatings : Ec 3

= 245 GPa = 245 GPa = . 8 GPa and

490. GPa

METHOD

u = v = o

Fig. 3

-

Representation of the influence coefficients

This vector is expressed as a function of the pressures written in matrix form. The matrix of influence coefficients is calculated, for the cylinder by the classical Boussinesq relations, and for the layered medium after a Fourier transform of the Lame's equations [ 6 ] . Adhesion between coating and substrate is assumed, and displacements are zero away from the contact (fig.3).

Unilateral contact conditions are used in formulating the problem. The distance between the deformed surfaces inside of the contact is zero (d=O), normal pressures are negative (P> a, the surface displacement is well approximated by, 2 uz(r,O) = A - r /2R (7) =

Chen and Engel approximate the pressure distribution as a linear combination of the functions q.(r) as follows:

Where the pi are n unknown coefficients and the functions qi(r) are defined as: 2 i-1/2 q.(r) = (1 - (r/a) ] (9) With this representation the total load P given by Eq (6) becomes:

P

=

nE,

n

2 l+Vl

c

pi/( 1 + 2i) i=l

In approximating q(r) by Eq (8) the choice n = 5 was made in the numerical results given in [lo]. The surface displacement caused by the application of the pressure distribution [E1/2(1 + v)]qi(r) to the coated body is denoted Xi('). From Eq(7) and the principle of superposition, the displacement due to q(r) is thus , .n

u (r,O)

=

o - C piXi(r) a i=l

(11)

From Eqs (7) and (11) the error in the surface displacement due to the approximation is

159

&(r)

=

u (r,O)

uz (r,O)

-

=

2

A - r /2R

-

p*

=

2 3n(l - vl) n 3(1 - vl )PR ._.. - --8 b --E pi/(l+2i) 4Ela3 i=l (20)

and, The relative error, i.e., the error as a fraction of the maximum surface displacement A is: c(r)

a

d(r)/A

=

2 1" 1 - r /2RA - - C piXi(r) (13) a i=l

3

CORRECTION FACTORS FOR AREA AND LOAD

Introducing the parameter When a rigid spherical indenter of radius R contacts hombgeneous elastic half plane, with a maximum penetration A, the load P and contact radius a are given by the ?allowing expressions due Hertz: (cf. Johnson [12])

a

2

@ = a /2RA

80

PH = 74j E,R1/2 A3/2

The mean square relative error over the contact area is expressible as: I

l aJ re2(r)dr 'a o

= -

where,

(16)

E'

=

E/(1 - vL)

aH

=

[RA]1 / 2

(23)

and,

The mean square error is thus a function of D (through the parameter @) and the n coefficients pi (i = 1, ...n). To find the values giving the smallest mean square relative error, one sets

The area AH of the circular contact region is:

A H - n aH 2 = m n

(25)

This leads to the set of n + 1 linear equations 12 a 3 - 2 8 - - J r3 piwi(r)dr = 0 (17) a4 o i=l

The same expressions apply if both bodies are elastic if A is taken as the total approach of points on the two bodies which are remote from the region of contact and E' is taken to be Eft,given by

7O rw.(r) J

(1 - v 2 )/E + (1 - vI 2)/EI (26) P P wherein the subscripts p and I refer to the plane and the indenter respectively. 1/E"

[l - @,'/a2

-

i=l

p.w.(r)]dr 1 1

= 0;

i=l,..n where,

=

Using E q ( 2 0 ) to express P in terms of P* gives,

P

4/3 E'

=

a3 P*/R

(27)

From E q ( 2 1 ) In [ l o ] Chen and Engel solve for the values of w.(r) corresponding to the functions q.(r) for i'= 1, 2...5 and satisfying the bAundary conditions (Eqs. (2)-(5)), using a numerical procedure developed by Chen [ll]. They performed the computations for 13 choices of t/a and four values o f the ratio E /E2 with the assumption that v1 = v2 = 113. They then determined the values of pi and @ by numerically integrating the functions of r in Eqs. (17) and (la), and solving the resultant set of simultaneous linear equations for p and i B. They do not list the individual values of p. and 6. Instead they give for each value of tya and E /E the values of the quantities: 1

2

'a

*

RA/S

=

and thus using (27) in (26), p

=

4/3 El R1/2A3/2 (P* 1 6*3/2) 1

(29)

Comparing (22) and (29) leads to P = CP

H'

(30)

P is the load corresponding to deformation A i? the half space is made entirely of the coating material. Cp defined as,

cp =

P*/6

*3/2

(31)

160

may be regarded as a correction factor that accounts for the fact that the surface coating has finite thickness t. By analogy, if the indenter is also a coated, elastic body made of the same material and having the same coating thickness as the half plane, one simply uses

so that

- E t 1 aH3

PH

When t -+ 0 , i.e. the substrate material governs the coated contact behavior, the contact radius a should be the value given by S

- (P/Er2)1/3

as From Eq(27) and (23): a

*

(RA/6 )

=

1/2 =

(33)

aH cR

But as we have seen, when t P

where CR

(1/6* ) 1/2

I

(34)

Like Cp, C may be viewed as a correction factor whereby ?he Hertz contact radius aH is adjusted to reflect the effect of the finite coating thickness and the substrate material. n

The area A is computed as naL so that from Eq(28) and (25): (35)

where

C P P H and therefore

cA

-=

=

cR

2

notftd, Cheg and Engel give tabled values of P and 6 as a function of t/a. This is less useful than to have the correction factors expressed in terms of t/a To transform one uses Eq(33) and wriaes

.

=

(t/a) (a/aH)

=

(t/a) CR

(37)

Using the tabled values in [lo] the factors CA, C and C were computed as functions of !/aH an5 are listed in Table 1. Figure 2 is a plot of C against t/aH for all 4 It is seen from values of the ratio E Fig. 2 that for smal11t,2C converges to E2/E1 signifying that the materig1 acts like the substrate when the coating thickness is small. Correspondingly, for large t, CP approaches unity indicating that the materlal behaves like the coating when the coating thickness is sufficiently large.

/E .

Figure 3 shows CR plotted against t/aH for E1/E2 = 1/3 and 3. CR is unity for small and large t values. For soft coatings CR exceeds unity at intermediate coating thicknesses. For hard coatings CR is less than unity indicating a smaller contact area than when the coating is thick. The behavior of CR at small t is explainable as follows: In general, from Eqs(22) and (24) A1/2 aH and

PH

- E'l

A3/2

EZ'/E1'PH

Thus CR

=

1 as t

-+

'P /E ' E ']'I3 H 1 2

=

aH

(42)

0.

A series of nonlinear curve fits were made for CA and Cp as functions of t/aH. These expressions are listed in Table 2. The maximum error is less than 7% for any of the fits. Where possible, the expressions were devised to give the required asymptotic behavior with small and large values of t discussed above. l4ICROCONTACT SIMULATION MODEL

A simulation model comparable to that described

As

t/aH

=

aS =[E2

4

* 1/6

=

= 0,

in [13], was developed to analyze the microcontact behavior of contacting coated rough surfaces using the Greenwood-Williamson Model adapted to account for the presence of a coating on both surfaces. Under the Greenwood-Williamson Model the contact of two isotropic rough surfaces is treated as the contact of a single equivalent rough surface and a smooth plane. The asperities are regarded as spheres of radius R whose height x above the mean plane is a Gaussian distributed random variable with standard deviation as. Figure 4 shows a number of such summits schematically for the case where the coated smooth plane is held at the distance d parallel to the summit area plane. The summits for which x > d become microcontacts and deform by the amount A = x - d

(43)

At a prescribed value of the separation d the objective is to determine the distribution of the asperity load, and the microcontact area and radius. The input to the model is the coating thickness t, the elastic modulus of the coating, El, the separation d, the appropriate ratio of coating to substrate modulus (E /E = 1/10, 1/3, 3, lo), the summit radius R a!id $he standard deviation oS of the summit height distribution. The simulation encompasses the following steps:

(39)

1. An asperity height value x is drawn from the Gaussian distribution of asperity heights

161

Figure 5 is a plot of mean real pressure RP against coating thickness for each value E /E of the modulus ratio of coating to shbszrate using the smooth specimen (301) results. The plot is drawn for a dimensionless separation d/us = 1.0.

If A = x - d is negative, step 1 is repeated. If A is positive, P and aH are computed using Eqs(22) and (247.

2.

3. t/a is computed and C and CP are evaluate! as a function of +/a using the fitted equations from Table 2 !or the appropriate ratio E1/EZ. 4. The asperity area and load are computed using A = CA

AH

(44)

and P = CP H'

(45)

The contact radius a is computed as a

=

(A/n) 1/2

(46)

5. Steps 1-4 are repeated as many times as desired and then, 6. The means and standard deviations of A, P and a are computed and histograms are compiled.

5

PARAMETRIC STUDIES

Roughness measurements were made on flat M50 steel specimens that were manufactured for use as test specimens in pin-on-disk tests of coated surfaces. The measurements comprised five repeated traces in three directions spaced at 4 5 O apart. The equivalent values of the RMS profile height Rq and slope Aq were determined as proposed by Sayles and Thomas [14]. Using these values the Greenwood-Williamson model parameters R and uS were computed by means of the spectral estimation approach proposed in [15] as implemented using the program RUFFIAN, described in [16]. In this determination the assumption was made that the mating surface is smooth. The results are listed in Table 3 for two specimens, Nos. 101 and 301 which span the roughness range to be explored in the planned pin-on-disk tests. Also shown, for reference, are the values of the estimated spectral exponent k (cf. (151) and the summit density DSUM.

A total of 4 x 4 x 5 x 2 = 160 simulation runs were made corresponding to all combinations of: 4 values of the modulus ratio, E1/E2 = 1/10) 1/3, 3 and 10 4 values of the coating thickness CT = 0, 0.5, 1.0 and 1.5 (w) 5 values of the dimensionless scaled separation d/os = 1, 1.5, 2, 2.5 and 3.0 2 roughness levels corresponding to specimens no. 101 and 301 For each run, 1000 microcontacts were simulated. The average value of the microcontact area and the microcontact load P as determined by the simulation were diviced to approximate the real contact pressure RP =P/A. RP is an important indicator of the severity of the surface loading.

All the curves on Fig. 8 have the same point of origin since at CT = 0, the material responds as the substrate steel. When the coating is sufficiently thick the substrate will cease to matter and the material will respond as if it were made entirely of the coating material. For the soft coatings a thickness of 1.5 pm appears to be as a large as necessary since the plots have leveled off. For the hard coatings, the asymptote appears to be beyond 1.5 pm. Figure 6 shows mean real pressure RP plotted for each coating thickness against dimensionless separation d/us for the 301 specimen with the hardest coating. Separation is seen to have a comparatively small effect on RP with the thinnest coatings but a larger effect with the thicker coatings. Figure 7 is comparable to Figure 6 but is drawn for the softest coating. The curves for coating thickness of 1 and 1.5 pin are quite close, confirming the observation that for soft coatings the behavior becomes asymptotic for thicknesses of 1-1.5 pm. Figure 8 shows average microcontact area A plotted for each coating modulus as a function of coating thickness. The plot is drawn for specimen 301 at a dimensionless separation of d/o = 3. With respect to contact area, unlike S RP, the asymptotic behavior with coating thickness sets in earlier. For the soft coatings there is negligible change in area beyond a coating thickness of 0.5 pm. The hard coatings have not quite leveled off at a thickness of 1.5 pm but the area is not changing greatly. Figure 9 shows RP plotted against the elastic modulus of the coating for the four coating thickness values. The plot is drawn for specimen No. 301 at a standardized separation of d/us = 1.0. When there is no coating, (CT = 0 ) ) the substrate determines the response so there is no variation in the plot with coating modulus. The plot suggests that linear interpolation could reasonably be used to compute the real pressure at values of the elastic modulus intermediate to the four values used in this study. Figure 10 is comparable to Figure 9 but shows the variation of microcontact area with modulus. As noted previously the differences in area due to coating thickness are small compared to the real pressure differences. Figure 11 compares the effect of the thickness of the hardest coating (E1/E2 = 10) on RP at d/us = 1.0, for the two specimens. RP is seen to increase at a faster rate with coating thickness for the rougher specimen (No. 101). For the soft coating, (not shown) RP also decreases more rapidly with coating thickness for the rougher than for the smoother

162

surface. At a fixed d/os, microcontact area is larger for the rougher surface but varies with coating thickness in approximately the same way. 6

DETERMINING TEE SEPARATION D/us

In elastohydrodynamic lubricated contact the separation may reasonably be talcen to be determined by the film thickness h, which is interpreted as the distance between the roughness mean planes of the contacting bodies. The relation between d/us and h involves the roughness spectrum and is given in [15]. For dry contact d/u may be determined as the separation at which '?he mean load Q over the nominal area of contact .A is equal to the load externally applied to the contact. To use the simulation results to make this determination one multiplies the mean asperity load P at the separation d/us by the expected number of microcontacts. The expected number of microcontacts is the expected number of summits per unit area DSUM, multiplied by the nominal area .A and by the probability that a summit is a microcontact. This probability is:

P[summit=microcontact] P[summit height x > d]

= =

l-+(d/os)

=

P

DSUM

*

[l-+(d/os)]

*

.A

=

DSUM[l-+(d/us)]

P

1. 2.

3.

4.

5.

7.

(48)

The load per unit nominal area, i.e. the nominal pressure, is thus: Q /Ao

References

6.

The mean load supported over the nominal contact area is

8.

(49) 9.

Figure 12 is a plot of the logarithm (base 10) of Q/AO against the dimensionless separation d/oS for the hard coating applied at a thickness of 1.5 pm. For a given applied load per unit nominal area, the dimensionless separation is seen to be smaller for the smoother surface (Spec. NO. 301) than for the rougher surface (Spec. No. 101). As an example, a load of Q2= 10 N applied over an area of .A = 1 mm giving log 10(Q/Ao) = 1.0, results in d/u cz 2.2 for specimen No. 301 and d/os = 2.7 for specimen no. 101. The absolute mean separation is computed from the individual us values in Table 2:

d301

=

2.2 x 0.052

=

0.114 pm

dlOl

=

2.7 x 0.254

=

0.686 pm

10.

11. 12. 13.

14. 15.

Repeating this calculation for different Q values will yield the Q vs. d relationship characterizing the stiffness of coated joints. Figure 13 shows the effect of coating type on the load/ separation relationship for specimen No. 301 with a 1.5 pm coating thickness.

ACKNOWLEDGMENT

This investigation was supported by DOE-ECUT under DOE Contract No.DE-AC02-87CE90001.AOOO. It was performed within the Tribology Program managed by Mr. David Mello. Dr. Fred Nichols, manager of the Tribology Project, was the technical monitor. This support is gratefully acknowledged.

(47)

where + is the standard normal cumulative distribution function.

Q

7

16.

McCool, J. I., "Comparison of Models for the Contact of Rough Surfaces", Wear, 107, pp. 37-60, (1986). Greenwood, J., and Williamson, J., "Contact of Nominally Flat Surfaces", Proc. R. Soc. London, Series A, 295, pp. 300-319, (1966). Burmister, D. M., "The General Theory of Stresses and Displacements in Layered Systems", Jnl. Appl. Physics, Vol. 16, pp. 89-94, Feb. (1945). Tu, Y., and Gazis, D., "The Contact Problem of a Plate Pressed Between Two Spheres", ASME Trans., Jnl. Appl. Mech., pp. 659-666, Dec. (1964). Kennedy, F., and Ling, F., "Elasto-Plastic Indentation of a Layered Medium", ASME Trans., Jnl. Engr. Matls. and Tech., pp. 97-103, April (1974). Chiu, Y., and Hartnett, M., "A Numerical Solution for Layered Solid Contact Problems with Application to Bearings", ASME Trans., Jnl. Lub. Tech., Vol. 105, pp. 585-590, Oct. (1983). Gupta, P., and Walowit, J., "Contact Stress Between an Elastic Cylinder and a Layered Elastic Solid", ASME Trans., Jnl. of Lub. Tech., pp. 250-257, April (1974). El-Sherbiney, M., and Halling, J., "The Hertzian Contact of Surfaces Covered with Metallic Films", Wear, Vol. 40, pp. 325-337, (1976). Halling, J., "The Tribology of Surface Coatings, Particularly Ceramics", Proc. Inst. Mech. Engrs., Vol. 200, No. C1, pp. 31-40, (1986). Chen, W., and Engel, P., "Impact and Contact Stress Analysis in Multilayer Media", Int. J. Solids Structures, Vol. 8, pp. 1257-1281, (1972). W. T. Chen, "Computation of Stresses and Displacements in Layered Media", Int. J. Engng Sci., 9, pp. 775-800 (1971). Johnson, K. L., Contact Mechanics, Cambridge University Press, 1985. McCool, J. I., and John J., "Flash Temperature on the Asperity Scale and Scuffing", ASME Transactions, Jnl. of Tribology, Vol. 110, No. 4, pp. 659-663, October (1988). Sayles, R. S. and Thomas T. R., "Thermal Conductance of a Rough Elastic Contact", Appl. Energy, 1, pp. 249-267 (1976). McCool, J. I., "Relating Profile Instrument Measurements to the Functional Performance of Rough Surfaces", ASME Transactions, Journal of Tribology, Vol. 9, No. 2, pp. 264-270, (April 1987). McCool, J. I., "Predicting the Upper Percentiles of Flash Temperature at Microcontacts", Surface Topography, Vol. 1, No. 3, pp. 343-355, (September, 1988).

163

El/E2=1/3 t/aH CA CR CP -----------_--___-____ -------0 0.117476 0.180841 0.244851 0.373081 0.499766 0.745414 1.206660 1.745012 2.262380 4.277158 8.275616 16.27156

1 1.380072 1.453488 1.498801 1.546551 1.561037 1.543448 1.456028 1.353363 1.279591 1.143380 1.070091 1.034233

1.17, 765 1.20! 507 1.224255 1.243604 1.249414 1.242356 1.206660 1.163341 1.131190 1.06928" 1.034452 1.016973

-t/aH -------

CA

CR

0 0.095695 0.14 1127 0.185615 0.271707 0.354663 0.515102 0.835017 1.259260 1.709714 3.625295 7.582342 15.60697

1 0.915751 0.885191 0.861326 0.820277 0.786164 0.737028 0.697253 0.704771 0.730780 0.821423 0.898:11 0.951475

1 0.956949 0.949846 0.923077 0.903692 0.886659 0.858504 0.835017 0.839507 0.854857 0.906324 0.947793 0.975436

I

0 0.106600 0.162593 0.219476 0.335075 0.451610 0.711218 1.129817 1.661648 2.177131 4.192909 8.194468 16.19304

10 7.278482 6.368164 5.652272 4.609759 3.895887 3.005700 2.162781 1.724623 1.515346 1.2 31162 1.107954 1.052838

0.3333 0.345010 0.350038 0.355083 0.365739 0.377457 0.403752 0.462048 0.532376 0.592040 0.738!70 0.850476 0.928010

TABLE 1

-

0.091762 0.132614 0.171499 0.243524 0.309261 0.428878 0.656193 0.970594 1.329146 3.012376 6.768974 14.60593

1 1.136364 1.174950 1.204239 1.247505 1.274697 1.405086 1.276487 1.227144 1.184975 1.098780 1.049208 1.024275

1 1.066004 1.083951 1.097378 1.116918 1.129025 1.185363 1.129817 1.107766 1.088565 1.048227 1.024308 1.012065

CA

CR

1 0.842034 0.781616 0.735294 0.658935 0.597764 0.510934 0.430589 0.418690 0.441657 0.567151 0.715922 0.833333

1 0.917624 0.884091 0.857493 0.811748 0.773152 0.714796 0.656193 0.647063 0.664573 0.75?0L;4 0.846122 0.912871

Correctign Factors CA, CR and C

3 2.773669 2.670842 2.573500 2.395744 2.238909 2.241148 1.659825 1.446389 1.330942 1 7573 1.075357 1.037670

___---------_-_ CP

vs.

0.1 0.106088 0.108283 0.110591 0.115750 0.121595 0.134947 0.166450 0.211642 0.258615 0.418917 0.604243 0.760498

t/aH

Modulus Ratio E1/E2 0.10

IF Te) :

Procedure

The unknown problem a r e :

quantities

of

the

+ t h e d e p t h of t h e v e l o c i t y f i e l d as a f u n c t i o n of t h e l o a d F ( i . e . t h e width 2a) : h * ( a ) +the

=

yield

stress

e q u a t i o n ( 5 ) becomes :

distribution

00 (h)

They would be deduced from e x p e r i m e n t a l data (the indentation pressure p r o f i l e a t increasing load, p ( F ) o r p ( a ) ) through equation (5) although they s h o u l d v e r i f y a l s o e q u a t i o n ( 4 ) a t any s t a g e of l o a d i n g . The r e s o l u t i o n needs consequently an incremental procedure.

S i n c e ool and oOs a r e c o n s t a n t , t h e p r o c e d u r e minimization g i v e s e a s i l y t h e v a l u e of H a t each l o a d i n g . Three c a s e s o c c u r : H i s s o l u t i o n of t h e problem f o r an homogeneous m a t e r i a l ,case ( 6 ) , H = G , e H=o r H i s s o l u t i o n of a t h i r d degree a , equation i n t h e case ( 7 ) .

178

4.2.Validation The p r e d i c t i o n s of t h i s s i m p l i f i e d model a r e compared t o t h o s e p r e s e n t e d i n a' p r e v i o u s t h e o r e t i c a l and e x p e r i m e n t a l work, [4], f o r t h e two c a s e s below : + s o f t layers ( l a y e r of copper vapour d e p o s i t e d on a s u b t r a t e of h i g h speed s t e e l : h = 0 . 1 2 ) D = 2 f i b

0

4

?

I

'

6

6/e

'O

o v e r view

0 e

= 6pm A e = 1.5pm

+ h a r d l a y e r s (boron n i t r i d e c o a t i n g mild steel chemically deposed on subtrate :h= 4 . 4 ) I

I

c r o s s s e c t i o n AA figure 3

one o b t a i n s : I

0

I

0.5

1,s

we

=

0.8pm

Oe

=

5.5

A

2

- ae

2.5

D

e == 20bni

p l a n e model [4] t h r e e dimensional e x t e n s i o n [41

+

:

p r e s e n t t h e o r e t i c a l . work

The p e n e t r a t i o n depth 6 w a s deduced from t h e l e n g t h D of t h e impression d i a g o n a l a f t e r unloading

(8

=

D

7 ) . The

2 f i b

a is

a

=

2

fiE

term

a

of

adjustment

experiments, one f i n d s a =

pm

figure 2 :

=

3

impression

d i a g o n a l D i s r e l a t e d t o t h e punch width 2a a s f o l l o w s :

t o

2

From f i g u r e 2 , w e can deduce t h a t o u r model i s r a t h e r good f o r s o f t coatings a s w e l l a s f o r hard c o a t i n g s . The i n d e n t a t i o n p r e s s u r e p r o f i l e i s n o t f a r from e x p e r i m e n t a l d a t a , a t l e a s t f o r a h a r d l a y e r . The approximation i s less v a l i d i n t h e case of a s o f t layer, n e v e r t h e l e s s it i s b e t t e r than t h e plane a n a l y s i s used f o r t h e more complex model [ 4 ] . Furthermore, t h e t h r e e dimensional model l e a d s t o t h e b e s t a p p r o x i m a t i o n for s o f t coating, while, f o r hard c o a t i n g , t h e performances of t h e 2 D and 3D models a r e q u i t e s i m i l a r .

179

4.3.Evolution

of

the

deforming-

zone L_

The r e s o l u t i o n o f the direct problem g i v e s i n f o r m a t i o n about t h e e v o l u t i o n o f t h e d e f o r m i n g zone t h r o u g h t h e function h ( a ). +hard coatings :

t

4.00

I

t

3.00

h i s f i r s t a l i n e a r f u n c t i o n of a u n t i l t h e velocity f i e l d reaches t h e layers u b s t r a t e ,interface. Since there, h becomes c o n s t a n t a n d e q u a l t o t h e f i l m t h i c k n e s s e . The v e l o c i t y f i e l d r e m a i n s longer confined within t h e s o f t layer a s t h e r a t i o h i s l o w e r . Then a n e x t e n s i o n i n t o t h e s u b s t r a t e can b e o b s e r v e d . The r e s o l u t i o n of the direct problem f o r b i l a y e r s validates our It shows also that the model. "inversion" procedure, for coated m a t e r i a l s , should be c a r r i e d out very carefully.For such materialsfthe d i g c o n t i n u i t i e s of flow stress, induces d i c o n t i n u i t i e s of t h e a u x i l i a r y q u a n t i t y h(a).

5.INVERSION

2.00

PROCEDURE

1.00

0.00

0.00

0.20

0.60

0.40

0.80

a -

1.00

To d e d u c e t h e i n t r i n s i c p r o p e r t i e s use from experimental data , we e q u a t i o n s ( 4 ) a n d ( 5 ) where :

e

h

figure 4 : e

+ p ( a ) i s a f i t t i n g of e x p e r i m e n t a l datas

a

= f

; i )

t h e velocity f i e l d is f i r s t located i n t h e hard l a y e r u n t i l extension t o t h e s o f t e r s u b s t r a t e would p r o v i d e l o w e r is a work rate. The consequence d i s c o n t i n u i t y of the function h ( a ), t h e d i s c o n t i n u i t y being a l l stronger a s t h e r a t i o h i s higher.After t h a t , t h e depth h o f t h e d e f o r m i n g zone i s a g a i n a q u a s i l i n e a r f u n c t i o n of a , t h e curve s l o p e v a l u e i s a p p r o x i m a t i v e l y G, s o l u t i o n o f t h e problem f o r homogeneous m a t e r i a l s .

+ h ( a ) , o o ( h ) , E o ( h ) a r e t h e unknown q u a n t i t i e s o f t h e problem 5.1.A

differential

method

This method , t h a t w e h a v e f i r s t tested, consists in successive d e r i v a t i o n s of equation (5) with respect t o t h e v a r i a b l e a . Thus, w e g e t a s y s t e m of f o u r l i n e a r e q u a t i o n s with t h r e e unknown q u a n t i t i e s E o ( h ), o0(h), o t o ( h ,)

+ s o f t coatings : By e l i m i n a t i n g t h e m , t h e p r o b l e m i s reduced t o t h e r e s o l u t i o n of a f i r s t degree d i f f e r e n t i a l e q u a t i o n of H with respect t o a :

"'h e

H p ( a ) (H2-2) + a p ' ( a ) (H2+2)+ a2p"( a ) ) H'=--( a p ( a ) ( H ~ - I ) + apl ( a ) ( H ~ + I )

0.0

2.0

9.0

6.0

h

figure 5 :e

= f

8.0

a (g)

1 e

10.0

The RUNGE-KUTTA method i s u s e d t o s o l v e it. The unknown quantities can a f t e r w a r d s e a s i l y be d e t e r m i n e d from t h e system. S i n c e t h e p r o c e d u r e r e l i e s upon d e r i v a t i o n s , t h e d e r i v a b i l i t y of t h e is implicitly unknown quantities s u p p o s e d . T h i s method c o u l d c o n s e q u e n t l y n o t b e a p p l i e d t o c o a t e d m a t e r i a l s which p r e s e n t a d i s c o n t i n u i t y of t h e f l o w s t r e s s d i s t r i b u t i o n . But t h i s method could be s u c c e s s f u l l y used f o r d i f f u s i o n 1 a y e r s . T h e example o f l i q u i d n i t r i d i n g i s p r e s e n t e d below :

180

t h u s , f o r t h e v a l u e h* ( s o l u t i o n of e q u a t i o n ( 4 ) ) which minimizes W a t a g i v e n l o a d , t h e e q u a l i t y between t h e experimental datas p ' ( a ) and the aP be v e r i f i e d : calculated -must aa

12.0

!!

10.6

9.2

7.8

6.4

0 experimental

data

5.0

0.

1W.

m.

2w.

'40.

a(pm) 500.

+ t o build appropriate intervals (where amax i s [ a k - l , a k l on [O,a,,,l a s s o c i a t e d t o t h e maximum l o a d a p p l i e d ) and t o s o l v e t h e p r o b l e m on e a c h of them.

5.2.2.Alqoritha Hv

9.w

=

f(a)

,

The p r o c e d u r e t i m e s resolution :

I

consists

in

a

two

+ w e suppose known t h e v a l u e s of h, Go(h) and r o ( h ) r e s p e c t i v e l y h,,Ool and 4, f o r an i n i t i a l v a l u e a=a,. These v a l u e s a r e s o l u t i o n s of t h e problem, t h e n t h e y v e r i f y e q u a t i o n s ( 5 ) and ( 8 ) . F o r a r e a s o n a b l e v a l u e of a,, w e can assume h t o have a l i n e a r v a r i a t i o n with r e s p e c t t o a on t h e i n t e r v a l [a,,a,l : h ( a ) = h, + P(a - a,) a, I a I a2

so t h e s o l u t i o n h,

=

h ( a , ) w i l l be known

s i n c e t h e v a l u e o f p w i l l be determined. + f o r a g i v e n v a l u e of v a r i a b l e a i s a f u n c t i o n of h : Oo=

f (h) a = a , + -

figure 6

global method

-

h.

P

Equation ( 5 ) can t h u s be c o n s i d e r e d a s a f i r s t o r d e r d i f f e r e n t i a l e q u a t i o n of co with r e s p e c t t o h :

so'( h ) + 5.2.A

h

the

c ( h ) e0(h) = r ( h )

which i s i n t e g r a t e d by t h e RUNGE-KUTTA method on t h e i n t e r v a l [h,,h2] .

5.2.1.Introductioq Thus w e have an e s t i m a t i o n of h , , o o ( h , ) , To s o l v e t h e problem i n any case, even when t h e flow s t r e s s d i s t r i b u t i o n Oo(h) i s n o t d e r i v a b l e , w e m u s t b u i l d a n o t h e r method of r e s o l u t i o n . W e have t e s t e d many a p p r o a c h e s of t h e problem and u s e d v a r i o u s n u m e r i c a l methods t o s o l v e i t . We have found t h a t t h e b e s t way i s : + t o a v o i d any d e r i v a t i o n w i t h r e s p e c t t o h . One can n o t i c e t h a t :

c o ( h 2 ) f o r a=a2 . S i n c e t h e s e q u a n t i t i e s m u s t v e r i f y e q u a t i o n ( 8 ) , we modify t h e v a l u e of p a n d s t a r t t h e procedure a g a i n in order t o obtain the best ( 8 ) . The approximation of equation method used i s a dichotomy on e q u a t i o n ( 8 ) w i t h r e s p e c t t o t h e v a r i a b l e p . We have t e s t e d b e f o r e more b e t t e r methods of r e s o l u t i o n (NEWTON-RAPHSON, G r a d i e n t ) we have finally adopted t h e but dichotomy one s i n c e any d e r i v a t i o n w i t h r e s p e c t t o h m u s t be a v o i d e d . The c a l c u l a t i o n i.9 a f t e r w a r d s e x t e n d e d t o t h e next i n t e r v a l [a2,a3].

181

5.2.3.Results

The two f o l l o w i n g t e s t c a s e s a r e t h o s e t h a t we have used b e f o r e t o v a l i d t h e d i r e c t problem. +soft steel) :

coating

/

(Cu

high

+ h a r d c o a t i n g ( N i B / mild s t e e l ) :

speed 5.00

1.00

8%. .t

1

I

=%.a

0.80

0.80

0.40

0.20

I

0 experimental 0.00 0.0

4.0

2.0

6.0

8.0

a

0.00

'

data I 5 5.00 e

~

0.00

10.0

1.00

3.00

2.00

4.00

0

-= HV

:

f i g u r e 8.1

f) ; (

a

Hv,

f

1.B

E 1.25

3'50E 3.00 1.

1.05

2.50

"

2.00

-'

1.50

.',

0.85

I

* . .

t

'

I

.

0.45

'

:

'

2.0

0.0

.

6.0

4.0

8.0

5

I

.

+

+

*

a

f

.

f

*

*

*

*

t

1.00

10.0

e

f i g u r e 8.2 : H

=

f(;)

a

1.54

3 8 , .

Eva 0.290

''

0.180

'

O.LM

.'

0.m

~'

1.a

0.90

0.69

-.

0 . m ' 0.0

0.3

0 adjuntment :

:

3.0

i

:

:

:

6.0

12.0

9.0

0.00

L!

0.00

1.00

2.00

3.00

4.00

figure 7.3 :

y= QO

VS

figure 7

f(;)

h

& e

0

figure 8.3 :

-= 00

HvS

figure 8

)€;(

h

5

182

We

can n o t i c e : +on f i g u r e 7 :

6.CONCLUSION

i)H : +is f i r s t constant s o l u t i o n of t h e problem and e q u a l t o f o r an homogeneous m a t e r i a l +decreases a s long a s t h e v e l o c i t y f i e l d s t a y s confined i n the layer +increases after

6,

u n t i l it reaches again t h e value

fi .

i i ) o , ( h ) :+is equal t o t h e l a y e r flow stress u n t i l t h e v e l o c i t y f i e l d reaches the layer-substrate interface +is discontinuous f o r h=e +reaches afterwards t h e v a l u e of t h e s u b s t r a t e y i e l d s t r e s s . +on f i g u r e 8 : i)H :

and e q u a l t o

-+is

first

constant

fi

+increases quickly since t h e substrate influences t h e test -+decreases after and r e a c h e s a g a i n

A k i n e m a t i c model, b a s e d on t h e punch analogy, and a resolution procedure w a s proposed i n o r d e r t o deduce t h e i n t r i n s i c p r o p e r t i e s of l a y e r e d m a t e r i a l s from t h e r e s u l t s of i n d e n t a t i o n t e s t s . The m a t e r i a l s a r e assumed t o b e r i g i d p e r f e c t l y p l a s t i c , the indentation pressure is calculated by m i n i m i z a t i o n o f t h e p l a s t i c work rate.

The model h a s b e e n f i r s t t e s t e d by analysing the direct problem of i n d e n t a t i o n of b i l a y e r s . I t h a s been v a l i d a t e d by c o m p a r i s o n t o e x p e r i m e n t a l t e s t s a n d t o r e s u l t s i s s u e d from a more complex model.The t h e o r e t i c a l r e s u l t s show t h e p r o p a g a t i o n o f t h e v e l o c i t y f i e l d i n r e s p e c t i v e l y s o f t c o a t e d and h a r d c o a t e d m a t e r i a l s . The i n f l u e n c e o f t h e s u b s t r a t e on t h e flow stress d i s t r i b u t i o n i s a l s o determined. The r e s o l u t i o n a l g o r i t h m t h a t h a s been c a r r i e d o u t f o r c o a t e d m a t e r i a l s i s a two t i m e s p r o c e d u r e w i t h o u t any derivation t o avoid d i s c o n t i n u i t i e s . However, for diffusion layers, a d i f f e r e n t i a l method c a n b e u s e d .

fi. ACKNOWLEDGMENTS

i i )o o ( h ) : + d e c r e a s e s from t h e l a y e r flow stress value t o t h e one of t h e s u b s t r a t e . For t h i s case, the s u b s t r a t e h a s an i n f l u e n c e f r o m t h e beginning of t h e t e s t .

The a u t h o r s a r e t h a n k f u l t o t h e D . R . E . T . f o r f i n a n c i a l support under c o n t r a c t

88/116. REFERENCES

The n u m e r i c a l b e h a v i o u r o f t h e two solutions suggested t h a t t h e curves o0 ( h ) m u s t ' b e s m o o t h e d . I n d e e d , t h e apparent workhardening f o r t h e s o f t apparent coating a s w e l l a s the a n n e a l i n g f o r t h e h a r d c o a t i n g which appears a f t e r t h e discontinuity i s probably a numerical a r t e f a c t r a t h e r t h a n a p h y s i c a l phenomena. a r e s u l t , w e can e s t i m a t e t h a t t h e method o f r e s o l u t i o n i s q u i t e s a t i s f y i n g f o r t h e model p r o p o s e d . F o r f u r t h e r works, t h e model s h o u l d b e more a c c u r a t e a n d a f i n i t e e l e m e n t s method should be used. As

.

H BUCKLE

L 'essai de microdurete et ses applications Publications scientifiques e t t e c h n i q u e s du m i n i s t b r e de l ' a i r (1960) J.F.W.BISHOP J . M e c h . P h y s . S o l i d s , 2 (1953)43-53

.

H PETRYK J.MeC.App1.

,4 (1980)255-282

D.LEBOUVIER

L'essai de duretC sur les mat Criaux revst us Th&se ENSMP (1987) W.JOHNSON I n t . J . M e c h . S c i . ,3(1961)229-238

J.B.HADDOW,

F.J.LOCKETT

J.Mech.Phys.Solids,ll(l963)345-355 J.SALENCON

C.R.Acad.Sci.Paris,Ser.A, 266 (1968)1210-1213

D.LEBOUVIER,P.GILORMINI,E.FELDER T h i n S o l i d s F i l m s , 172 (1989)227-239

183

Paper VII (iii)

Damage mechanisms of hard coatings on hard substrates: a critical analysis of failure in scratch and wear testing R. Rezakhanlou and J. von Stebut

For hard brittle coatings on hard substrates single pass scratch testing is shown to produce shallow tracks whose depth prior to fatal damage does not exceed one third of the coating thickness. The singular cause for fatal damage (chipping, spalling) is tensile type surface cracks generated behind the trailing edge of the indenter. The crack features observed correspond to a quasi-bulk mechanical response of the coating. By increasing the tip radius of the indenter the measured critical load for crack generation becomes increasingly sensitive to coating/substrate interface brittleness and flaws. Multipass sclerometric wear experiments done on the same scratch tester provide for more realistic testing of fatigue wear likely to be dominant for hard coatings on hard substrates. They reveal delamination in the substrate/coating interface region. Friction is shown to amplify brittle surface damage both for scratch and multipass wear testing. Damage caused by both techniques appears to be controlled by the same basic mechanism of surface crack generation and propagation.

1- INT R 0D U C TI 0N Coating is a well-known technique used to increase the resistance of mechanical parts with respect to friction and wear. As rigorous testing of a coated surface under real contact mechanical conditions is i n general too expensive and time consuming there has been a long standing need for laboratory tests, sufficiently close to the required contact mechanical reality to yield the necessary feed-back for coating process optimization. For hard, brittle coatings the scratch test [ l , 2, 31 is commonly used t o obtain quantitative information on the strengh of what should be considered the substrate-coating composite (S.C.C.). This test yields the critical load Lc for fatal coating damage (chipping, spalling, buckling, etc.) when drawing a 0.2 niin tip radius indenter under progressively increasing normal load F n , in dry friction, over the coating to be tested. C o m m er c i a 11y a v ai I a b I e scratch testers are generally factory equipped with reflected light microscopes for post test damage inspection as well as on line acoustic emission (A.E.) and friction force (Fl) detectors. In case of hard, brittle coatings critical damage

coincides with abrupt variation in A.E. and Ft [3, 41. These two parameters are easily monitored during the test and yield very useful, indirect hardcopy information on contact mechanics and surface damage. However they should not be used to define Lc [4] unless validated before by appropriate surface analysis. Lc is often taken as a measure of coating adhesion. This is somewhat adequate for poorly adhering coatings. However for well adhering systems there is abundant literature [ 5 , 61 showing that Lc is related to S.C.C. strength (also called "practical adhesion" [ 7 ] or "load bearing capacity" [S]) and depends on the prevailing mechanical test conditions (indenter tip radius and composition, surface roughness, load rate dL/dx and friction coefficient p). Lc values can be considered as S.C.C. strength specific only if these conditions are completely identical [ 5 , 61. Even if these conditions are met the crucial question remains whether the scratch test and in particular the corresponding measured Lc value can give the required predictive information concerning wear r e s i s t a n c e . Therefore comparative studies of scratch testing and realistic wear testing are badly needed. When doing such comparative testing

184

an additional problem is how to choose a realistic wear test. T. Arai et al. [9] have run field experiments like hammering, rolling with slip, coining and stamping in conjunction with indentation and scratch testing. Because of a lack of contact mechanical similarity i t is practically impossible to establish any valid cross correlation. In a particular case Nierni et al. [ l o ] found that field results on wear resistance of TiN coated gear cutting hobs were in contradiction with what would have been expected from the critical loads measured by standard scratch testing. Therefore Lc alone is often insufficient to predict wear behaviour of a coated system. For ion beam assisted deposition von Stebut et al. [ l l , 121 have shown that detailed damage analysis after scratch testing and pin/disc wear testing reveal common damage mechanisms where the measured absolute values of Lc were of little practical interest. However such direct comparisons of failure mechanisms in real, dynamic wear experiments and standard scratch testing are delicate because of very different contact mechanical conditions. For this reason we have compared in [13] surface damage i n standard scratch testing with sclerometric, multipass unidirectional wear damage obtained by means of the same C.S.E.M. scratch tester and the same Rockwell C stylus under (tribologically more realistic) constant normal loads well below L c . This study revealed that the sclerometric wear life (expressed in passes to failure, Nc at Fn =10 N) may not correlate with the standard critical load, L c , of fatal coating damage but- rather with another critical load, L,, related to the onset of tensile-type surface cracks behind the trailing edge of the indenter. Such tensile-type cracks, at normal loads Fn < Lc have been observed by various researchers [6, 8, 14, 1-51 but their contribution to damage in wear has never been studied i n detail. I n [I31 we also showed that another brittle failure mechanism is responsible f o r coating delamination in sclerometric wear testing of hard, brittle coatings on hard substrates, a composite system of particular technological interest. In the present paper the aforementioned e x p e r i m e n t s have been scaled u p to tribologically more realistic conditions by increasing the tip radius of the rider and by changing its chemical nature (WC and ball-bearing steel instead of diamond). One of the questions we are trying to answer is

whether the same brittle failure mechanisms prevail when adhesive friction is paramount. 2

-

2.1

EXPERIMENTAL

-

Specimens

The substrates were flat, 5 mm thick and 30 mm wide high speed steel (H.S.S.) discs, heat treated to 790 HV. Details on the surface substrate preparation and the microstructure of TiN coatings obtained by means of a hot cathode P.V.D. technique can be found in [16, 171. The deposition temperature was controlled in between 4.50 and 500 "C. The major features of the specimens studied are compiled in Table I. Specimens M44 and M45 are the same as those discussed in [13]. Table I: Major

specimen fcaturcs coatings on H.S.S. substrates).

Specimen code

I

M1

I

Substrate Hardness (HVO.OS) 790

I

Composite hardness (HV0.0S) 1600

2.2 - Scratch testing scleromertic wear

and

(P.V.D.

TiN

Coating thickness

I

( PI

5

I

multipass

A modified C.S.E.M. scratch tester [ l ] , factory equipped with A.E. detection and a metallographic light microscope was implemented by a piezoelectric transducer to measure the friction force, Ft. Multipass unidirectional sliding wear testing in the ball/flat geometry was done under constant normal load F n 1 and gives a reasonable description of experimental data only f o r indentation depth/coating thickness ratios well above 1 a s indicated by the authors 1141. The model is therefore inadequate for our situation (hp/t < 1/3).

2- The first part of the derivation is based on an assumption of pure ploughing while in the end the relation Ft = pc . Lc is used which describes total friction. In case of a large adhesive contribution this is not proportional to A1 but rather to the real contact area A2 (cf. ref. 14). For systems consisting of brittle bulk material the influence of friction on the critical load for cracking, Lc(p), has also been studied by Gilroy and Hirst [24]. Their experimental data show that the proportionality constant L c ( p ) / R strongly depends on the effective total friction coefficient (increase of Lc(p) by roughly an order of magnitude when increasing p from 0.15 to 0.5). This is in qualitative agreement with our data showing that with increasing p the contact becomes more severe causing higher crack density (Fig. 5 ) and lower life (Table IV). Based on t h e work of Hamilton and Goodman [20], Gilroy and Hirst give an analytical expression for the total tensile stress, o t , behind the trailing edge of a spherical indenter sliding on a flat of a bulk material: 27t a

1"

8

a is the Hertzian contact radius which is proportional to Fn lI3. What is striking in this expression is the predominant effect of the friction contribution (second term i n braces) as compared to the contribution related to static indentation (first t e r m ) . When considering the ratio Fn(O)/Fn(p) of critical normal loads without sliding (static indentation) and with sliding (scratch testing) this yields:

By inserting our experimental data for the standard Rockwell C indenter on sample M44, Fn(O)/Fn(p) = 5 (with p = 0.1 and v = 0.25 from t h e literature), we got fairly good agreement ( 5 vs. 8) which means that t h e basic mechanism of brittle coating damage can be reasonably well accounted for by tensile stress behind the trailing edge of the indenter sliding on bulk material. Admittedly this approach assimilates

191

coating and bulk failure and should be taken only as a starting point for a more general description. We shall take i t as an indication that fatal brittle damage is triggered at the surface via intrinsic brittleness of the coating. What can be seen i n Fig. 2 is the simultaneous presence of tensile cracks all along the track where the coating did not spa11 off. Even at the point where the substrate is stripped off its coating there are line patterns altogether similar to the corresponding crack patterns in the coating itself. I t is not clear whether these are some kind of replica of the cracks in the spalled off coating or real cracks continuing into the substrate. However this d o e s i n d i c a t e that t h e s u r f a c e c r a c k propagation took place before interfacial detachment. We suggest that coating failure is the result of two effects: 1 ) surface cracks propagating towards the interface; 2) activation of interface crack propagation by these surface cracks when arriving at the substrate. The efficiency of this interface crack propagation should then be enhanced with increasing brittleness and/or flaw density at the interface.

-

4.2 coating

Failure related to interface strength

substrate-

So-called “adhesive spalling failure” as shown in Fig. 1, 3 and 5 are experimental proof that the intrinsic strength contributes i n an important way to S.C.C. damage. Just how this occurs quantitatively must be questioned when considering the analysis i n section 4.1. An additional question is: “where does t h e damage start?” - at the coating surface as suggested by the preceding discussion, - or rather at the substrate/coating interface as proposed by Rickerby et a1 [25] by relating it to the interface flaw density. This may well depend on the contact mechanical situation.

4.2.1 testing

-

Interface

failure in

scratch

Blister formation as shown on Fig. 2 for conventional scratch testing with a blunt WC indenter is striking evidence that there is an interface specific dam‘age mechanism for sample M45 absent for the other two specimens and which the sharp indenter did not reveal.

4.2.2 wear

-

Interface testing

failure

in

sclerometric

For all samples tested under the blunt diamond and WC riders the loading becomes Hertzian after a few initial passes and no d e t e c t a b l e w e i g h t l o s s i s seen. T h i s corresponds to a situation of severe fatigue wear. As the friction coefficients are small the maximum in the principal shear stress is well below the coating surface (= a/2 = 30 pm - cf. Table IV and ref. 20, 22). Therefore fatigue cracks might well be initiated not at the surface but rather at interface flaws and their propagation would finally lead to coating detachment. This is an open question because we never observed any blistering without surface cracks. When doing a quality evaluation of the three composites M1, M44 and M45 based on their respective wear lives, as measured by Nc, M1 ranks first, followed by M44 and M45. The strength evaluations based on Lc for the sharp diamond indenter (Table 111) yield a quite different order (M44, M45 and M1 last), whereas we get the same order as in the wear experiments when taking the Lt values of Table I11 (blunt indenters). This suggests that same basic damage mechanism (surface cracks) triggers spalling in sclerometric wear testing and in scratch testing with the blunt indenter. If this can be confirmed it would be an important step in the understanding of damage mechanisms in scratch and sclerometric wear testing as the “industry standard” for adhesion testing [26] which is not the case at the present time. CONCLUSION We have shown that scratch testing and multipass sclerometric wear testing are useful tools only if one studies the corresponding surface damage. A major part of coating failure is in fact due to the intrinsic brittleness of the coating. The common interpretation of the critical load as a measure of the coating adhesion should be abandoned. It is related to the strength of the substrate/coating composite. It should never be taken blindly from on-line acoustic emission measurements which must be accompanied by thorough inspection of the prevailing damage features. When defining the critical load related to the onset of surface cracks this parameter provides for a better measure of the multipass

192

sclerometric wear resistance which has been used to scale up the method to contact mechanically more realistic conditions with respect to "common wear". The electronic detection of these surface cracks which is impossible with the present device would be a considerable progress for reliable and physically more significant testing. Intrinsic coating br i t t 1en e s s and c oat i n g /s u b s t r a t e interface brittleness are important parameters that should be accounted for in future modelling. A cknow 1ed gem ent s

T h e present authors gladly appreciate specimen preparation by K. Anoun. The major part of the 3D mapping device has been conceived in the Laboratoire de MicromCcanique des Surfaces, Besanqon.

References 1 - P.A. Steinmann, P. Laeng and H.E. Hintermann, Le vide, les Couches Minces 220 (1984), 87. 2- A.J. Perry, Thin Solid Films 107 ( 1 9 8 3 ) , 167. (1986), 3 - J. Valli, J. Vac. Sci. Tecnol. 3007. Surface 4 - J. von Stebut, in Plasma Engineering, p. 1215; Ed. E.Broszeit, W.D. Munz, H. Oechsner, K.T. Rie, G.K. Wolf; D.G.M. Informationsgesellschaft, Oberurse1,FRG (1989). 5- P.A. St einmann, Y. Tardy and H.E. Hintermann, Thin Solid Films 154(1 987), 333. 6- A.J. Perry, Surf. Eng. 2(1986), 183. 7- D.S. Rickerby, Surf. Coat. Technol. 36 (1988), 541. 8 - A.J. Perry, Thin Solid Films 81 ( 1 9 8 1 ) , 357. T. Arai, H. Fujita and M. Watanabe, Thin 9Solid Films 154 (1987), 387. 1 0 - E. Niemi, A.S. Korhonen, E. Harju and V. Kaudpinen, J. Vac. Sci. Technol. A4 (1 986), 2763. 1 1 - J. von Stebut, J.P. Riviere, J. Delafond, R.C. Sarrazin and S. Michaux, Proceedings Int. Congr. Surface Modification of Metals by Ion Beams, Riva del Garda 1988, in press Mat. Sci. Eng. A l l 4 (1988). 1 2 - J. von Stebut, K. Anoun, J.P. Riviere and R.J. Gaboriaud, Proc. 16th Int. Conf. on Metallurgical Coatings, San Diego 1989, Thin Solid Films, i n press.

13- J. von Stebut, R. Rezakhanlou, K. Aoun, I-I. Michel and M. Gantois, ibid [12]. 14- S.J. Bull, D.S. Rickerby, A. Mathews, A. Leyland, A. Pace and J. Valli, Surf. Coat. Technol. 36 (1988), 503. 15- A. Schulz, P. Mayr, G. Ludenbach and R. Reichel, Harterei. Technische Mitteilungen 43(1988), 128. 1 6 - H. Michel, M. Gantois and C.H. Luiten, Proc. Heat Treatements 84, The Metals Society, London 1984. 17- K. Anoun, H. Michel and M. Gantois, Proc. 1 2 t h World C o n g r e s s on S u r f a c e Finishing, Interfinish 88, AITE, Paris 1988. 1 8 - H.J. Leu, R.D. Scattergood, J . Mater. Sci. 23 (1988), 3006. 1 9 - B. Lawn, R. Wilshaw, J. Mater. Sci. 10 (1975), 1049. 2 0 - G.M. Hamilton, L.E. Goodman, J . Appl. Mech. 33 (1966), 37. 2 1 - K.L. J o h n s o n , C o n t a c t M e c h a n i c s , Cambridge University Press, Cambridge 1985. 2 2 - M.J.W. Schouten, Schmiertechnik + Tribologie 5 (1973), 147. 2 3 - D.S. Rickerby, Surf. Coat. Technol. 36 (1988), 541. 2 4 - D.R. Gilroy, W. Hirst, Brit. J. Appl. Phys. (J. Phys. D) 2 (1969), 1784. 2 5 - D.S. Rickerby, D.S. Whitmell, C.F. Ayres, p. 911, ibid [4]. 2 6 - P.J. Burnett, D.S. Rickerby, J. Mater. Sci. 2 3 (1088), 2429.

SESSION Vlll MULTILAYER THEORY Chairman:

Dr. W.H. Roberts

PAPER Vlll (i)

Stress determination in elastic coatings and substrate under both normal and tangential loads

PAPER Vlll (ii)

A survey of cracks in layers propelled by contact loading

PAPER Vlll (iii)

A statistical approach for cracking of deposits: determination of mechanical properties


195

Paper Vlll (i)

Stress determination in elastic coatings and substrate under both normal and tangential loads J.M. Leroy and B. Villechaise

A 2D study of an elastic coated medium submitted to a static or a quasi-static sliding cylinder is presented. The method of resolution is based on Fourier transform techniques, to calculate the influence coefficients in the coated medium, and on an algorithm to solve unilateral contact conditions. Evolutions of different stresses (maximum contact pressure, interfacial shear stress, maximum Von Mises stress, ...) versus the coating thickness are presented.

I Introduction Stiff and compliant coatings are used more and more to increase the wear resistance of surfaces in contact. Theoretical analyses were then developped to study elastic media [1,2,3,4] or thin layers deposited on rigid substrates [5]. Generally, these studies only present the surface pressures [2,3,5] or stresses under a thick coating [6]. A study of an elastic coated medium loaded with a static or sliding rigid cylinder is presented here. Coating thickness, coating properties and friction vary in a wide range. Their influence on stress fieds (maximum pressure, maximum interfacial shear stress, maximum traction,etc) are given both in the coating and in the substrate. Variations of these stresses versus the coating thickness are important. Fracture, plastic deformations or interface delamination can then appear.

I1 Model A 2D, plane-strain contact between a rigid cylinder and an elastic coated medium is studied (fig. 1). E , ES, 3,; v s are the Young's moduli an2 Poisson s coefficients of the coating and the substrate. eCI eS represent the coating and substrate thicknesses. Lx is the dimension of the coated medium in the x direction. u, v are the lateral and normal displacements.

- the coating is perfectly bonded to the substrate. - The substrate is assumed to be a half space compared to the contact width ( L ~ >> 2a, eS >> za). Thus the uncoated case is the Hertzian case, with a . and po the half contact width and maximum pressure. .a and po are used to normalise results. - The normal load N is constant. Coulomb's law of friction is used when friction is taken into account (ax = f.u ) . In this case, the cylinder &idesY%n the coated surface without rolling (T=f.N). Inertial effects and residual stresses are neglected. Quasistatic conditions are assumed. N

Y

L Lx --

fig.1 Model 2.2 Stress notation

Stresses are noted with:

2.1 Assumptions and boundary condi-

tions

- a lower subcript C or S which represents the coating or the substrate. - an upper subscript s or i which repre-

sents the surface or the interface. The following assumptions and boundary conditions are includes in this analysis:

196

See for example figure 2. Note that with our sign convention a compressive stress is negative.

I11 Method

3.1 Equations Unilateral contact conditions are solved to obtain the contact size ( r ) and pressures. These conditions are:

(s)

. .

(1)

r =

o out of

r

(2) (3)

(4)

fl

*

I

A Fourier transform applied in the x direction is used to solve Lame's equations and to find the influence coefficients.

With this method, used by others authors [1,7], an analytical formulation of Fourier transforms of displacement and stress fields is obtained. Note that : - a Fast Fourier Transform algorithm is used to perform direct and inverse transforms [8]. This algorithm gives good precision and requires low computer calculation time [9]. - The effect of tangential stresses on normal displacements is taken into account in our calculation.

fig. 2 Stress notation

.d=Oinr . C T ao), whereas a stiff layer acts in the reverse way. Quite separately, there must be a stress concentration effect associated with the interface. The trend is clear; a compliant layer is beneficial both because of loadspreading and because the stress concentration is weak. What is difficult to estimate is the required layer thickness: other considerations such as cost will enter the engineering decision, and the optimal design will theoretically require the layer to be a fixed fraction of the contact width: it is essential, therefore, that the design is based on the heaviest load encountered, when the contact width is greatest. King and O'Sullivan also looked at the maximum tension developed in the wake of the contact. They found only a weak influence of the presence of the strip for normal indentation, but for frictional contacts the same trend was followed as that described above for yielding: a compliant layer is beneficial. There are some solutions in the literature for axi-symmetric indentation on layers [40,411 but only for normal indentation. 4. CRACKS IN LAYERS AND AT INTERFACES

Ultimately, having found the contact stress field, we shall need to solve for the stress intensity factors for a cracked layer (fig 3), where the crack may lie either adjacent to the interface (i) or along it (ii). The application of fracture mechanics to the layered problem should actually be more fruitful than for the

E

=

El = E2

v

=

v1 = v2

(1)

homogeneous problem, as the crack trajectory is well defined by the interface. But the problems in an applied mechanics formulation of the geometry are formidable: the crack is inevitably in an extremely steep stress gradient, although the 'dislocation' technique can cope with that, it is at (or very near to) an interface which produces a further stress concentration, and lastly there are the strange phenomena associated with elastic interfaces which further complicate the picture. We will address the last point first, and then return to the layer and contact problems. Figure 4 shows two bonded, elastically dissimilar half-planes loaded by uniform tension. Intuition tells one that there will be a significant mode I component of loading and probably a small mode I1 owing to the different Poisson effects. Early applied mechanics solutions with these assumptions proved unrealistic as material near the crack tip interpenetrated [42]. There are essentially two ways to overcome this problem; (a) Assume that the crack tips are closed, ie there is no l / h T stress singularity there, as in the celebrated Comninou solution [43]

(b)

Observe that at real interfaces the transition from one material to the other occurs over a finite thickness, as suggested by Atkinson [44]. The conventional KI value then reappears.

Current thinking is veering towards the latter, as the thinnest transition region permits a conventional fracture mechanics approach, which is comforting [45]. Assuming that ordinary fracture mechanics & valid, we can postulate a theoretical "fracture toughness" of the interface, and hence predict conditions for detachment of a badly-adhered layer. At this point a slightly more detailed exposition of the behaviour of interface cracks

206

characterise a flaw between layer and substrate are the Dundurs' constants [46] which, under transverse plane strain conditions are:

-

l-u1

1 - u2 1-12

1-11

c L =

1 - u

1

l

+

-

1-11 1

(2)

- u2 p2

- 29

1 - 2u

-

2

T21.12 B =

(3)

1 - u1 1-11

1 - 1-12

+ -

1-12

hence E < 0.08 - in most cases it is considerably less. Therefore, it is proposed that since the zone of oscillation is minute we systematically take E -+O, and hence rie -)1, whence equation (4), (6) and ( 8 ) take on their familiar meanings. The above discussion relates to pairs of bonded half-planes and similar simplified geometries. For the tribology problem we require to replace one half-plane by a strip (fig 1) which introduces further difficulties in the applied mechanics, although all comments relating to the nature of the crack-tip fields apply a fortiori. Erdogan and Gupta [49] studied the case of a crack within the layer ( s o that the above difficulties are avoided) and in the presence of an arbitary stress field. They also considered the case of an interface crack in a multi-layer system [50], using conventional fracture mechanics ideas. The axi-symmetric

Where ui is the modulus of rigidity. These parameters both vanish when the bonded materials are elastically identical and under certain other conditions; an extensive table of their values has recently been given by Suga et a1 [47]. As with conventional fracture mechanics the stress field in the neighbourhood of the crack tip is singular, but now varies as [48]

+ iu12

u22

=

layer

lid 3.

ic (K1 + K2) r

(4)

substrate

Cracked layers subject to contact loading, (i) Crack meandering either side interface, (ii) crack propagating along interface.

J2nr where i

= &,and 1 - P

E =

(5)

2 n

K1, K2 being "interface intensity factors." Similarly, the crack opening displacements are known, and corresponding to (4) we have

s2 + i s1

(K1 + i K2)

4

V'

r riE

=

*

(1 + 2i E) cosh R E

2 n E

where 1

1

E

- u1

+

(6) 1 - u 22

4. Two dissimilar elastic half-planes bonded together everywhere except over a finite crack.

=

*

&2

(7) In an analogous way to the derivation of Irwins' celebrated result in fracture mechanics we can derive an expression for the work done in closing an element of the interface, giving a strain energy release rate

2

*

E

2

cosh n

E

The analogy with "ordinary" fracture mechanics is clearly strong. For practical combinations of materials f3 < 0.24 [47], and

equivalent to [49] was considered in [51] and in a more recent paper Farris and Keer examine the interface crack in both plane and axi-symmetric geometries, with internal pressurization, although the method could be adapted to deal with contact loading. Dislocation methods discussed in an above section in relation t o homogeneous problems can in principle be extended to solve layered contacts [53], but the kernels become formidably complicated, and there will inevitably be some loss of generality in the technique. Lastly, the recent paper by Suo and Hutchinson [54] does seek to solve the problem of an interface crack accurately, but the loading chosen is very different from the contact geometry, and it is not clear that the method could be extended to the contact loading cases.

201

5. DISCUSSION

The separate elements which need to be drawn together to understand the problem posed at the outset are cited above. It is clear that the first step in understanding the problem is to extend the result for the internal stress state in the layer, following King and OfSullivan [39]. In doing so, we should focus on the practical points that normally the substrate and contacting body are already known, ie pl, vl, p3, u3, fig 1. Also, the maximum contact load and relative radius of curvature, P,R are fixed. We want to know the influence of h, p2, u2 on the severity of the internal stress state, bearing in mind that the contact halfwidth is itself dependent on p2, v2. It is, of course, generally true that a compliant coating produces a larger contact patch which diffuses the contact force: separately there is the effect of stress concentration. Turning to cracks, the most frequently occurring ones we might expect are those at the interface, where recent work has shown that only slight modification to fracture mechanics is needed. On the other hand there is virtually no work on cracks in layers subject to severe stress gradients, and this is an area where the dislocation technique has much to offer. What is needed here first is a thorough appraisal of the kernel involved, and this is currently being undertaken by the authors. When i t is known we will be in a position to solve the contactlayer-crack problem rigorously. References 1. Bryant, M.D., Miller, G.R. and Keer, L.M. ‘Line contact between a rigid indenter and a damaged elastic body’. Q.J. Appl. Maths. (1984)p 21, 3, 467-478.

2. Johnson, K.L. ‘Contact Mechanics‘, (1985), Pub. by CUP, pp 84-106. 3. Gladwell, G.M.L. ’Contact problems is the classical theory of Elasticity‘ (1980) Alphen aan den Rijn: Sijthoff and Noordhoff.

4. Deresiewicz, H. Bodies in contact with Applications to Granular Media. In R.D. Mindlin and Applied Mechanics, pub. by Pergamon Press, 1974 Ed. George Herrmann, pp 105-147.

9. Hills, D.A. and Sackfield, A. ‘Yield and shakedown states in the contact of generally curved bodies’. Jnl. Strain Anal., (1984), 19, 1, 9-14. 10. Uzel, A.R., Hills, D.A. and Sackfield, A.

‘Stress intensity factors for a cracked half-plane’. Jnl. Strain Anal., (1985) 20, 4, 209-216.

11 * Nowell, D. and Hills, D.A. ’Open cracks at or near free edges‘. Jnl. Strain Anal., (1987), 3, 3, 177-185. 12. Hills, D.A. and Nowell, D. ‘Stress intensity calibrations for closed cracks’. Jnl. Strain Anal., (1989), 2, 1, 37-43. 13. Schmueser, D., Comninou, M and Dundurs, J. ‘Separation and slip between a layer and a substrate caused by a tensile load‘. Int. Jnl. Eng. Sci (1980), g,1149-1155. 14. Schmueser, D., Comninou, M. and Dundurs, J. ‘Frictional slip between a layer and substrate‘. A.S.C.E. Jnl. Eng. Mech., 1981, 1103-1119. 15. Chang, F-K, Comninou, M., Sheppard, S. and Barber, J.R. ’The subsurface crack, under conditions of slip and stick caused by a surface normal force‘. Jnl. Appl. Mech. (1984), 51, 2, 311-316. 16. Chang F-K, Comninou, M and Barber, J.R. Slip between a layer and substrate caused by a normal force moving steadily over the surface. Int. Jnl. Mech. Sci., (1983), 11, 11, 803-809. 17. Sheppard, S., Barber, J.R. and Comninou, M. ’Subsurface cracks under conditions of slip, stick and separation caused by a moving compression load’. Jnl. Appl. Mech, 1987, 3, 393+. 18. Keer, L.M., Bryant, M.D., and Haritos, G.K. ‘Subsurface and surface cracking due to Hertzian Contact’. Jnl. Lub. Tech, (1982), 104, 347-351. 19 * Keer, L.M., Bryant, M.D. and Haritos, G.K. ‘Surface cracking and delamination‘. Presented at ‘Solid contact and Lubrication. ASME conf’. 1980, AMD-39, 79-95. 20 Keer, L.M. and Bryant, M.D. ‘A pitting model for rolling contact fatigue’. Jnl. Appl. Mech., (1983), 105, 198-205. 1

5. Hills, D.A. and Sackfield, A. ‘Sliding contact between dissimilar elastic cylinders‘. Jnl. Tribology, (1985), 107, 4, 463-466.

6. Sackfield, A. and Hills, D.A. ‘A note on the Hertz contact problem; a correlation of standard formulae‘. Jnl. Strain Anal. (1983), Is, 195-197,

7. Sackfield A. and Hills, D.A. ’Sliding contact between dissimilar elastic bodies‘. 110, 4, 592-596. Jnl. Tribology, (1988), 8.

Johnson, K.L. and Jefferis, M.A. ‘Plastic flow and residual stresses in rolling and sliding contact’. Proc. of the Symp. on Fatigue in Rolling contact. (I. Mech. E. London) 1963 pp 54-65.

21 Bower, A.F. ‘The influence of crack face friction and trapped fluid on surface initiated contact fatigue cracks’. Jnl. Tribology. In press. I

22. O’Regan, S.D., Hahn, G.T. and Rubin, C.A.

‘The driving force for mode I1 crack nrowth under rolling contact‘. Wear, 1985, 333-346

&,

e

23. Lei, S., Bhargava, V., Hahn, G.T. and Rubin, C.A. ‘Stress Intensity factors for small cracks in the rim of disks and rings subjected to rolling contact’. Jnl. of Tribology, 1986, 108, 540-544.

208

24. Yoshimura, H., Rubin, C.A. and Hahn, G.T. 'Cyclic crack growth under repeated rolling contact'. 11th Canadian Fracture Conference, June 1984, University of Ottawa, Ontario, Canada.

40. Jaffar, M.J. 'A.numerica1 solution for axisymmetric contact problems involving rigid indenters on elastic layers'. Jnl. Mech. Phys. Solids. (1988), 36, 4, 401-416.

25. Nowell, D. 'An Analysis of fretting fatigue', D.Phil thesis, Oxford University Dept of Engineering Science, Trinity 1988.

41. Jaffar, M.J. 'Asymptotic behaviour of thin elastic layers bonded and unbonded to a rigid foundation'. Int. Jnl. Mech. Sci, (1989), 31, 3, 229-235.

26. Sato, K., Fujii, H. and Kodama, S. 'Crack propagation behaviour in fretting fatigue', Wear, 1986, 107, 245-262.

42. England, A.H. 'A crack between dissimilar media'. Jnl. Appl. Mech., (1965), 32, 400-402.

27. Meijers, P. 'The contact problem of the rigid cylinder on an elastic layer'. App. Sci. Res. (1968), Is, 353-358.

43. Comninou, M. 'The interface crack'. Appl. Mech, (1977), 44, 631-636,

28. Koiter, W.T. 'Solution of some elasticity problems by asymptotic methods'. In Proc. Int. Symposium on Applications of the theory of functions in continuum mechanics, held in Tiblisi, 17-23 September, 1967, pp 15-31. 29. Conway, H.D. and Engel, P.A. 'Contact stresses in slabs due to round rough indenters'. Int. Jnl. Mech. Sci., (1969), 11, 9, 709-722. 30. Conway, H.D. Vogel, S.M., Farham, K.A. and So,S. 'Normal and shearing contact stresses in indented strips and slabs'. Int. Jnl. Eng. Sci., (1966), 4 , 343-359. 31. Jaffar, M.J. and Savage, M.D. 'On the numerical solution of line contact problems involving bonded and unbonded strips'. Jnl. Strain Anal., (1988), 2 , 2, 67-77. 32. Hannah, M. 'Contact stress and deformation in a thin elastic layer'. Quart. Jnl. Mech. and App. Maths. (1951), 4 , 1, 94-105. 33. Bentall, R.H. and Johnson, K.L. 'An elastic strip in plane rolling contact'. Int. Jnl. Mech. Sci., (1968), 2 , 637-663. 34. Pao, Y.C., Wu, T.S., and Chiu, Y.P.,' Bounds on the maximum contact stress of an indented elastic layer'. Jnl. Appl. Mech., (1971), 38, 608-614. 35. Nowell, D. and Hills, D.A. 'Contact problems incorporating elastic layers'. Int. Jnl. Solids Structures (1988), 2,1, 105-115. 36. Nowell, D. and Hills, D.A. 'Tractive rolling of tyred cylinders'. Int. Jnl. Mech. Sci., (1988), 2 , 12, 945-957. 37. Barovich, D., Kingsley S.C. and Ku, T.C. 'Stresses on a thin strip or slab with different elastic properties from that of the substrate due to elliptically distributed load'. Int. Jnl. Eng. Sci., (1964), 2, 253-268. 38. Gupta, P.K., Walowit, J.A. and Finkin, E.F. 'Stress distributions in plane strain layered elastic solids subjected to arbitary boundary loading'. Jnl. Lub. Tech, 4, 427-432. (1973) g, 39. King, R.B. and O'Sullivan, T.C. 'Sliding contact stresses in a two-dimensional layered elastic half-space'. Int. Jnl. Solid Structures. (1987), 2 , 5, 581-597.

Jnl.

44. Atkinson, C. 'On stress singularities and interfaces in linear elastic fracture mechanics'. Int. Jnl. of Fracture (1977) 13, 807-820. 45. Hutchinson, J.W. 'Mixed mode fracture mechanics of interfaces'.. Harvard University, report no. Mech -139, Feb 1989. 46. Dundurs, J. 'Discussion of edge-bonded dissimilar elastic wedges under normal and shear loading'. Jnl. Appl. Mech., 1969, 36, 650-652. 47. Suga, T., Elssner, G. and Schmauder, S. 'Composite parameters and mechanical compatibility of material joints'. Jnl. Composite Matls., 1988, 22, 917-934.

48. Suga, T., Schmauder, S. and Elssner, G. 'On the interface crack models'. Jnl. de Physique 1988, 49, 10, C5, 539-544. 49. Erdogan, F. and Gupta, G.D. 'Layered composites with an interface flaw'. Int. Jnl. Solid Structures, 1971, 7, 1089-1107. 50. Erdogan, F. and Gupta, G.D. 'The stress analysis of multi-layered composites with an interface flaw'. Int. Jnl. Solid Structures. 1971, 7, 39-61.

51. Arin, K. and Erdogan, F. 'Penny-shaped crack in an elastic layer bonded to dissimilar half-spaces'. Int. Jnl. Engineering Sci., 1971, 9 , 213-232. 52. Farris, T.N. and Keer, L.M. 'William's blister test analysed as an interface crack'. Int. Jnl. Fracture, 1985, 27, 91-103. 53. Tsamaphyros, G.J. and Theotokoglu, E.N. 'Integral equation solution of the infinite strip with cracks and holes'. Mech. Res. Commun. 1986, 2,3, 133-140. 54. Zhigang Suo and Hutchinson, J.W. 'Interface crack between two elastic layers'. Harvard University internal report no. MECH-118, 1988.

209

Paper Vlll (iii)

A statistical approach for cracking of deposits: determination of mechanical properties A. Mezin, R. Ramboarina and J. Lepage

Compared with materials as a bulk, stressed coatings exhibit certain pecularities which can be used in studying the mechanical properties of the system constituting of the deposit and the substrate. The reliability of a statistical analysis, complementary to the classical mechanical approach, is emphasized. With the intent to take into account the random nature of the fracture of brittle Films, we propose a simple statistical approach of the cracking of deposits, which offers a large applicability under the condition that the problem can be considered as one-dimensional. This method is applied to metal-metal and ceramic-metal systems. 1

INTRODUCTION

The use of thin films or coatings is now widespread in the modern technology. The coupling between the film and the substrate gives rise to a new material with unique properties. However, the derived properties, either optical, electronical, protective, etc., may be without use if the mechanical strength of the system cannot withstand the internal or external imposed stresses. The first type of stresses encountered in thin film technology are intrinsic. They originate from the non-uniform character of the deposition process. During the growth process, there are also numerous heterogeneities such as grain boundaries, dislocations, which are a potential source of mechanical defects. The other class of internal stresses is thermomechanical which arise from the difference of thermal expansion coefficient between the film and the substrate. When porous, the deposit can absorb a great amount of gases, especially water vapour. The resulting swelling of the network may lead to the appearance of strong compressive stress which lead to the buckling of the deposit, if the adherence between the film and the substrate is too low. Internal tensile stresses may cause cracking of brittle coatings, eventually associated to decohesion. An externaly imposed tensile stress can be an easy means of studying the mechanical properties of deposits. It is to be noted that in the literature, the deterioration of the coating is generally treated from a mechanical point of view whereas the physical basis of the problem, where numerous defects intervene, would suggest a statistical approach. In a first step, with the help of the results of previous authors, we try to link the mechanical and statistical approach, and to put in evidence the reliability of a complementary statistical analysis. In a second step, we propose a simple one-dimensional statistical approach illustrated by some experimental results.

2

RELATION BETWEEN MECHANICAL AND STATISTICAL APPROACHES

It is possible to describe schematically the deterioration of a brittle coating with the help of three eventually connected phenomena, namely cracking, decohesion (or delamination), and spalling. Dealing with the study of this deterioration, we may distinguish two points of view, which in a first attempt can be independently treated, before a synthesis enables the genesis of the deterioration to be described as a whole. The first point of view relates to the mechanical approach : the objective is to study the effect on the deterioration, resulting from the different mechanical characteristics connected with the deposit, interfacial zone and substrate. After a crack has formed in the coating, it is not possible any more to call in the only concepts of continuum mechanics. A pre-existing crack or defect with given size, geometry and localisation, is then considered. Many papers (1,2,3) deal with the stress intensity factors at coating cracks of defects. The analysis, using particularly the theory of fracture mechanics, intendsto theoreticallydetermine the evolution under mechanical solicitation of the considered defect, which may lead to cracking, scientific team ( 4 , 5 , 6 ) , decohesion... A interested in a more practical point of view, has been dedicated to this study for some years. When the interest is not shown only in behaviour of one defect but also in combined behaviour of the different defects, analysis has to permit the determination of the evolution of the mechanical state of the system (especially the stress in the deposit) resulting from the presence of the defects. Indeed, the formation of new cracks is conditioned by the new mechanical state. Such attempts are not yet very numerous ( 7 , 8 , 9 ) ; so in fact for this purpose, the stress in the deposit around a crack is generally (10,11) considered as linear (shear lag model), a hypothesis widely used in the framework of study of composite materials. The results

210

of this approach cangenerally find an expression in the notion of the size of the zone relieved of stress around the crack. The second point of view is answerable to statisticics. The random character of the distribution of size and position of the flaws which are the origin of the damage, naturally leads to the problem looked at from the statistical point of view. Especially in the case of brittle coatings, substrate and deposit gener.ally exhibit behaviours different enough such that the first crack does not fracture the specimen entirely. Thus it is possible to observe a great number of cracks on the same sample (for simplicity, the discussion can be restricted to the case of only cracking without decohesion nor spalling). Concerning the statistical analysis, certain mechanical, and of course geometrical characteristics will necessarily have to figure in a formal way. However, under certain conditions, the statistical analysis can be worked out without pecularities of the mechanical characteristics associated to every kind of deposits, being necessarily taken into account. For this, the effect of the cracks or defects on the mechanical state of the system have to be expressed in a form synthetical enough. For instance this can be done with the help of the notion of the size of the failure-protected zone introduced in our approach (paragraph 3 ) . The studies which exploit multiplicity of the cracks forming in the coating lead to establishing a more or less formal relationship between the effect of the crack (or more generally the geometrical discontinuity) on the mechanical state of the system, and the influence of the new mechanical state on the formation of the new cracks. Difficulty and interest of the synthesis of the mechanical and statistical approaches lie particularly in the quality of the interpretation in terms of mechanical characteristics attributed to this relationship. All the different studies of the mechanical properties of brittle coatings generally involve, in a very variable proportion, the two mechanical and statistical approaches. Nevertheless we can remark that the statistical approach is not often very amplified. GROSSKREUTZ and McNEIL (7) have long ago noted the regularity of the fracture spacings of certain coatings. Their mechanical approach induce naturally a symetric stress relaxation in the coating between neighbouring cracks. So, they model the cracking of the deposit by assuming that every new crackforms at the midpoint of the uncracked segment. At any deformation, all the neighbouring cracks are equidistant. They actually allow the intercrack discrete distances belonging only to a set of values Do/2”, where Do is an arbitrary quantity and n an integer positive, nil or negative. A complementary statistical approach would have permitted to take into account all the intercrack distances allowed by the modelling (between D0/2~+l and DO/^^. The mean intercrack distance is then a continuous function which is equal to Ln2 Dm(E), where Dm( E ) is the largest intercrack distance permissible with regards to the stress in the deposit resulting from the deformation E imposed to the substrate.

Besides, a very great regularity of the fracture spacings actually appears only for the high crack densities ; indeed, in the first steps of cracking, the cracks are too far from each other as to interact in a significative manner and then they randomly appear in the coating, which once again could be taken into account with the help of a statistical approach. Besides its quality, the study of GROSSKREUTZ and McNEIL essentially involves mechanics, and well illustrates the importance of a complementary statistical analysis in studying cracking of deposits. GILLE and WETZIG (10) are among the first authors who have considered the random nature of cracking in brittle coatings. Moreover, their modelling takes into account the twodimensional character that may exhibit cracking of deposits. This generalisation is achieved at the cost of a sophistication which makes the understanding of their analysis rather difficult. Quantification of cracking permits them to identify and measure different mechanical characteristics related to the coating (residual strains, density of probability of rupture, influence of deposit thickness, of substrate nature ) (12). The purely mechanical approaches can be of course quite reliable. Nevertheless, EVANS and al., whose the studies up to present exhibit essentially a mechanical nature, have as well pointed out the interest of a complementary statistical analysis (9).

...

3

A

STATISTICAL DEPOSITS

3.1

APPROACH

FOR

CRACKING OF

Position of the problem

The study that we propose is restricted to the one-dimensional case. It is workable when the observed cracks are relatively long and parallel, which is generally the case with brittle deposits subjected to unidirectional tensile stress. It is then possible to count the formed cracks and to measure their relative position. Considering a thick substrate coated with a relatively brittle coating (thickness h) subjected to uniaxial loading in the direction of the Ox axis (figure l), then N(E ) is the number of cracks that have appeareSd on the length L of the sample when the strain of the substrate is E

.

I

li 0

x

c

Figure 1 The formation of a crack in the deposit alters the stress field in the film and substrate. The resulting strain in the film E ~ ~ ( X )is , abbreviated as E for simplicity. Due to the thickness of the substrate, the substrate strain far from the deposit is assumed

21 1

not altered by the presence of the cracks and remains equal to the imposed strain E Let f(E)dEdx be the probability gf rupture of an infinitesimal element of the deposit, of length dx, unit width, and thickness h, when the imposed strain increases from E to E+dE. The cumulative probability of rupture at strain E is : r

.

F( E)dx =

I-

f( E ' )dE'dx

(1)

J O

3.2

Theoretical case without stress relaxation

Our entire approach is based on the analysis of the purely theoretical case where the formation of a crack does not alter the stress in the coating ( E = E 1. So the creation of a crack is not influence3 by the previously created ones, i.e. cracking is a purely random process. Under this hypothesis, we can show (13) that the density of probability g(E,x) for the distance between two neighbouring cracks to be equal to x, is given by : lim x/dx F(E){~-F(E) dx) g(E,x) = dx+O = F( E)exp{-F(E)x }

Within g( E , X ) number to the 2-a).

(2)

the limit of statistical fluctuations, can be considered as the ratio of the n(E ,x) of pavements which length is x, total number of pavements N( E ) (figure

As discussed above (paragraph 21, the statistical approach can be further worked out without precising the nature of the mechanical phenomena which accompany cracking. The effect of these phenomena on cracking results from the existence of a stress-free zone around the cracks. In our case of the one-dimensional problem, the existence of this stress-free zone will be formally taken into account with the help of a quantity homogeneous to a length. 3.3.1 Density of probability of rupture of the deposit Beyond a given distance noted R/2, characterizing the size of the stress-free zone, we can in practice consider that the strain and stress field is not altered by the presence of the crack. All that is needed is for the neighbouring crack to be far enough. So, outside the relaxed zones, the formation of cracks is not altered since the mechanical state in these regions remains unchanged. The zone I1 (figure 2-b) corresponds to the pavements far much greater than R , which have failed to give pavements larger than R. Then in this zone, the experimental distribution of the pavement lengths fits the distribution of the theoretical case without stress relaxation. The zone I1 of the experimental distribution then permits to determine the evolution with imposed strain of the density of probability of rupture of the coating F(E). 3.3.2 Cracking rate. Size of the failureprotected zone The study of the cracking rate (evolution with the imposed strain of the density of cracks) can give us a measure of the size of the zone relieved of stress around the cracks. From definition, we have :

I I

N ( E ~ )=

0

X

0

a) without stress relaxation

X

b) real case

Figure 2 According to (2), the mean intercrack distance is m( E ) = _ ~ / F ( E )while , its physical meaning is clearly x=L/N( E ) . So without stress relaxation, the cumulative density of probability of rupture is simply equal to the density of cracks :

1:

n(ss,x)dx

the For a strain increment d E s around E s '. increase of the density of cracks can be written as : dxn(Es,x)p(Es,x)dEs

dN(E ) = S

/

where p( E , , X ) ~ E ~ denotes the probability of rupture at strain E of a pavement of length x :

iu

P(E~,X)= ~ E1-exp[~

3.3

Theoretical approach of the real case

In a real system, the formation of a crack in the coating alters the stress field around the crack, which, according to the relative properties of the substrate, film and interfacial region, may lead to plastic flow of the substrate, to decohesion... (paragraph 2). In any case, the induced stress relaxation in the coating around the crack prevents the formation of a new crack within a given zone. For this reason, we experimentally observe few narrow pavements (figure 2-b), in opposition to the previous case (figure 2-a).

(5)

I0

L

a relation which is not obvious from the definition of F(E).

(4)

duf(e(u))des]

(6)

The existence of the relaxed zone (size R( E~,,x))is taken into account via E ( u ) , the strain along the considered pavement. Finally the cracking rate is given by :

d

N(E )

- 2= ES

L

- -o 1

L

X

d x n ( ~ ~ , x ) Jduf(e(u)) ~ (7)

The introduction of the notion of the failureprotected zone (size r(E ,x)) can provide a more tractable expression thag the above formulation (7).The probability of rupture of the pavement is modelled by considering the density of probability of rupture, f(E (u)) nil within a zone of size r( E ~ , x ) /at ~ every end of the pavement, and independent on the abscissa u in

212

t h e c e n t r a l p a r t of t h e equals f ( E s ) (figure 3 ) .

pavement

where

it

cracking rate

4

Under t h e s e c o n d i t i o n s , p ( c S , x ) c a n b e r e w r i t t e n as : p ( E ~x ,) d E =1-exp[ - {x-r( E

~x ,

f ( E ~ dES ) ]

(8)

Then t h e c r a c k i n g rate is g i v e n by :

Although t h e c r a c k i n g r a t e i s f o r m u l a t e d i n t h e framework o f a model, i t i s t o b e p o i n t e d o u t t h a t t h e e x p r e s s i o n ( 9 ) c a n b e c o n s i d e r e d as rigourous, for it is always p o s s i b l e to f i n d a l e n g t h r(E x ) s u c h t h a t t h e r e l a t i o n ( 8 ) i s e x a c t . But we%ave t o n o t e t h a t t h e q u a n t i t y r is a p r i o r i a f u n c t i o n o f t h e imposed s t r a i n E and s i z e x o f t h e pavement. r is d e f i n e d by i d e n t i f y i n g The‘quantity t h e p r o b a b i l i t i e s o f r u p t u r e of t h e pavements ( i . e . t h e cracking rates) r e l a t i v e t o t h e g e n e r a l f o r m u l a t i o n and t h e modelled form. I t comes :

A s already mentioned, t h e s i z e o f t h e stressf r e e zone R ( E ,x) i s i n c l u d e d i n E ( u ) . The q u a n t i t i e s R ‘and r are then l i n k e d with t h e help of t h e r e l a t i o n (lo), F ( E ) and t h e n f ( E ) , h a v i n g been p r e v i o u s l y d e t e r m i n e d .

3.3.3 S i m p l i f y i n g c o n d i t i o n s

Under c e r t a i n c o n d i t i o n s some h e l p f u l s i m p l i f i c a t i o n s c a n be a c h i e v e d . When t h e s i z e x o f t h e pavement is l a r g e r t h a n t h e stress-free z o n e , t h e q u a n t i t i e s r and R are o b v i o u s l y independent of x , s i n c e i n t h i s case i n t h e c e n t r a l p a r t o f t h e pavement : f ( E ( u ) ) = f ( E S ) . Under t h i s a s s u m p t i o n t h e r a t e o f c r a c k i n g may b e e x p r e s s e d i n a s i m p l e r form t h a t d o e s n o t need t h e knowledge o f t h e h i s t o g r a m s o f t h e intercrack distances : d

N ( E ~ )

--=

“s

WES)

f(ES)

L

L1-r(ES)

-3

(11)

L

T h i s r e l a t i o n is a c t u a l l y s u i t a b l e when t h e mean i n t e r c r a c k d i s t a n c e X i s large r e l a t i v e t o t h e s i z e R o f t h e s t r e s s - f r e e z o n e . So, it i s a p p r o p r i a t e i n t h e s t r a i n r a n g e where t h e c r a c k d e n s i t y remains r e l a t i v e l y l o w ( l / x = N ( E s ) / L < l / R ) . Under v e r y more r e s t r i c t i v e c o n d i t i o n s , i t is p o s s i b l e t o assume t h a t t h e q u a n t i t y r is i n a d d i t i o n i n d e p e n d e n t o f t h e imposed strain The q u a n t i t y r i s t h e n d i r e c t l y determine$ by indentifying the measured

.

and

the

theoretical

one, i.e.

DISCUSSION

In p r i n c i p l e t h e density of probability o f r u p t u r e F ( E ) and t h e s i z e r o f t h e f a i l u r e p r o t e c t e d zone can be determined e x p e r i m e n t a l l y with t h e h e l p o f the e s t a b l i s h e d theory. I t is t o be p o i n t e d o u t t h a t s t u d y i n g c r a c k d e n s i t y , t h e s i z e o f t h e f a i l u r e - p r o t e c t e d z o n e is t h e q u a n t i t y a c c e s s i b l e t o measurement. I n d e e d , t h e q u a n t i t y r (and not R ) t a k e s , through f ( E ) , t h e b r i t t l e n e s s of t h e d e p o s i t i n t o a c c o u n t . A t t h i s s t a g e , it i s a l r e a d y p o s s i b l e t o compare t h e b e h a v i o u r of some d e p o s i t s u s i n g t h e o n l y measured q u a n t i t y r . E x p e r i m e n t a l o b s e r v a t i o n s may o f c o u r s e g i v e some i m p o r t a n t i n f o r m a t i o n on t h e n a t u r e o f t h e m e c h a n i c a l phenomena r e l a t i v e t o t h e measured s i z e o f t h e failure-protected zone ( p l a s t i c f l o w of t h e substrate, decohesion at interface...). For f u r t h e r d e v e l o p m e n t , i t is n e c e s s a r y t o d i f f e r e n c i a t e t h e q u a n t i t y R from t h e measured q u a n t i t y r, u s i n g a complementary m e c h a n i c a l a p p r o a c h . With t h i s o b j e c t i v e , t h e d i s t r i b u t i o n of stress o r s t r a i n E ( u ) a l o n g a pavement, r e s u l t i n g from a n e x t e r n a l s t r a i n E ~ ,is import a n t ( 7 , 9 ) . A good p r o g r e s s c o u l d be made on this subject with numerical calculations. The p r o p o s e d s t a t i s t i c a l a p p r o a c h g e n e r a l l y p r o v i d e s a n e a s y means of s t u d y i n g t h e i n situ mechanical properties of deposits which e x h i b i t a more b r i t t l e c h a r a c t e r t h a n t h e i r s u b s t r a t e . When u s i n g t h e g e n e r a l formul a t i o n (91, some f u r t h e r r e f i n e m e n t s w i l l b e useful. Due t o t h e f a c t t h a t t h e s i z e o f t h e failure-protected zone is a f u n c t i o n o f t h e d e p o s i t t h i c k n e s s and m e c h a n i c a l c h a r a c t e r i s t i c s of t h e f i l m , i n t e r f a c i a l r e g i o n and s u b s t r a t e , t h e method c a n b e u s e d i n s t u d y i n g t h e i n f l u e n c e of c e r t a i n p a r a m e t e r s ( n a t u r e of the substrate, condition of deposition, deposit thickness...). For instance, it c o u l d b e a p p l i e d when t a k i n g i n t o a c c o u n t t h e effect of intrinsic stresses appearing during growth of deposits. It is hoped t h a t t h e a p p r o a c h s e r v e s a s a model t o t e s t t h e a d h e s i o n between l a y e r s . An a p p l i c a t i o n t o welded j o i n t s and more g e n e r a l l y t o c o m p o s i t e materials, seems also clearly possible. For t h i s p u r p o s e , w e have t o p o i n t o u t t h e c l o s e c o n n e c t i o n which e x i s t s between our problem a n d some s t u d i e s r e l a t e d t o c o m p o s i t e materials, i n p a r t i c u l a r t h e r u p t u r e of a monof i l a m e n t imbedded i n a s t r a i n e d p l a s t i c m a t r i x . The proposed statistical approach h a s b e e n a p p l i e d t o C . V . D . molybdenum c o a t i n g s on n i c k e l r i b b o n s ( 1 4 ) . The e v o l u t i o n o f the density of probability of rupture F ( E ) has been d e t e r m i n e d i n t h e s t r a i n r a n g e 0-6 % o f the deposit, a large domain r e l a t i v e t o f r a c t u r e . The measured d e n s i t y of p r o b a b i l i t y of rupture increases with thickness of t h e d e p o s i t . F o r i n s t a n c e , c o n s i d e r i n g 1 mm of d e p o s i t , t h e p r o b a b i l i t y of r u p t u r e i s a b o u t 0.3, 0.45 and 0.6 when t h i c k n e s s e q u a l s 14 pm, 18 p m and 20 pm r e s p e c t i v e l y . By u s i n g t h e s i m p l e s t form ( 1 2 ) s u i t a b l e i n our case, t h e i n f l u e n c e of t h e q u a l i t y of t h e i n t e r f a c e (presence of i n t e r f a c i a l microcavities) has been p u t t o e v i d e n c e .

:

213

Another system under study in the laboratory is alumina on aluminum, a system largely studied otherwise (15,16). The metal-oxide interface is the weak boundary layer in the adhesive bonding of aluminum alloys under humid environment. Experiments are conducted at present to correlate the size of the failure-protected zone of the deposit, to the interfacial adhesion of the oxide on the metal under controlled atmosphere. From a physical point of view, the cracking of alumina is very intringuing. It is accompanied by emission of slow electrons of unknown origin (exo-electrons). This emission is an extra term beside the surface energy term in the energy balance during cracking. Its relative importance has to be taken into account in the context of fracture mechanics of brittle solids. The cracking rate dN/dc is of fundamental importance for the electronic current emitted by the sample during straining. This current is proportional to dN/dt = (dN/dE)(dc/dt), a relation interpreted with the help of the Grosskreutz's formula (16). Further work is certainly needed on the subject

.

References MING-CHE LU and ERDOGAN, F. 'Stress intensity factor in two bonded elastic layers containing cracks perpendicular to and on the interface - I. Analysis', Engng. Fract. Mech. 1983, 18, no3, 491-506. VIJAYAKUMAR, S. and CORMACK, D.E. 'Stress behaviour in the vicinity of a crack approaching a bimaterial interface', Engng. Fract. Mech. 1983, 17, n04, 313-321. GECIT, M.R. 'Fracture of a surface layer bonded to a half space', Int. J. Engng. Sci. 1979, 17, 287-295. EVANS, A.G. and HUTCHINSON, J.W. 'On the mechanics of delamination and spalling in compressed films', Int. J. Solids Structures 1984, 20, n05, 455-466. HU, M.S., THOULESS, M.D. and EVANS, A.G. 'The decohesion of thin films from brittle substrates', Acta Metall. 1988, 36, n05, 1301-1307. DRORY, M.D., THOULESS, M.D. and EVANS, A.G. 'On the decohesion of residually stressed thin films', Acta Metall. 1988, 36, n08, 2019-2028. GROSSKREUTZ, J.C. and McNEIL, M.B. 'The fracture of surfaces coatings on a strained substrate', J. Appl. Phys., 1969, 40, nol, 355-359. EVANS, H.E. 'The role of oxide grain boundaries in the development of growth stresses during oxidation', Corros. Sci. 1983, 23, n05, 495-506. MEZIN, A. and LEPAGE, J. 'Relaxation de contrainte dans un dbpBt fissurb', Thin Solid Films, to be published. (10) HU, M.S. and EVANS, A.G. 'The cracking and decohesion of thin films on ductile substrates', Acta Metall. 1989, 37, n03, 917-925. (11) GILLE, G. 'Investigations on mechanical behaviour of brittle wear-resistant coatings - 11. Theory', Thin Solid Films 1984, 111, 201-218.

(12) GILLE, G. and WETZIG, K. 'Investigations on mechanical behaviour of brittle weerresistant coatings - I. Experimental results', Thin Solid Films 1983, 110, 37-54. (13) MEZIN, A., LEPAGE, J., PACIA, N. and PAULMIER, D. 'Etude statistique de la fissuration des revztements - I. Thborie' Thin Solid Films 1989, 172, 197-209. (14) MEZIN, A., PACIA, N., NIVOIT, M. and WEBER, B. 'Etude statistique de la fissuration des revGtements - 11. Application aux cas de revGtements de molybdGne', Thin Solid Films 1989, 172, 211-225. (15) DOERING, D.L., ODA, T., DICKINSON, J.T. and BRAUNLICH, P. 'Characterization of anodic oxide coatings on aluminum by tribostimulated exoemission', Appl. of Surf. Sci. 1979, 3, 196-210. (16) ROSENBLUM, B., BRAUNLICH, P. and HIMMEL, L. 'Spontaneous emission of charged particles and photos during tensile deformation of oxide-covered metals under ultra-vacuum conditions', J. Appl. Phys. 1977, 48, n012, 5262-5273.


SESSION IX YOUNG’S MODULUS Chairman:

Professor J. Frene

PAPER IX (i)

Young’s modulus of TiN and TIC coatings

PAPER IX (ii)

A method for in situ determination of Young’s modulus of deposits


217

Paper IX (i)

Young's modulus of TiN and TIC coatings L. Chollet and C. Biselli

This paper presents an experimental technique which allows the determination of the Young's modulus of thin films deposited on comparatively thick substrates. It is based on the measurement of the flexural resonance frequency of a vibrating composite sample. This technique was applied to Tic, TiN and Ti(CN) coatings deposited by CVD and PVD processes on hard metal and steel substrates. A Young's modulus of 439 GPa was obtained for CVD TiN, and of 640 GPa for TiN deposited by reactive sputtering on a stainless steel substrate. Young's modulus of Tic and Ti(CN) will be discussed. Finally, a tentative determination of the elastic modulus by means of a depth sensitive microindenter will be presented. 1 INTRODUCTION

Ceramic type coatings such as Tic and TiN are now widely used in different technological applications. They are hard and present generally a low friction coefficient, they are corrosion and wear resistant. However their mechanical characteristics need to be known better. Values given for the Young's elastic modulus, for example, cover a wide range, as already mentioned in an earlier paper (1). For TiN, this range extends between 81 and 616 GPa, and for Tic between 200 and 460 GPa. Most of these values were determined for bulk materials or even for single crystals, but very few data are available for coatings.

detection electrode, forming thus an oscillating capacitance which modulates the frequency of a detection oscillator. The frequency modulated signal thus produced is fed into a FM demodulator which gives at its output a voltage proportional t o the instantaneous deformation of the vibrating sample. This signal, filtered and fed into the excitation amplifier, develops an electrostatic force between the excitation-detection electrode and the sample, maintaining the vibration of the latter in its own resonance frequency.

The Young's modulus can be measured by different techniques, such as for example in static mode by tensile or flexural tests. It can also be measured in a dynamic mode, studying the propagation of ultra sounds or determining the flexural resonance frequency of a vibrating specimen. This last technique, used in the present work to determine the Young's modulus of thin coatings deposited on comparatively thick substrates, will be described. The results obtained will be discussed. 2 YOUNG'S MODULUS MEASUREMENT 2.1

Measurement of frequency

the flexural resonance

The experimental method, based on the measurement of the flexural resonance frequency of a vibrating sample, was described by Torok (2), and applied by Hausch and Torijk (3) and by Torok et a1 (1). The sample, in the shape of a beam of about 50x5~1 mm3, is suspended at its nodes (Fig.1). It faces an excitation-

Fig. 1 a) The vibrating sample suspended at its nodes b) The vibrating sample facing the excitation-detection electrode

218

The Young's modulus of the vibrating beam is calculated by the classical relation E =

l4

P

___________

f2

(GPa)

1)

1.061 t2 where 1 and t are the length and the thickness of the beam, f its resonance frequency and p its density. The data for the coated samples are evaluated after having adapted equations developed by Tanjii et a1 ( 4 ) in a work on the vibrational characteristics of a composite vibrator. Their analysis is based on the assumption that the flexural rigidities of each component can be superposed. If the thickness of the composite is small enough t o allow the deformation in the cross-sections Si to be ignored, then the relations

2.1.1 Apparatus The instrument used for the elastic modulus measurements was built at CSEM, following the development described by Torok (2). It is designed to allow the measurement of the modulus as a function of the temperature. The mechanical part consists essentially of the specimen holder, which can be fitted in a cylindrical vacuum chamber, and of the excitation-detection electrode. The specimen holder, shown in Fig. 2, is composed of a stainless steel head maintaining four tungsten wires 4 supporting the sample 2. It is suspended to ceramic bars assuring its thermal isolation. The excitation-detection electrode 1 and the thermocouple 3 are also visible in Fig. 2.

hold true where pi and Ii are the density and the secondary moment of the cross-section around the neutral axis of the composite for each component i. The coatings studied here were deposited on both faces of the substate, their thicknesses varying between 5 and 20 wn. The deposition processes were carefully controlled t o assure the same film thickness on both sides, the composite specimen being thus symmetrical. For such symmetrical composite specimens, the Young's modulus of the coating can be expressed by a relation containing E,, the modulus of the substrate, and the thicknesses and densities of the coating and the substrate respectively: ( A - 1) to3

E

=

..................... 2t1(4t12+ 6t,t1 + 3tOZ)

EO

3)

where A = (CSipi/S,p,)(f/f,)2, f, is the vibration frequency of the substrate alone, f is that of the composite and to and t, are the thicknesses of the substrate and composite respectively. The Young's modulus E, of the uncoated substrate has to be determined for each individual substrate before the coating process. To obtain a correct value for the coating's modulus, any modification of the substrate's modulus by the deposition process must be avoided. Introducing the expression for E, given by l ) , the relation 3) becomes: E1

Fig. 2 Detail of the specimen holder. 1: excitation-detection electrode. 2: vibrating sample. 3: thermocouple. 4 : tungsten wires supporting the sample.

- fo2] The block diagram of the electronic part, ____________________----------------4) is represented in Fig. 3. The instrument is 0.9464 14p0[(l + 2t,pl/topo)f2

=

2(t,/to)3[i

+ 3((tO+tl)/t1)2i

t,2

The relation 4), containing the ratios and (t,/t,)3 which are of the order of and respectively, shows the importance of a very precise determination of the thicknesses to and t,. t,/t,

computer controlled, allowing the programmation of the temperature cycle. The computer is also used for the automatic data acquisition and for the online calculation of the Young's modulus.

219

Frequency modulated signal

F i l t e r and

Vibrating sample

Excitation

I L----

*Switching control ( f r o m t h e decrementmeter) F i l t e r e d signal ( t o measuring part) 3 Block diagram of the electronic part of the instrument.

Fig.

2.2 Depth-sensing indentation F : Force

High resolution depth-sensing indentation instruments have been developed to measure the microhardness of thin films. It has been shown that such instruments provide a means for studying the elastic and plastic properties of thin films. Doerner and Nix (5) give a review of this application, describing in detail a method for obtaining Young's modulus from data obtained from these types of instruments.,

InNl

20

FMX -ax

[mNl [nnl

19.52

: :

I

186.0

' ! I 10

I

! I

i!

I'

i !

I

I

I

I

I00

I

1

200

P : Depth inn1

It is based on the separation of the plastic and elastic contributions to the indentation. The hardness is obtained from the plastic indentation, while the Young's modulus may be obtained from the elastic contribution. However, the knowledge of the exact shape of the pyramidal diamond indenter is critical to the determination of both plastic and elastic properties. Figure 4 illustrates a typical load-displacement curve obtained using the ultramicrohardness tester developed at CSEM and described by Schmutz et a1 (6). 3. SPECIMENS STUDIED

Fig.

4 Typical load-desplacement curve obtained using the ultramicrohardness tester illustrating the plastic and final depths of a TiN coating on steel.

Based on their characteristics and on their applications, the following substrates were chosen: cemented carbide K10 stainless steel 1.4301 high speed steel 1.3343 martensitic steel 1.4112

220

Before any CVD deposition, the substrates were heat treated for 20 h. at 900 OC under an argon atmosphere. This treatment compares to that imposed to the samples by the CVD deposition. The Young's modulus E, of the substrates is measured after this heat treatment, just before the deposition process, and it can thus be assumed to be equal to that of the coated sample. TiN, Tic and Ti(CN) coatings were deposited by CVD and PVD techniques on these substrates. The deposition conditions and the geometrical arrangement of the substrates in the reactors are carefully selected to obtain regular coatings with equal thicknesses on both sides. When possible, the coating's thickness is increased up to 20 pm, improving thus the precision in the coating's Young's modulus determination. The deposition techniques used may summarized as follows:

be

d.c. magnetron reactive sputtering r.f. magnetron reactive sputtering (ion plating) MT CVD (medium temperature CVD) conventional CVD MT CVD means a CVD deposition at a medium temperature, near 700 OC. It gives presently only good Ti(CN) coatings deposited on cemented carbides. All the coatings were analysed by the microprobe. The TiN and Tic coatings are all practically stoichiometric, i.e. have the composition Ti,N, and Ti,C,. The MT CVD Ti(CN) coatings contain 13.6 and 8.5 weight % C and N respectively, or may be given as Tic.6 9N. 3 7 4. RESULTS AND DISCUSSION The results are summarized in table 1. The very large scattering of the results can be explained as follows. 4:-1 CVD coatings on hard metal'K10

Hard metal or cemented carbide substrates were chosen due to their high stability at elevated temperatures. CVD deposition in particular can be processed without modifying the elastic properties of such substrates. Furthermore, hard metal substrates show a very regular variation of their Young's modulus as a function of the temperature and they seemed thus appropriate for the study of the temperature dependence of the modulus of coatings Surprisingly, all coatings deposited by CVD on hard metal substrates show apparently low Young's moduli, much lower than expected. The study of these coatings has revealed rather high tensile residual stresses (9-10). These stresses produce a network of cracks in the coatings. Such cracked coatings can not be considered as continuous films and the applied method to determine their Young's modulus is thus no more valid. The values given in table 1. for the CVD coatings on hard metal have to be considered as irrelevant.

.

4.2 Tic coatings on steel substrates

large discrepancy is observed between the Young's modulus measured for the PVD and CVD coatings. Unfortunately only one adequate Tic coating was obtained by reactive sputtering. However, the Young's modulus of 460 GPa determined for this coating is in full agreement with those measured by Torok et a1 (1). The study of the Tic coatings deposited by CVD on the stainless steel 1.4301 revealed a s6mewhat inhomogenous thickness, and, what is still more detrimental, slightly different thicknesses on both sides. The decisive influence of the coating's thickness on the accuracy of the Young's modulus has been discussed earlier. That is why the values given for samples 3 to 7 have to be considered with care. However, the different microstructures of PVD and CVD coatings may also affect their Young's modulus. CVD coatings exhibit no strongly preferred orientations and the grain size is of the order of hundreds of nm. They can be considered as isotropic. Moderate compressive residual stresses were measured in these coatings.

A

Table 1. Sample Sub.

Depos. Coating Thick. (Clm) (GPa)

E mod.

CVD CVD CVD CVD CVD CVD CVD sputt.

Tic Tic Tic Tic Tic Tic Tic Tic

5.9 7.5 21.6 =5 =5 =5 =5 4.7

302 304 512 591 566 586 551 460

9 K10 10 K10 11 steel*

CVD CVD CVD

TiN TiN TiN

12.6 22.6 1'0.3

264 164 416

12

1 K10 2 K10 3 steel* 4 1.4301 5 1.4301 6 1.4301 7 1.4301 8 1.4301

13 14 15 16 17 18 19

1.4301 1.4301 1.4301 1.4301 1.3343 1.3343 1.3343 1.3343

CVD CVD CVD CVD CVD CVD CVD CVD

TiN TiN TiN TiN TiN TiN TiN TiN

6.47 6.51 6.62 6.60 9.61 9.80 9.88 9.88

454 446 439 445 385 387 384 380

20 21 22 23 24 25

1.4112 1.4112 1.4112 1.4112 K10 1.4301

CVD CVD CVD CVD sputt. sputt.

TIN TiN TiN TiN TiN TiN

15.44 16.10 16.16 15.95 2.1 4.5

428 430 436 433 450 640

26

K10

MT CVD Ti(CN) 18.5

264

this steel was not unambigously identified. It is a high carbon, high chromium steel ( = 1 w% C, = 13 w% Cr).

22 1

In contrast, PVD coatings are very strongly textured and very finely crystallized, the grain size being of the order of tens of nm. They can no more be considered as isotropic. Furthermore, very high compressive residual stresses were observed in these coatings. For the time being, the influence of the microstructure on the Young's modulus has not yet been systematically studied.

4.4 MT CVD Ti(CN)

coatings

Although the tensile residual stresses are usually much smaller in MT CVD coatings than in those deposited by conventional CVD, cracks networks are also often observed in these MT CVD Ti(CN). Thus, the low Young's modulus measured for these coatings have to be considered as irrelevant, as it was for the CVD coatings on hard metal substrates.

4.3 TiN coatings

4.5 Depth-sensing microindentation

The results obtained for the Young's modulus of TiN coatings are coherent and reproducible. Each of the three series of coatings deposited by CVD on the different steel substrates give moduli with a moderate scattering around the mean value. However, the Young's modulus of the coatings on the high speed steel 1.3343 is much lower than those of the coatings on stainless steel 1.4301 and martensitic steel 1.4112 substrates. It could be possible that the nature of the substrate has an effect on the elastic properties of the coatings, but it has been observed that the heat treatment at 900 OC induces a rather large decrease of the Young's modulus of the substrate 1.3343. It is possible that the heat treatment was not adequate for this substrate and that a stable state was not obtained. Considering only the two series 1.4301 (samples 12-15) and 1.4112 (samples 20-23), a mean value of 439 GPa can be given for TiN coatings deposited by CVD on steel substrates. The Young's modulus obtained for the TiN coating # 24 deposited by PVD on a hard metal substrate is 450 GPa, a value very similar to those obtained for CVD coatings on steel substrates.

Microhardness and Young's modulus of series of Tic and TiN coatings have been measured by means of the ultramicrohardness tester developed at CSEM. The measurements were made on the as received surfaces of the coatings. Surprisingly high values were obtained for the hardness as well as for the Young's modulus. The instrument was tested by measuring the microhardness and the modulus of polished steel substrates, where correct values were obtained. Thus, it can be assumed that the depth-sensing indentation must be practicable, and that the CSEM's instrument is correctly calibrated. The difficulties encountered with the Tic and TiN coatings must be related to their rugosity. The microindentations were performed with a maximum load of 20 mN, producing a maximum penetration of the order of 200 nm. Surface irregularities of the order of the maximum penetration will obviously induce a large scattering in the measurements and give erroneous results. Unfortunately, to keep them usable for further Young's modulus measurements as a function of the temperature, the samples could not be polished to allow better indentation tests. One series of measurements were then made on the polished cross section of a PVD TiN coating deposited on a stainless steel substrate. A mean value of 590 GPa was obtained for its Young's modulus, a value rather close to that obtained in the flexural mode, confirming thus the applicability of the microidenter.

By contrast, a Young's modulus of 640 GPa was obtained for the TiN coating deposited by reactive sputtering on a stainless steel substrate. This last value is in a full agreement with those published by Torok et a1 ( 1 ) for similar coatings.

As already mentioned above about the Tic coatings, noticeable differences appear in the microstructure of CVD and PVD films. However, the microstructure of the TiN deposited by PVD on the hard metal substrate is closer to that of CVD coatings on steel than to that of the reactive sputtered film on steel. These observations confirm that both the nature of the substrate and the deposition process affect the microstructure of the coatings, which in turn affects the Young's modulus of the films. Doerner and Nix (l), in a study of tungsten coatings on silicon substrates by means of their depth-sensitive indentor, already observed a significant difference in Young's modulus of the crystalline and amorphous phases. Rickerby and Burnett ( 1 1 ) have also presented a study of the correlation of the process and system parameters with the structure and properties of PVD hard coatings.

5 . CONCLUSIONS

dynamical method based on the measurement of the flexural resonance frequency of a vibrating slender bar has proved to be a suitable means for measuring the Young's modulus of thin films deposited on comparatively thick substrates. To obtain correct results for the coatings, the Young's modulus of the substrate, which must be determined before the deposition, should not be affected by this process. This condition may represent a serious handicap depending on the type of substrate on which coatings are deposited by CVD. Nevertheless, significant results were obtained mainly for TiN coatings deposited by CVD or PVD on steel and hard metal substrates. These results indicate that the Young's modulus depends on the microstructure of the coatings, and that this dependance needs to be studied in more detail. A

222

The depth-sensitive indentation instrument may also provide a means for studying the elastic properties of thin films, but it has been shown that such a method can be applied only on carefully polished surfaces. 6. ACKNOWLEDGEMENTS

The authors would like to thank Mr Torok for his assistance in the construction of the instrument, Mr Lauffenburger for his help in its informatisation, Mr Gindraux and Mr Morel for the deposition of coatings by CVD, Miss C. Schmutz for the tests made by means of the ultramicrohardness tester and Mr Beguin for the microprobe analyses. They also gratefully acknowledge the financial support of the CERS which made this investigation possible. References Torok, E., Perry, A. J., Chollet, L. and Sproul W. D. 'Young's modulus of TiN, Tic, ZrN and HfN', Thin Solid Films 1897, 153, 37-43.

Torok, E. 'Gerate zur Bestimmung elastischer und anelastischer Eigenschaften verschiedener Materialien', Vortrag an der Technischen Akademie Esslingen, Kurs Nr. 2728 "Federwerkstoffe", 11 Dezember 1975.

Hausch, G. and Torok, E. 'Thermal expancivity and elastic constants of CrFe 1977, 40, alloys', Phys.Stat.Sol.(a), 55-62

e

Tanji, Y., Moriya, H. and Nakagawa, Y. 'Measurement of Young's modulus of thin plate by composite vibrator method', Sci.Repts Res.Inst., Tohoku Univ. Series A, 1978, 27(1), 1-8. Doerner, M. F. and Nix, W. D. 'A method for interpreting the data from depthsensing indentation instruments', J.Mater.Res. 1986, 1(4), 601-609. Schmutz, C., Jeanneret, J. P., Tranganida, S. and Hintermann, H. E. 'Characterization of thin PVD coatings by microidentation', IPAT, Geneva, May 1989, 341-346.

Chollet, L. stresses in coatings', Treatments,

and Perry, A.J. 'Residual CVD and PVD refractory in Surface Advances Vol. 4, Pergamon Press,

1986, 147-161.

Chollet, L. and Perry, A. J. 'The stress in ion-plated HfN and TiN coatings', Thin Solid Films, 1985, 123, 223-234. Perry, A. J. and Chollet, L. 'States of residual stress both in films and in their substrates', J. Vac.Sci.Techno1. A, 1986, 4(6), 2801-2808. (10) Perry, A. J. and Chollet, L. 'Physical vapor-deposited TiN on cemented carbide: tempering effects', Surface and Coatings Technology, 1988, 34, 123-131. (11) Rickerby, D. S. and Burnett, P. J. 'Correlation of process and system parameters with structure and properties of physically vapour-deposited hard coatings', Thin Solid Films, 1988, 157, 195-222.

223

Paper IX (ii)

A method for in situ determination of Young's modulus of deposits J.P. Chambard and M. Nivoit

The s u b s t r a t e Y o u n g ' s modulus i s i d e n t i f i e d by u s i n g t h e f i r s t n a t u r a l f l e x u r a l f r e q u e n c y of a r e c t a n g u l a r s a m p l e . The s i m u l a t i o n o f t h e "free-free" boundary c o n d i t i o n s makes t h e r e p r o d u c t i b i l i t y of t h e e x p e r i m e n t a l c o n d i t i o n s p o s s i b l e . T a k i n g t h e g e o m e t r i c a l i r r e g u l a r i t i e s , mainly t h e t h i c k n e s s v a r i a t i o n s , i n t o c o n s i d e r a t i o n when i n t e r p r e t i n g t h e f r e q u e n c y s p e c t r a , g i v e s Y o u n g ' s modulus o f t h e m a t e r i a l v e r y a c c u r a t e . Young's modulus o f t h e f i l m d e p o s i t e d on t h e s u b s t r a t e i s measured u s i n g t h e same method o f i d e n t i f i c a t i o n . A l l t h a t i s needed is t o i n t e r p r e t t h e s h i f t of t h e f i r s t n a t u r a l f l e x u r a l f r e q u e n c y o f t h e s a m p l e a f t e r c o a t i n g .

1

INTRODUCTION

h I

The g r e a t i n t e r e s t t a k e n i n d e p o s i t s , which promotes t h e i r p r e s e n t development, i s w e l l known ( 1 ) . They make i t p o s s i b l e t o combine t h e s u r f a c e q u a l i t i e s o f n o b l e materials w i t h t h e u s u a l q u a l i t i e s o f more common m a t e r i a l s s u c h as s t e e l s . We a r e i n t e r e s t e d i n t i t a n i u m n i t r i d e coatings, s i n c e t h i s material is a c e r a m i c w e l l known f o r e x h i b i t i n g a h i g h h a r d n e s s and good wear p r o p e r t i e s . These materials are o b t a i n e d as c o a t i n g s by c h e m i c a l o r p h y s i c a l v a p o u r d e p o s i t i o n and v e r y o f t e n e x h i b i t d i f f e r e n t b e h a v i o u r s from t h a t shown by t h e same material i n b u l k . So it is necessary t o study t h e behaviour of t h e f i l m " i n s i t u " , i . e . w i t h t h e s u b s t r a t e on which i t is u s u a l l y d e p o s i t e d . The aim o f t h i s s t u d y i s t o p r e s e n t a s i m p l e methodology o f t h e d e t e r m i n a t i o n o f Young's modulus o f c o a t i n g s . To t h i s p u r p o s e , Young's modulus o f t h e s u b s t r a t e must be accurately determined. So, the first part of the presentation deals with the substrate, and t h e s e c o n d one w i t h t h e c o a t i n g . 1.1

-

v Poisson r a t i o p mass p e r u n i t volume p S mass p e r u n i t l e n g t h 2

SUBSTRATE YOUNG'S MODULUS

The s u b s t r a t e Y o u n g ' s modulus is i d e n t i f i e d u s i n g t h e first n a t u r a l f l e x u r a l frequency o f a r e c t a n g u l a r s a m p l e ( d i m e n s i o n s 70 x 5 x 0 . 3

mm

3).

Within t h e framework of t h e EulerB e r n o u l l i beam t h e o r y a n d i n t h e case o f an homogeneous and i s o t r o p i c material , Young's is r e l a t e d t o t h e first n a t u r a l modulus E f l e x u r a l F r e q u e n c y f s by t h e e q u a t i o n :

Main n o t a t i o n s

f

S u b s c r i p t s s, d and s d r e f e r t o t h e s u b s t r a t e , c o a t i n g and t w o - l a y e r e d s a m p l e c o n s i s t i n g o f t h e s u b s t r a t e and t h e c o a t i n g , r e s p e c t i v e l y . Absence o f u p p e r i n d i c e s r e f e r s t o quantities given by the E u l e r - B e r n o u l l i beam model, t h e i n d e x t t o t h o s e from T i m o s h e n k o ' s t h e o r y and t h e i n d e x p from Love-Kirchhoff p l a t e theory. b width D flexural rigidity for plates :

e

d i s t a n c e between t h e m i d d l e p l a n e o f t h e s u b s t r a t e and n e u t r a l p l a n e o f t h e twol a y e r e d material E Young's modulus E I f l e x u r a l r i g i d i t y f o r beams f frequency

G

thickness bh: bhi moment of i n e r t i a : I = and I = 12 12 K s h e a r form f a c t o r 1 length S c r o s s - s e c t i o n area : S = bh and S = bh s s d d X slenderness r a t i o :

s h e a r modulus : G

=

ES

2(l+vs)

-

x: 2Tl*

1/35 psss

where t h e c o e f f i c i e n t X boundary c o n d i t i o n s . 2.1

d e p e n d s o n l y on t h e

Boundary c o n d i t i o n s

The s i m u l a t i o n o f t h e "free-free" boundary c o n d i t i o n s makes t h e r e p r o d u c t i b i l i t y o f t h e e x p e r i m e n t a l c o n d i t i o n s p o s s i b l e , t h e sample l y i n g on e l a s t i c s u p p o r t s . I n t h i s c a s e , t h e c o e f f i c i e n t X' e q u a l s 2 2 . 3 7 3 . F o r a g h e n sample, r e p r o d u c t i b i l i t y i s t e s t e d with respect t o t h e frequency f : it h a s been a d m i t t e d t h a t "free-free" b o h d a r y c o n d i t i o n s were s a t i s f i e d when t h e p o s i t i o n of the s u p p o r t s had no and stiffness more e f f e c t on t h e f r e q u e n c y f

.

2.2

Comparison between beam t h e o r y and p l a t e theory

Due t o t h e g e o m e t r i c a l c h a r a c t e r i s t i c s of t h e t e s t e d samples, i t appears t h a t t h e p l a t e t h e o r y s h o u l d be u s e d a p r i o r i f o r m o d e l l i n g

224

t h e i r dynamical behaviour. For l o n g enough s a m p l e s , t h i s t h e o r y c a n be r e p l a c e d by beam theory. I n t h e framewcrk o f t h e Love-Kirchhoff model, w e can w r i t e :

where t h e c o e f f i c i e n t Xp d e p e n d s n o t o n l y on t h e boundary c o n d i t i o n s bu? a l s o on P o i s s o n r a t i o and l e n g t h t o w i d t h r a t i o :

For " c o m p l e t e l $ 2 f r e e " b o u n d a r y c o n d i t i o n s , the coefficient X i s d e t e r m i n e d by t h e R a y l e i g h - R i t z metho8 ( 3 , Appendix 1 ) . The l a t e r a l d e f l e c t i o n o f t h e p l a t e is d e s c r i b e d l o n g i t u d i n a l l y by beam f u n c t i o n s and t r a n s v e r s a l l y by Legendre p o l y n o m i a l s : a l t h o u g h c h o o s i n g Legendre p o l y n o m i a l s d o e s n o t s a t i s f y t h e boundary conditions exactly, t h e y l e a d t o an e x c e l l e n t p r e c i s i o n compared w i t h c a l c u l a t i o n s made u s i n g t h e f i n i t e e l e m e n t s method. Writing : "P

t h e comparison between t h e beam and p l a t e t h e o ries is equivalent t o t h e s t u d y of t h e e v o l u t i o n o f Q a s a f u n c t i o n o f @, v b e i n g f i x e d . I t is th$n p o s s i b l e t o o b t a i n an &timat e of t h e e r r o r incurred i n t h e determination o f Young's modulus E , when u s i n g beam t h e o r y r a t h e r t h a n p l a t e the& : Ebeam - E p l a t e AEs s S Eplate

2.3

The E u l e r - B e r n o u l l i t h e o r y d o e s n o t t a k e i n t o account t h e effects of s h e a r i n g , nor t h o s e of rotary inertia. T h e s e e f f e c t s are modelled i n t h e framework o f T i m o s h e n k o ' s beam t h e o r y ( 2 ) . One c a n t h e n w r i t e :

where t h e c o e f f i c i e n t Xt d e p e n d s on t h e bound a r y c o n d i t i o n s a n d alsg on t h e P o i s s o n r a t i o vs, s a m p l e s l e n d e r n e s s r a t i o X and s h e a r i n g form f a c t o r K (K=5/6 f o r a r e c t a n g u l a r c r o s s section). Putting :

t h e c o m p a r i s o n between t h e two t h e o r i e s is e q u i v a l e n t t o s t u d y i n g t h e e v o l u t i o n of Q t as a function o f A s , v being f i x e d . A s previgusl y , i t is shown t h a t : AE

F i g u r e 2 shows t h e r e s u l t s f o r v d . 3 a n d very K=5/6 : w e o b s e r v e t h a t t h e e r r o r ' i s small f o r o u r e x p e r i m e n t a l c o n d i t i o n s where t h e s a m p l e s l e n d e r n e s s r a t i o i s a b o u t 800. This r e s u l t is only i n f l u e n c e d very s l i g h t l y by t h e v a l u e of P o i s s o n r a t i o .

AES

ES

_ES

S

I d e n t i f y i n g f p with f

S'

D i s c u s s i o n o f t h e model

2.

we find :

x;4 A- Es = ( 1-v; )

ES

x;

- 1 = Q g - 1

1o - ~

Figure 1 gives the corresponding r e s u l t s f o r v = 0 . 3 : w e c a n n o t e t h a t f o r @ > 8 ,t h e e r r o r 'does n o t exceed 2.10-3 , which is a v e r y l o w v a l u e . The v a l u e o f t h e P o i s s o n r a t i o only influences t h e s e r e s u l t s very slightly.

0

200

400

600

800

A

Figure 2 The E u l e r - B e r n o u l l i theory does n o t a l s o t a k e i n t o a c c o u n t t h e e f f e c t of t h e e x t e r n a l and internal dampings. From a measure of t h e l o g a r i t h m i c d e c r e m e n t o f t h e f r e e v i b r a t i o n s of t h e s a m p l e , t h e damping c o e f f i c i e n t a is e s t i m a t e d as 16s-' , i n t h e l e a s t f a v o r a b l e case. When t h i s damping is c o n s i d e r e d as e x t e r n a l (31, i t l e a d s t o an e r r o r i n Young's modulus of : AEs a2 - =

ES

4

6

8

10 1 2 14 Figure 1

16

@

a2+4v f 2

i . e . a b o u t 3.10-4 i n o u r e x p e r i m e n t a l c o n d i t i o n s , which i s n e g l i g i b l e . When t h e damping i s c o n s i d e r e d as i n t e r n a l ( 3 ) , w e f i n d : a2 AES

- = ES

8.rr2f;

225

, which is a g a i n n e g l i g i b l e .

i.e.

a b o u t 2.lO-'

2.4

Influence o f geometrical inhomogeneities

The above s t u d i e s show c l e a r l y t h a t i n o u r case, u s i n g t h e E u l e r - B e r n o u l l i beam t h e o r y t o deduce Young's modulus from t h e f i r s t n a t u r a l f r e q u e n c y f , is q u i t e j u s t i f i e d . However, many experimenta7 r e s u l t s a c q u i r e d on d i f f e r e n t s a m p l e s show t h a t t h e d i s p e r s i o n of t h e Es v a l u e s are r e l a t e d t o t h e g e o m e t r i c a l i r r e g u l a rities, especially with respect to the thickness. For i n s t a n c e , i f Young's modulus is d e t e r mined t o be a b o u t 212 GPa f o r a s a m p l e w i t h a relative t h i c k n e s s v a r i a t i o n n o t exceeding 2 . 1 0 - 3 , t h i s modulus c a n r e a c h a v a l u e o f 1 6 8 GPa when Ahs/hs e q u a l s 0.2. Thus i t is a b s o l u t e l y n e c e s s a r y t o c o n s i d e r sample thickness variations in the analysis of our results. These irregularities are taken into a c c o u n t n u m e r i c a l l y when u s i n g t h e m a t r i x method ( 4 , Appendix 2 ) i n t h e framework o f t h e Euler-Bernoulli or Timoshenko beam t h e o r i e s . Thus, i n t h e above example, w e f i n d E =208 GPa, i . e . w i t h a r e l a t i v e e r r o r e q u a l to 2.10-'. T h i s e r r o r becomes n e g l i g i b l e when t h e t h i c k n e s s v a r i a t i o n s a r e s u c h t h a t Ah / h < 5 . 1 0 - 2 , s s which is t r u e o f most of o u r s a m p l e s . 2.5

Error evaluation

T a k i n g i n t o a c c o u n t t h e geometrical i r r e g u l a r i t i e s of t h e samples provides u s with a s i m p l e and precise method of determining Young's modulus. Moreover t h i s method d o e s n o t r e q u i r e p r i o r knowledge o f P o i s s o n r a t i o . T h i s c o n c l u s i o n is o n l y m e a n i n g f u l f o r o u r s t a t e d h y p o t h e s e s ; i n p a r t i c u l a r , t h e s a m p l e s must b e r e l a t i v e l y long, i.e. @>8. * Experimental s e t u p : The sample r e s t s on e l a s t i c s u p p o r t s , t h e p o s i t i o n and s t i f f n e s s o f which c a n b e v a r i e d . The measurement equipment is c o n v e n t i o n a l . I t c o n s i s t s of a vibration e x c i t e r (Bruel & Kjaer BN8418), a p r o x i m i t y p r o b e ( B r u e l & Kjaer 4165 m i c r o p h o n e ) and a real-time f r e q u e n c y anal y s e r ( B r u e l & Kjaer 2 0 3 2 ) . Error evaluation : The main s o u r c e o f i n c e r t i t u d e is due t o t h e measurements. I n t h e case o f s t e e l XC75 s a m p l e s ( s i z e 70x5x0.3mm3), t h e n e x t t a b l e summarizes t h e e f f e c t of e a c h k i n d o f measure on t h e r e l a t i v e e r r o r i n t h e d e t e r m i n a t i o n of Y o u n g ' s modulus. On t h e w h o l e , t h i s i n c e r t i t u d e e q u a l s 8.10-3.

Es = 2 0 5 . 5 GPa ? 0.8 %

total dispersion being 1.5 % c o n s i s t e n t with t h e claimed r e s u l t . 3

Frequency

Length

is

FILM YOUNG'S MODULUS

Young's modulus o f t h e f i l m d e p o s i t e d on t h e s u b s t r a t e i s measured u s i n g t h e same method o f identification. A l l t h a t is needed is t o i n t e r p r e t t h e s h i f t o f t h e first n a t u r a l f l e x u r a l f r e q u e n c y o f t h e s a m p l e a f t e r it i s coated. The two-layered sample, c o n s i s t i n g o f homogeneous and i s o t r o p i c m a t e r i a l s , is modell e d using Euler-Bernoulli beam t h e o r y ( 2 ) . After h o m o g e n e i s a t i o n , t h e f i r s t n a t u r a l frequency f i s g i v e n by : sd

where ( E I ) s d a n d ( P S ) a~r e~ t h e f l e x u r a l r i g i dity and the e q u i v a l e n t mass e: l e n g t h r e s p e c t i v e l y . The c o e f f i c i e n t pX sunit till d equals 22.373 for "free-free" ioundary conditions. If E. denotes Young's modulus of t h e d e p o s i f , t h e e x p r e s s i o n f o r ( E I ) s d and ( P S ) a~r e~ : hs+hd z ( E I ) s d = EsLIs+e2Ss]+E [I +(- e ) sd] d d 2

where : hd Ed(hs+hd) e = 2 E h +Edhd s s

thus : f s d = fs

11

--

s o t h a t when t h e r a t i o f / f i s known, t h e i s t h e s o l u ? ido n s o f t h e s e c o n d r a t i o Ed/E degree e q u a k o n :

+

Mass

which

A(-)Ed

+ B(-) Ed

ES

ES

+

C = 0

-

fs'd ' s -fs'd ) ( - ) +h( 4d-2- ) ( - )

with : hd

A =( -)

hS

B = 4 ( -hd )

Thickness Width

+

(6

'd

hS

fs'

hs

fs'

hd hs

~

% -

51.10-~

1.5

c

5

1 - (1

+

'd

--)

hd

ps hs

ES

3.1 2.6

=

Results

For a s e t o f t h r e e s t e e l XC75 s a m p l e s ( s i z e 70x 5 x 0 . 3 mm E

=

) w e f i n d an a v e r a g e v a l u e : 198.1 GPa t O . 8 %

t h e d i s p e r s i o n o f r e s u l t s between s a m p l e s b e i n g a b o u t 0 . 7 %. For a s e t o f t h i r t e e n s t e e l 35CD4 s a m p l e s (size 1 0 0 ~ 5 ~ 0 m . 3~ n . ~ ) we , f i n d an av erag e v a l u e :

d:f

-

f:

Comparison between beam t h e o r y and p l a t e theory

I n t h e framework of t h e Love-Kirchhoff p l a t e t h e o r y and a f t e r homogeneisation, it i s possible to write :

226

where bD and ( P S ) are ~ ~ t h e equivalent flexural rig?$ity and e q u i v a l e n t mass p e r u n i t length. The coefficient Xp depends on t h e boundary conditions a n 8 d a l s o on a l l of t h e m e c h a n i c a l and geometrical c h a r a c t e r i s t i c s o f t h e t w o - l a y e r e d material , e s p e c i a l l y t h e l e n g t h t o w i d t h r a t i o I$ The f o l l o w i n g e x p r e s s i o n s are f o u n d :

.

5.1

bDsd =

Ed

ES rIs+e”’s,l+

-

1-

1-v2

g’

d

hS+hd [Id+(---eP) 2

2

sd 1

where : 0.2

0.3

V

d

Figure 3 Under t h e ” c o m p l e t e l y f r e e ” boundary coni s d e t e r m i n e d as d i t i o n s , t h e c o e f f i c i e n t Xp sd p r e v i o u s l y u s i n g t h e R a y l e i g h - R i t z method ( 3 , Appendix 1 ) . Thus :

t h e c o m p a r i s o n between t h e beam and p l a t e t h e o r i e s is e q u i v a l e n t t o s t u d y i n g t h e e v o l u t i o n of Q as a f u n c t i o n of a l l of t h e mechan i c a l anr?dgeometrical characteristics of the t w o - l a y e r e d material. I t is t h e n p o s s i b l e t o g i v e a n estimate o f t h e e r r o r made w i t h r e s p e c t t o Young’s modulus E o f t h e d e p o s i t , when u s i n g beam t h e o r y ratfler t h a n p l a t e t h e o r y : Ebeam - E p l a t e d d - = Eplate Ed d Knowing : E = 210 GPa hS = 0 . 3 mm = 7800 kg.mW3 PS v = 0.3

b = 5 mm 1 = 70 mm

E = 300 GPa d h = 0 . 0 1 mm p d = 5000 k g . n ~ - ~ d

=

fs

-’

x:

-(Wsd

a l l o w s t h e r a t i o f p / f p t o b e c a l c u l a t e d . Idenin the t i f y i n g t h i s r a t i o s i i t E t h e r a t i o f /f sd s r e l aIt i o n : ,

beam possible t o calculate E and then AEd/Ed., Figure 3 shows the results for v v a r y i n g i n t h e r a n g e 0 . 2 t o 0 . 4 : we o b s e r v e t i a t t h e e r r o r d o e s n o t e x c e e d 10- ’, a q u i t e reasonable value.

it

D i s c u s s i o n of t h e model

The i n f l u e n c e o f s h e a r i n g and o f rotary i n e r t i a can be t a k e n i n t o a c c o u n t w i t h i n t h e framework o f T i m o s h e n k o ‘ s beam t h e o r y ( 2 ) . I t i s shown ( 3 ) t h a t t h i s e f f e c t i s q u i t e n e g l i g i b l e with r e s p e c t t o t h e determination of Young’s modulus of t h e d e p o s i - t . Knowing t h a t f o r o u r s a m p l e s , steel c o a t e d w i t h t i t a n i u m n i t r i d e , t h e t o t a l damping c o e f f i c i e n t is b u t very s l i g h t l y i n f l u e n c e d by t h e p r e s e n c e of t h e d e p o s i t , i t is assumed as p r e v i o u s l y t h a t damping d o e s n o t i n f l u e n c e Young‘s modulus i n a s i g n i f i c a t i v e manner. I t is h i g h l y p r o b a b l e t h a t , d u e t o t h e method of elaboration, our deposits are anisotropic. N e v e r t h e l e s s , t h e y a r e assumed t o be t r a n s v e r s a l l y i s o t r o p i c , t h e i s o t r o p y plane being t h e deposition plane : i n such a case, and in t h e framework of beam or p l a t e t h e o r y , t h e r e s u l t s are i d e n t i c a l . Inclusion of geometrical i r r e g u l a r i t i e s

3.3

The above s t u d i e s c l e a r l y show t h a t u s i n g beam theory to deduce Euler-Bernoulli Young’s modulus i s a d e q u a t e . The p r o p o s e d methodology d o e s n o t a l l o w the geometrical irregularities of the s a m p l e s t o b e t a k e n i n t o a c c o u n t . So, mean v a l u e s are used. Error e v a l u a t i o n

3.4

the relation : f:d

3.2

Though

lack

ratio

vd

o f knowledge c o n c e r n i n g P o i s s o n l e a d s t o an i n c e r t i t u d e w i t h r e s p e c t t o Young’s modulus E d a p p r o x i m a t e l y e q u a l t o lo-’ , t h e main s o u r c e o f e r r o r r e m a i n s e x p e r i m e n t a l m e a s u r e m e n t s . For s t e e l XC75 c o a t e d w i t h t i t a n i u m n i t r i d e s a m p l e s ( s i z e 70x5x(0.3+0.014)mm3), t h e n e x t t a b l e summarizes t h e i n f l u e n c e of e a c h of t h e measur e m e n t s on t h e r e l a t i v e e r r o r i n t h e d e t e r m i n a t i o n o f Young’s modulus. On t h e w h o l e , t h i s i n c e r t i t u d e i s e q u a l t o 4 . 5 lo-’.

is

Ed c

Mass

Frequency

6.10-3

11.10-3

Width Length

2.10-’

ES

8.10-3

221

3.5

Results

F o r a s e t o f t h r e e s t e e l XC75 s a m p l e s c o v e r e d with titanium n i t r i d e T i 2 N ( s i z e 70x5x(0.3+ 0.014)mm3), we f i n d an a v e r a g e v a l u e : E = 284.9 GPa 4.5 % d . t o t a l d i s p e r s i o n b e i n g of t h e o r d e r o f 6 %, a v a l u e which is c o n s i s t e n t w i t h t h e c l a i m e d result.

*

4

CONCLUSION

Young's modulus of an homogeneous sample w i t h a l a r g e s l e n d e r n e s s r a t i o ( g r e a t e r t h a n 800) and l e n g t h t o width r a t i o (greater than 8 ) , c a n be i d e n t i f i e d from i t s f i r s t n a t u r a l f l e x u r a l f r e q u e n c y u s i n g E u l e r - B e r n o u l l i beam t h e o r y . T h i s methodology d o e s n o t r e q u i r e knowledge o f P o i s s o n r a t i o o f t h e m a t e r i a l . Young's modulus o f a t h i n f i l m ( t h i c k n e s s a p p r o x i m a t e l y e q u a l t o 0 . 0 1 4 m m ) d e p o s i t e d on a s u b s t r a t e o f t h e above k i n d is i d e n t i f i e d u s i n g t h e same method. Al.1 t h a t is needed i s t o i n t e r p r e t w i t h i n t h e framework o f E u l e r B e r n o u l l i beam t h e o r y t h e s h i f t of t h e f i r s t n a t u r a l f l e x u r a l f r e q u e n c y o f t h e sample a f t e r c o a t i n g . Here a l s o , t h e methodology d o e s t n o t require knowledge of Poisson ratio of t h e d i f f e r e n t materials, f o r t h e t r a n s v e r s a l s h e a r i n g e f f e c t is n e g l i g i b l e . T h i s c o n c l u s i o n i s c o n f i r m e d by an a n a l y s i s o f t h e n a t u r a l higher order frequencies, which leads t o t h e same v a l u e o f Y o u n g ' s modulus o f t h e film.

5

'

.

and o€ f i t t i n g ,the coefficients A in s u c h a way t h a t 6' is minimum. T h i s c o n v i t i o n is e x p r e s s e d a s : sp

6s: ---_ - 0 6A

i.e.

Study o f t h e s u b s t r a t e

F i g u r e 4 g i v e s a s c h e m a t i c o f t h e p l a t e , where t h e Oxy p l a n e is t h e m i d d l e p l a n e .

3; 2d3

where w i s t h e f r e q u e n c y of v i b r a t i o n o f t h e p l a t e . ?t is w e l l known t h a t t h e n a t u r a l f r e q u e n c i e s a r e d e t e r m i n e d by m i n i m i z i n g t h e e x p r e s s i o n o f 6p4 The R a y l e i g h - R i t z method c o n s i s t s of a p p r o 5 i m a t i n g t h e d e f l e c t i o n o f t h e p l a t e w i t h t h e h e l p of a d o u b l e s e ri e s :

APPENDIX 1

5.1

J

with :

p = lto M q = It0 N

for

Pq

:

[

c

Mc

Amn [(fiX:dG

N

m=1,2 n = 1 , 2

.I 1

t" i*y

'[I

+@

.fYqYnd;] -1

'[I

1

XpXmdx

-1

1

Y$Yndy] +Us@

-1

[l

-1

l-Vs

)#

XbX:dx

-1

-1

-1

.I 1

1

.(Y:Yndy]+2(

P Xl'dx m

X;XmdG.(YqY:d;+(X

-1

Y:Y:dy]

-1

1

1 -6:4k<md

;.l:.....1j-:qYnd7]]

= 0

for p

=

lto M

9 = It0 N

1

(x)

Figure 4

f

Let :

1 = 2a b = 2c The following introduced : X = x/a

y_

I1

11

-

XiXjdx

=

-1 reduced

(7)

If t h e f u n c t i o n s X and Y a r e two s e t s o f o r t h o g o n a l f u n c trni o n s , a n d nmoreover a s s u m i n g that :

1

coordinates

are

11

-

=

-1

= Y/C

u = u/a where u ( x , y ) d e n o t e s t h e maximum d i s p l a c e m e n t o f a p o i n t o f t h e middle p l a n e o f t h e p l a t e . I n t h e framework o f t h e Love-Kirchhoff p l a t e t h e o r y , t h e R a y l e i g h r a t i o is g i v e n by the relation :

I1

YiYjdy

we o b t a i n :

*

p f m and

-

Apq ' :6

228

X.

(x) =

x+-

[cos(Ki-)+ch(Ki-)] 1

x+ 1 +R. [ s i n ( Ki-)+sh(Ki-) 1 2

x+1 ,.

x+l

]

2

for i > 2 a n d w i t h : COSK. - ChK.

-

R. =

sinKi - shKi where K. i s s o l u t i o n of t h e e q u a t i o n : 1

*

cosK. chK. = 1

p = m and q = n

1

1

Besides, using only t h e first f o u r polynomials:

I

2

L

Y y

i . e . i n m a t r i x form : BX = GP4X where B i s a s q u a r e m a t r i x o f d i m e n s i o n MN and X t h e column m a t r i x c o n s i s t i n g of t h e unknown quantities A Knowing t h a t i = ( p - l ) M + q and j = ( m - I ) N + n , tR8 c o e f f i c i e n t B . . i s e x p r e s s e d as 1J * i f j

.

3

4

2

3 ( 3 -y 2 - 1 ) ( y ) = v4

1 4 (5Y3-37) (7) = v-

4 Although choosing Legendre polynomials d o e s n o t s a t i s f y t h e " c o m p l e t e l y f r e e " boundary c o n d i t i o n s , t h e y l e a d t o an e x c e l l e n t p r e c i s i o n compared w i t h c a l c u l a t i o n s u s i n g t h e f i n i t e e l e m e n t s method, e s p e c i a l l y f o r t h e s o - c a l l e d flexural frequencies, which correspond t o a d e f l e c t i o n w i t h o u t n o d a l l i n e on t h e l o n g i t u d i n a l a x i s . The f o l l o w i n g t a b l e a l l o w s t o compare t h e c o e f f i c i e n t s Xp2 r e s u l t i n g from t h e R a y l e i g h - R i t z method (17'beam f u n c t i o n s and 4 Legendre polynomials) and resulting from t h e f i n i t e e l e m e n t s method ( g r i d lOOxlO), f o r (I=8 a n d v = 0 . 3 :

Frequency

Rayleigh-Ritz

21.364

21.365 * i = j

1

1

1

1

1

1.

7

+2(1-vs)(12

[f

X;X,:d;.f

-1

YbYAdy] -1

So t h e n a t u r a 1 , f r e q u e n c i e s are deduced from t h e of t h e m a t r i x B . eigenvalues 6' With t h z aim t o make t h e b e s t approxiniat i o n o f t h e d e f l e c t i o n of t h e p l a t e , t h e X . ( x ) have been c h o s e n as t h e beam f u n c t i o n s sakisf y i n g t h e "free-free" boundary c o n d i t i o n s and the as Legendre p o l y n o m i a l s . Thus :

Yi(y)

X,(X) = 1

VF 2

vz ; x 2 (X) = 2

We exceed 5.2

observe

F i n i t e Elements

59.046

59,053

116.147

116.182

192.754

192,825

289.014

289.224

405.926

405.557

542.054

541.962

that

discrepancy

does n o t

Study o f t h e d e p o s i t

The p l a t e h a s t h e same c h a r a c t e r i s t i c s a s t h e p r e v i o u s l y d e f i n e d one [ f i g u r e 41 the 0xy plane is t h e n e u t r a l p l a n e , t h e -thickness of the substrate and deposit a r e n o t e d h and h r e s p e c t i v e l y . d

229

I n t h e framework o f t h e Love-Kirchhoff p l a t e t h e o r y , t h e c a l c u l a t i o n of t h e n a t u r a l f r e q u e n c i e s is unchanged, a l l t h a t i s needed is t o replace i n t h e e x p r e s s i o n o f t h e Rayleighr a t i o :6 by d 6: and Vs by Vsd such t h a t :

6zd = w z d a 2

\i

respectively. The the ith element vectors V. a n d Vi 1-1

matrix Ai of the two state

transfer

relates :

V. = A . V. 1

1-1

1

Due t o t h e f a c t t h a t t h e beam e l e m e n t is assumed t o b e of c o n s t a n t c r o s s - s e c t i o n , t h e e x p r e s s i o n A . is e a s i l y d e r i v e d :

(PS)sd

bDsd

el

-Xi e4

-Xi EsIsi e3 h iEsIsi e2

e2

el

EslsieO

'iEs1sie3

e3/EsIsi

e2/EsJsi

el

'ie4

-e2

el

A,= 1

I -e 4 / ES IS l. -e 3 /ES S

l.

knowing t h a t :

e

=

O

e

e 6 6.1

2

3

APPENDIX 2 Euler-Bernoulli

Bi

-

(shB.1.

sinB.1. )

1 1

2

1 1

+

sinR.1.)

_ (chB.1. 1 1

cosBili)

(shBili

= -

1 1

2 Pi

2 P;

theory

The beam ( f i g u r e 5 ) is d i v i d e d i n t o e l e m e n t s small enough t h a t t h e y can b e c o n s i d e r e d t o b e of constant cross-section.

1

E I . s s1

l't

The t r a n s f e r m a t r i x A o f t h e beam r e l a t e s Vo and V : V with :

A =

= A V

0

1

n

A.

i=n

___+

X

T h u s , f o r t h e "free-free" we obtain the matrix :

0

0

J

1

A12

-

en U

Figure 5

A21

A22

A31

A32

A41

A42

boundary c o n d i t i o n s ,

A13

A14

A23

A24

A

0 0

33

A34

00

A43

A44

0

which l e a d s t o a non t r i v i a l s o l u t i o n i f : The e l e m e n t o f s u b s c r i p t i , c r o s s - s e c t i o n S , and i n e r t i a I , is c o n n e c t e d w i t h t h e stag; Sl' vector V. : M.

v.

=

6.2

0. U

T h i s c o n d i t i o n e n a b l e s t h e f r e q u e n c y o r Young's modulus, a c c o r d i n g t o t h e unknown q u a n t i t y c h o s e n , t o be n u m e r i c a l l y d e t e r m i n e d . Timoshenko's t h e o r y

The method i s q u i t e i d e n t i c a l , o n l y t h e e x p r e s the elemental transfer m a t r i x is s i o n of changed :

1

t h e components of which a r e t h e l a t e r a l d e f l e c t i o n u., angle of slope o f t h e d e f l e c t i o n s h e a r f o r c e T. c u r v e l o i , b e n d i n g moment M . I'

230

e l +%e3

- Xie4

e2

el- q . e 1 3

e3/Es1si

(e2-ye4)/EsIsi

-e / E I . 4 s s1

-e / E I . 3 s s1

A. =

+ ( e2+Sie4 )/KGsSsi

- X .1E

I..e

XiEsIsi(e2+Sie4)

S S l 3

E I .(e - e ) s s 1 0 9 2

X.E I . e 1 S S l 3

el-Z e 3

?e4

-e

e

2

+ W / m ) 3.069 1.391 1.974 30.69 2.557 45.20 1.974 45.20 45.20 1.391 16.49 1.391 1.391 35.65 45.s4 1.391

17w

(Pa s) 0.2461 0.2461 0.2461 0.2461 0.2461 1.469' 1.363' 1.307*

*non-Newtonian lubricant (SOOW gear oil) Experiment No. 1 was chosen from a region where the friction coefficient seemed to be increasing as the Sommerfeld parameter decreased. According to Unsworth et a1 (1988), this behaviour indicated fluid film breakdown. Experiments No.'s 2, 3 and 4 were chosen to span the scatter in the data in a region where friction coefficient increased with increasing Sommerfeld parameter. Again according to Unsworth et al, this behaviour indicated fluid film breakdown. Experiment No. 5 had the highest Sommerfeld parameter of the experiments with the Newtonian lubricant. Experiments No.'s 6, 7 and 8 were selected to represent the experiments with the non-Newtonian lubricant. During the friction experiments, the inertia of the upper bearing assembly apparently introduced fluctuations in the friction force signal so that the maximum friction did not always occur close to the point of maximum entrainment velocity as expected from theory. It was felt that this distortion in the friction force signal shifted the point of maximum friction coefficient in time rather than increasing its amplitude significantly. Thus, a comparison was made between the measured maximum friction coefficient and the value predicted by the PI Model (Fig.9). ooooo EXPERlMENTr

w THEORY ULU

THEORY (non-Newtonian lubricant)

Pmaz

0.01

-I

0.001

'

14-1

I

I

I

T

I .

I I

16-5

16-6

a-4

S

Fig. 9

Comparison of the experimental and theoretical values for the maximum coefficient of friction in the cycle.

The measured value for Experiment No. 1 was much higher than the predicted value and this finding was consistent with the hypothesis that fluid film breakdown had occurred. The theoretical line ran into the midst of the data for Experiment No.'s 2, 3 and 4 which were chosen to represent the scatter in the full set of collected data. The friction coefficient for Experiment No. 5 was less than that predicted for reasons as yet undetermined but the data of Experiment No.'s 6, 7 and 8 fell remarkably close to the theoretical predictions despite the fact that further approximation had been introduced into the PI Model to account for the non-Newtonian lubricant. The lambda ratio (A,) at the point of maximum friction coefficient was calculated for each of the eight experiments. The lambda ratio required only the RMS surface roughness (0)of the silicone rubber layer because the glass plate had a much lower RMS surface roughness. Assuming film breakdown occurred at about A, = 3 (Johnson et al, 1972), the calculations indicated that only Experiment No. 1experienced film breakdown (Fig.10). This finding was consistent with the criteria of Unsworth et a1 (1988) which was described previously.

Fig. 10 The lambda ratio when

p = pmaI for each

experiment.

A detailed comparison of theoretical and measured (7stimates of cyclic variation of the friction coefficient \\'iLs performed for each of the eight experiments (Fig.11). In general, the agreement between theory and experinieiit was very good with the exception of the expected tlisagreement for Experiment No. 1. The measured variation of friction coefficient with time for Experiment No. 4 indicated a flattened region at high entrainment velocities. For the Newtonian lubricants, this phenomena only occurred for Experiment No. 4 and thus a malfunction o l this measurement system was suspected. The limitations of the modelling of the non-Newtonian lubricant became evident in the theoretical curve for Experiment No. S i n that the values of friction coefficient remained essentially constant, at the high values of entrainment velocity, a i i t l fell below the measured values. The use of the avcr;~ge viscosity might have caused an over-estimate of the film thickness in this region when used in the PI Modcl. As a result, the friction coeflicient calculated by equation ( 14) would be under-estimated.

248

The PI Model assumed film lubrication throughout the cycle and at the point of maximum friction coefficient some theoretical evidence was presented to support this assumption (Fig. 10). However, during the portions of the cycle when entrainment velocity was low, film breakdown could occur unless squeeze film action niaintained thick enough films. To investigate this possibility, the variation of lambda ratio over the cycle was calculated for Experiment No. 2 (Fig.12). The PI Model did predict that squeeze film action would maintain thick enough films because the lambda ratio remained greater than 3 throughout the cycle. Experiment No. 2 had the lowest predicted lambda ratio except for Experiment No. 1.

\

-0.01 o?

8.0

0.01

I-L 0.00

-0.01

T

-I

A 6.0

MPERlMENT No. 4

4.0

2.0

1-

x=3

1

MPERlMEHl No. 5 0.0

a2

-0.01

0.4

WF.

0.6

0.8

1.o

Fig. 12 The cyclic steady state variation of the lambda ratio for Experiment No. 2.

6 CONCLUSIONS 0

The transient friction coefficient was measured successfully for a contact consisting of a cylindrical surface with an attached elastomeric layer against a recriprocating glass plate under constant load in the presence of a liquid lubricant.

0

In general, good agreement was obtained between the experimental values for cyclic steady state friction coefficients and the theoretical values predicted by the PI Model. In one experiment, poor agreement was found and attributed to the brcakdown of fluid film lubrication.

0

In some of the experiments a non-Newtonian lubricant was employed. The P I Model was adapted to include a representation of the non-Newtonian influences and good agreement between theory and experiment was maintained.

0

For the present study, it was shown that the cyclic steady state behaviour could be represented by the maximum friction coefficient in the cycle and a Sommerfeld parameter based on average conditions over the cycle. An increasing maximum friction coefficient with increasing Sommerfeld parameter indicated the existence of fluid filiii lubrication.

No.

-0.03

f........., 0.2

0.0

I ~ - I I I I I I ~ I . I

0.4

0.6

0.8

1 .o

t/tP

Fig. 11. The cyclic steady state variation of the coefficient of friction for each experiment. (To clarify the comparison between theory and experiment, the coefficients of friction were permitted to be negative quantities).

249

0

Given the current understanding of the lajrcred contact in the present apparatus, the next s t q ) in the overall investigation would be to conduct w a r tests of candidate implant materials under specific regimes of lubrication. Sub-surface fatigue would be examined by testing in the regime offull fluid film lubrication while adhesive and abrasive wear would be examined by testing in the regime of partial film lubrication.

7 ACKNOWLEDGEA!IENTS The authors wish to thank the technical staff of both the Universities of Waterloo and Leeds for their help with the various measurements needed to complete this experimental investigation. Furthermore, the authors are indebted to Dr. C.J. Hooke of the Department of Mechanical Engineering, University of Birminghani for sending us the discrete data upon which his 1986 paper was based and thus allowing us to curve fit the data in ways which he would probably not approve. Financial support was provided by the Natural Science and Engineering Research Council of Canada and the Ontario Centre for Materials Research.

ISAAC, G.H., ATICINSON, J.R., DOWSON, D., KENNEDY, P.D. and SMITH, M.R. (1987) ‘The Causes of Femoral Head Roughening in Explanted Charnley Hip Prosthesis’, Engng in Med., 16, 3, 167-173. JOHNSON, K.L., GREENWOOD, J.A. and POON, S.Y. (1972) ‘A Simple Theory of Asperity Contact in Elastohydrodynamic Lubrication’, Wear, 19, 91-108. LABERGE, M., BOBYN, J.D., DROUIN, G. and RIVARD, C.H. (1986) ‘The Effect of Custonlizcd Hemiarthroplasty on the Canine Patello-Femoral Joint on Cartilage Properties’, Trans. 3211d Annual Meeting of the Orthopaedic Research Society, 1, 362-363. MATTHEWSON, M.J. (1981) ‘Axi-Symmetric Contact on Thin Compliant Coatings’, J. Mech. Phys. Solids, 29, 2, 89-113. MEDLEY, J.B., PILLIAR, R.M., WONG, E.W. and STRONG, A.B. (1980a) ‘Hydrophylic Polyurethallc Elastomers For Hemiartllroplasty: A Prelinlinary In Vitro Wear Study’, Engng in Med., 9, 2, 5945. MEDLEY, J.B., STRONG, A.B., PILLIAR, R.M. and WONG, E.W. (1980b) ‘The Brealcdown of Fluid Film Lubrication in Elastic-Isoviscous Point Contacts’, Wear, 63, 25-40.

References BENNETT, A. and HIGGINSON, G.R. (1970) ‘Hydrodynamic Lubrication of Soft Solids’, J. Mech. Engng Sci., 12, 218-222.

MEDLEY, J.B. and DOWSON, D. (1984) ‘Lubrication of Elastic-Isoviscous Line Contacts Subject to Cyclic Time-Varying Loads and Entrainment Velocities’, ASLE Trans., 27, 3, 243-251.

CLARKE, I.C. (1981) ‘Wear of Artificial Joint Materials I, Friction and Wear Studies: Validity of Wear-Screening Protocols’, Engng in Mcd., 10, 3, 115-122.

MEDLEY, J.B., DOWSON, D. and WRIGHT, V. (1984) ‘Transient Elastohydrodynamic Lubrication Models For the Human Ankle Joint’, Engng in Med., 13, 3, 137-151.

CRUESS, R.L., KWOK, D.C. ct al (1084) ‘The Response of Articular Cartilage to Weight-Bearing Against Metal - A Study of Hemiarthroplasty of the Hip in the Dog’, J. Bone Joint Surg., 66-B, 592-600.

MEIJERS, P. (1968) ‘The Contact Problenl of a Rigid Cylinder on an Elastic Layer’, Appl. Sci. Res., 18, 353-383.

DOWSON, D. (1989) ‘Are Our Joint Replacement Materials Adequate?’Proc. International Conference on the Changing Role of Engineering in Orthopaedics, Mechanical Engineering Publications, London, 1-5.

SEEDHOM, B.B. (1981) ‘Bio-mechanics of the Lower Limb B. Knee’, An Introduction to the Bio-mechanics of Joints and Joint Replacement, Edited by D. Dowson and V. Wright, Mechanical Engineering Publications, London, 73-81.

FINIKIN, E.F. (1972) ‘The Determination of Young’s Modulus from the Indcntation of Rubber Sheets by Spherically Tippcd Indentors’, Wcar, 19, 277-286. GLADSTONE, J.R. (1988) ‘The Tribology of Elastomeric Layers for Use in Hemiarthroplasty’, MASc thesis, University of Waterloo. HOWIE, D.W., VERNON-ROBERTS, B., OAKESHOTT, R. and MANTHEY, B. (1988) ‘A Rat Model of Resorption of Bone at the Cement-Bone Interface in the Presence of Polyethylene Wear Particles’, J. Bone Joint Surg. 70-A, 2, 257-263. HOOKE, C.J. (1986) ‘The Elastohydrodynamic Lubrication of a Cylinder on an Elastomeric Layer’, Wear, 111, 83-89.

SMITH, T.J. and MEDLEY, J.B. (1986) ‘Development of Transient Elastohydrodynamic Models For Synovial Joint Lubrication’, Proc. 13th Leeds-Lyon Symposium on Tribology, Elsevier, Amsterdam, 369-374. SMITH, T.J. (1985) ‘Numerical Modelling of the Transient Elastohydrohynamic Lubrication of Compliant Surface Layers’, MASc Thesis, University of Waterloo. UNSWORTH, A., PEARCY, M.J., WHITE, E.F.T. and WHITE, G. (1987) ‘Soft Layer Lubrication of Artificial Hip Joints’, Proc. International Conference entitled Fifty Years On, Mechanical Engineering Publications, London, 715-724.

250

UNSWORTH, A., PEARCY, M.J., WHITE, E.F.T. and WHITE, G. (1988) ‘Frictional Properties of Artificial Hip Joints’, Engng in Med., 17, 3, 101-104. YEADON, A.J., LABERGE, M., MEDLEY, J.B. and McNEICE, G.M. (1989) ‘Mechanical Feasibility Study of a Thermoplastic Elastomer For Application as Artificial Cartilage’, Proc. 2nd International Conference on Development and Design With Advanced Materials, August 16-18, 1989, Montreal, Quebec.

Awwendix A Newton’s Method For Finding a h Following the expressions and procedures developed by Meijers (1968), the following equation was derived for A 2 0.7:

+ 10D:A3 + 2.5 (D3 - 40:) - D3DI)A - 0.375D5 + 2.5030;

f(A) = A5 - 5D1A4

+

5 (D:

- D!---

1.250; A - D1

A2

F’R

22.5-

Eti

where a

A = th 1 1 D1 = 0.076025- - - 2Cl c 2 1 2 D3 = 0.12535- - - -

c,3 c;

12

24 Ds = 0.2454- - - -

c:

c;

Ci = 2.746011 C2 = 0.739085 To apply Newton’s method to find A for a given F’, R, E and th the above equation was differentiated with respect to A as follows: - -

dA

+ 5 (D3 - 40:)

- 5A4 - 20D1A3 + 30D:A2

+

5 (D: - D3D1)

+ 1.25 (-)

A

0 3

A - D1

A starting guess of A = 2. was used in all cases and a converged solution was obtained without difficulty. Finally, bdry was evaluated using the converged A value as follows:

25 1

Paper X (iii)

A preliminary investigation of the 'cushion bearing' concept for joint replacement implants D.D. Auger, J.B. Medley, J. Fisher and D. Dowson

The cushion bearing concept involved the potential application of elastomeric surface layers, with a compliance similar to cartilage, in total joint replacement implants. In the present study, experiments were performed on a cushion bearing to investigate the possibility of fluid film lubrication and to compare the measured friction coefficients with theoretical predictions. A pendulum simulator apparatus was modified extensively for the experiments. The measured friction coefficients had a rising characteristic with increasing Sommerfeld parameter which suggested fluid film lubrication and a comparison of predicted film thickness to surface roughness supported this contention. However, the measured friction coefficients did not show good qualitative agreement with theory.

1 INTRODUCTION Current forms of total joint replacement are constructed from polymers, metals and ceramics with physical properties very different from that of the cartilage and bone which they replace, During the past decade, interest in adopting joint replacement bearing materials with properties similar to articular cartilage has been growing, since these materials could promote fluid film lubrication and hence reduce friction and, most importantly, wear. Dowson (1989) introduced the term 'cushion bearing' to describe this type of bearing which would be designed to promote fluid film lubrication in total joint replacements. The cushion bearing examined in the present study consisted of a compliant elastomeric layer bonded to a much stiffer metal substrate. 1.1 The cushion bearing concept The most obvious advantage of a cushion bearing in orthopaedic practice would be a reduction in wear, provided the elastomeric layer was protected from direct surface contact by a full fluid film and provided the elastomer was sufficiently resistant to fatigue. In addition, a reduction in the incidence of loosening might be possible. Isaac et a1 (1988) proposed that the level of frictional torque and the adverse reaction to wear debris contributed to the loosening of conventional implants. Howie et a1 (1988) showed subsequently that the cellular response to wear debris caused loosening of acrylic bone plugs inserted into the knee joints of rats. Their results confirmed the importance of polyethylene wear debris as a factor in prosthetic loosening. By maintaining fluid film lubrication, the cushion bearing should have lower friction and less wear than conventional implants. Dowson (1989) stated that natural synovial joints already benefit from fluid film lubrication, O'Kelly et a1 (1978) and Roberts et a1 (1982) had concluded from friction measurements that under physiological conditions, synovial joints operated in the fluid film regime. Dowson and Jin (1987)

performed numerical analysis which indicated that natural joints could experience fluid film lubrication by microelastohydrodynamic action. Thus, both experiment and theory provided strong support for the importance of fluid film lubrication in synovial joints. On the other hand, O'Kelly et a1 (1979) concluded that conventional joint implants experienced only boundary or mixed film lubrication. Various research groups had recognized that it might be possible to develop joint implants that experienced fluid film lubrication. In hemiarthroplasty, which involved placing an implant surface directly against cartilage, Medley et a1 (1980) proposed the use of an elastomeric layer to promote fluid film lubrication and reduce stress levels in the cartilage. They performed wear tests with a reciprocating pin-on-disc configuration to examine the role of fluid film lubrication in protecting the elastomeric surface from wear. In hip arthroplasty or total hip replacement, Unsworth et a1 (1987, 1988) performed friction measurements on an elastomeric layer which had been placed in a metallic acetabular cup. A pendulum simulator apparatus was used in their tests to impose conditions similar to those encountered in vivo. From their results, they concluded that fluid film lubrication had occurred in their hip prostheses. In Japan, Murakarni and Ohtsuki (1987) considered total knee replacement and examined the lubrication of a tibial component of low elastic modulus sliding against a stainless steel femoral component. Electrical resistance measurements indicated that fluid film lubrication had occurred over most of the walking cycle but they did not suggest specifically that the compliant tibial component be developed for clinical application in total joint replacement.

1.2 Purpose of the present study The cushion bearing concept was considered well suited to investigation by laboratory experiments and engineering analysis. The present project examined the possibility of establishing fluid film action in a cushion bearing subject to

252

dynamic loads and oscillating motion. Bearing friction was measured in a pendulum simulator apparatus. The results were compared to a theoretical analysis which assumed continuous fluid film lubrication and predicted both friction and film thickness. 1.3 Notation

A

constant in the viscosity-temperature relationship

B

constant in the viscosity-temperature relationship

F load F' load per unit width \

hC

central film thickness

L . 0 mm

width of the cushion bearing lW radius of curvature of the upper surface of R1 the cushion bearing

T

Fig. 1 The cushion bearing used in the present study.

lubricant temperature

Tf frictional torque t period of the cycle P velocity of the upper surface of the cushion bearing rl

viscosity

lJ

coefficient of friction

0

combined surface roughness for both bearing surfaces

S =

0% 2F'

A = - hC 0

2 THE CONTACT The chosen geometry for the cushion bearing (Fig. 1) was based on the geometry of the ankle joint as measured by Medley et a1 (1983). The upper cylindrical surface was made of stainless steel. Each side of the upper bearing surface was tapered slightly in the longitudinal direction to approximate a crowning profile. The taper ran about 15 mm from each side and gave up to a 28 pm reduction in the radius of curvature of the cylindrical surface. The lower surface consisted of an aluminium sleeve with an attached silicone rubber layer (RTV 3112 made by Dow Corning). The radius of curvature of the upper surface (R = 20 mm) was slightly smaller than the radius1of curvature of the sleeve (22 mm) as shown in Fig. 2 A reduced radius of 0.22 rn was calculated and when compared to the measurements of Medley et al, it fell within the range of values recorded for the human ankle joint. The width (lw= 100 mm) of the cushion bearing was larger than the human ankle to allow side-leakage to be neglected in the theoretical model. The thickness of the silicone rubber layer was less than the combined thickness of the articular cartilage in the ankle joint. However, under the loads applied, the ratio of contact length to layer thickness remained within the range of the ankle as estimated by Medley et a1 (1984).

.

Fig. 2 A side view of the cushion bearing (an early prototype with a layer thickness of 1.5 mm rather than 1.0 mm). 2.1 Elastomeric layer The silicone rubber elastomer was cast at ambient temperature and pressure in a mould to obtain a uniform layer thickness as described by Auger (1989). A polished stainless steel cylinder formed the mould surface against which the silicone rubber was cured. The elastic modulus of the silicone rubber was determined by O'Carroll (1989) using an optical technique. A transparent spherical surfaced indentor was pushed into a thick block of the silicone rubber at 0.5 mmlminute and held at various levels of indentation while a photograph was taken of the circular contact area and a value was recorded for the load. The contact was lubricated with petroleum jelly to ensure that adhesion forces were minimal and a standard Hertzian formula was used to calculate an average value for elastic modulus of 5.51 MPa. Although the value of the elastic modulus was influenced somewhat by both strain rate and strain amplitude, the chosen value was

253

assumed to be accurate enough for the present study. The usual value of 0.5 was assumed for Poisson's ratio of the silicone rubber layer. 2.2 Lubricant

A number of Shell HVI series oils were employed to lubricate the cushion bearing along with a mixture of HVI 650 and a polybutene thickening agent (BP HVIS 10). This mixture was prepared in a ratio of 2 : l by volume and thus was named HS 2:l in the present study. Viscosity was measured using a Ferranti-Shirley cone-on-plate viscometer at shear rates up to about 17000 11s. These measurements were made at temperatures of 35"C, 42.5"C and 50°C in order to cover the range of operating temperatures that occurred in the pendulum simulator apparatus during the friction testing. Over the range of shear rates employed, the lubricants were judged to be Newtonian (Auger, 1989). In addition, water was used as a lubricant but its viscosity was taken from Kaye and Laby (1986) in the range of 2OoC to 70°C. A least squares curve fit was performed on each lubricant' s viscosity-temperature data with the following general form: q = A e-BT The constants (A and B) in the above equation were calculated (Table 1) and later during the friction experiments, the calculated viscosities ranged from 0.0006 Pa s for water to 0.36 Pa s for HS 2 : l

.

Table 1 The constants for the temperatureviscosity relationship.

water HVI 60 HVI 160 HVI 650 HS 2 : l

1.391~10-~ 0.0914 0.4801 0.7354 2.540

2.4 Load and sliding velocity Cyclic time varying loads and sliding velocities were imposed on the cushion bearing (Fig. 3 ) . The maximum values of both load and velocity were similar to those given by Smith and Medley (1987) for the ankle joint. However, the values of load per unit width were much smaller because the present cushion bearing was wider than the human ankle joint. Furthermore, the synchronization of load and sliding velocity functions was adjusted away from that of the human ankle joint during walking so that the maximum load and sliding velocity occurred at about the same time as indicated by the circled region in Fig. 3 This adjustment was made to reduce the influence of mechanical vibrations on the signal from the frictional torque transducer. The theoretical studies of the human ankle joint by Medley et a1 (1984) had indicated that despite significant changes in the magnitudes of load and sliding velocity, the film thickness remained essentially constant throughout the walking cycle. Thus, it was expected that the value of film thickness might be increased because of the lower load per unit width but the change in sychronization would not have a significant effect. Furthermore, the ratio of contact length to layer thickness was maintained in the same range as estimated for the human ankle joint by making the silicone rubber layer thinner than the combined thickness of the natural cartilage. It was argued, therefore, that the basic lubrication mechanisms, which would act on a cushion bearing implant in vivo would occur in the present study despite the differences in the load per unit width and sliding velocity functions.

.

0.0181 0,0379 0.0468 0.0465 0.0489

2.3 Surface roughness

The roughness of the upper cylindrical surface was measured in the longitudinal direction using a Talysurf 5 profilometer and in the circumferential direction using a Talyrond profilometer. The largest values for the RMS surface roughness were obtained on the tapered regions at the sides of the cylinder. An average value for RMS surface roughness of 0.297 urn was determinedfor these tapered regions and used to represent the upper surface. The roughness of the silicone rubber surface was obtained indirectly by measuring the roughness of the cylindrical surface against which it had been moulded. This strategy eliminated the distortion caused by the stylus of the profilometer indenting or penetrating the surface but assumed that the silicone rubber surface had the same roughness as the mould surface. An average value for RMS surface roughness of 0.054 pm was determined and used t o represent the roughness of the silicone rubber surface. Following Johnson et a1 (1972) a combined surface roughness of 0.302 urn was calculated and used in subsequent analysis to examine the possibility of film breakdown.

Fig. 3 The load and one of the sliding velocity functions applied to the cushion bearing. 3 THEORY A complete theory for the cushion bearing would have to include the following features:

a deformation calculation for an elastomeric layer with a Poisson's ratio of 0.5 and an elastic modulus similar to articular cartilage. conditions of time varying loads and entrainment velocities in the physiological range.

254

0 a contact zone of finite width and an account

taken of two dimensional lubricant flow. a full representation of the squeeze velocity including local variations throughout the contact zone.

The cushion bearing was placed at the fulcrum of the driven pendulum (Fig. 5).

Riclion Carriage

O t h e possibility of lubricant starvation if .the range of motion of the surfaces was not sufficient to entrain lubricant into the central region of the contact zone. Hooke (1987) performed analysis which included all these requirements except an elastomeric half space was considered rather than a layer and a constant load was applied rather than a dynamic one. The extension to elastomeric layers had been achieved by Hooke (1986) for steady state conditions and presumably could be done for transient conditions but the inclusion of dynamic loads might be very difficult. Furthermore, micro-elastohydrodynamic lubrication and the rheology of synovial fluid in thin films might have to be considered. Another approach was used in the present study. The plane inclined surface model (PI Model) had been applied in earlier studies (Medley and Dowson, 1984; Medley et al, 1984; Smith and Medley, 1987) to estimate, in an approximate fashion, the cyclic variation in central film thickness and coefficient of friction for the human ankle joint during the walking cycle. The film shape was represented by a plane inclined surface of suitable geometry and the squeeze velocity was assumed constant over the contact zone at an instant in time. It was assumed that lubricant would always be entrained into the centre of the contact zone. The PI Model was applied to the cushion bearing with some minor modifications. The required steady state formula for mi-nimum film thickness was taken from a curve fit of the results obtained recently by Hooke (1986) and a less complicated friction formula was introduced. A succinct description of this most recent version of the PI Model was given by Gladstone and Medley

lary Poknliomeler

Cam and Iollower Master Cylinder-

-Loading

Cylinder

Fig. 4 The pendulum simulator apparatus.

(1990). The frictional torque was calculated from the results of the PI Model using the following equation:

Tf

=

uF'lwRI

The most recent version of the PI Model did not require much computer memory and thus a successful run was made on a personal computer (IBM PS-2). However, the analysis performed for the present study was completed using an Amdahl mainframe computer bwause it had much faster execution times.

4 APPARATUS 'The pendulum simulator (Fig. 4 ) used in the present study was designed and built originally by O'Kelly et a1 (1977). The load cam was modified subsequently by Medley (1981). Further modifications were made by Auger (1989) for the present study in order to accomodate slight misalignments of the test bearing with respect to the centres of rotation of the pendulum simulator and to improve both the instrumentation and the data acquisition system. The apparatus consisted of two components, a moving frame and a fixed frame. The moving frame was free to slide up and down on linear bearings which were connected to the fixed frame.

Fig. 5 The friction carriage and upper yoke with a cushion bearing in place for testing.

4.1 The moving frame Variable loads were applied to the test bearing through the moving frame by a cam and follower hydraulic system. The cam was driven by a variable speed electric motor. Full details of the hydraulic system was provided by Auger (1989). The same shaft which drove the cam was connected to a scotch yoke mechanism (Fig. 5) which ran a rack and pinion assembly to oscillate the upper yoke and bearing surface in simple harmonic motion. The frequency of the oscillation was altered by changing the speed of the electric motor. The amplitude of the oscillations, o r the stroke length, was altered by adjusting the radius of the connecting point on the scotch yoke mechanism. 4.2 The fixed frame The fixed frame supported the lower surface of the cushion bearing in a friction carriage (Fig. 5) which was mounted on a set of hydrostatic

255

bearings. Four hydrostatic bearings were mounted directly on the fixed frame and allowed the carriage to move in the fore and aft directions (in and out of the page in Fig. 5). The remaining two hydrostatic bearings were placed on top of the fore and aft bearings and allowed the carriage to rotate freely. The oscillation of the upper surface of the cushion bearing generated a frictional torque on the lower surface. This torque tended to rotate the carriage in the hydrostatic bearings and the carriage was prevented from rotating by a small load cell which thus recorded the frictional torque. The hydrostatic bearings which allowed the rotation were designed to operate on large oil films so that the friction arising from the rotation of the carriage (caused by the deflection,of the small load cell and coupling) would be much less than the friction in the cushion bearing. Alignment of the cushion bearing in the apparatus involved two sets of centres, The first set consisted of the upper surface of the cushion bearing aligned with the centres of the rolling element bearings of the upper yoke assembly. The second set of centres consisted of the lower surface of the cushion bearing aligned with the hydrostatic bearings on which the friction carriage rotated. The alignment within the second set of centres ms important, since misalignments would result in a torque acting on the friction carriage as a normal load was applied and this torque could not be distinguished with certainty from the frictional torque in the cushion bearing. However, slight misalignment within the first set of centres resulted in a moving centre of rotation of the upper bearing surface as the yoke oscillated. This movement could be accomodated by movement of the friction carriage in the fore and aft directions, allowing the second set of centres to follow the movement of the upper bearing surface. In addition, this same behaviour allowed slight misalignment between the two sets of centres to be accomodated Some misalignment between the two sets of centres was inevidible because the compliance of the cushion bearing caused the upper surface to move up and down as the normal load varied while the lower surface remained fixed in space. The fore and aft hydrostatic bearings were designed originally to prevent this inevidible misalignment from producing torques on the friction carriage which would masquerade as frictional torques. The fore and aft hydrostatic bearings were designed to operate on large oil films so that their friction would not influence the measurement of the frictional torque in the cushion bearing. Further details regarding the alignment were given by Auger (1989). 4.3 Instrumentation The pendulum simulator was modified by Auger (1989) for the present study to allow continuous simultaneous measurement of load, upper yoke position and frictional torque. A load transducer (from R.D.P. Electronics Ltd.) was added to the apparatus. It had a full scale capacity of 4448 N and was mounted between the loading cylinder and the moving frame (Fig. 4). For zero load to occur on the cushion bearing, the loading cylinder had to push up with a force equal to the full weight of the moving frame which was about 418 N. For loads greater than 418 N , the loading cylinder had to pull down on

the moving frame. Thus, the load cell had both tensile and compressive forces acting on it. A rotary potentiometer was mounted on the end of the shaft of the upper poke in order to monitor the position of the upper surface of the cushion bearing. The voltage drop between ground and the sweep arm of the potentiometer was measured and calibrated for conversion into angular position. The vertical dead centre position of the yoke was set to zero degrees. As described earlier, the oscillation of the upper bearing surface generated a frictional torque on the lower bearing surface which tended to rotate the friction carriage. This rotation was resisted by a piezoelectric force transducer (Kistler 9203) attached to an arm which protruded from the front of the friction carriage (Fig. 5). The piezoelectric crystal was a capacitance type of measuring device. It was chosen because it offered high sensitivity (in the order of millinewtons), a fast response (in the order of microseconds) and a good loading range (k500 N). The frictional torque in the cushion bearing was expected to be very low under fluid film conditions and therefore high sensitivity was needed. However, if surface contact occurred in the bearing, the torque could be very high and a large load range was necessary to prevent damaging the transducer. A charge amplifier (Kistler 5001) was used with the transducer and gave capacitance time constants of 16 to 1600 minutes. To maintain drift and decay free measurements for several hours required cleaning of all electrical connections with freon and the use of a special insulated coaxial cable (Kistler 1601). A major difficulty encountered with the torque transducer occurred in the mechanical coupling between transducer and carriage. The coupling tended to stick in one direction o r the other leaving a preload on the transducer. This problem was solved by introducing polyethylene washers in the coupling (Fig. 5) and by leaving a small clearance between the locking nuts and the carriage arm. This configuration gave a slight dead spot in the torque measurement at the cycle reversals but the error was deemed small compared to other factors. 4.4 Data acquisition and processing

A data acquisition system (Fig. 6) was installed which conditioned and recorded the transducer signals for load, position and frictional torque. An analogue to digital conversion board (Metrabyte Dash 16) was installed in a personal computer (IBM PS-2) and a multi-channel signal conditioner (R.D.P. Electronics Ltd.) allowed the transducer signals to be both amplified and trimmed to produce the maximum possible resolution, Within the personal computer, a high speed data collection and processing software package (Unkelscope) was used to store and manipulate the data. The conversion of transducer outputs into the corresponding physical values was performed on-line. Data values were collected at 200 samples per second per channel for 2.56 seconds to give a total of 512 samples per channel at any chosen instant in time. Also, continuous monitoring of the channels was possible. The slew rate across a sample from one channel to the next was less than 10 nanoseconds so each transducer output was collected at virtually the same instant in time,

256

Load Cell

Piezoelectric Crystal

Rotary Potentiometer

allowed a reasonably sophisticated approach to the study of friction in the cushion bearing.

Multichannel Signal Conditioner Analogue/Digital Conversion Card

Personal Computer IBM-PS2

Fig. 6 The data acquisition system. Positional information was collected from the rotary potentiometer as described previously. To reduce signal noise, the data values were sent through a low pass, second order Butterworth filter with a cutoff frequency of 10 Hz using the Unkelscope utilities. To ensure that relative phase lags did not occur between the channels, all three transducer signals were filtered. The highest frequency of oscillation of the upper bearing surface was 1.8 Hz and the low pass filter cutoff of 10 Hz did not alter the magnitude of the transducer outputs significantly. Once filtered, the positional data values were digitally differentiated, using the Unkelscope utilities, to give sliding velocities in degrees per secondfor the upper bearing surface. For subsequent calculations and graphing, the data was converted into a format to be read into a spreadsheet program (Lotus 1-2-3). Within the spreadsheet, a data sample of 1 second was selected from the midsection of the 2.56 seconds of data collected for each test in order to eliminate the end effects from the previous processing procedures. In addition, the sliding velocity in degrees per second was converted into millimeters per second and the measured coefficient of friction for each point in time throughout the cycle was calculated using the formula:

Also a Sommerfeld number for the cushion bearing was calculated using the formula:

s = - qul 2F' Graphs were plotted from the processed data using another software package (Grapher by Golden Software Inc.) and hardcopy was produced on an HP 74708 plotter. The entire apparatus including the data acquisition system (Fig. 7)

Fig. 7 The pendulum simulator apparatus, signal conditioner unit and personal computer. 5 FRICTION EXPERIMENTS The present study involved several stages of investigation. Preliminary tests were performed on the pendulum simulator apparatus using a conventional hip implant as a test specimen. Details of the operating procedures were established during this stage of familiarization. The next stage was to commission the apparatus for testing of a cushion bearing. The cushion bearing with a layer thickness of 1.5 mm (Fig. 2) was used to assess the capabilities and limitations of the apparatus and to develop the experimental protocol. Unfortunately, during the commissioning, the layer was damaged and thus the final tests were performed on a cushion bearing with a layer thickness of 1.0 mm (Fig. 1). Over 250 tests were completed during the first two stages of investigation and the protocol used in the final stage of actual testing was the result of a great deal of experience with the machine. A rather complicated alignment procedure was developed to minimize the experimental error. A rod of 3.18 nun diameter was passed through the centres of the rolling element bearing, the hydrostatic bearing, the upper bearing surface and the hydrostatic bearing on the other side. The upper bearing surface was clamped in place and the yoke was rotated back and forth, The change in the centre of rotation of the upper bearing surface was measured with a dial gauge, The upper bearing surface was undamped, minor adjustments were made and measured again until the change in centre of rotation was minimized. Then, the lower bearing surface was placed against the upper bearing surface, A lubricant was injected into the contact and under a constant load, which was achieved by disconnecting the loading cylinder from the moving frame, the apparatus was run and the frictional torque was monitored. The

251

lower bearing surface was adjusted until equal torque amplitudes occurred in both directions of oscillation. Once this position was located, the lower bearing surface was clamped down tightly and not moved for the duration of the experiments. To change lubricant, the upper bearing surface was removed from the apparatus and subsequently re-aligned using the rod and dial gauge. Three sets of experiments were used to investigate the behaviour of the present cushion bearing (Table 2 ) . The first set (la, lb, lc) involved testing of five lubricants and was repeated once at the beginning and once at the end of the testing program. In this manner, the repeatability of the test results was ascertained. lhesecond set (Za, 2b) examined the effect of increasing frequency and the third set (3a, 3b, 3c) examined the effect of both increasing the stroke angle and varying the cycle frequency. The temperatures of the lubricants (Table 2 ) were higher than ambient because the hydrostatic bearings had a steady state operating temperature in excess of about 40°C. Table 2 The conditions imposed on the cushion bearing in the order that they were performed.

.

dimensionless time (t/t ), as shown in Fig. 8 When the upper bearing Psurface reversed its direction of rotation, at t/t of 0.15 and 0.65, P the torque values changed in sign and thus direction as expected. The torque was especially low, compared to the rest of the cycle, during the interval where the load and sliding velocity increased towards their peak values (t/t between 0.2 and 0.4). In this interval,Pthe level of torque was influenced by changes in lubricant viscosity and sliding velocity. However, in some of the experiments, the frictional torque was apparently negative within this interval which meant it had changed direction. Results of this nature were not included in subsequent comparisons to the other experiments or to theory because they violated the basic physical premise that only a reversal in the direction of rotation could cause a reversal in the direction of the torque. These unrealistic results only occurred in the third set of experiments as shown in Table 2. Their cause was not determined but some excitation of new modes of mechanical vibration might have occurred as a result of the increase in the stroke angle. 0.40

I

Set Stroke Cycle Lubricant Lubricant No. Angle Period Temperature

("C)

(s)

la

+15"

1.o

HS 2:l

HVI 650 HVI 160 HVI 60 Water lb

2a

+15"

+15"

1.0

0.785

2b

+15"

0.555

3a

+24"

0.555

3b

3c

lc

+24"

+24

+15"

0.775

1.0

1 .o

41 42 43 43 43

HVI 160 HVI 60 HVI 650 HS 2 : l

36

Water

40

HS 2 : l HVI 160 HVI 650

41 42 42

HVI 650 HVI 160 HS 2:l HS 2:l HVI 160 HVI 650 HVI 650 HVI 160

43 42 42

37 38

40

44 44" 43" 44"

HS 2:l

42" 43

HS 2:l HVI 160

44" 44"

HVI 650 HVI 650 HVI 60

44" 41 42 42 42

HS 2:l HVI 160 Water 41 *not included in comparisons to other expt. or theory 6 RESULTS AND DISCUSSION The cushion bearing was run for about 5 minutes until cyclic steady state behaviour was established. The frictional torque was generally within the range of k0.4 N m with typical features, when plotted against

0.60 Heel

strike

0.20

0.40

t/t,

....................

0.60 Toe

0.80

1. 3

Off

Fig. 8 A typical frictional torque curve (tp is the cycle period). In the interval following the peak load and sliding velocity, the frictional torque increased in every experiment. In this case, severe mechanical vibrations were observed and probably contributed to the peak in the measured torque. These vibrations might have been caused by the rapidly changing load acting on the backlash in the rack and pinion system which drove the upper yoke and on any misalignment of the various centres of rotation. Finally, the torque during the swing phase of the cycle (t/t greater than 0.65) usually reached similap magnitudes to those occurring during the stance phase. The results of the experiments were compared to each other by plotting the coefficient of friction at peak load and sliding velocity versus the Sommerfeld parameter (Fig. 9). When only the first set of experiments was considered, the scatter in the results was relatively small. The friction coefficient started at a high value when the Sommerfeld

parameter was low and dropped to a minimum then increased again as the Sommerfeld parameter increased. Unsworth et a1 (1987) had noted that the region of increasing friction coefficient with increasine. Sommerfeld oarameter indicated full fluid fili lubrication: Essentiallv. ,. the same behaviour seemed to occur for the results of the second and third sets of experiments. However, the magnitudes of the friction coefficients were much higher. These results seemed to indicate that changing the frequency of oscillation o r the stroke angle (ie. stroke length) gave a distinct change in the behaviour of the friction coefficient versus Sommerfeld parameter. On the other hand, the results might simply indicate scatter about a single characteristic curve. As mentioned previously, a number of the results from the third set of experiments were discarded because the torque reversed its sign while the direction of rotation remained the same. This behaviour indicated that the scatter in the data was even more pronounced than indicated in Fig. 9

.

0.010

comparison, between both theoretical results and experimental results with the uncertainty ranges, was required to gain further insight into the friction of the cushion bearing.

7 COMPARISON WITH THEORY Comparisons were made between the measured dynamic frictional torques and those predicted by the PI Model f o r most of the individual experiments, In general, the agreement was poor, although in some cases such as set lc with HS 2:l lubricant shown in Fig. 10, the agreement was within the estimated experimental uncertainty in the interval surrounding the point of peak load and sliding velocity. However, the theoretical predictions and experimental values were very different in the low load portions of the cycle for all the experiments. Set lc with the HS 2:l lubricant was considered again in A plot of friction coefficient versus Fig. 11 dimensionless time showed the same behaviour as the frictional torque except that the high measured friction coefficients just after toe-off were not obvious from the frictional torque plot.

.

0.40

0.008

fi

Set 1 c Lubricant: HS 2:l Experiment Theory

00001~

0.30 -

0.20 n 0

z

0.10

W

a, 0.00 3

P-0.10

+0 0.000

, ‘ I , I , , , , , , , , , , , , 1 , , ~ , , , , , , , , ,

O.OE+OOO

ZOE-007

4.OE-007

rrl

-0.20

I , , , , , ,

6.OEhO7

8.OE-007

Sommerfeld parameter Fig. 9 A comparison of the coefficient of friction at peak load and sliding velocity versus Sommerfeld parameter for the three sets of experiments. An attempt was made to quantify the uncertainty in the experimental values for friction. The estimates of uncertainty were based on experience with the apparatus and small assessing tests. This analysis included influencing factors such as alignment of the cushion bearing in the apparatus, mechanical vibrations of the apparatus, load sharing between the bearing and the friction transducer, hysteresis friction, layer deformation, errors in the measurement of the elastic modulus of the layer, temperature rise of the lubricant through the contact, dimensional accuracy and errors in instrument readings. The analysis was presented in some detail by Auger (1989) who indicated that two factors seemed to be the dominant in the experimental uncertainty and thus in both the precision and accuracy of the present results. These two factors were misalignment of the cushion bearing and mechanical vibrations. However, in the analysis itself difficulty was encountered in accurately estimating the uncertainty caused by the mechanical vibrations and in establishing the link between misalignment and vibrations. A detailed

-0.30

1

-0.40 II 0.00 I

I I I I

,,

/

I

, , , ,,,

0.20

I

I I , I

0.40

Heel strike

,,

I,,,,,,,,,I,, ,, , , I , 0.80 1.00

0.60

Toe

off

t/t, Fig. 10 A comparison between the predictions of the PI Model and the measured values of frictional torque with uncertainty ranges indicated. Although it might be argued that the PI Model itself provided only an approximate prediction of frictional torques and coefficients, the differences between theory and experiment were large enough to indicate that the torque transducer was measuring other quantities besides friction in the cushion bearing. Throughout the present study, design modifications were made to reduce the experimental error but it was apparent that basic problems existed with the pendulum simulator apparatus. Some agreement with theory, however, was obtained by examining the friction coefficient at peak load and sliding velocity versus the Sommerfeld parameter as shown in Fig. 12. The estimated experimental uncertainty was calculated and plotted for each experiment. In addition, a measurement threshold was introduced which

259

.

represented the average uncertainty for all the experiments. Data which fell below this threshold had bands of uncertainty on their frictional torque values that extended below zero at the point of peak load and sliding velocity.

greater than 3.0 Thus, the experimental results of the present study did seem capable of identifying conditions of fluid film lubrication in the manner suggested by Unsworth et a1 (1988). The apparatus, however, did not seem capable of determining friction coefficients with accuracy or precision even at the point of peak load and sliding velocity. In general, the theoretical curve fell below the data and was contained within the measurement threshold. Thus, if the theory did provide a good prediction of friction in the cushion bearing, the experimental results did indeed lack accuracy. The existence of a measurement threshold which contained the theoretical predictions showed the lack of precision. The present values of friction coefficient in the fluid film regime were all lower than the friction factors measured by Unsworth et a1 (1987, 1988) and the amount of scatter in the data was similar. Since Unsworth et a1 used a pendulum simulator apparatus, the findings of the present study might provide an indication of the accuracy of their friction factors. Furthermore, various forms of pendulum simulator had been used to measure the friction of human synovial joints (O'Kelly et al, 1978; Roberts et al, 1982). The limitations of the pendulum simulator apparatus might explain the lower values of friction coefficient predicted by theory (Medley et al, 1984) compared to the higher measured ones (Roberts et al, 1982).

Set jf 1 c Lubricant: HS 2:l D Experiment

00

-y

0.060

c

a, .-0

.-

% Ll-

0.040 0 C

.-0 .-L0 0.020 -id

LI

0.000 0.00

0.20

0.40

0.60

Heel strike

0.80

1.00

Toe off

t/t, Fig. 11 A comparison between the predicted friction coefficients and the measured values with uncertainty ranges indicated.

8 CONCLUSIONS

I

L

.Dynamic coefficients of friction for a cushion bearing were measured in a pendulum simulator apparatus and values less than 0.005 were obtained at peak load and sliding velocity. @The presence of fluid film lubrication was indicated by the increase in the friction coefficient at peak load and velocity with increasing Sommerfeld parameter. Theoretical predictions using the PI Model supported the contention that fluid films had been generated.

I

O.OE+OOO

I ' " ' I ~ ' ' '

2.OE-007

~

4.OE1007

~

~

6.OE-007

~

~

8.OE- ,007

~

Sommerfeld parameter Fig. 12 A comparison of theoretical and experimental friction coefficients at peak load and sliding velocity with the experimental uncertainty indicated. The value of the Somrnerfeld parameter at which the lambda ratio (central film thickness divided by combined RMS surface roughness) was equal to 3.0 was identified in Fig. 12. The central film thickness was predicted by the PI Model and the combined RMS surface roughness was measured as described previously. The lambda ratio increased with increasing Sommerfeld parameter. According to Johnson et a1 (1972), when the lambda ratio exceeded about 3 , a full fluid film separated the bearing surfaces. The region of increasing friction coefficient with increasing Sommerfeld parameter corresponded to the region of lambda ratio

-

*An analysis of experimental uncertainty in the friction measurements suggested that misalignment of the cushion bearing and mechanical vibrations caused the scatter in ~ ~ l ~ @ precision ~ ~ ~ v m the data. The was not sufficient to determine from the experimental results whether the friction coefficient at peak load and velocity was a unique function of the Sommerfeld parameter. .The measured friction coefficients at peak load and velocity were less than the friction factors recorded by Unsworth et a1 (1987, 1988) but higher than the friction coefficients predicted by the PI Model. Thus, the accuracy of these measured friction coefficients could not be established.

9 ACKNOWLEDGEMENTS The authors wish to thank the technical staff of the University of Leeds, in particular Mr. D. Darby and Mr. B. Jobbins, for their valuable assistance and advice throughout this experimental investigation. Financial support was provided by the Science and Engineering Research Council of the

United Kingdom, the Natural Science and Engineering Research Council of Canada and an Ontario Graduate Scholarship for one of u s (D.D.A.) from the Government of Ontario in Canada. References AUGER, D.D. (1989) 'A Preliminary Investigation of the Cushion Bearing Concept for Total Joint Replacement', MASc Thesis, University of Waterloo. DOWSON, D. (1989) 'Are Our Joint Replacement Materials Adequate?' Proc. International Conference on the Changing Role of Engineering in Orthopaedics, Mechanical Engineering Publications, London, 1-5. DOWSON, D. and JIN, Z.M. (1987) 'An Analysis of Micro-elasto-hydrodynamic Lubrication in Synovial Joints Considering Cyclic Loading and Entraining Velocities', Proc. 13th Leeds-Lyon Symposium on Tribology, Elsevier, Amsterdam, 375-386. GLADSTONE, J.R. and MEDLEY, J.B. (1990) 'Comparison of Theoretical and Experimental Values for Friction of Lubricated Elastomeric Surface Layers Under Transient Conditions', Proc. 16th Leeds-Lyon Symposium on Tribology, Elsevier, Amsterdam. HOWIE, D.W., VERNON-ROBERTS, B., OAKESHOTT, R. and MANTHEY, B. (1988) 'A Rat Model of Resorption of Bone at the Cement-Bone Interface in the Presence of Polyethylene Wear Particles', J. Bone Joint Surg., 70-A, 2 , 257-263.

HOOKE, C.J. (1986) 'The Elastohydrodynamic Lubrication of a Cylinder on an Elastomeric Layer', Wear, 111, 83-89. HOOKE, C.J. (1987) 'The Calculation of Film Thickness on Soft, Highly Deformed Contacts Under Dynamic Conditions', Proc. Instn. Mech. Engrs., 201, C3, 171-179. ISAAC, G.H., ATKINSON, J.R., DOWSON, D.,

KENNEDY, P.D. and SMITH, M.R. (1987) 'The Causes of Femoral Head Roughening in Explanted Charnley Hip Prosthesis', Engng in Med., 16, 3 , 167-173. JOHNSON, K.L., GREENWOODl J.A. and POON, S.Y. (1972) 'A Simple Theory of Asperity Contact in Elastohydrodynamic Lubrication', Wear, 19, 91-108. KAYE, G.W.C., LABY, T.H. (1986) 'Tables of Physical and Chemical Constants', Longman, New York, 36. MEDLEY, J.B., PILLIAR, R.M., WONG, E.W. and STRONG, A.B. (1980) 'Hydrophylic Polyurethane Elastomers For Hemiarthroplasty: A Preliminary In Vitro Wear Study', Engng in Med., 9, 2 , 59-65. MEDLEY, J.B. (1981)' The Lubrication of Normal Human Ankle Joints', PhD Thesis, University of Leeds, MEDLEY, J.B., DOWSON, D., WRIGHT, V. (1983) 'Surface geometry of the Human Ankle Joint', Engng in Med., 12, 1, 35-41. MEDLEY, J.B. and DOWSON, D. (1984) 'Lubrication of Elastic-Isoviscous Line Contacts Subject to Cyclic Time-Varying Loads and Entrainment Velocities' , ASLE Trans,, 27, 3, 243-251.

MEDLEY, J.B., DOWSON, D. and WRIGHT, V. (1984) 'Transient Elastohydrodynamic Lubrication Models For the Human Ankle Joint', Engng in Med., 13, 3 , 137-151.

MURAKAMI, T. and OHTSUKI, N. (1989) 'Effects of Lubricants on Improvement of Fluid Film Formation in Knee Prostheses Under Walking Condition', Progress and New Directions of Biomechanics, Edited by Fung, Hayashi and Seguchi, 403-412. O'CARROLL, S. (1989) 'Investigation of LOW Elastic Modulus Materials Used as Bearing Surfaces in Artificial Joints', Final Year Project, Department of Mechanical Engineering, University of Leeds. O'KELLY, J., UNSWORTH, A. DOWSON, D., HALL, A. and WRIGHT, V. (1977) 'Pendulum and Simulator Studies of Friction in Hip Joints', Evaluation of Artificial Hip Joints, Biological Engineering Society, London, 19-29. O'KELLY, J., UNSWORTH, A,, DOWSON, D. HALL, A., and WRIGHT, V. (1978) 'A Study of the Role of Synovial Fluid and Its Constituents in the Friction and Lubrication of Human Hip Joints', Engng in Med., 7 , 2 , 73-83. O'KELLY, J . , UNSWORTH, A,, DOWSON, D. and WRIGHT, V. (1979) 'An Experimental Study of Friction and Lubrication in Hip Prostheses', Engng in Med., 8, 3, 153-159. ROBERTS, B.J., UNSWORTH, A. and MIAN, N. (1982) 'Modes of Lubrication in Human Hip Joints', Ann. Rheum. Dis., 41, 217-224. SMITH, T.J. and MEDLEY, J.B. (1987) 'Development of Transient Elastohydrodynamic Models For Synovial Joint Lubrication', Proc. 1 3 t h LeedsLyon Symposium on Tribology, Elsevier, Amsterdam, 369-374. UNSWORTH, A,, PEARCY, M.J., WHITE, E.F.T. and WHITE, G. (1987) 'Soft Layer Lubrication of Artificial Hip Joints', Proc. International Conference entitled Fifty Years On, Mechanical Engineering Publications, London, 715-724. UNSWORTH, A., PEARCY, M.J., WHITE, E.F.T. and WHITE, G. (1988) 'Frictional Properties of Artificial Hip Joints', Engng in Med., 17, 3, 101-104 Note: Since writing this paper, it has been learned that the elastic modulus estimates of O'Carroll ( 1 9 8 9 ) were based on an incorrect value for the radius of curvature of the indentor. The elastic modulus should be 2.86 MPa rather than 5.51 MPa as reported in the paper. Calculations with the new elastic modulus gave increases of about 2% in the friction coefficient, thus not changing our discussion or conclusions substantially.

SESSION XI SOFT COATINGS 2 Chairman:

Professor H.S. Cheng

PAPER XI (i)

The influence of elastic deformation upon film thickness in lubricated bearings with low elastic modulus coatings

PAPER XI (ii)

Frictional mechanism in uncoated and zinc-coated steel sheet forming theoretical and experimental results

PAPER XI (iii)

Effect of nitrogen ion implantation on the friction and wear properties of some plastics

-


263

Paper XI (i)

The influence of elastic deformation upon film thickness in lubricated bearings with low elastic modulus coatings D. Dowson and Z. Jin

The elastic deformation of a layered surface firmly bonded to a rigid substrate has been calculated for an infinitely wide nominal line contact between a cylinder and a plane using both a simplified model, the so-called constrained column model, and a full elasticity model. The results are presented for different values of Poisson's ratio and loading width. The effects upon contact and lubrication analyses have also been examined. The general conclusion is that the constrained column model can be reasonably applied to predict the elastic deformation and hence to perform the contact and lubrication analyses if Poisson's ratio is less than about 0.45 and the ratio of the loading width to the layer thickness is greater than about 2. 1.

INTRODUCTION

Compliant surface layers now find application in a number of tribological devices, including solid tyres on wheels, certain fluid seals, some journal and thrust bearings and synovial joints. The advantages of compliant surface bearings have been summarized by Benjamin and Castelli (1971), who noted; the tolerance for impurities in the lubricant; the ability to conform to irregularities in the bearing walls; the capacity to operate at low lubricant film thicknesses and the capability to function at low lubricant feed rates. In addition to these advantages, compliant surfaces can be adopted to protect the substrate from impact and abrasion and, most importantly, to generate by elasto-hydrodynamic action a satisfactory lubricant film thickness while supporting a sufficiently large load. Many experimental and theoretical investigations have been carried out on compliant surface bearings and reported in the literature. Fogg and Hunwicks (1937) showed experimentally that a continuous lubricant film could be developed with a rubber surface journal bearing under loading conditions for which they would otherwise have failed. Cudworth and Higginson (1976) examined the effect of a compliant layered surface coating on a more rigid substrate. They showed the persistence of hydrodynamic lubrication to a very low value of entraining velocity, showing a major improvement over the rigid surface bearing. Darbey et a1 (1979) further showed experimentally that for compliant rough surfaces, the film thickness could be of a similar value to the combined surface roughness for hydrodynamic lubrication to persist. On the theoretical aspects of the problem many solutions exist for various conditions. Herrebrugh (1968) solved the sliding elastohydrodynamic lubrication problem for a compliant semi-infinite solid, for which the increase of viscosity with pressure can generally be neglected, using an integral solution method. Later, the same author extended his analysis to the situation of a

cylinder approaching a plane surface in the squeeze-film process (Herrebrugh, 1970). In the case of a compliant surface coating, Higginson (1966) adopted a simplified elastic deformation model, the so-called constrained column model, to consider the effect of the elasticity of a soft layered liner in a journal bearing on lubrication performance. The general elastohydrodynamic lubrication theory for a cylinder sliding against a plane, soft layered surface has been presented by Hooke and his colleagues (Hooke and O'Donoghue, 1972; Hooke, 1986). Other references in this area, concerning sliding conditions, normal approach motion, transient conditions and rough surfaces, have been detailed recently by Jin (1988).

The purpose of the present study is to investigate the elastic deformation models of a compliant layered surface firmly bonded to a rigid substrate under plane strain conditions and its consequence on the contact and lubrication analyses. 1.1

Notation

a

Semi-width of dry contact or of a parabolic pressure distribution in equation (7).

ci j

Displacement coefficients defined in equation (5).

d

Layer thickness.

D

Non-dimensional layer thickness, d/R.

E

Elastic modulus.

E'

Equivalent elastic modulus, 2E/(1-v2

h

Film thickness.

H

Non-dimensional film thickness, h/R.

P

Pressure.

Po

Central pressure value of a parabolic form in equation (7).

)

.

*:

264

P

Non-dimensional pressure, p/Ef.

R

Radius.

U

Entraining velocity.

U

Non-dimensional entraining velocity,

dE.v

r(u/E'R.

(a) Elastic Deformation

W

Load per unit length.

W

Non-dimensional load per unit length, wpR.

X

Axial coordinate.

X

Non-dimensional axial coordinate, x/d.

d

Elastic deformation.

A

Non-dimensional elastic deformation, d/d.

n

Coefficient of viscosity.

V

Poisson's ratio.

m

I

d5,v-a-

X

a

(b) Dry Contact

2. ELASTIC DEFORMATION MODELS

The calculation of elastic deformation is essential for both contact and lubrication analyses. The problem, depicted in Figure l ( a ) , is to determine the elastic deformation for a given pressure distribution. 2.1

Constrained Column Model

The constrained column model, or 'column model' for short, assumes that the deformation of the layer takes place normal to the hard substrate surface and that the lateral expansion can be neglected. This can reasonably be expected to be valid for a relatively large loading width and a large deformation of the layer, but would not be acceptable for a Poisson's ratio close to 0.5. Johnson (1985) has shown that the nondimensional elastic deformation for this situation is given by;

X

3

(c) muid-Film Lubrication Figure 1

K(X-S)

=

Theoretical Analysis Associated with a Compliant Surface Coating Firmly Bonded to a Rigid Substrate [(3-4v)sinh(2w)-2wl cos[w(X-0.45), the use of the column model results in an appreciable error. In the central region, the deformation predicted by the column model is considerably less than that predicted by the full solution. Near the edge, the bulge effect also increases due to the increasing incompressibility of the layer and the column model clearly cannot be applied with any confidence under these conditions.

Figure 4 Comparison of Elastic Deformation under a Parabolic Pressure Distribution according to Column Model and Full Elasticity Model (Po = 0.10; a/d = 4.00) The deformation at the centre of the contact is shown for different values of (a/d) and ( v ) in Figure 5. It is clear that for large values of (a/d) and values of (u) less than or equal to about 0.4, the column model can be adopted to predict the deformation of the layer with reasonable accuracy provided that the loading width is much larger than the layer thickness and Poissonrs ratio is not too close to 0.5. Furthermore, the agreement between the two predicted deformations appears to be better in the central region of the conjunction than near to the edge of the conjunction as shown in Figure 3. 1 0.16 0. 14

..

-/r-

2

0. 12 - * 0. 10 .. 0. 08 -. 0. 06 -. 0. 04

-.

0. 02 -r 0.00

1

4 :

e/d

0 1 2 3 4 5 Figure 5 Deformation at Centre Under a Parabolic Pressure Distribution (Po = 0.1) 1. v = 0.0 2. v = 0.3 3. v = 0.4 4. v = 0.5 Solid Line : Full Model Dashed Line : Column Model

266

4.

necessary for the analysis for a value of (v) of 0.5 ( JOhnSOn, 1985).

CONTACT WIDTH ANALYSIS

using the elastic deformation models developed in the previous section, the contact width analysis can readily be performed (Figure l(b)).

2

2

4wR (1-v 1 / (xEa 1 1 2

4.1 Column Model Solution

\J

L,

= 0.45 = 0.48 A

Based upon the assumption of the column model, the contact width can readily be determined (Johnson, 1985):

--- Column

3

Modei

4.2 ~ u l lElasticity Solution The full analysis was carried out by Meijers (1968) using an asymptotic expansion method and results were presented in terms of formulae relating the applied load, the radius of the indenter, the elastic modulus, the Poisson's ratio and the ratio of the thickness of the layer to the semi-width of the contact. Comparisons between the contact width predictions based upon the column model and the full solution for Poissonrsratios of 0.0, 0.3 and 0.4 are shown in Figure 6. It is generally noted that the agreement between the two solutions is very good for (a/d) greater than about 2. Furthermore, it is interesting to note that for the same load, the contact width predicted from the column model is larger than that from the full elasticity solution for ( v ) less than or equal to about 0.3. However for ( v ) equal to 0.4 and (a/d) larger than two, the opposite effect is found. This has a large effect upon the lubrication analysis as shown in the next section.

3

0 1 2 3 4 5 6 7 8 9 1 0 Figure 7

5.

Comparison of Contact Width Predictions for the Present Model (Full Model from Meijers, 1968).

LUBRICATION ANALYSIS

For lubrication problems (Figure l(c)) it is necessary to couple and solve the Reynolds' and elasticity equations. 5.1 Solution Methods With the application of the column model, both the Reynolds equation and elasticity equation can be combined into a single ordinary differential equation. Gear's method is found to be particularly suitable for the solution of this equation (Medley et al, 1984). For the full elasticity model, an effective straight forward iterative method has been developed to solve the Reynolds and elasticity equations and the detailed solution technique will be presented elsewhere (Dowson and Jin, 1989). 5.2 Comparison of Results

2 1

a/d

0

1

Figure 6

2

3

4

5

6

7

8

9

1

0

Comparison of Contact Width Predictions for the Present Model (Full Model from Meijers, 1968) Another set of comparisons of contact width predictions for Poissonrsratios close to 0.5 is shown in Figure 7. It can be seen that the contact width predicted from the column model is considerably smaller than that from the full solution for ( v ) equal to 0.45 and 0.48. This trend is reversed, however, for v = 0.5 even though some modifications were

The film profiles and pressure distributions for different loads (hence a/d)) and for a fixed value of ( v ) of 0.4, a dimensionless layer thickness (D) of 0.1 and a value of the dimensionless speed parameter (U) of 1.31253-06 are shown in Figures 8 and 9. It is noted that for small loads (a/d about 11, a relatively large difference is predicted between the column model solution and the full solution. However as (W) increases (a/d 2 2), the differences in the overall film profiles become very small. Furthermore, it is interesting to note the exit nip predicted by the full model. This leads to a relatively large difference in the minimum film thickness predicted by the two procedures. For a value of the dimensionless load (W) of 0.1397, the difference in the central film thickness predicted by the two solutions is only 2.8%, but 16.4% for the minimum film thickness. Figure 9 shows the corresponding pressure distributions. It is noted that in the central region, the pressure predicted from the column model is larger than that from the full solution, while in both the inlet and outlet regions the opposite trend can be seen.

261

FI

F I l m Thlckness (h/R]

Lm Th 1 c kness (h/R)

~

X/d

x/ d

-3

-2

-1

0

1

2

3

Figure 10 Comparison of Film Thickness for Different Poisson's Ratios. (U = 1.31253-06; D = 0.1; W = 4.5553-02) l : =~ 0.0; 2 : = ~ 0.3; 3:v = 0.4; (Solid Line: Full Model; Dashed Line: Column Model) Presaure D I 8 t r 1 but I on (p/E' )

t

Om20

-4

-3

Figure 9

3 4 Comparison of Pressure Distribution for Different Loads (U = 1.31253-06; D 0.1; v = 0.4) -2

1:W 3:W

-1

= =

0

1

7.2893-03; 2:W 1.3973-01;

-3

2

=

4.5553-02;

(Solid Line : Full Model; Dashed Line : Column Model) The effect of Poissonfsratio is shown in Figures 10 to 13 for a fixed value of ( W ) of 4.5553-02, (U) Of 1.31253-06 and (D) Of 0.1. For small values of Poisson's ratio ( < 0.4), the agreement between the two solutions is generally very good. It is noted that for this particular case, the best agreement between the two solutions is for ( v ) of 0.4, while for both ( v ) of 0.0 and 0.3, the film thicknesses predicted from the column model are larger than those from the full solution, This is mainly because of the difference in the contact width predictions as discussed in the previous section. For the corresponding pressure distributions shown in Figure 11, it can readily be noted that the smaller the Poison's ratio the better the agreement between the two solutions. This is particularly evident in the central region of the conjunction. However, as Poisson's ratio increases ( 2 0.45), an appreciable error results from the use of the

-2

-1

0

1

2

3

Figure 11 Comp3rison of Pressure Distribution for Different Poisson~sRatios. (U = 1.3125E-06; D = 0.1; W 4.5553-02) l:v = 0.0; 2 : = ~ 0.3; 3 : =~ 0.4; (Solid Line : Full Model; Dashed Line : Cohmn M o d e l ) column model for both the film profiles and pressure distributions. It can also be noted from Figures 12 and 13 that Poisson's ratio has a smaller effect upon the predictions from the full solution than from the column model. Furthermore, it can be seen that the minimum film thickness predicted from the column model is larger than that from the full solution for ( v ) less than 0.4 and smaller for ( v ) larger than 0.4 (Figure 14). A similar variation is also true for the central film thickness. 6.

DISCUSSION AND CONCLUSION

The elastic deformation of a layered surface firmly bonded to a rigid substrate has been calculated using both the constrained column model and the full elasticity model. the effects of the loading width and Poisson's ratio have been examined in detail and it has been shown that the constrained column model

268

FI l m Thlckness (h/R)

0.0016

o.oo14 0.001 2 0.001 0

x

h/R

---------------____

t--------! Ir ...

0.0008 0.0006 0.0004 0.0002 0.0000 J ~

I-

---+

*.--

x/d

-.-+-

-3 -2 -1 0 1 2 3 Figure 12 Comparison of Film Thickness for Different Poisson's Ratios. (U = 1.31253-06; D = 0.1; W = 4.5553-02) l : =~ 0.45; 2 : = ~ 0.48; 3 : =~ 0.50; (Solid Line: Full Model; Dashed Line: Column Model) Pressure D t etr t but ton (PIE' 1

A

m

: v

0.0 0. 1 0.2 0.3 0.4 0.5 Figure 14 Comparison of Film Thickness for Different Values of PoissonrsRatio (U = 1.31253-06, W = 4.5553-02, D = 0.1) 1. Hmin (Full Model) 2. A H (Column Model) 3. Hmln (Full Model) (ColunU~Model) 4. * HZ:

-

--_-

,

REFERENCES

Benjamin, M K and Castelli, V, (1971). A Theoretical Investigation of Compliant Surface Journal Bearings. Trans. ASME, J. Lub. Technol, 93(1), pp 191-201. cudworth, C D and Higginson, G R, (19761, Friction of Lubricated Soft Surface Layers. Wear, 37, pp 299-312. Darbey, P L, Higginson, G R and Townend, D J, (1979). Lubrication of Rough Compliant Solids. In Elastohydrodynamics and Related Topics, Proc. of the 5th LeedsLyon Symposium on Tribology, D mwson, C M Taylor, M Godet and D Berthe, eds. Mech. Eng. -1. BUT St EdmundSr Suffolk, pp 398-403.

-3 -2 -1 0 1 2 3 Figure 13 Comparison of Pressure Distribution for Different PoissonrsRatios. (U 1.31253-06; D = 0.1; W = 4.555E-02) 1:V = 0.45; 2 : =~ 0.48; 3 : =~ 0.50; (Solid Line : Full Model; Dashed Line : Column Model) can be applied with fair accuracy €or Poissonrs ratios less than about 0.45 and the ratio of the loading width to the layer thickness larger than about 2. Furthermore, it has been shown that under these conditions, the constrained column model can also be applied to perform the contact width and lubrication analyses with acceptable accuracy. The use of the simple, constrained column model does, of course, greatly increase the efficiency of the numerical procedure. In the present study, the validity of the constrained column model has been demonstrated for smooth surfaces and steady-state conditions. However, for transient elastohydrodynamic lubrication or micro-elastohydrodynamic lubrication analysis, the use of this model appears to be not only efficient but necessary. Under these conditions, the computing time required for the full solution becomes excessive, typically 100 to 1000 times greater than that for the column model.

DOWSOn, D and Jin, 2 M, (19891, A Full Numerical Solution to the Micro-Elastohydrodynamic Lubrication Problem for an Elastic Wavy Layered Surface Firmly Bonded to a Rigid Substrate under Steady-State Conditions. To be published. FOgg, A and Hunwicks, S A, (1937), Some Experiments with Water Lubricated Rubber Bearings. In General Discussions on Lubrication and Lubricants, vol. 1, Instn. Mech. Engrs., London, pp 101-106. Herrebrugh, K, (19681, Solving the Incompressible and Isothermal Problem in Elastohydrodynamic Lubrication through an Integral Equation. Trans. ASm, J. ~ub. Technol, 90(1), pp 262-270. Herrebrugh, K, (19701, Elastohydrodynamic Squeeze Films between two Cylinders in Normal Approach, Trans. ASME, J. Lub. Tech. pp 292-302. 81 Higginson, G R, (19661, The Theoretical Effects of Elastic Deformation of the Bearing Liner on Journal Bearing Performance. Proc. Instn. Mech. Engrs., 180, Pt 3B, pp 31-38. 91 Hooke, C J, (1986), The Elastohydrodynamic Lubrication of a Cylinder on an Elastic Layer, Wear, 111(1), pp 83-99.

269

[lo] Hooker C J, and O'Donoghue, J P, (19721, Elastohydrodynamic Lubrication of Soft Highly Deformed Contacts. J. Mech. Eng. Sci, 14(1), pp. 34-48.

[13] Nedley, J B, (1981), The Lubrication of Normal Human Ankle Joints. Ph.D. Thesis, university of Leeds.

[14] Heijers, P, (1968), The Contact Problem of a Rigid Cylinder on an Elastic Layer. Appl. Sci. ReS., 18, pp 353-383.

[11] Jin, Z M, (1988), The Micro-ElastoHydrodynamic Lubrication of Synovial Joints. Ph.D. Thesis, University Of Leeds

.

[12] Johnson, K L, (1985), Contact Mechanics. Cambridge University Press. Appendix A

The Displacement Coefficient Calculation of a Layered Surface Firmly Bonded to a Rigid Substrate As

shown by equation ( 5 1 , the displacement coefficient (Cij)can be calculated as:

Integrating with respect to ( 5 )

o2 [ (3-4~)cash(2 ~ +) 23+5

0

do

- 1 2 +~ 8u2 ]

Splitting the integration domain (Or-) as ( 0 , ~ and ~ ) (ao, m) and choosing (to) sufficiently large so that (Cij)can be written as follows:

1 ' 1 J~

[ (3-4u)sinh(2o)-2w]

4

cij

[p-

o2 [ (3-4v)cosh(2w) + 202 + 5 .(D

+

[sin@

J

Xi j]+ sinw[F

- 1 2 +~ 8

V*

+ Xi j)]dw

]

1 [sinw [F- xij) + sino [F+ xij)] do] 0

NO

The first integral in the above equation is numerically evaluated using a 10 point Gaussian quadrature formula and the second one can be integrated analytically as follows: - 0 1

J.

[ sino [F- xij) + sinw[F

WO

-

sin o,

'[

[p- xi

j)

- xij) + sin o,

ci

[No

+ xij)] do

[F + xij)

IF - xi I 1

where (C,) is the cosine integral defined as: Ci (X) =

-

[ Ft dt


27 1

Paper XI (ii)

Frictional mechanism in uncoated and zinc-coated steel sheet forming - theoretical and experimental results V. Samper and E. Felder

A b r i e f review of t h e t o o l / m e t a l c o n t a c t c o n d i t i o n s i n deep-drawing [1,21, l e a d s u s t o compare t h e f r i c t i o n a l behaviour of uncoated and zinc-coated s h e e t s . Experimental r e s u l t s show v a s t d i f f e r e n c e s : * t h e u n c o a t e d s h e e t , which p r e s e n t s good f r i c t i o n a l c h a r a c t e r i s t i c s , i s s u p e r f i c i a l l y work-hardened by f r i c t i o n ; * c o n v e r s e l y , worse f r i c t i o n a l behaviour ( h i g h e r f r i c t i o n , d e b r i s f o r m a t i o n ) i s observed f o r t h e c o a t e d s h e e t . Furthermore, t h e z i n c l a y e r s o f t e n s , by dynamic r e c r i s t a l l i z a t i o n , during i t s p l a s t i c deformation. I n o r d e r t o s t u d y t h e a n a l y s i s of t h e phenomena t h o r o u g h l y , a k i n e m a t i c a l v e r s i o n of t h e wave model of f r i c t i o n has been developped: t h e s t r a i n - h a r d e n i n g law introduced, O O = ( T ~ E ~t,a k e s i n t o account t h e work-hardening (n>O) o r s o f t e n i n g (ne (in the substrate)

oo=.p F i g . 5 Galvanized m i l d - s t e e l s h e e t a f t e r friction a) frictional characteristics b ) topography

ooz=hool i f O 1 t h e l a y e r i s h a r d e r t h a n base m a t e r i a l

the

214

This theoretical model, more d e t a i l e d i n [ 5 ] , provides t h e e v o l u t i o n of normal h a r d n e s s w i t h t h e r e l a t i v e p e n e t r a t i o n 6/e f o r g i v e n v a l u e s of h. These curves present some slope d i s c o n t i n u i t i e s which c o r r e s p o n d t o a b r u p t t r a n s i t i o n s on t h e f l o w f i e l d induced by t h e i n d e n t e r a t some c r i t i c a l v a l u e s of 6.

a) tL

IHY 5.8

t

I

3.6

i.3

*

h plateaux 1.0

t

valleys r

b

0.7

-e 6

b)

z0.513

l.0

0.9

0.8

0.7

0.c

0.5

after

friction 6

-6

0.4

Fig.7 T h e o r e t i c a l r e s u l t s ( l i n e s ) and experimental p o i n t s of i n d e n t a t i o n t e s t s a ) uncoated m i l d - s t e e l s h e e t b) galvanized mild-steel sheet

2 . 3 . 3 Results a n d d i s c u s s i o n I n o r d e r t o compare t h e o r e t i c a l r e s u l t s and experiments, t h e hardness v a l u e s a t d i f f e r e n t l o a d s have been d i v i d e d by HvO , t h e s u b s t r a t e h a r d n e s s . T h i s r a t i o

HV has Hv0

@)The m i l d s t e e l s h e e t a f t e r f r i c t i o n H a r d n e s s measurements r e v e a l a h i g h s u p e r f i c i a l strain-hardening due t o sheet/tools friction: the surface h a r d n e s s a f t e r f r i c t i o n i s approximately t w i c e a s h i g h a s t h e b u l k v a l u e . The comparison of t h e * e x p e r i m e n t a l r e s u l t s w i t h t h e t h e o r e t i c a l o n e s p r o v i d e s an e s t i m a t i o n of t h e t h i c k n e s s of t h e pm) . hardened s u p e r f i c i a l l a y e r ( e ~ 6 C o n s t a n t a t low d e p t h i n d e n t a t i o n (hard l a y e r ) , t h e hardness decreases the l i n e a r l y a s t h e l o a d P, i . e . p e n e t r a t i o n 6, i n c r e a s e s ( F i g . 7 . a ) . T h i s result, already observed i n other e x p e r i m e n t a l works, i s c o n f i r m e d h e r e experimentally a s in theory. This decrease begins a t a c r i t i c a l depth 6,r2.4 p m and c o r r e s p o n d s t o a sudden s p r e a d i n g of t h e d e f o r m a t i o n zone, due i n depth. The to indentation, correlation between theory and experiments demonstrates t h a t the h a r d n e s s of t h e s u p e r f i c i a l l a y e r i s almost uniform, as p r e v i o u s l y assumed. W e can e s t i m a t e t h e t o t a l s t r a i n of t h e hardened l a y e r . The f o l l o w i n g s t r a i n h a r d e n i n g law h a s been d e t e r m i n e d by a n u p s e t t i n g t e s t performed on a m i l d s t e e l s h e e t covered with Teflon a s a l u b r i c a n t ( n e g l i g i b l e friction) [6] : (To = 97.3 + 6 1 3 . 8 MPa (1) From t h e r e l a t i o n between t h e h a r d n e s s and t h e y i e l d s t r e s s of a m a t e r i a l : Hv 3 (50 (2) and t h e extreme s u r f a c e h a r d n e s s v a l u e , we g e t (Tor730 MPa. Thus, from Eq.(l), t h e t o t a l s t r a i n v a l u e undergone by t h e hardened l a y e r can be e s t i m a t e d t o about one.

been p l o t t e d v s :

f o r coating s o f t e r than t h e s u b s t r a t e f o r c o a t i n g harder than t h e s u b s t r a t e These r e s u l t s a r e p r e s e n t e d i n F i g . 7 GPa, t h e measured b u l k w i t h H,0=1.2 hardness of t h e mild s t e e l .

(ii) The a a l v a n i z e d s h e e t b e f o r e and a f t e r friction T h e mean t h i c k n e s s of t h e z i n c l a y e r , measured by scanning electron microscopy, i s a b o u t 1 0 pm b e f o r e and after friction. The low and c o n s t a n t h a r d n e s s v a l u e a t 6 l e s s t h a n 6 pm, f o r t h e two c u r v e s ( F i g . 7 . b ) , shows t h a t t h e z i n c i s s o f t e r than the mild steel and almost As the penetration homogeneous. i n c r e a s e s , t h e s u b s t r a t e h a s an e f f e c t upon the measures: the hardness i n c r e a s e s g r a d u a l l y and t e n d s t o t h e m i l d s t e e l v a l u e HVO when t h e d e p t h i s greater. Comparing t h e r e s u l t s b e f o r e and a f t e r f r i c t i o n , it may b e observed t h a t the zinc layer hardness markedly d e c r e a s e s a f t e r f r i c t i o n : t h e r a t i o h of t h e z i n c s u r f a c e hardness t o t h e bulk v a l u e i s about 0 . 6 5 f o r t h e o r i g i n a l s h e e t and 0 . 5 a f t e r f r i c t i o n . The c o r r e l a t i o n between t h e o r y and experiments demonstrates f i r s t l y t h a t t h e h a r d n e s s of t h e z i n c c o a t i n g i s almost uniform b e f o r e as a f t e r f r i c t i o n , and s e c o n d l y t h a t f r i c t i o n h a s n o t modified t h e hardness of t h e s t e e l substrate.

275

2.4 xmc

pheoloaical laver

e v o l ~ i o n of

the

I n order t o approach t h e deformation mechanism o f t h e z i n c c o a t i n g , an u p s e t t i n g t e s t h a s been c a r r i e d o u t : t h e schematic diagram of t h e experiments i s presented i n Fig.8. A galvanized sheet of lasert e x t u r e d t y p e ( n o t i c e i n i t i a l roughness a t t h e edge of t h e p r i n t s represented i n F i g . 9 ) h a s been covered w i t h a t h i c k f i l m of Teflon so t h a t during upsetting the friction at the punch/sheet i n t e r f a c e s i s n e g l i g i b l e . The s h e e t specimen h a s b e e n punched a t d i f f e r e n t l o a d s F ( p r e s s u r e r a n g e u p t o 580 M P a ) ; t h e mean p r e s s u r e f o r e a c h p r i n t i s g i v e n by Eq. ( 3 ) :

s l i g h t l y deformed ( F i g . 9 . a ) . Then, a t high pressure values, an important i n c r e a s e o f t h e r o u g h n e s s may b e s e e n : the initial laser impression has completely disappeared ( F i g . 9 . c ) . This i s c h a r a c t e r i s t i c of a good l u b r i c a t i o n with a continuous s o l i d film.

-

p = - F (3) 2a L The f i n a l s h e e t t h i c k n e s s h r e l a t e d t o t h e i n i t i a l t h i c k n e s s ho y i e l d s t h e corresponding deformation:

F

I

PUNCH

T

A- A

L

2a

Fig. 8 S c h e m a t i c d i a g r a m o f a n u p s e t t i n g test

The t h r e e - d i m e n s i o n a l profiles p r e s e n t e d i n F i g . 9 show t h e e v o l u t i o n o f t h e s h e e t roughness a s t h e normal p r e s s u r e i n c r e a s e s (from 300 t o 580 MPa): a t t h e beginning, the sheet s u r f a c e keeps i t s o r i g i n a l roughness a p p r o x i m a t i v e l y , as t h e p l a t e a u x are

Fig.9 Some t h r e e - d i m e n s i o n a l p r o f i l e s of t h e g a l v a n i z e d s h e e t deformed by upsetting tests The r h e o l o g i c a l e v o l u t i o n o f t h e z i n c l a y e r h a s been followed thanks t o tests, as previously indentation d e s c r i b e d , p e r f o r m e d o n e a c h p r i n t . The c o n s t a n t a p p l i e d l o a d i s low e n o u g h s o the indenter stays i n the layer: its penetration i s a l m o s t a l w a y s t h e same, 8 s 4 pm. E a c h h a r d n e s s v a l u e i s a n a v e r a g e f r o m s i x m e a s u r e m e n t s made n e a r t h e p r i n t s edges, which a r e h i g h s l i d i n g zones. These r e s u l t s are p r e s e n t e d i n F i g . 1 0 . Owing t o t h e f a c t t h a t t h e s m a l l d i m e n s i o n s o f t h e p r i n t s (D=30 pm) a r e m e a s u r e d on a n i r r e g u l a r s u r f a c e , t h e r e s u l t s a r e s l i g h t l y s c a t t e r e d . B u t , it i s obvious t h a t t h e z i n c has softened f o r s t r a i n values greater than 0.3. Consequently, t h e p l a s t i c deformation of t h e zinc coating causes i t s softening d u e t o i t s dynamic r e c r i s t a l l i z a t i o n . By c o m p r e s s i o n t e s t s p e r f o r m e d on b u l k z i n c , S U Z U K I a n d A1 [ 7 ] o b s e r v e d v e r y s i m i l a r v a l u e s of i n i t i a l f l o w stress and s o f t e n i n g f o r s t r a i n above 0.3.

276

.

.

3 . 1 pescrzDtion

H v (Cl'a)

-

E

Rheological e v o l u t i o n of t h e z i n c l a y e r a s i t i s deformed w i t h o u t friction

Fig. 1 0

3 A MICROSCOPIC MODEL OF FRICTION Numerous a u t h o r s have l a i d down c o n t a c t models between t h e m e t a l and a hard a s p e r i t y of t h e t o o l , f o r s t u d y i n g f r i c t i o n phenomena a t a m i c r o s c o p i c s c a l e . These t h e o r i e s d e a l w i t h complex mechanisms such a s p l a s t i c d e f o r m a t i o n of a m e t a l wave, m e t a l adhesion on t h e [ 8 ] . They a s p e r i t y and m i c r o - c u t t i n g show t h e e f f e c t of two main p a r a m e t e r s on t h e e x i s t e n c e of e i t h e r of t h e s e mechanisms : t h e t o o l a s p e r i t y s l o p e ( t g a ) and t h e l o c a l f r i c t i o n c o e f f i c i e n t m a t the junction. I n o r d e r t o b e t t e r account f o r t h e r e a l phenomena ( s t r a i n hardening of t h e s u r f a c e s , p a r t i c u l a r rheology of c o a t e d . m a t e r i a l s ) , we have c o n s i d e r e d a p l a n e f r i c t i o n model. Those r e c e n t l y proposed for homogeneous perfect plastic [9,10,11], based upon materials kinematical o r s l i p l i n e f i e l d analyses, give similar t h e o r e t i c a l solutions as regards t h e f o r c e s involved. I t i s t h e r e a s o n why we h a v e d e v e l o p e d t h e most s i m p l e model: a kinematic version with t h r e e free g e o m e t r i c a l p a r a m e t e r s where s t r a i n hardening has been i n t r o d u c e d .

-

+"

-

th e

Droblm

W e consider a semi-infinite metallic body which p r e s e n t s a b u l g e (DEA) a t i t s surface (see Fig.11). A rigid indenter (whose s l o p e i s t g a ) r e s t s on t h e f a c e AE of t h e m e t a l wave, and i t s v e r t e x A o u t c r o p s a t t h e p l a n e s u r f a c e of t h e m e t a l . We p r o p o s e t o d e t e r m i n e t h e v e l o c i t y and deformation f i e l d s induced by t h e t a n g e n t i a l d i s p l a c e m e n t of t h e m a t e r i a l (applied v e l o c i t y UO p a r a l l e l t o t h e plane s u r f a c e ) . To s o l v e i t , we make t h e f o l l o w i n g assumptions: - p l a n e and s t a t i o n a r y flow - p l a n e f r e e s u r f a c e DE - i s o t r o p i c , i n c o m p r e s s i b l e , and workhardening m a t e r i a l - Tresca's local friction a t the i n t e r f a c e AE ( c o e f f i c i e n t iii) Given t h e p a r a m e t e r s 5 and a and the rheological constants of the m a t e r i a l , w e can deduce t h e v e l o c i t y f i e l d and t h e r e s u l t i n g normal and t a n g e n t i a l f o r c e s (N and T ) on t h e indenter.

3 . 2 Presentation

of

the

method

The k i n e m a t i c method u s e d , p r e s e n t e d e a r l i e r [ill, c o n s i s t s i n d e t e r m i n i n g among t h e g i v e n f a m i l y of v e l o c i t y f i e l d s , t h e one t h a t d i s s i p a t e s t h e l e a s t energy. W e f i r s t s t a t e a v e l o c i t y f i e l d of block r i g i d t y p e a s a f u n c t i o n of t h e t h r e e g e o m e t r i c a l p a r a m e t e r s a , b, d of t h e wave. As t h e metal flows a c r o s s a line of (tangential) velocity d i s c o n t i n u i t y ( i n t e n s i t y Av), t h e normal Vn is constant v e l o c i t y ( i n c o m p r e s s i b i l i t y ) and t h e t o t a l s t r a i n of t h e m e t a l v a r i e s by AT [ 1 2 ] :

(5) From t h e s t r a i n - h a r d e n i n g l a w , deduced from u p s e t t i n g t e s t s ( s e e 2 . 3 . 3 ) :

t h e f l o w s t r e s s a l o n g t h i s l i n e can be e s t i m a t e d by t h e formula: T

tool asperity

metal

Fig.11 Kinematic a n a l y s i s of t h e wave mechanism: a 3 p a r a m e t e r s model

of

r i g i d blocks

F i n a l l y , t h e t o t a l power c a l c u l a t e d , due t o t h e f r i c t i o n and t o t h e v e l o c i t y d i s c o n t i n u i t i e s , h a s been minimized by a c o n j u g a t e g r a d i e n t method. Thus, t h e l e n g t h s a , b , and d , r e p o r t e d t o t h e h e i g h t h of t h e w a v e f a r e d e t e r m i n a t e d a s f u n c t i o n s of t h e t h r e e p a r a m e t e r s a,= and n, t h e s t r a i n - h a r d e n i n g c o e f f i c i e n t .

271

3.3 P e s u l t g F i r s t , w e have v a l i d a t e d o u r model by comparing t h e r e s u l t s f o r n=O ( p e r f e c t p l a s t i c m a t e r i a l ) with t h o s e a l r e a d y p u b l i s h e d [ll] These p r e v i o u s works had shown t h e a p p l i c a t i o n l i m i t s of t h e models: f o r ,t hie) given f r i c t i o n c o n d i t i o n s ( f i x e d % wave model e x i s t s o n l y f o r a lower t h a n

.

a c r i t i c a l a n g l e a,. * A s r e g a r d s t h e k i n e m a t i c method w e have taken up, the minimization d e g e n e r a t e s towards t h e t r i v i a l s o l u t i o n f o r a>a,: i n t h i s case, o t h e r phenomena w i t h d i r e c t m a t e r i a l removing, such a s micro-cutting, occurs. * The e f f e c t of t h e s t r a i n - h a r d e n i n g c o e f f i c i e n t n on t h i s l i m i t curve (i?i,ac) i s represented i n Fig.12. - F o r a g i v e n s t r a i n - h a r d e n i n g law ( f i x e d n ) , t h e phenomenon i s a l l t h e more s t e a d y t h a t t h e a s p e r i t y s l o p e and t h e f r i c t i o n a r e lower. - T h i s wave e x i s t e n c e f i e l d widens a l l t h e more t h a t n i n c r e a s e s . E s p e c i a l l y , t h e m a t e r i a l s t r a i n - h a r d e n i n g makes t h e wave s t a b l e f o r E=l, t o t h e e x t e n t t h a t is relatively flat. the indenter Conversely, the material softening markedly reduces t h i s f i e l d .

-

0.0

0.4

0.6

0.8

Fig.13 V a r i a t i o n of t h e g e o m e t r i c a l p a r a m e t e r s , r e l a t e d t o h, w i t h ii~ s t r a i n - h a r d e n i n g i n f l u e n c e f o r a=aO a ) r e l a t i v e t h i c k n e s s of t h e sheared layer b ) l e n g t h of t h e bulge Experimentally, l o w s l o p e s ( a ~ 8 " ) are usually observed for tool a s p e r i t i e s . Consequently, t h e f o l l o w i n g r e s u l t s have been s e t up f o r t h i s l a s t v a l u e , i n o r d e r t o b e t t e r judge t h e s t r a i n - h a r d e n i n g i n f l u e n c e i n most of t h e cases. * F i r s t of a l l , c o n s i d e r t h e g e o m e t r i c a l e v o l u t i o n of t h e wave w i t h n ( F i g . 1 3 and 1 4 ) . Whatever t h e f r i c t i o n a l c o n d i t i o n s , t h e material h a r d e n i n g ( h i g h n v a l u e s ) increases t h e thickness, a , of t h e s h e a r e d l a y e r , and d e c r e a s e s t h e b u l g e slope (varying a s t h e i n v e r s e of d ) : strain-hardening tends t o spread t h e deformation f i e l d i n depth; conversely, t h e m a t e r i a l s o f t e n i n g c o n c e n t r a t e s it near t h e s u r f a c e .

m

z Others phenomena

\ \

(microcutting)

\

\ \ \o

0

5

10

15

1

a (degree)

Fig. 12 Three p a r a m e t e r s k i n e m a t i c model: s t r a i n h a r d e n i n g e f f e c t on t h e e x i s t e n c e f i e l d of t h e wave Fig.14 G e o m e t r i c a l e v o l u t i o n wave w i t h n f o r a=aO

of

the

* A s r e g a r d s t h e f o r c e s a p p l i e d on t h e T/N, may be indenter, the ratio interpretated as a global f r i c t i o n c o e f f i c i e n t of Coulomb t y p e . I t s l i g h t l y i n c r e a s e s w i t h n ( F i g .1 5 ) : p a r t i c u l a r l y f o r low l o c a l f r i c t i o n v a l u e s ( i i X o . 2 ) i t s influence i s negligible.

T N

*

For a metal a b l e t o be s t r a i n - h a r d e n e d ( n > O ) , t h e wave, s h a p e d by p l a s t i c d e f o r m a t i o n , i s s t a b i l i z e d , comparing t o a p e r f e c t p l a s t i c m a t e r i a l (n=O), a s t h e t o o l a s p e r i t y p a s s e s . Indeed, a s shown f o r a=8', t h e velocity f i e l d spreads towards t h e b u l k m a t e r i a l . * However, t h e s t a b i l i t y f i e l d of t h e i s considerably reduced f o r model other softening materials (n

1.5

2.0

2.5

3.0

3.5

The P-V diagram of different oxide

Fig.3

in the case with .oxide coating, its thickness is much

1.0

coating thickness

larger than that of oxide film,

For the same oxide coating thickness

therefore, when the load reaches Pcrl the

of 1 um, its load bearing capacity on the

boundary

by

substrate with different hardness shows even

the oxide coating and the first transition

lubrication can be maintained

bigger difference. The P-V diagram of three

is thus prevented, Only when the load reaches

substrate hardness is shown in Fig.4.

enough high

can be found that the effect of substrate

thoroughly

level, the broken,

oxide coating is

the

transition

It

from

hardness is much greater than that of coating

boundary lubrication to severe scuffing will

thickness. The load bearing capacity of coatings on the substrates of 16 HRC and

occur. Just this thick oxide layer enlarges significantly the extent of boundary lubrication region and increase the load bearing

4646 HRC are quite similar to each other and to the case without coating, But a big

capacity to a very high value. However, the

rise

oxide coating can’t bear the action of higher

reaches 70 HRC, the load bearing capacity

sliding speed and

bearing

can increase about more than 10 times and

capacity in the high speed range, its value

the effect is even more obvious in the high

of Pcr is even lower than that of specimen

speed range.

loses the load

appears when

the

substrate hardness

without coating. 3.2 The effect of coating thickness and and

substrate

hardness

on

the

P-V

diagram The P-V diagram of different oxide coating thickness is shown in Fig.3.

It can be seen

that,

o

thickness. the

The

lower

effect

of

the

speed, the

When

46 liRC

16 PRC

25013

the

1500 1030 539

0

-

Y

L

a

A.

U

thickness. But

in the high speed range the effect of thickness is vanished. (2)

A

-

2000

(1) The load bearing capacity increase along with the increasernent of oxide coating greater

- 70 R R C

3500. 5000

oxide coating thickness is

larger than 1 um, its effect is already not very obvious. However, if the coating is too thin, like specimen No.1, its

Fig.4

The P-V diagram of oxide coating on substrate

with

different

hardness

3.3 The microanalyses of oxide coatina The result of analysis by X-ray diffraction on specimen N O S is shown in Fig.5. It can be seen that the strength of Fe3 O4 peak

308

is very high and no peaks of other oxides appear

pY1

in the diagram of diffraction. It indicates

0.2

that the composition of oxide coating is only Fe3 0 4 , Owing to the high penetration power of X-ray the

min.

0.8 a1n.

F 3 N peaks come from the substrate

of nitride layer appear as well. Fig.6 shows

1.25 m1n.

the distribution of oxygen content in the oxide coating by WDX analysis, the thickness of

1.75 mln.

coating is about 1.5 um.

Fig.7

The distribution of Fe and 0 content along the depth of specimen taken from the boundary lubrication region (left) and the transfer of valence state M

VV of Fe (right)

293

0 min.

0.1 mi".

1 m1n.

. 2 mi".

Fig.5 The

disgram

of

X-ray

diffraction

of

oxide coating on nitrided steel Fig.8

The distribution of Fe and 0 content along the depth of specimen taken from

the

scuffing

region

(left)

and the transfer of valence state

M2,3VV of Fe (right) Fig.7 shows the distribution of Fe and 0 content along the depth of oxide film and the transfer of valence state M2,3VV of Fe, the specimen for analysis was taken from the boundary

lubrication region.

It

can be found that the oxide film of a Fig.6

The distribution of oxygen content in oxide coating analysed by WDX

In order to understand deeply the structure of oxide coating originally attempted

certain thickness can be formed due to the high

frictional temperature even

case

without

pretreated

oxide

in

the

coating.

According to the position of M2,3VV

peak

to do its AES analysis, but this work met

of Fe in the transfer diagram the valence

trouble due to the non-conductivity

of too

state of oxide film can be determined (10).

thick oxide layer. Considering that in essence

The bonding energy of two peaks on the very

the structure of oxide coating and oxide film

surface is 44 and 52 eV, it is corresponding

should be quite similar, this paper conducted

to the oxide Fe203. After 0.2 min. of sputtering the peak position is transfered

the analysis of AES on the specimens without oxide coating, the results are shown in Fig.7 and Fig.8.

to 48 eV, corresponding to Fe3 0 4 , until to 1.75 min. of sputtering it is remained

309

unchanged. Only when the sputtering time reaches

and FeO.

3.25 min. the peak position changes to 55 eV,

The second (11) sublayer is the transi-

it shows that the majority of Fe atoms are

tional layer of diffusion and reaction with

non-oxidized', only very

the thickness of several tens A, in which

a

few content of FeO

exist in this depth of oxide film. Fig.8 specimen

is taken

the

result

from

the

of

the content of oxygen is already lower than analysis

severe

on

scuffing

that of iron.

It indicates that the iron

has

been

not

yet

oxidized

sufficiently,

region. The diffence between it and Fig.7 is

however, the oxygen absorbed from the super-

that, on the surface there isn't already the

ficial layer can diffuse inward and oxidize

layer of high oxygen content, i.e. the super-

the iron element in this layer.

ficial oxide layer has been peeled during scuffing. The M2,3VV

rapidly

position of Fe

in transfer diagram proves the same result.

A large number of AES analysis of oxide

The most inner (111) sublayer is the stably

oxidized

layer with

the

thickness

0

more than several hundred A, in which the oxygen and

iron content are basically

in

film show the similar characteristics as Fig.7

stable state, but the content of oxygen is

and 8. So, it can be infered that the much thicker oxide coating must be of the same

much lower than that of iron, i.e. only very few iron element can be oxidized, the rest

behavior of oxide film, the only difference

are in free state.

is that the transfer from the state of Fig.7 to that of Fig.8 will be completed under the higher P,V condition.

Such a structure of oxide coating is not permanent but of the

4

THE MODEL OF STRUCTURE AND ROLE OF OXIDE COATING

in the dynamic balance

continuous breakdown friction

process.

and The

formation

in

transition

of

states in the P-V diagram can be explained by this simple model. When the wear occurs only in the I sublayer (Fig.lOa)

Based

on

above

analyses a

coating structure may

model

be proposed

of

oxide

as shown

in Fig.9.

coating can give full play

the oxide

to protecting

the surface of steel throughout the rubbing process. Because this layer is quite thick, it will take more time and higher load to wear away the whole layer. Only when the wear rate is too fast, the frontier of wear enters

the

I11 sublayer, i.e.

the

oxide

coating has been broken thoroughly (Fig.lOb), the direct contact of steels will result in scuffing.

Oxide coating

I 11

I11

Distance below t h e s u r f a c e

Fig.9 The model of oxide coating structure The superficial (I) sublayer is the friction-reductive layer with the thickness of about 1 um, whose main composition is

Oxide coa tine

Fe304, it plays the most important role to

I

I1 IT1

reduce friction of steels, The content of oxygen is higher than that of iron, but they are changing continously, oxygen decreases and iron increases from the very surface to depth. The composition in the deeper depth of this layer may be the mixture of Fe304

b)

Fig.10

Scheme of two caess of oxide coating a) Boundary lubrication failure: can be maintained b) Scuffing can

be caused

310

But it is not true that the larger the

5.4

bearing

capacity.

Because

the

Based

on the analyses of oxide film

by AES and XPS a model of three-sublayer

thickness of coating, the higher the load

structure of

superficial

layer of oxide coating with thickness more

proposed,

than 1 um is far from the substrate, which

of

gives the strong support to the coating,

explained.

oxide

with

states

coating

which P-V

in

has

the

been

transition

diagram

can

be

it may be worn off easily due to its weakness,

until

the

thickness

1

of

urn

is

6

ACKNOWLEDGEMENT

remained. Meanwhile, the thicker oxide may contain more and

larger defects, such as

pores or microcracks than the thinner oxides,

The authors would like to thank the senior engineer

Mrs.

Wang

Yi-Zhen

thus it is also easily damaged by delamina-

Institute

of

Mechanical

tion (11).

Technology

for

her

For the same thickness of oxide coating

nitrided

from

and

help

in

Beijing

Electrical

offering the

specimens with oxide coating and

the hardness of substrate plays even more

Professor Suen Yang-Ming from the Analytical

important role.

Center of Tsinghua University for his help

The weaker

the

substrate

is, the larger the deformation (elastic and plastic) will

occur. Once the weak

oxide

in the elctron oxide film.

spectroscopic analyses

of

coating loses the support of substrate, it will be broken easily, and when the growth

References

rate of oxide layer can't catch up with its the frontier of wear is

damage rate, i.e.

located in the I11 sublayer of the model, the scuffing will certainly occur. Only when

Kirschke, K. 'InvestiCZICHOS, H. and gations intofilm failure of lubricated concentrated contacts', Wear. 1972,

the hardness of substrate reaches enough high level, its deformation can be basically

22, 321.

Begelinger, A. and de Gee, A.W.J.

'Thin

prevented, the oxide coating can be preserved

film

point

reliably on the substrate and can bring the

contacts of

full play to protecting the surface of steel

1974, 28, 103-114.

lubricaton

of

AISI

sliding

steel' , Wear.

52100

Odi-Owei, S., Roylance, B.J.

from wear damage.

and Xie

L.Z. 'An experimental study of initial 5 CONCLUSIONS

scuffing and recovery in sliding wear

The

using a four-ball machine', Wear. 1987, 117, 267-287. Quinn, T.F.J. 'The role of oxidation

5.1

pretreated

oxide

coating

instead

of the oxide film formed naturallv in the rubbing Process can increase significantly

the' load

bearing

capacity

of

There exist an optimum thickness of oxide coating about 1 um.

Too thick

coating is of less effect and unecono-

mic. 5.3

wear

of

steel',

British

Journal of Applied Physics. 1962,

13,

33.

steels. 5.2

in the mild

The hardness of

substrate d a y s more

important role than thickness of oxide coating. When the hardrless reaches

Sakurai Toshio the

'Role of

lubrication

contacts',

of

Journal

chemistry in concentrated

of

Lubrication

Technology. 1981, 103, 473-485. Ludema, K.C. 'A review of scuffing and running-in of lubricated surfaces, with asperities and oxides in perspective',

c

enough hinh

level, the deformation of

-substrate can

be

basically

the oxide coating can bring

prevented the full

play to reducing friction and wear of steels.

Wear. 1984, 100, 315-331. Zhao, Yong-Wu, Liu, Jia-Jun and Zheng, Lin-Qing 'The study on P-V diagram of steel/steel lubrication',

rubbing Journal

pair of

under Tsinghua

31 1

University. to be published, 1989. Zhao Yong-Wu, Liu Jia-Jun , Zheng LinQing 'The new development in study on

P-V diagram of steel/steel rubbing pair lubrication', to be published 1989. Zhao Yong-Wu, Liu Jia-Jun, Zheng LinQing

'The effect of hardness on

the

P-V diagram of steel/steel rubbing pair under

lubrication',

to

be

published

1989,

(10) Seo, S. et a1 'An AES analysis of oxide films on iron', Surface Science. 1975, 50, 541-552. (11) Komvopoulos, K., Suh, N.P. and Saka,

N. 'Wear of boundary lubricated metal surfaces', Wear. 1986, 107, 107-132.


SESSION XIV NEW TOOLS AND MODELS Chairman :

Professor B. Jacobson

PAPER XIV (i)

A survey of research in acoustic microscopy applied to metallurgy

PAPER XIV (ii)

Detection of interface defects in layered materials by photothermal radiometry

PAPER XIV (iii)

A low cycle fatigue wear model and its application to layered systems


315

Paper XIV (i)

A survey of research in acoustic microscopy applied to metallurgy J. Attal, R. Caplain, H. Coelho-Mandes, K. Alarni and A. Saied

ABSTRACT

The scanning acoustic microscope is a new non destructive technique of investigation at a microscopic scale which is discussed throughout this paper. Specific applications are shown in the field of metallurgy for surface and in-depth examination with high resolving power.Imaging

interfaces between materials

is shown and local

quantification of elastic properties are reported.

After

1 INTRODUCTION

In

the

field

of

metallurgy,

many

a

technique

general

survey

principles,

we

of

the

show

some

techniques are available for surface

metallurgical

analysis.

Scanning Acoustic Microscope (SAM) such

The techniques are mostly

interface

destructive and concern thickness or

as:

in-depth investigation generally less

analysing,

metallography

non-destructive techniques which can a

determination.

1

micrometer.

Among

bonding,

cohesion

the

than

applications

and

of

thin

the

layer

measurements,

elastic

constants

p r i o r i compete with acoustic microscopy we will say : eddy currents which give

2 PRINCIPLES OF THE TECHNIQUE (1,2)

informations about flaws in metals and X The physical phenomenon underlying the

rays which can tell about elasticity of material

especially

through

their

SAM is the interaction of an ultrasonic

diffraction techniques. But none has the

wave with

flexibility of ultrasounds which cover

(density, velocity, viscosity) of the

several decades in terms of frequency and

sample to be examined. This acoustic wave

thereby

is

optimize

resolution

and

the mechanical properties

generated

by

a

piezoelectric

penetration of a focused beam governing

transducer, typically ZnO or LiNb03 which

the final image.

transforms a high frequency electrical

316

signal

into

an

ultrasound

wave

p r o p a g a t i n g a t t h e same f r e q u e n c y . means

of

a

spherical

By

or

near

surface

imaging

and

charac-

terization.

sapphire lens a

convergent a c o u s t i c beam wave i s f o c u s e d

2 - 1 Subsurface t e s t i n g

on t h e sample s u r f a c e . A c o u p l i n g f l u i d

is

necessary

for

acoustic signal

transmitting

from t h e

the

lens t o the

One of t h e most p r o m i s i n g a p p l i c a t i o n s of t h e SAM i s t o probe deeply

(more t h a n

sample. Water i s commonly u s e d , but t h e

one a c o u s t i c wavelength) i n t o m a t e r i a l s .

i n s t r u m e n t performances

increased

T h i s a b i l i t y a r i s e s from t h e f a c t t h a t

when l i q u i d m e t a l s such a s mercury a r e

t h e r e i s p r a c t i c a l l y no a t t e n u a t i o n of

employed. I n t h e r e f l e c t i o n mode which

the

covers a wide range of a p p l i c a t i o n s , t h e

compared t o l i q u i d s . Moreover, t h e l a r g e

SAM o p e r a t e s

a

with

are

single

lens

for

acoustic

energy

in

most

solids

change i n sound v e l o c i t y o c c u r i n g a t t h e

t r a n s m i t t i n g and r e c e i v i n g t h e a c o u s t i c

couplant liquid-sample

interface leads

s i g n a l . T h e image i s o b t a i n e d b y moving

t h e a c o u s t i c waves t o be r e f r a c t e d i n s i d e

t h e focused beam on t h e sample. This can

t h e sample,

be c a r r i e d o u t b y scanning t h e sample i n

r e f r a c t i o n as i n Optics. P e n e t r a t i n g i n t o

two p e r p e n d i c u l a r d i r e c t i o n s r e l a t i v e t o

material,

obeying t h e

same l a w s o f

t h e b u l k waves

(longitudinal

by

and t r a n s v e r s e ) a r e r e f l e c t e d where t h e y

d i s p l a c i n g t h e l e n s towards t h e o b j e c t .

encounter d i s c o n t i n u i t i e s i n t h e e l a s t i c

The r e s o l u t i o n i s determined b y t h e f o c a l

p r o p e r t i e s , i .e, where a c o u s t i c impedance

spot

the

( d e n s i t y x sound v e l o c i t y ) changes. Thus,

d i f f r a c t i o n t o about one wavelength. I n

t h e y g i v e i n f o r m a t i o n on t h e i n t e r n a l

t h e h i g h frequency range (above 1 GHz),

features

t h i s resolution

d e f e c t s and inhomogeneities a t s e v e r a l

the

lens.

Focusing

and

size

is

is

obtained

limited

by

i s comparable t o t h a t

of

hundreds

achieved by o p t i c a l microscopes.

of

surface. The main r e a s o n s t h a t make t h e SAM a

the

and

micrometers

Owing

attenuation

material

to

detect

below

acoustic

occuring

mostly

the wave

in

the

f o r deep i n v e s t i g a t i o n s

powerful t e c h n i q u e employed where o t h e r s

coupling f l u i d ,

a r e i m p r a c t i c a l o r provide i n s u f f i c i e n t

t h e SAM employs low f r e q u e n c i e s r a n g i n g

r e s u l t s are : f i r s t , a c o u s t i c waves a r e

from

s e n s i t i v e t o t h e e l a s t i c p r o p e r t i e s of

r e s o l u t i o n between r e s p e c t i v e l y 5 0 and 1 0

materials

;

micrometers w i t h i n a specimen, depending

different

forms,

second,

they

i . e .,

appear

in

longitudinal,

t r a n s v e r s e and s u r f a c e modes. This l a t t e r p a r t i c u l a r i t y allows two p o s s i b i l i t i e s of imaging

by

the

instrument

which

are

a p p l i e d t o s u b s u r f a c e t e s t i n g and surface

100 t o

500

MHz.

This

allows

a

on t h e n a t u r e of t h e sample. In

the

instance, control circuits

microelectronic the

SAM

has

been

non-destructively throughout t h e

field, used

for to

integrated

thickness

of

317

t h e i r substrate, i n order t o evaluate for

2

- 2 Surface

example, t h e wires b o n d i n g on t h e c i r c u i t

eutectic

and

charac-

terization

( 3 ) . I n t h e same way,

m e t a l l i z a t i o n pads different

imaging

processes

like

welding,

etc...

bonding,

have

been

d i s t i n g u i s h e d and inspected t o o ( 4 ) . This k i n d of a p p l i c a t i o n has been c a r r i e d o u t on power s e m i c o n d u c t o r m o d u l e s .

The s e c o n d i m p o r t a n t a p p l i c a t i o n i s s u r f a c e imaging and t h e d e t e r m i n a t i o n of t h e e l a s t i c p r o p e r t i e s of m i c r o s t r u c t u r e s l o c a t e d a t less t h a n o n e w a v e l e n g t h u n d e r

Indeed,

f o r e l e c t r i c a l and thermal c o n d u c t i v i t y ,

t h e sample s u r f a c e .

High r e s o l u t i o n is

therefore

and

required

the

operating

t h e d i f f e r e n t levels o f t h e s e components f r e q u e n c y c a n b e e x t e n d e d b e y o n d t h e GHz

a r e made o f v a r i o u s m a t e r i a l s and c o n t a i n range. t h e r e f o r e d i f f e r e n t bonding a r e a s .

I n t h a t case, t h e acoustic signal

The a r i s i n g from t h e sample is t h e r e s u l t of

SAM

h a s b e e n employed t o c h e c k j o i n t s i n a n i n t e r f e r e n c e e f f e c t b e t w e e n two k i n d s

order t o evaluate the circuit r e l i a b i l i t y of and

to

eventually

know

the

cause

waves

propagated

in

different

of d i r e c t i o n s ( f i g u r e 1 ) : t h i s phenomenon

f a i l u r e s , w h i c h may a l l o w t h e improvement has

of

the

assembling

process.

Most

no

counterpart

theory

were

experiments

achieved

at

i n electromagnetic

of and

is

responsible

for

the

in

the

200 MHz contrast

variations

occuring

w h i c h seems t o be a n a d e q u a t e f r e q u e n c y surface

imaging.

This

variation

of

f o r t h e resolution of d e t a i l s expected. contrast

is

more

displayed

when

the

Mercury i s o f t e n u s e d a s a c o u p l i n g f l u i d lens-sample spacing i s decreased. s i n c e i t i s more p o w e r f u l t h a n w a t e r f o r s u b s u r f a c e i m a g i n g . T h i s a r i s e s from t h e

f a c t t h a t m e r c u r y impedance i s s i m i l a r t o t h a t of

most

s o l i d s which r e d u c e s t h e Y

impedance d i s c o n t i n u i t y a t l i q u i d - s a m p l e interface

and

improves

the

energy

p e n e t r a t i n g t h e sample. Moreover, b e i n g

f o u r times l e s s a b s o r b e n t t h a n w a t e r , mercury a l l o w s

t o double t h e operating

f i g 1 schematic d i a g r a m showing R a y l e i g h

frequency and t o i n c r e a s e consequently

wave p r o p a g a t i o n

t h e r e s o l v i n g power by a f a c t o r o f a b o u t

2 . However, it c a n amalgamate w i t h m e t a l s s u c h as g o l d , copper, silver e t c . . so, t o a v o i d damages,

a protective thin layer

deposited

the

required.

on

sample

surface

is

Furthermore, the

i n t h e non-scanning s t a t e ,

v a r i a t i o n of t h e r e f l e c t e d acoustic

signal

recorded

as

a

function

of

the

s a m p l e d e f o c u s i s a v a l u a b l e method f o r measuring

quantitatively,

on

a

318

microscopic

scale,

properties

of

explaining

the

surface

the

the sample,

contrast

images.

acoustic and

for

observed

Several

authors

transducer

reflectance

connected

f u n c t i o n and z

thickness

resolution

variations.

In

the

that

f i l m

manner,

l a c k of a d h e s i o n o f d e p o s i t e d l a y e r s and

have

i n h o m o g e n e i t i e s i n l o c a l i z e d r e g i o n s can

where V i s t h e v o l t a g e r e c e i v e d on

the

lateral

in

s t u d i e d t h i s t e c h n i q u e which i s c a l l e d V(z)

high

to

the

t h e sample

be detected. Moreover,

ion implantation

and d e f e c t

s t r u c t u r e s such a s c r a c k s ,

v o i d s .etc..

c h a n g e t h e R a y l e i g h wave

v e l o c i t y and c a n be t h e r e f o r e o b s e r v e d .

defocusing d i s t a n c e . V ( z ) curves e x h i b i t a

pseudo-periodic

response

which

3 -METALLURGICAL APPLICATIONS

r e p r e s e n t s a r e a l a c o u s t i c s i g n a t u r e of t h e m a t e r i a l s i n c e it c o r r e s p o n d s t o t h e

it

As

has

been

said

in

the

upper

p e r t u r b a t i o n i n t h e propagation of t h e

s e c t i o n , t h e most i n t e r e s t i n g r e s u l t s a r e

R a y l e i g h waves d u e t o t h e n a t u r e o f t h e

obtained

i t s topology.

the

acoustic

beam

is

by

u n f o c u s e d . The p a r t o f t h e specimen under

m e a s u r i n g t h e c u r v e p e r i o d i c i t y Az , t h e

e x a m i n a t i o n i s s e t t l e d w i t h i n t h e volume

surface

and

Thus,

when

of Rayleigh determined

wave

velocity

according t o

can

VR

the

be

following

relation :

the

focal

defined

by

spot

whose p o s i t i o n

the

lens-sample

according

t o

the

propagation.

O f course,

laws

is

distance of

wave

one has t o t a k e

i n t o a c c o u n t t h e e n e r g y damping down which i s a f u n c t i o n o f f r e q u e n c y , Imaging w h e r e v i i s t h e v e l o c i t y i n t h e l i q u i d and and F i s t h e frequency ( 5 ) .

t e s t and e v e n t u a l l y i t s c r y s t a l l o g r a p h i c

Rayleigh independent

For

velocity but

crystallographic grain

bulk

structure.

specimens, is

orientation a

the

with

and

metallic

thin

layer

v e l o c i t y of t h e s u r f a c e wave i s a l t e r e d and becomes a f u n c t i o n o f b o t h

bonding,

of

cohesion

thin

layers,

m e t a l l o g r a p h y , r o u g h n e s s and e l a s t i c i t y .

3

-

1 I n t e r f a c e v i s u a l i z a t i o n o f bonded

materials

the

d e p o s i t e d on a s u b s t r a t e , t h e p r o p a g a t i o n

and

a

the

frequency

change

For

of

V(z)

s t r u c t u r e c a n g i v e some i n f o r m a t i o n s upon

Hence, w e can i d e n t i f y t h e m a t e r i a l u n d e r

orientation.

signature

frequency

l a y e r t h i c k n e s s . The V ( z ) t e c h n i q u e

i s t h e n o f a g r e a t i m p o r t a n c e s i n c e it i s

possible t o characterize a t h i n deposited f i l m and t o m o n i t o r p o i n t by p o i n t w i t h a

The

visualization

of

the

material

under t h e s u r f a c e , w i t h o u t any damage, i s the

most

spectacular

technology. makes

thin

For

the

foils,

sight

this

of

metallurgist and

who

proceeds

to

s u c c e s s i v e a b r a s i o n s i n o r d e r t o have d e p t h i n f o r m a t i o n s by m e t a l l o g r a p h y , t h i s non

destructive

aspect

is

very

319

fascinating. Any perturbation of the acoustic impedance makes possible the observation of structures different from the matrix. Then, a free space, like disbonding or a bubble which exhibits a strong impedance discontinuity induces a high contrast in the image. In the same way of investigations, one is interested by the detection of inclusions, cracks etc

...,

fig. 2

Delamination zone of a dielectric

all sorts of defects interesting thin layer (F

=

1 GHz)

the industrial engineer.

This possibility is very useful for

3 - 2 Adhesion of coatings

making electronic devices, for multilayer One of the most crucial problem is to

analysing etc...

control and to improve our understanding about adhesion of coatings. All surfaces covered with

Since the mechanism connected

of

Metallography

to

a

candidates

for

It is well known that answering a

is

metallurgical problem should begin by a

mechanical

metallographic analysis which can be

adhesion

problem, no doubt that ultrasounds are good

-3

protective layers deposited

by different techniques are concerned.

directly

3

this

type

correlated to processing (6)

.

of

the

thermomechanical

investigation. In many processes, the grain boundary In the figure 2 we can see an example is an essential parameter. For instance of a delamination zone of a dielectric it controls the properties but also the thin

layer upon

its substrate.

The ruin

of

materials.

During

the

disbonding is characterized by numerous solidification the thermodynamics shows interference fringes. that

boundaries

may

contain

high

Quantitative measurements by means of concentration of impurities, like sulfur, V(z) signature help to characterize the rejected

in

the

important

example

liquid.

Another

uncohesion between the layer and the substrate.

Then,

it

is possible

affects

sintering

by technics where the boundaries control the

scanning the sample to count and map the densification kinetics. uncohesion

areas

between

the

two More than optical metallography wich

materials. gives only planar informations, acoustic microscopy,

sensitive

technique

to

v a r i o u s m i s o r i e n t a t i o n s of g r a i n s between

reference

them,

p o l i s h e d . I f t h i s s u r f a c e i s rough,

can f o l l o w t h e g r a i n boundary i n

depth.

This

is

an

introduction

of

the

imaged

following

has

the

disturbs

to

be

induced

well

the

surface

a c o u s t i c wave and i t s p r o p a g a t i o n w i t h i n

in-depth metallography. In

relief

surface

we

example

have

a p i e c e of copper a t a d e p t h of

1 5 0 pm under t h e s u r f a c e . The o p e r a t i n g

t h e f i r s t wavelength of t h e m a t e r i a l . The

two

following

p o s s i b i l i t i e s of

examples

show

the

s u r f a c e and i n t e r f a c e

roughness imaging. frequency was 2 0 0 MHz. The sample s u r f a c e has

been

only

polished,

and

we

I n t h e f i r s t case

( f i g . 4 ) which i s a

can

c l e a r l y s e e t h e g r a i n s t r u c t u r e s without

p r i n t i n t o Zr02 of t h e diamond p i n used f o r m i c r o h a r d n e s s measurements,

any e t c h i n g .

observe t h e q u a s i square print

delineating

interferences

a

form of

zone

pattern

w e can

of

this

surface

which g i v e s t h e

contour l i n e of t h e topography. The d e p t h of

this

print

can

be

estimated

by

counting t h e f r i n g e s d i s t a n t b y h / 2 . I t is also

fig. 3

A c o u s t i c metallography of copper

a t 1 5 0 pm depth (F

= 200

MHz)

I n t e r f e r e n c e f r i n g e s appear p a r a l l e l to

some

grain

boundaries.

The

space

between t h e s e f r i n g e s g i v e t h e r e l a t i v e o r i e n t a t i o n of t h e boundary w i t h r e s p e c t fig.4

Print

of

h diamond p i n

for

t o t h e s u r f a c e . The image t a k e n a t t h a t

microhardness depth

in

Zr02

(F

=

1

( 1 5 0 pm) i s n o t d i s t u r b e d b y t h e

GHz) surface defects.

I f t h e sample s u r f a c e

h a s been p o l i s h e d b u t

not

etched the

o b s e r v a t i o n of g r a i n s i s easy ( f i g . 3

.

possible

to

observe

the

microcrack

induced a t t h e a n g l e s of t h e p o i n t . A t l a s t , l a r g e f r i n g e s around t h e p o i n t can

3 -4

S u r f a c e and i n t e r f a c e roughness

b e i n t e r p r e t e d a s t h e change of r e s i d u a l

I n o r d e r t o have a c o r r e c t e v a l u a t i o n

stresses. I n t h e second case ( f i g . 5 ) , w e see an

of t h e n e a r s u r f a c e c h a r a c t e r i s t i c t h e

example of b r a z i n g d e f e c t between copper

T

c o n d i t i o n s , l o n g i t u d i n a l waves c a n a l s o be

generated

detected

and

t o

by

V(z)

technique.

According

this

new

possibility,

Young a n d P o i s s o n Modulus

c a n be f u l l y d e t e r m i n e d . In

figure

6 w e show a n e x a m p l e o f

t h e s e d e t e r m i n a t i o n s made on a t u n g s t e n sample.

f i g . 5 B r a z i n g d e f e c t between c o p p e r and s t a i n l e s s s t e e l . (F= 2 0 0 MHz)

picture,

the

central

characterizes straight

spot

black

[

OUTPUT VOLTAGE

0

500

t h e d i s b o n d e d zone and

lines indicate that the steel fig. 6

h a s been b r u s h e d b e f o r e b r a z i n g .

V ( z ) curve of tungsten p l o t t e d

at

change

of

elasticity

1 3 8 MHz

with

as

mercury

coupling l i q u i d .

3 - 5 M i c r o e l a s t i c i t y measurements

Local

zCm)

1500

1000

can

be The volume o f a n a l y s i s a t t h e o p e r a t i n g

measured w i t h h i g h a c c u r a c y u s i n g t h e V(z)

technique.

This is of

t h e upmost

i m p o r t a n c e f o r s t r e s s mapping, which c a n locate cracks,

f r e q u e n c y o f 138 MHz i s o f t h e o r d e r o f

l i k e w i s e f o r f a t i g u e and

lmm2x10 pm. was

The

measured

R a y l e i g h wave v e l o c i t y

from t h e

frequency

part

of

the

p l a s t i c i t y which can be m o n i t o r e d a s w e l l

oscillations in

a s homogeneity i n s u r f a c e p r o c e s s i n g .

c u r v e , whereas t h e l o n g i t u d i n a l v e l o c i t y

I n p a r t 2 - 2 , w e have shown t h a t from

the

high

left

was d e t e r m i n e d from t h e low f r e q u e n c y

t h e p e r i o d i c i t y o f t h e V ( z ) c u r v e , w e can

oscillations in the right part.

d e t e r m i n e t h e R a y l e i g h wave v e l o c i t y .

values are t h e following:

This

is not

sufficient

if

we

are t o

o b t a i n p r e c i s e l y t h e Young Modulus of t h e material studied. F o r t u n a t e l y , i n a r e c e n t work ( 7 1 , w e have demonstrated t h a t ,

under specific

V,

=

2545 m / s

VL

=

Their

2814 m / s

g i v i n g a Young Modulus E

=

4 4 6 GPa

(8)

322

4

-

(4) A.

CONCLUSION

SAIED,

J.M.

w e have i n v e s -

Journal

tigated

metallurgical

suppl.au

applications results

of

of

are

the

SAM.

directly

a c o u s t i c images,

Qualitative

obtained

whereas V ( z ) t e c h n i q u e

new

This

way

of

de

physique.

no9,

Colloque

C4

(1988)

p.

49

tome

C4.801

from

g i v e a d i r e c t measurement o f t h e e l a s t i c properties.

CHAFFAUT,

DU

SAUREL and J . ATTAL

Through t h e s e e x a m p l e s , some

C.AMAUDRIC

non

(5) R.D.WEIGLEIN: IEEE

A c o u s t i c MicroMetrology

Transactions

on

sonics

and

u l t r a s o n i c s . V o l . SU32 no 2 ( 1 9 8 5 ) .

d e s t r u c t i v e i n v e s t i g a t i o n f i r s t developed f o r f l a t s u r f a c e s and i n t e r f a c e s c a n b e extended

to

cylindrical

symetries.

Acoustic

propagation

in

developed

models

different

i n order

or

to

spherical

d e s S u r f a c e s t 1 Ed. b y D .

for

CAPLAIN (EYROLLES 1 9 8 8 ) .

wave

the

give a

of

presence

DAVID e t R .

materials are complete

i n t e r p r e t a t i o n o f t h e o b s e r v e d phenomena like

( 6 ) "MBthodes U s u e l l e s de C a r a c t e r i s a t i o n

longitudinal

skimming waves i n t h e V ( z ) c u r v e s .

( 7 ) J . ATTAL, ALAMI,

Role

C.AMAUDRIC DU CHAFFAUT,

K.

H . COELHO-MANDES and A . SAIED: of

acoustic

the

fluid

in

.(to

be

C.AMAUDRIC

DU

coupling

signature

V(z)

pub1 i s h e d ) REFERENCES ( 8 ) J.M.SAUREL,

(1) A. BRIGGS

CHAFFAUT, 0 . D U G N E a n d A . GUETTE

introduction

"An

to

scanning

a c o u s t i c microscopy"

Microscopy Handbook

( 2 ) J.M.SAUREL,

A.

Ecole du CNRS

Society:

12 ( 1 9 8 5 ) .

SAIED and

J. ATTAL

Saint-Valery s u r Some

a v r i l 1988 ( t o be p u b l i s h e d ) .

(3) J . ATTAL, A. SAIED, J . M . C.C.

SAUREL and

LY

Acoustical Imaging V o l . 1 7 ( P r o c e e d i n g of

17th

May-June

International 1988)

Ed.

by

Symposium Shimizu,

C h u b a c h i a n d K u s h i b i k i Plenum P r e s s New-York 1989

European M a t e r i a l s R e s e a r c h S o c i e t y S t r a s b o u r g F r a n c e May-june

Microscopical

Royal

K.ALAM1,

be p u b l i s h e d ) .

1989 ( t o

323

Paper XIV (ii)

Detection of interface defects in layered materials by photothermal radiometry M. Heuret,

E. Van Schel, M. Egee and R. Danjoux

Photothermal radiometry is a promising method for the non destructive testing and the characterization of thin materials and has already been suggested to study various kinds of layered materials. A bonding defect at the interface of two materials leads to a thermal contact resistance which is usually low and hardly detectable with the existing NDT techniques. We wish to present here the results of three studies of modulated photothermal radiometry for which such defects can be observed. At first , we have studied several metallic-electrochemically induced deposits. A statistical treatment allows to distinguish various samples, when prepared in different conditions. Then, a similar coating (black polyurethane paint) has been deposited on two plates (steel and glass), for which the bonding strength is known as different. Evidence is given of the existence of an interface thermal resistance for the coating deposited on glass. At last, we have studied the mechanical contact quality between two coaxial metallic pipes. A mathematical model has been developed, including a focalized laser excitation. We were thus able to measure very low contact resistances (about S.I.).

1 INTRODUCTION

We have first studied the case of electrolytic deposits on a metallic substrate which has been submitted to various chemical preparations in order to cause adhesion

Photothermal radiometry is a non destuctive testing method which has been developed for a few years for thin layers. The knowledge and evaluation of the thermophysical properties of the coating and of the support generally constitute the first stage for such a testing method. It can then allow to detect various types of defects inside the coatings, or at the coating-substrate interface. We can thus, with the help of that method, obtain information about the nature and the quality of the mechanic contact at the layer-sublayer interface, as both influence the value of the thermal contact resistance. We briefly present here the results of three studies of photothermal radiometry under modulated excitation, which show the presence of adhesion defects at the interface of layered materials.

alterations. A statistical exploitation of the results allows to confirm the classification, established in relation with the modes of the preparation. Then, we have studied the properties of a similar paint deposit on various sorts of substrate (metal and glasses) leading to different adhesion qualities. These properties can be interpreted in term of thermal resistances of the interface thanks to an unidimensionnal mathematical model. At last, we have been able to characterize the crimping of two coaxial metallic pipes. Because of the conductive nature of the samples, we had to use a tridimensionnal model. The good accordance between the theoretical calculations and the experimental results allows to foresee the elaboration of a convenient and automatic testing method for the crimping of metals.

324

2 PRINCIPE OF PHOTOTERMAL RADIOMETRY A continuous laser beam of low power (a few watts), mechanically modulated (frequency between 10 Hz and about 200 Hz), is send on to the surface of a material. The part of the absorbed radiation produced a local and periodical rise of temperature, which creates an internal thermal flux. This variation is observed and measured from a distance with a localized infrared detector [l]. The photothermal signal depends on different parameters according to the excitation (spectral energy, frequency.. .), the nature of the material (optical absorption coefficient, thermal diffusivity.. .), the geometry of the materials, and the nature of its interface (thickness, layered structure, contact thermal resistance between layers.. .) [2].

3 RESULTS 3.1 Adhesion of electrolvtic deuosits on a metallic substrat. The first results presented here concern industrial parts in solid brass covered with a layer of cobalthickel electrolytically deposited on a continuous conveyor-belt that is completely automatic. Very slight variations in the preparation conditions can lead after some time to the damaging of the deposited layers. We have tested a few parts, chosen from a lot which had undergone a similar fabrication as well as a similar manufacturing and, which were then prepared in different chemical conditions that were likely to induce different adhesion qualities between the support and the deposit. We have used 5 sorts of parts prepared in the following conditions : l-optimal preparation of the substrate : electrolytic polishing before the electrolytic deposit. 2-use of alcohol before polishing. 3-stains caused by a wetting agent before the deposit. 4-use of sulfochromic acid, rinsing, drying and 30 mn wait before the deposit. 5-intermediate deposit of a nickel iron layer. Each part to be studied is set on a X-Y stage that is monitored by a computer. This one is also responsible for the excitation function. A point of the test part provides us with a phase value and an amplitude value. A phase and/or an amplitude Cartography is then obtained by displacement of the sample (the laser beam remaining fixed). The results are saved in the form of binary files with a dynamic coded on a byte, an image analysis software allows to read and treat.

Figure l a and figure l b represent amplitude cartographies obtained on 1 (optimal preparation) and 3 (bad preparation) parts under the following conditions : modulation frequency 15 Hz, argon laser power 1.5 W, 1920 measurements points (15 lines of 128 .columns :measured area 32 * 7.5 mm2), the total time-duration of the measurement is about 200 mn.

Fig. l a Amplitude cartography on brass part, covered with CoNiP :optimal preparation.

Fig.lb Amplitude cartography on brass part, covered with CoNiP: bad preparation.

Figure 2 represents the results of a statistical treatment on the 5 sorts of parts.We can find there, for the phase and amplitude the histograms of the average and of the normalized standard deviation. The analysis of the normalized histograms allow a rapid comparison - which is hardly possible when working on primary values. Yet, it must be remarked that the amplitude histograms depend not only on the properties of the interface deposit/substratebut also on the aspect of the surface - a parameter which has nothing to do with the one we wish to measure.The evolution of the 1 to 4 standard deviations perfectly follows the predifined classification; as far as the 5th one is concerned the extra layer of iron seems to modify noticeably the bonding characteristics without our being able to tell that the quality be seriously altered (normalized values are even better than for 3 and 4).

325

3.2 Adhesion of a coat of paint onto various substrates A coat of black polyurethane paint has been applied onto several steel (Q Panels) and glass supports. The thickness checking of each one has been achieved with a PIG gauge (the coating has been incised throughout its whole thickness and then observed with an optical microscope). This operation has also allowed us to remark the poor adhesion in the case of the glass support; indeed there was some detachment along the cut. The optical absorption coefficient at the excitation wavelength has been estimated to a value of 220000 m-l (spectrometer PERKIN ELMER LAMBDA 9). The effects of the diffusion of light have been neglected. Figure 3 shows the phase lag and the amplitude of the photothermal signal according to the modulation frequency. Both have been obtained for a 12 pm thick-coat of paint on a 0.8 mm thick-steel plate. The confrontation of experimental results with calculations performed with a bilayered unidimensionnal model [3] allows us to determine the thermophysical properties of the paint : -thermal diffusivity = 1.06 m2 s-l -considering a very good mechanical adhesion of the paint on that type of support, we have let the interface thermal resistance to be nil

We can now find on figure 4, the results obtained with a glass support, with a 15 pm thick-coat of paint. We observe a good accordance in phase as well as i n amplitude between the experimental results and the theoretical ones when the contact thermal resistance is 4 m2 K W-l. This value is equivalent to that a 1.2 pm thick-blade of air would have, to the atmospheric pressure. Having checked that the surface of glass was much smother (roughness R, = 0.01 pm) than that of steel (roughness R, = 0.5 pm), we must thus consider that the coating behaves - in the case of glass- as a weakly adhering layer that is quite independent from its support.

Fig.2 Phase and amplitude histograms on 5 differents parts.

326

“lase

PhaSC .30

0

Glms subsualc. Thcorctical c m c

t

wilhR=O

-40

Glass subsuaw.. Experimental cur\’c

.lo

.5c 20

Glass subsuatc. Tlwretical curve

.6t

uiilh R = 4 10

-3c

-’

Steel subsuate. Thcoreucalcurve

-71 100

0

200

-4c I

100

0

Frequency

Amplitude (Arb. Unils)

Amplitude (Arb. Units) 200

80

Glass substrate. Theoretical curvc 150

-5

wilh R = 4 10 70

Glass substrate. Experimcnlal curve 100

60

5c

j l ~ substrate. s Thcorctical curve

wih

5c

r 1.0, then there is a tendency for positive peaks in the friction force, and if D < 1.0, then negative deviations tend to characterize the frictional behavior. Friction force data for a series of five passes of sapphire and steel balls on the plate-like diamond film are shown in Fig. 4(a) and (b). The nominal value and deviation of the sliding friction coefficient are given at the right of each trace. The two prominent peaks in the sapphire experiment produced deviations greater than 1.0, and an anomalous dip produced deviations less than 1.0 for the steel experiment. One might consider how characteristic the deviation is of the majority of the sliding contact if it is affected strongly by a single anomalous event; however, the fact that such a variation can occur is valuable in attempting to predict the best and worst possible behavior for given film-slider combinations. Table 1 summarizes the friction coefficient data for one- and five-pass runs on three diamond film morphologies, and Fig. 5(a) and (b) plot the nominal values for the friction coefficient as a function of number of passes. In general, the one-pass friction values corresponded to the first-pass values of the five-pass experiments. One exception was for the plate-like morphology specimen rubbed on the steel, but in this case, there was a pronounced drop in friction at one point in the trace on the five-pass experiment [see this example in Fig. 4(b). This localized anomaly was not observed on the single-pass experiment done parallel to it about 2.0 mm away on the same film and therefore may have been due to a small heterogeneity in the film structure. Such heterogeneities are not uncommon in films of this type.

5 DISCUSSION The friction coefficient values obtained in the current experiments are about ten times those previously reported for sliding various materials on smooth diamond surfaces in air at room temperature. We must conclude that plowing and cutting of the slider ball surfaces by sharp asperities on the diamond films add additional mechanical resistance to motion (two-body abrasion), but there are additional considerations as well. Scanning electron microscopy of the wear paths on the films was used to determine the causes for the levels and variability of the frictional sliding behavior. There was clear evidence of microcutting of the steel surface by sharp diamond points, and the steel debris tended to accumulate in pockets in the surface on the pyramidal and plate-like films [see Fig. 6(a) and (b)]. On the microcrystal film, evidence for transfer o f the

steel was obtained (see Fig. 7). Transfer build-up and self-mated sliding probably caused the increase in nominal friction with number of passes displayed in Fig. 5(b). The deposits of sapphire debris (see Fig. 8 ) did not have the same effect as the transferred steel, and the nominal friction coefficient remained about the same as pass number increased, Fig. 5(a). The nominal friction coefficient was the highest for the pyramidal film since a major contribution of asperity plowing was present. The microcrystal film had lower nominal friction, but transfer and debris accumulation significantly affected the friction. The platelike specimen had the lowest nominal friction coefficients, probably because the sliding surface was smoother and because abrasive wear debris could accumulate between the diamond crystals rather than remain in the interface to add to the sliding resistance. The variability of sliding friction coefficients per pass was lowest for the pyramidal film even though the nominal values of friction coefficient were the highest of all three films on both sapphire and steel. The variability reflects point-to-point changes in sliding conditions along the surface. Even though the sliding resistance was high, the uniformity of the shapes of the pyramids in the contact area produced no large variations in friction force as the sliders passed by. While the microcrystal film was somewhat smoother, transfer and debris accumulation led to greater frictional variability. Likewise, localized accumulations of debris at the cutting edges of favorably oriented crystals in the plate-like film created variability in the contact conditions. The plowing contribution was probably less for the plate-like films; however, cutting processes were still present and prevented the friction force from dropping lower. Positive deviations in the friction coefficient (D > 1.0) were greatest for the microcrystal film because localized rises in sliding resistance were produced by steel and sapphire deposits on the sliding surface. Negative deviations (D < 1.0) were more pronounced on the pyramidal film possibly because the process involved cutting, and when a chip broke off, there would be a momentary drop in the sliding resistance. Where debris deposits are involved, momentary breakage of the debris layers can also produce drops in friction force. To some extent, the duration of momentary drops in friction force can be controlled by the stiffness of the slider fixtures and the time until the next encounter with an asperity ( 1 3 ) . While diamond film technology has the potential to make a significant impact on applied tribology, processes have to be improved to provide smooth, nonabrasive surfaces.

6 SUMMARY AND CONCLUSIONS

In sliding experiments of 52100 steel and sapphire on diamond films with three morphologies, the following conclusions were drawn:

402

1. In no case were the friction coefficients of the diamond films tested as low as those reported in published studies of sliding on smooth diamond surfaces in roomtemperature air. Sometimes, the friction coefficients were as much as ten times higher than those obtained on smooth diamond surfaces. 2. Films with pyramidal facets produced the highest sliding friction due to cutting and plowing contributions to friction, but they displayed the least variability in friction coefficient because the geometrical conditions of sliding contact remained more constant along the surface.

3. Microcrystal films, although smoother than the pyramidal films, experienced the effects of steel transfer and alumina debris accumulation, and they had higher variability in friction force along the stroke length. 4 . Plate-like film morphologies produced the lowest nominal sliding friction coefficients, but some cutting of the counterfaces was still observed. The variability in friction force was also relatively high.

CASEY, M. and WILKS, J., 'The Friction of Diamond Sliding on Polished Cube Faces of Diamond.' J. Phys. D Appl. Phys., 6 , 1973, pp. 1772-1781. (8) BOWDEN, F.P. and BROOKES, C.A. 'Frictional Anisotropy in Nonmetallic Crystals.' Proc. Royal SOC. London, A295, 1966, pp. 244-258. (9) MOORE, D. F. Principles and Applications of Tribology, Pergamon Press, 1975, pp. 94-97 (10) YUST, C. S . , McHARGUE, C. J., and HARRIS, L. A . 'Friction and Wear of Ion-Implanted TiB2.' Mater. Sci. and Eng., A105/106, 1988, pp. 489-496. (11) GARDOS, M. N. and RAVI, K. V. 'Tribologica Behavior of CVD Diamond Films,' Paper 115, presented at the Electrochem. SOC. Meeting Los Angeles, California, May 7-12, 1989. (12) CLAUSING, R. E., HEATHERLY, L., BEGUN, G., AND MORE, K., 'High Resolution Electron Microscopy of Growth Features on Filament Assisted CVD Diamond Film' presented at the International Conference on Metallurgical Coatings, San Diego, California, April 1721, 1989. (13) BLAU, P. J. Friction and Wear Transitions of Materials, Noyes Publications, 1989, pp. 391-395.

(7)

Faceted, microcrystal, and plate-like diamond film morphologies all abraded the sliding counterface and experienced cutting, plowing, debris accumulation, and transfer sufficient to overwhelm the low friction normally found when diamond slides on many materials in room-temperature air. Further modifications of the film-growing conditions are required to obtain the smooth films required for low friction.

7 ACKNOWLEDGMENTS Portions of this work were sponsored by the Department of Energy, Office of Basic Energy Sciences, and by the Department of Energy, Energy Conversion and Utilization Technologies (ECUT) Tribology Project. The authors thank L. Heatherly, Oak Ridge National Laboratory, for his help in film preparation, and C. A. Valentine for her editorial and cameraready copy prepa.ration assistance. References GRAFF, G. 'Diamond Power,' Popular Science, Sept. 1988, pp. 58-60 and 90. BACHMA", P. K. and MESSIER, R. 'Emerging Technology of Diamond Thin Films.' Chem. and Engr. News, May 15, 1989, pp, 24-39. DEUTSCHMAN, A. H. and PARTYKA, R. J. 'Diamond Film Deposition.' Adv. Mater. and Proc., June 1989, pp. 29-33. SPEAR, K. E. 'Diamond - Ceramic Coating of the Future.' J. Am. Ceram. SOC., 72(2), 1989, pp. 171-191. BOWDEN, F. P. and TABOR, D. The Friction and Lubrication of Solids, Oxford Press, 1986 ed., pp. 162-163. TABOR, D. 'Adhesion and Friction,' Chap. 10, in The Properties of Diamond, ed. J . E. Field, Academic Press, 1979, pp. 345349.

Fig. 1. Schematic diagram of the hot-filament CVD film-growing apparatus.

403

Table 1.

FRICTION COEFFICIENTS FOR STEEL AND SAPPHIRE ON DIAMOND FILMS

(0.98 N normal force, 3.0-mm-diam ball sliders) Friction Coefficients Film Type

Slider

Pyramids Steel

Pass

Microcryscals

Steel

0.51

0.98

1

5

0.42 0.42 0.42 0.44 0.46

0.49 0.49 0.49 0.47 0.49

0.53 0.51 0.51 0.69 0.60

0.98 0.96 0.96 1.21 1.09

1

0.35

0.40

0.60

1.19

1 2 3 4 5

0.38 0.33 0.38 0.42 0.38

0.43 0.38 0.44 0.47 0.43

0.49 0.46 0.51 0.57 0.46

1.03 1.06 1.03

1

0.23

0.28

0.35

1.06

1

0.27 0.23 0.34 0.36 0.43

0.42 0.40 0.44 0.49 0.57

0.88

3 4 5

0.05 0.05 0.07 0.09 0.18

1

0.27

0.32

0.35

1.00

1 2

0.28 0.34 0.34 0.36 0.36

0.38 0 53 0.86 0.84 0.55

1.00

5

0.18 0.24 0.28 0.27 0.31

1.16 1.70 1.55 1.21

1

0.02

0.25

0.71

1.49

1 2 3 4 5

0.07 0.07 0.05 0.07 0.05

0.23 0.18 0.18 0.20 0.18

0.64 0.42 0.44 0.5i 0.51

1.58 1.36 1.36 1.43 1.54

1

0.02

0.25

0.53

1.13

1

0.07 0.09 0.09 0.13 0.09

0.23 0.25 0.20 0.27 0.27

0.49 0.42 0.51 0.55 0.55

1.24 1.04 1.48 1.28 1.20

4

Steel

Sapphire

Deviation

0.47

3

Plates

Maximum

0.40

2

Sapphire

Nominal

1

2 3 4

Sapphire

Minimum

2 3 4 5

1.07

1.00

1.00

0.77 0.82 0.90

404

Fig. 2. study .

P Y R A M IDS

M ICRO-CRYSTALS

P L A T E - L IK E

fa

fb

fc/

Scanning electron micrographs of the three film morphologies investigated in this

ATTRIBUTES OF FRICTIONAL BEHAVIOR

t

f

n

Z \

IU

II w-

0

TIME OF SLIDING

-

Fig. 3. Various attributes of the firction traces which can lead to understanding of the contact conditions.

405

0.6

I

I

I

I

I

0.5

0.4

0.2 PLATES 0.1 0

2

0

4

6

PASS NUMBER

0.6

0.5 0.4 NOMINAL 0.3 (TIN) 0.2

0.i 0

I

0

I

I

2

I

4

6

PASS NUMBER

Fig. 4 . S l i d i n g f r i c t i o n f o r c e t e s t records obtained for ( a ) sapphire b a l l s and (b) s t e e l b a l l s .

406

w

Q

0

w

C

4-

0 .c

L

E

L

U

w 0

J

v)

A W W I-

Fl

v) 0 0

In

81 0

2

b

s 7

0

9

m

2

m

2

z

U

N

0

]: L

0

h

v

W 0

$

a

ld

Fig. 5. Friction force/normal force ratio for stroke-by-stroke tests of (a) sapphire and (b) steel sliding on diamond films of various morphologies.

407

Fig. 6 . Scanning electron micrograph illustrating the manner by which diamond pyramids (a) and plates (b) cut the steel ball surface and accumulate cutting debris. Note the thin streaks of transfer (arrow) from steel adhering to the square face of the plate in (b).

Fig. 7 . Scanning electron micrograph showing the development of patches of steel debris on the microcrystal surface after five passes.

Fig. 8 . Scanning electron micrograph of fine granular deposits of sapphire on the microcrystal surface after five passes.


409

Paper XVlll (ii)

Factors affecting the sliding performance of titanium nitride coatings F.E. Kennedy and L. Tang

The tribological behavior of TiN-coated Inconel 625 rings in dry sliding contact with carbon graphite was investigated with the aid of ring-on-ring sliding tests, computer-assisted profilometry, optical microscopy and scanning electron microscopy. Residual stresses and preferred orientations in TiN coatings were determined by X-ray diffractometry methods. Both hardness and Young's modulus of the TiN coatings were measured by nanoindentation hardness testing. Friction, wear, and spalling results were related to the hardness, residual stress, preferred crystallographic orientation, and thickness of the coating. To better understand the effects of coating and substrate properties on coating performance, thermal and thermoelastic models of the sliding contact were developed. Finite element methods were used to study the thermomechanical behavior of the thin TiN coatings.

1 INTRODUCTION

The objective of this research was to gain a better understanding of the tribological behavior of titanium nitride (TiN) coatings on ring-shaped metallic substrates in dry sliding. One of the potential applications of TiN-coated rings is as a component of mechanical face seals, where they could slide against carbon graphite rings. Previous work [ 11 had shown that hard titanium nitride coatings can have nearly as good wear resistance as monolithic ceramics in face seal configurations. There are several concerns that prevent the use of TiN coating in seals and other mechanical components, however. Because they are applied by slow vapor deposition processes, they are usually quite thin and, despite their good wear resistance, they have finite wear lives. In addition to wear, another failure mechanism, spalling, has been noted with TiN coatings [l]. Spalling of the protective coating is very undesireable, especially when the spalled debris remains within the contact, as is usually the case with conformal contacts. For these reasons, this research set out to answer two questions: (1) What is the effect of coating thickness on wear and durability of titanium nitride coatings? and (2) What other factors influence wear and spalling of TiN coatings in conformal contacts? Among the other factors considered were: residual stress in the coating resulting from the coating process, hardness of the coating, elastic modulus of the coating, and preferred crystallographic orientation of the coating.

2 MATERIALS All tribotests in this study were run with a conformal ring-on-ring configuration. The stationary ring was a commercial seal ring made of carbon graphite. It had a mean diameter of 5 cm and a face width of 2.5 mm, and those dimensions dictated the nominal contact area (approximately 4 cm2) between the contacting rings. The rotating ring was concentric with the stationary ring and was made from Inconel 625 with a titanium nitride coating on its contact surface. The thickness of the TIN coating ranged from 4.6 pm to 28 pm. The carbon graphite, grade P658RC, is one of the most common face seal materials. It is a composite of pyrolitic amorphous carbon from petroleum coke and crystalline graphite bound by carbon.

Inconel 625 is a good corrosion-resistant nickel-based alloy, which has moderate thermal and mechanical characteristics. This solid-solution strengthened, matrix-stiffened alloy whose microstructure contains carbides has the face-centered cubic crystal structure. The high alloy content of Inconel 625 makes it almost completely resistant to mild environments such as the atmosphere, fresh water, sea water, neutral salts and alkaline media. Since many mechanical components used in corrosive environments are made of Inconel 625, it was chosen as the substrate material for all tests in in our study. TiN has extremely high hardness, chemical inertness and a low friction coefficient against hard metals and carbon graphite. It is regarded as one of the most favorable thin hard coatings to improve the wear resistance and durability of mechanical components [2]. The TiN-coated Inconel 625 rings used in our study were produced by Union Carbide Corporation using the PVD arc evaporation technique. The coating procedure was as-follows: [3] The surface of the Inconel 625 ring was mechanically polished through 240, 400 and 600,grit S i c papers first, then it was finished by using a nylon cloth and 1 pm diamond paste until the surface roughness value Ra reached 0.1 pm. Before deposition, the ring to be coated was cleaned ultrasonically in a bath of methanol. The vacuum chamber was evacuated to a pressure below ~ x I O Pa - ~ and then the chamber was filled with argon (purity, 99.99%) to a pressure of 0.7 Pa. In order to remove the surface contaminants, the substrate was sputter cleaned by applying a negative bias of -1 KV d.c. Subsequently, the coating deposition was carried out in an atmosphere of nitrogen (purity, 99.998%). Under a high current-low voltage d.c. arc discharge, titanium was evaporated from the titanium cathode, where the temperature was about 2000OC. Both titanium and nitrogen were ionized to form plasmas within the region between the titanium cathode and the trigger. Since a negative bias of -150 V d.c. was applied to the substrate, the ionized titanium and nitrogen particles were accelerated toward the substrate. TiN formed and deposited on the surface of the substrate. The deposition temperature was about 5OOOC and the deposition rate was about 4 pmhr. Table 1 shows some property data of carbon graphite, titanium nitride and Inconel 625.

410

I

Carbon

NORMAL LOAD

property Young's modulus

I

Poisson's r a t i o

I 0.278 I

0.2

I

0.3

I ROTARY RING HOLDER T I N COATED

INCDNEL 625 RING

-CARBON

GRAPHITE RING CTlON TORQUE ARR BON GRAPHITE G HOLDER

T her ma1 conductivity W/m°C

9.8

17.0

9.0

Specific heat J/kg°C Density Kg/m3

41 0

627

1047

8440

5430

1830

Hardness

812**

2550**

PLATFORM

BALL

2

Figure 1 Schematic diagram of wear test apparatus.

95

Table 1 Thermal and mechanical properties of materials used in this study.

3 PROCEDURES 3.1- W The wear experiments were done on a test machine previously used for wear and seal investigations [ 11. Figure 1 shows a schematic configuration of the test machine. Normal load on the test rings is applied through the spindle by static weights hung on the loading arm. A specimen-holding platform is mounted on a thrust bearing beneath each spindle. The rotation of the specimen holder is restricted by a torque-sensing system, which is used to measure the friction on the surfaces of rings during the test. For this test program, the stationary carbon graphite ring was mounted in the specimen holder on the test platform. The TiN-coated Inconel 625 ring was mounted on the end of the rotating spindle. Before each test, the specimens were cleaned in an ultrasonic cleaner and carefully dried. Both ring specimens were weighed on an accurate analytical balance. Then surface profiles of both the TiN-coated Inconel 625 ring and the carbon graphite ring were taken using a computer-assisted linear profilometer system. During the wear test, a normal load of 50 N was applied, producing a nominal contact pressure of 0.125 MPa. Normally, the wear tests were run at a speed of 1800 rpm for six hours under dry sliding conditions. This produced a sliding speed of 4.7 m/s and a sliding distance of approximately 100 km in a 6 hour test. For each material combination there were five tests of six hour duration, along with one test of thirty hours (500km sliding distance). The strain on the friction torque bar, corresponding to friction force and friction coefficient, was monitored continuously during each test. After the tribotests, the test rings were cleaned, dried and weighed, and surface profiles were again characterized. The surfaces of specimens after wear test were examined under both an optical microscope and a scanning electron microscope. Special attention was focused on the transfer films and the failure region.

3.2 Measurements of Residual S t r e w S-wc i m e n ~ The residual stress in the coating can induce a change of lattice parameters and, in combination with other factors, may influence surface cracking that could initiate spalling and other failure modes. The residual stresses was measured by X-ray diffraction methods, using a sin*W technique. This employed the diffraction of copper radiation from the (333}/(511) planes of the FCC crystal structure of TiN coating [4].W is the angle between the normal to the surface of the specimen and the bisector of the incident and the diffracted beams, which is also the angle between the normals to the diffracting lattice planes and the specimen surface. The angular positions of the (333)/(511) diffraction peaks were determined for W tilts of 0, -35.0, 35.0 and 45.0 degrees. X-ray diffraction residual stress measurement was made at the surface of TiN-coated Inconel 625 rings along the circumferential direction. It was assumed that the stress distribution could be described by two principal stresses existing in the plane of the surface with no stress acting normal to the surface. The problem with the technique above is choosing the appropriate value of the elastic modulus of the TiN coating for the calculation of the macroscopic residual stress from the strain measured perpendicular to the (333)/(5 11) planes of TiN. Numerous different values were found in the literature. To resolve the discrepancy, the elastic moduli of our samples were measured by nanoindentation hardness testing at Oak Ridge National Laboratory. 3.3 Measurements of Hardness of TiN Coatinrrs For a thick coating, the microhardness can be determined directly by using a conventional microhardness tester. For thin coatings, however, microhardness tests often give incorrect results because the measured hardness is influenced by the substrate. A new ultra-low load microindentation system has been developed in the Metals and Ceramics Division of Oak Ridge National Laboratory [ 5 ] . Several mechanical properties, including hardness and elastic modulus, can be determined from volumes of material with submicron dimension. Both hardness and elastic modulus of TiN coatings of our samples were measured by nanoindentation hardness testing at Oak Ridge National Laboratory. The indentation depth was 150 nm and the width was less than 1 pm. The applied load ranged from 20 to 30 mN.

41 1

3.4 Measurements of Preferred Orientat ions in TiN Coatings Generally, each grain in a polycrystalline aggregate has a crystallographic orientation different from others nearby. The orientations of all grains may be randomly distributed in relation to some selected frame of reference, or they may tend to cluster to some degree about particular orientation(s). Any aggregate characterized by the latter condition is said to have a preferred crystallographic orientation, which may be defined as a condition in which the distribution of crystal orientations is nonrandom. The preferred orientations of TiN coatings were determined using an X-ray diffractometer in the Materials Laboratory of Thayer School of Engineering. 3.5 Determination of Influences of Temperature and Stress on Coating Durabilitv Thermo-mechanical analyses were carried out to study the influences of friction- induced temperature and stresses on thermocracking, spalling and excessive wear of sliding rings. The analysis used a suite of finite element programs developed earlier for studying temperatures and stresses in the contact region of sliding components [6]. Temperatures in the contact regions between sliding rings were determined using the THERMAP thermal analysis program, a specially-developed finite element program used for thermal analysis of frictionally heated regions [7]. The resulting stresses in the contacting bodies were determined using the ADINA finite element stress and deformation analysis program. Previous experiments had shown that the real area of contact between two flat conforming rings during sliding was concentrated in several patches and there were small solid-solid contact spots within each patch, with the patches remaining approximately stationary with respect to the surface of the ceramic-coated ring [ 11. The geometry of the contact model in our research was based on the determination of the spots sizes and locations of contact in that previous experimental study. All contact spots were assumed to be identical, and five contacts were assumed to be equally spaced along the ring circumference. Therefore only one section of the ring needed to be analyzed. Previous work had shown that a pseudo- two-dimensional analysis (axial and circumferential directions) was sufficient to model the most important temperature gradients and stresses in the contact region [6]. Figure 2 shows a typical two-dimensional ring sector used in this analysis, along with boundary conditions applied to the sector. The boundary conditions for the thermal analysis included setting temperatures on the top and bottom surfaces of the ring section shown in Figure 2. From previous experimental results [l], 1500C and lOOOC were assumed to be the temperatures of the non-contacting face of the carbon graphite ring and the TiN-coated Inconel 625 ring respectively.

Figure 2

Schematic diagram of ring section for thermal and mechanical analyses.

load: 50 N, speed: 1800 RPM, coating process: PVD

Table 2

Average friction and wear results.

4 RESULTS AND DISCUSSION

4.1 Wear Test Results Average wear and friction results of PVD TiN coatings with different coating thicknesses are shown in Table 2. In the wear tests, changes in mass of the specimens per linear sliding distance, i.e. mg/km, gave a good measurement of the degree of severity of the wear process. During the constant speed sliding tests, the friction coefficients were approximately 0.1 for all the TiN coatings, independent of thickness. The wear rates of the differen1 thickness coatings were also nearly equal, but the wear rate of 4.6 pm TiN coating was a little bit higher than those of other two thicknesses. Similar sliding tests were also carried out on uncoated Inconel 625 rings in contact with carbon graphite [14]. It was found that the wear rate of uncoated Inconel 625 was at least seven times higher than the wear rates given in Table 2 for the coatcd specimens. The friction coefficient of the uncoated rings W;IS also much higher. The friction coefficient of TiN-coated Iiiconel625 was about 0.1 whereas the uncoated Inconel 625 had a friction coefficient of 0.18. A comparison was made with the wear rates of other ceramic and cermet coatings on the same Inconel 625 substrate [8]. The wear rate of the TiN coatings was slightly less than the wear rates of tungsten carbide coatings but was slightly greater than those of chromium carbide and chromium oxide coatings. The surface roughness of the as-coated TiN-coated Inconel 625 rings was generally about 0.3 pm Ra. The roughness of all TiN coatings decreased dramatically during the first six-hour test to about 0.04 pm Ra and then remained in the range 0.03 - 0.045 pm Ra in later six-hour tests. No relapping of the TiN coati:igs was done before any tests. The original surface of TiN-coated Inconel 625 rings consisted many valleys and asperities due to the PVD process itself. In the initial stage of the first wear test, a burnishing wear process made the surface smoother by polishing away the tops of the highest asperities. This produced tiny TiN particles which could become embedded into the surface of the carbon graphite ring or act as third body particles. In either case, they could calrse an abrasive wear process to occur, even though the TiN particles are very tiny. Figure 3 provides evidence of TiN particles embedded in the surface of carbon graphite. The fluctuating surface roughness average during the subsequent wear tests results from the combination of polishing and abrasion processes. Optical microscopy and scanning electron microscopy showed that some pores were present on the surface of TIN coating before wear tests. These pores had formed during the coating process. Energy Dispersive Spectrometry (EDS) analysis showed there were no penetrations of pores through the coating to the substrate.

412

Earlier studies of other ceramic coatings had shown that in those cases the highest tensile stresses also occurred just beneath the surface of the coatings [8]. In this analysis it was found that the maximum Von Mises stress also occurred below the surface of coating (8.9 pm below the surface for a 150 pm thick coating). This leads to the conclusion that, as deformation of the subsurface continued, some fatigue cracks may have nucleated below the surface. Further loading and deformation could cause the cracks to extend and propagate and join with neighboring cracks. As in other delamination wear cases, the cracks tended to propagate parallel to the surface at a depth which was controlled by the properties of the material itself and the state of loading [9]. Finally, when the cracks sheared to the surface, thin wear sheets delaminated as shown in Figure 6. In some cases, if sufficient damage accumulated before the subsurface cracks had propagated parallel to the surface, the cracks could be turned toward the surface by the near-surface tensile stress, and this would result in the spalling of a particle, as in Figure 5.

Figure 3

TiN particle embedded in the surface of the carbon graphite ring.

Figure 4

Carbon transfer films on the surface of TiN coating.

As shown in Figure 4,during the wear tests carbon transfer films formed on some parts of the surfaces of TiN coatings. The relatively soft carbon transfer film would be beneficial i n improving the wear resistance of the coatings since it reduces direct contact between the two ring surfaces during the sliding process. Scanning electron microscopy showed several different kinds of coating failures. Figure 5 shows spalling of coating and Figure 6 shows a combination of spalling and delamination. EDS analysis showed that, in general, the spalling and delamination were cohesive failures that occurred within the TiN coatings, and did not expose the substrate. The only exception is at the center of the spalled area shown in Figure 5(a), where the substrate materials were exposed in the small (25 pm diameter) circular region. An explanation for the appearance of spalls and delamination on the coating surface can be found from an analysis of the stresses in the TiN coating. Thermal and thermoelastic stress analysis of TiN coatings showed that the maximum tensile stresses for different coating thicknesses all occurred just behind the contact and just beneath the coating surface (2.4 pm beneath the surface for a 150 pm thick coating). The location of the maximum tensile stress went deeper into the coating with increasing coating thickness.

Figure 5 Spalling of TiN coating in two different locations.

413

Figure 6 Combination of spalling and delamination of TiN coating.

Observation of the worn surfaces in the scanning electron microscope showed that some delamination and/or spalling had occurred on the surfaces of worn 12 pm and 28 pm thick TiN-coated Inconel 625 rings. There was no evidence of such failures on 4.6 pm thick TiN coatings, however. It might be noted that recent tests at Northwestern University [lo] have shown a similar influence of coating thickness on delamination and debonding of thin TiN coatings in rolling contacts. They have found that thinner coatings have improved fatigue life, whereas thicker coatings lead to debonding and delamination more readily.

4.2 Residual Stresses in Coa~ E and S Thermal Stress Analvsis The results of residual stress measurements are given in Table 3. They show that the residual stresses in the TiN coatings are compressive in the circumferential direction and are very high in magnitude. The residual stress in the 12 pm thick coating was higher than in the thicker (28 pm) coating. Diffractometry was unsuccessful in measuring the residual stress in 4.6 pm TiN coating because the coating was so thin that the presence of a substrate (4201 diffraction peak prohibited the use of the (333)/(511) diffraction peak technique.

Table 3

Results of residual stress measurements in TiN coatings. *

coating thickness residual stress standard deviation (wm) ( MPa) (MPa)

- 2560

12

I

28

I I

Table 4

Predicted temperatures and stresses in TiN coating and Inconel 625 substrate.

coating thickness (pm>

(OC)

10

I I

2o

150

197.7

197.8

196.4

507.4

503.2 493.7

185.1

188.3

Yon Mises stress in coating ( MPa)

-2290

100

maximum temperature

I

I * provided by the X-ray diffraction laboratory of LAMBDA Research Incorporated, results of residual stresses were calibrated using accurate value of Young's modulus. E=280 GPa I

The residual stress could have been induced either by an intrinsic growth stress or thermal mismatch between coating and substrate on cooling from the deposition temperature [I 11. Intrinsic stress in a TiN coating depends on the deposition parameters, such as deposition rate, bias voltage, pressure of nitrogen in the vacuum chamber and the evaporater current [12]. The nucleation and growth of TiN by PVD arc evaporation occurred under conditions of certain disruption by the impact of high energy particles due to the effect of bias voltage. Since kinetics of grain growth were limited because of the relatively high deposition rate and low deposition temperature, very fine grains were retained [ 131. The bombardment of energetic particles induced lattice defects, such as nitrogen interstitids at tetrahedral sites in the structure of TiN, which resulted in distortions within the grains and corresponding residual stresses. In general, such residual stresses were influenced by the gas-to-metal ratio N:Ti and gas ion to metal ion ratio N+:Ti+during the deposition process 1121. Changes in the stoichiometry of the coating can result, and these would contribute to the residual stresses in the TIN coating. Table 4 shows the results of the thermal stress analysis. Maximum temperatures during sliding were relatively unaffected by the thickness of the TiN coating. Von Mises stresses within both TiN coating and substrate increased with decreasing coating thickness. The maximum principal stress in the TiN coating was tensile and its value decreased as the thickness of coating became smaller. Thus, the compressive residual stresses were beneficial to the stability of coatings, since they reduced the magnitude of the damaging tensile stresses that occurred during sliding, especially in thinner coatings. The value of maximum principal stress decreased while the value of compressive residual stress increased with decreasing coating thickness, so the thinner coating was more resistant than the thicker one to failures of the type that would be caused by tensile stress. This coincides with the observation of delamination and spalling only in the thicker coating. A major reason for the presence of thermal stress during sliding as well as residual stress after deposition is the difference in thermal expansion coefficient between coating and substrate. Although the tensile stress resulting from frictional heating is probably responsible for spalling failure of TIN coatings, the tensile stresses would be even higher with coatings whose thermal expansion coefficient is lower than that of TiN [8].

maximum principal stress i n coating ( MPa)

'on Mises stress i n substrate 392.6 ( MPa)

191.2

386.1 375.3

414

coating thickness hardness (GPa) (P>

Young's modulus (GPa)

4.6

29.3

4.7

28 1.7 2 1 6.0

12

25.7: 4.6

247.82 12.5

Matthews and Sundquist have found that TiN coatings with [ 200) preferred orientation are more wear resistant than coatings such as ours with [ 111 ) texture even though both of them may have the same hardness. This improvement may be partly due to the increase in densification of TiN coating which can be obtained under the conditions of higher ion bombardment to get (200) preferred orientation [ 161.

5 CONCLUSIONS 28

29.0 2 4.5

241.31: 8.9

* measured b y nanoi ndentation hardness testing at Oak Ridge National Laboratory

Table 5 Measured values of hardness and Young's modulus of TiN coatings. *

4.3 Effect of Coating Hardnea Table 5 lists the hardness and Young's modulus data of TiN coatings measured by nanoindentation hardness testing at Oak Ridge National Laboratory. The Young's modulus was found to be slightly higher for the 4.6 pm thick coating than for the other two thicknesses. Hardness, on the other hand, was lower for the 12 pm thick coating. Since the mobility of dislocations is low for nitrides when the temperature is below 1000 OC, the strength of the grain boundaries becomes an important factor in determining the hardness of polycrystalline coatings. Coatings containing voids in grain boundaries tend to have low strength and hardness [18], because voids and microcracks have been found to be weak points which may initiate crack propagation and fracture when external forces are applied. In almost all cases of coating deposition using the PVD process, the hardness of coating gets higher with increases in the deposition rate [18]. On the basis of SEM studies, Gabriel has observed smaller columnar grains and denser coatings with increasing deposition rates [ 191. These very fine grain sizes and dense structures improve the strength of coating. On the other hand, the hardening of coating may be caused by lattice distortion during the deposition process. The susceptibility to brittle fracture tends to increase as the possibility of shear crack nucleation is minimized when increasing the hardness of a coating [20]. For this reason, there should be an optimal coating hardness for a certain application. 4.4 Preferred Orientations in the Coatings The measurements of preferred orientations showed that all the PVD arc evaporation TiN coatings had very high intensities of ( 11 1 ) diffraction peaks and corresponding high ( I 1 1 ) preferred orientations [14]. The 12 pm TIN coating was found to have a higher degree of ( 11 1 ) preferred orientation than the other two coating thicknesses. Preferred crystallographic orientation is now regarded as an important factor affecting the tribological performance of TiN coatings [12,15,16]. In general, the deposited coatings from any PVD process probably have a preferred orientation to some degree. The reason for preferred orientation has not been fully identified, but the degree of preferred orientation of TiN coatings is obviously dependent on the process and deposition parameters, such as deposition rate, ion current density and bias voltage [12,16,17]. Referring to the measured hardness values listed in Table 5, the changes i n hardness of coating correspond to the degree of preferred orientation. The reason for this is not clear yet. From Table 2 it can also be seen that the coating with the greatest degree of preferred orientation also had the highest friction. It is clear that the preferred orientation does have an influence on sliding behavior of TiN coatings because it changes the surface conditions of the coatings.

1. TiN is a favorable thin hard coating to improve the wear resistance of sliding mechanical components. The wear rate of Inconel 625 without TiN coating was at least seven times higher than that with coating and the friction coefficient was also higher. The friction coefficient of TiN-coated Inconel 625 was about 0.1 whereas the uncoated Inconel 625 had a friction coefficient of 0.18. Polishing and abrasion processes were the major wear mechanisms of TiN coating. 2. Coating thickness is an important factor affecting the durability of the TiN coatings. The tendency of spalling and delamination of the coatings increased with increases in the coating thickness. Unlike thicker coatings, the failure mode of the 4.6 pm thick TiN coating was a gradual wear process, even though the wear rate was a little bit higher than for the 12 pm and 28 pm thick coatings. 3. The modulus of elasticity of the 4.6 pm thick TIN coating was higher than those of the 12 pm and 28 pm thick coatings. The wear rate decreased as the coating modulus decreased, but the tendency for spalling and delamination of the coatings increased. 4. The residual stresses in the PVD arc evaporated TiN coatings were compressive and a relatively higher compressive residual stress occurred in the thinner coating. The residual stresses were beneficial to the stability of coatings because the tensile stresses that occurred in the coatings during sliding were reduced. This effect was more obvious in the thinner coating.

5. All PVD arc evaporated TiN coatings had very high ( 11 1 ) preferred orientations. The 12 pm coating had a higher degree of ( 111 ) preferred orientation and also had the

lowest hardness. The preferred orientations have an influence on the sliding behavior of TiN coatings because they change the surface conditions of the coatings, such as hardness and densification.

6 ACKNOWLEDGEMENTS This work was sponsored by the U.S.Office of Naval Research, Tribology Program. M.B. Peterson was the ONR Project Monitor. Coatings were generously donated by Union Carbide Corporation, Coatings Service Group. The assistance and useful information provided by Dr. J.Albert Sue of Union Carbide is gratefully acknowledged. Nanoindentation testing to determine modulus of elasticity and hardness of the coatings was done by James R. Keiser of Oak Ridge National Laboratory. The care taken in those measurements was greatly appreciated. Residual stress measurements in the coatings were done by Lambda Research Inc. The authors are grateful for the assistance of Victor A. Surprenant of the Thayer School of Engineering in X-ray diffractometry and optical microscopy and Louisa Howard of the Dartmouth College Electron Microscopy Center in scanning electron microscopy.

415

REFERENCES 1. Kennedy, F.E., Hussaini, S.Z. and Espinoza, B.M., Lubrication Engineering, v.44 (1988), pp. 361-367. 2. Ramalingam, S., in M.B. Peterson, ed. Wear Contro1 Handbook, ASME, New York (1981), pp 385-411. 3. Sue, J.A., Union Carbide Corporation, personal communication, (1989). 4. Prevey, P.S., Adv. in X-Rav A n a l m ' , v. 29 (1986), pp. 103-112. 5: Oliver, W.C. and McHargue, C.J., Solid Films, V. 161 (1988), PD 117-122. 6. Kennedy,-F.E. and Hussaini, S.Z., m u t e r s a nd Structures, v. 26 (1987), pp. 345-355. 7. Kennedy, F.E., Colin, F., Floquet, A. and Glovsky, R., in D.Dowson, et al, eds. Developmem in Numerical and Experimental Methods Amlied to Triboloey, Butterworths, London (1984), pp. 138-150. 8. Kennedy, F.E., Espinoza, B.M. and Pepper, S.M., Lubrication Engineering, in press, (1990). 9. Suh, N.P., in D.A. Rigney, ed., bndamentals of Friction and Wear of Materials, American Society of Metals, Metals Park, OH (198l), pp 43-72. 10. Cheng, H.S., Chang, P.T. and Sproul, W., to be published in Proc of 16th Leeds-Lvon Svmposium on Tribology, Lyon, France, 1989. 11. Rickerby, D.S., ,I. Vac. Sci. Technol,, v. A4 (1986), p. 2813. 12. Sue, J.A. and Troue, H.H., Surface and Coat ingz Technologv, v.36 (1988), pp 695-705. 13. Quinto, D.T., Wolfe, G.J. and Jindal, P.C., Thin Solid Films, v.153 (1987), pp. 19-36. 14. Tang, L., Master of Science Thesis, Dartmouth College, 1989. 15. Matthews, A. and Lefkow, A.R., Thin Solid Films, V. 126 (1985), pp. 283-291. 16. Matthews,-A. and Sundquist, H.A., Proc. Int'l. Ion Engineering Congress, Tokyo 1983, pp 1325-1330. 17. Kobayashi M. and Doi, Y., Thin Solid Films, v. 54 (1978), p. 67. 18. Sundgren, J.E., Thin Solid Films, v.128 (1985), pp. 2 1-44. 19. Gabriel, H.M., Proc. Int'l. Ion Engineering Congress, Tokyo 1983, UP 1311. 20. Kramer; B . , Thin Solid Films, v. 108 (1983), pp. 117-125. ~


417

Paper XVlll (iii)

The mechanism of failure of coatings in roller tests J. Viiintin

To clarify t h e effect of TIN coatings on the fa ilure resistance and frictional c ha ra c te ristic and compare t h i s effect w i t h t h a t produced by t h e heat tre a te d coatings t w o roller t e s t s have been made and t h e s t r e s s resulting from t h e combination of t h e Hertzian s t r e s s field and frictional force field on and below t h e contacting su r f ace aswell as t h e flash t em pe ra ture rise w e re calculated. On t h e basis of t h e r e s u l t s obtained on a t w o roller machine and by calculation, i t w a s found out t h a t the fa ilure re sista nc e of t h e TIN- coated roller pair was g r eat e than that of t h e heat tre a te d roller pair. The mechanism of failure resistance can be explained by t h e shearing s t r e s s (Hertzian s t r e s + frictional force) acting on t h e contact surface. This s t r e s s modifies t h e s t r u c t u r e in t h e vicinity below t h e TIN layer which is then sheared in t h e wear t r ack direction.

1 INTRODUCTION

2

To increase wear resistance of cutting tools, hard coatings such as titanium carbide, titanium nitride and aluminium oxide a r e applied t o t h e s u r f a c e of tools. These coatings a r e also widely applied t o wear - r es i s t an t p ar t s and mechanical components. There a r e a g r eat number of r e ports in which t h e scoring resistance of gears and mechanism of scoring was investigated using a two-roller machine. Scoring r es i s t an ce of TiCand TIN-coated gears w a s investigated by Terauchi / I / who found out t h a t t h e s e iz ure resistance of t h e coated roller pairs w a s higher than that of t h e roller pair which consisted of uncoated upper and lower r o l l er s . The mechanism of seizure in a two-roller t e s t w a s investigated by Nadano /2/, He has found o u t t h a t a part of t h e wear t r a c k on t h e upper roller is f r acture d due t o t h e action of shearing s t r e s s a t t h e position w h e r e t h e hardness of t h e roller Is minimum, and adheres t o t h e contacting s urfa c e of t h e lower roller. In t h i s r ep o r t , on t h e basis of microhardness, of the of observations s t r u c t u r e at t h e failured portion of the heat treated- and TIN- layer in t w o - r o l l e r t e s t s , and o n t h e basis of calculation of t h e s t r e s s on and below t h e s u r f ace of t h e roller, t h e mechanism of t h e f a i l u r e of t h e TiN-layer i n comparison w i t h t h e f r a c t u r e of t h e heat t r eat ed roller pa irs w a s examined in t h e incipient stage of failure.

The profile and dimension of t h e rolle rs used In t h e tw o-rolle r t e s t a r e shown in Fig. 1. The rolle rs w e r e made of XI55 C r VMo 12-1 (c .4850) and S6-5-2 Cc.7680) tool ste e ls. The combination of roller pa irs, heat t r e a t m e n t and coating tre a tm e nt a r e shown in Tab. 1. The TIN-coating of a thic kne ss of 2 t o 4 p w a s produced by t h e physical vapour deposition (PVD) process. The the rm a l properties and hardness of t h e material of t h e rolle rs and t h e coatings a r e shown in Tab. 2.

TEST SPECIMENS METHOD

AND

EXPERIMENTAL

Fig. 1: The profile’and dimensions of t h e rol lers

1 :; I !iat&.ri21

Rollar

Upper roller

Lnuer roller

pair

AlSi

Heat treatment

coating

Heat treatment

X I 55crvno

1215 C.oil.2min

II

S6-5-2

/

Table

1:

TIN

ITIN

Combination of roller pa irs, t r e a t m e n t and coat 1 ng t r e a t m e n t

heat

418

3 RESULTS AND DISCUSION 3.1. Failure r e s i s t a n c e

Table

2:

Hardness and thermal properties r o l l e r - a n d coating m a t e r i a l s

of

T h e s u r f a c e r o u g h n e s s of t h e c y l i n d r i c a l r o l l e r s in t h e a x i a l d i r e c t i o n is s h o w n in Tab.3. T h e s u r f a c e r o u g h n e s s of t h e coated r o l l e r s was s i m i l a r t o t h a t b e f o r e t h e coating was applied. T h e p e r i p h e r a l v e l o c i t i e s , t h e s p e c i f i c sliding a n d o t h e r t e s t conditions of t h e t w o - r o l l e r t e s t a r e s h o w n in Tab.4.

!‘:gure 2 s h o w s t h e c a l c u l a t e d v a l u e s of t h e f l a s h t e m p e r a t u r e r i s e and t h e m a x i m u m H e r t z i a n ‘;tress Pmax at t h e start a n d at t h e i n c i p i e n t i a p u f f a i l u r e of d r y f r i c t i o n a n d l n c i p l e n t qtage of l u b r i c a t e d f r i c t i o n of t h e roller p a i r s t e s t e d . T h e f l a s h t e m p e r a t u r e r i s e was c a l c u l a t e d by t h e e q u a t i o n given in r e f e r e n c e / 3 / , a n d t h e value of t h e c o e f f i c i e n t of f r i c t i o n w a s t h a t m e a s u r e d j u s t b e f o r e f a i l u r e o c c u r r e d a n d at t h e begjnning of t h e r o l l e r p a i r t e s t s . The H e r t z i a n s t r e s s was c o n s t a n t d u r i n g t h e t e s t s . T h e f l a s h t e m p e r a t u r e r i s e of t h e roller pairs Type B and Type D of d r y f r i c t i o n was a p p r o x i m a t e l y by 370 t o 430 K h i g h e r t h a n t h a t i n T y p e A and Type C , w h i l e t h e t e m p e r a t u r e rise of t h e r o l l e r p a i r s Type B a n d Type D in l u b r i c a t e d f r i c t i o n was a p p r o x i m a t e l y by 70-95 K h i g h e r t h a n t h a t In Type A a n d Type C . T h e m i n i m u m oil f i l m t h i c k n e s s c a l c u l a t e d by D o w s o n i s e q u a t i o n /4/ i n a l i n e c o n t a c t on t h e r o l l e r p a i r s w a s a p p r o x i m a t e l y 0,7 mm. As t h e v a l u e d e f i n e d by W e l l a u e r /5/ ( t h e r a t i o of t h e f i l m t h i c k n e s s t o combined s u r f a c e t e x t u r e ) , was f r o m 0,095 t o 0,248. t h e t e s t s w e r e r u n under t h e c o n d i t i o n s of a l m o s t m e t a l l i c contact.

.

3.1.1. L u b r i c a t e d f r i c t i o n

Table 3: S u r f a c e r o u g h n e s s b e f o r e a n d a f t e r t h e roller test

900

--

* Bulk

temperoture : Tb = 300-350 I

Kl

tgW

Table 4: S p e c i f i c a t i o n of t h e test conditions

T h e t e s t c o n d i t i o n s w e r e kept c o n s t a n t d u r i n g t h e test. T h e test w a s c a r r i e d o u t using a t w o r o l l e r m a c h i n e . T h e rollers w e r e l u b r i c a t e d w i t h EPOL SP 150, w i t h k i n e m a t i c v i s c o s i t i e s of 214 l o v 8 m 2 / s at 313 K a n d 17.2 m’/s at 373 K w h i c h is a s t r a i g h t m i n e r a l oil w i t h a d d i t i v e s . T h e r o l l e r tests w e r e c a r r i e d o u t w i t h u n f o r c e d l u b r i c a t i o n as s h o w n i n Fig. 1. The oil t e m p e r a t u r e w a s c o n t r o l l e d t o - 4 K by a thermostat.

Fig. 2.: S u r f a c e t e m p e r a t u r e rise a n d m a x i m u m H e r t z i a n s t r e s s at t h e i n c i p e n t s t a g e of f a i l u r e a n d at t h e i n i t i a l s t a g e

419

T h e r e l a t i o n s h i p b e t w e e n t h e c o e f f i c i e n t of f r i c t i o n a n d t h e w e a r l e n g t h is s h o w n in Fig. 3. T h e m e a s u r e m e n t of t h e c o e f f i c i e n t of f r i c t i o n was c a r r i e d o u t t w i c e f o r e a c h r o l l e r p a i r . As t w o m e a s u r e d v a l u e s of t h e c o e f f i c i e n t of f r i c t i o n w e r e s i m i l a r , t h e i r m e a n v a l u e is shown.

T h e c o e f f i c i e n t of f r i c t i o n v a r i e s d u e t o t h e d i f f e r e n c e In t h e b a s e m a t e r i a l a n d c o a t i n g of t h e roller. For all t h e roller pairs i t appears t h a t t h e surface w a s uniformly t o r n out due to frictional force and wear however t h e contacting s u r f a c e became s m o o t h e r as s h o w n i n Table 3.

3.1.2. Dry friction

0.05

!

A s t h e f a i l u r e r e s i s t a n c e of t h e coated a n d uncoated r o l l e r s could n o t be e s t i m a t e d f r o m t h e test r e s u l t s obtained u n d e r l u b r i c a t i o n , t h e f a i l u r e test was c a r r i e d o u t u n d e r d r y f r i c t i o n . T h e t e s t i n g w a s stopped w h e n , on t h e b a s i s of visual evaluation, failure o c c u r r e d on the contacting surface. The initial friction c o e f f i c i e n t s w e r e a b o u t 0,12 t o 0,16 r e s p e c t i v e l y . T h e r e l a t i o n s h i p b e t w e e n t h e c o e f f i c i e n t of f r i c t i o n a n d t h e wear l e n g t h is s h o w n in Fig. 4 .

i----001

L

Fig.3.:

WEAR LENGTH

llbml

Relationship between coefficient of friction and wear length - lubricated f r i c t i o n conditions

For a l l r o l l e r p a i r s , t h e c o e f f i c l e n t of f r i c t i o n j u s t a f t e r t h e befinning of t h e test had a m a x i m u m v a l u e . A f t e r t h a t , i t w a s reduced t o a constant value w i t h increasing wear length. The c o e f f i c i e n t of f r i c t i o n of t h e r o l l e r p a i r s Type A a n d C was 0,065, t h a t of t h e r o l l e r pair Type D w a s 0,078, a n d t h a t of t h e r o l l e r pair Type B w a s h i g h e s t 0,OLl.

Fig.5. s h o w s t h e r u n n i n g t i m e u n t i l f a i l u r e o c c u r r e d . The t e s t w a s c a r r i e d o u t t w i c e f o r e a c h r o l l e r p a i r , a n d t h e m e a n v a l u e o u t of t w o m e a s u r e d v a l u e s is s h o w n . T h e l i f e of t h e c o a t i n g s of t h e r o l l e r p a i r s Type B and D was longer t h a n t h a t of roller pairs Type A a n d C .

-

I

5 T

R O L L E R PAIR

Flg.5.:

F a i l u r e r e s i s t a n c e of d r y friction

roller

pairs

under

4 OBSERVATION OF FAILURE PORTION 4.1. Lubricated friction

Fig.4.:

Relationshlp between coefficient of f r i c t i o n a n d w e a r l e n g t h in d r y f r i c t i o n condi t i o n s

F l g u r e s 6 A,B s h o w a m i c r o g r a p h of t h e w e a r t r a c k of t h e r o l l e r s Type A a n d C a f t e r a 1,Z. m w e a r l e n g t h . T h e s u r f a c e l a y e r of t h e roller Type C was s l i g h t l y m o r e s h e a r e d in t h e d i r e c t i o n of f r i c t i o n a l f o r c e . Along t h e c o n t a c t

420

(8)

MICROPHOTOGRAPH OF SECTIONAL PLANE CUT IN THE AXIAL DIRECTION OF HOLLER AND DLSTRI8UTION OF HARDNESS ALONG

LINE A-A

Fig.6.: Microphotograph of t h e wear track, type A , C

16) WCFQFYOTDCIUPR OF S E c r ~ o ~ l l ~ PWNE CUT I N TH& mIAL

DIRECTION OF ROLLER AND DISTRI6UTION OF H4FU"SS ALONG LINE A-h

LEI HICROPWOMOIUPH OF BECTIOWAL PLANE CUT I N THE AXIAL DIRECTION OF ROLLER AND DISTRIBUTION OF HARDNESS AMNG LIMA A-A

Fig. 7 . : Microphotograph of failure portion of roller, type B

F i g . 8 . : Microphotograph of failure portion of roller, type A

42 1

s u r f a c e and in t h e vicinity of t h e s u r f ace t h e r e a r e distinct modifications of mi cr o s t r uc ture induced by t h e action of shear s t r e s s e s and te m p e r a t u r e during t h e t e s t s . This can be confirmed by t h e fact t h a t t h e hardness is considerably higher. Figure 6 B s h o ws t h e distribution of Vickers microhardness measured along t h e line A - A . I t can be considered t h at the y a r e caused by. work-hardening due t o t h e action of compressive s t r e s s , frictional force and cooling w i t h lubricating oil. Figure 7A shows a micrograph of t h e wear tra c k of t h e roller Type B af t er f ai l u r e at about 1.2 m. An undulation w a s observed in t h e circumferential direction of roller, and t h e s u r f a c e layer of t h e roller w a s fatigue-damaged in t h e direction of t h e frictional force. Figure 7 8 shows a mlcrograph of t h e section plane c u t and t h e in axial direction of t h e roller distribution of Vickers microhardness measured along t h e line A-A. From t h i s micrograph i t can be seen t h a t t h e metal in t h e vicinity below t h e TIN layer w a s distinctly deformed. The TiN layer w a s then on t h e same places separated from t h e base material. The hardness in t h e vicinity of t h e boundary of t h e TIN layer w a s t h e same as t h a t before t h e t e s t s . I t can be considered t h a t t h e TIN layer has a larger elasticity modulus th a n t h e base material, and t h a t t h e compressive, shear and thermal s t r e s s e s cause a much larger deformation in t h e base material in t h e vicinty of t h e TIN layer than that in t h e TIN layer. On t h e other hand t h e s u r f ace t emp er at u r e w a s lower than t h a t used for heat t r e a t m e n t . The degree of s u r f ace fatigue damage of t h e TIN layer of t h e roller Type B w a s more substantial than t h a t of t h e roller Type D.

.

and t h e surfa c e layer of t h e roller w a s sheared in the direction of t h e frictional force. Along the tested surfa c e t h e r e is a n approx. 1 p thick layer of a uste nite .This layer w a s produced in t h e same way a s t h a t on roller pa irs type A. Figure 9, A,B s h o w s a micrograph of t h e wear tra c k and t h e sectional plane c u t In t h e axial of the roller Type B after direction failure.Comparing t h e roller Type D w i t h t h e roller Type B, t h e degree of surfa c e fatigue damage by fa ilure w a s higher tha n t h a t found on t h e r o l l e r s pa irs type D. Fig.9 B show s t h e distribution of Vickers microhardness which 1s t h e same as that before t h e t e s t s . The mechanism of t h e fa ilure of TIN-layer w a s on t h e basis of our observations slightly different tha n that with lubricated. The e lastic deformation of t h e base material w a s larger than elastic deformation of t h e TIN-layer and larger than t h a t of. t h e heat-treated base material of t h e roller in t h e lubricated friction conditions.

4.2. Dry friction Flgure 8 A sh o ws a micrograph of t h e wear t r a c k of t h e roller Type A a f t e r failure. An undulation w a s observed in t h e circumferential direction of t h e roller, and t h e surface layer of t h e roller w a s sheared In t h e direction of t h e frictional force. Fig. 8 B s h o ws a micrograph of t h e sectional plane cu t in t h e axial direction of t h e roller and the distribution of Vickers microhardness. Along thb s u r f ace t h e r e a r e no signs of deformation. There is an approx. 1 p thick layer of a u s t en i t e. This confirms that t h e te m p e r a t u r e w a s above t h e AC3 point which, according t o t h e catalogue, amounts t o 875'C.The a u s t e n i t e layer could not be separated from t h e wear track w i th a hammer impact. Therefore, t h e a u st e n i t e layer w a s regarded a s a s t r u c t u r e affected by t h e actions of frictional force and frictional heat. An undulation was observed in the circumferential direction of t h e roller Type C ,

Fig.9.: Micrograph of fa ilure portion of t h e rolle r, Type B

5 MECHANISMS OF FAILURE An analysis of thermal s t r e s s in rolling contact has shown t h a t by Nadano and Terauchi /2/ thermal s t r e s s could be analytically evaluated under t h e assumption of a one dimensional heat flow in which t h e heat flux e n t e r s in t h e

422

n o r m a l direction of t h e c o n t a c t a r e a w h e n a parabolically d i s t r i b u t e d h e a t s o u r c e moves w i t h a r e l a t i v e l y high velocity on t h e c o n t a c t i n g s u r f a c e . F i g u r e 10 s h o w s t h e c o o r d i n a t e s of t h e r o l l e r in t w o - r o l l e r tests. In t h i s f i g u r e , t h e s u b s c r l p t s 1 and 2 r e l a t e t o t h e upper and l o w e r rollers, r e s p e c t i v e l y . The m a x l m u m value of t h e h e a t i n t e n s i t y qo g e n e r a t e d per u n i t of t i m e is given KF

I

V1 - V2 = 4qo a/3

w h e r e F ... is t h e n o r m a l load per u n i t of l e n g t h , V ... Is t h e p e r i p h e r a l v e l o c i t y , a ... Is a half of t h e H e r t z l a n c o n t a c t l e n g t h , p ... is t h e c o e f f i c i e n t of f r l c t i o n .

c o n t a c t i n g s u r f a c e of t h e r o l l e r a n d t h e s t r e s s e s o c c u r r i n g on a n d below the surface were c a l c u l a t e d by t h e a u t h o r a n d s h o w n i n r e f e r e n c e /6/. T h e c a l c u l a t e d v a l u e of t h e h e a t i n t e n s l t y on t h e upper roller w a s r e l a t i v e l y s m a l l and t h e i n f l u e n c e on stresses was m u c h s m a l l e r t h a n t h a t of t h e f r i c t i o n a l f o r c e . As an e x a m p l e . t h e d i s t r i b u t j o n of t h e e q u i v a l e n t s t r e s s o k , s h e a r stresss 5 45' a n d r e v e r s e d u n i d i r e c t i o n a l s t r e s s azy r e s u l t i n g f o r m t h e combination of t h e H e r t z l a n s t r e s s field and t h e f r i c t i o n a l f o r c e f i e l d of t h e upper rollers a r e s h o d n in Fig. 12 and Flg. 13, r e s p e c t i v e l y . The value of t h e c o e f f i c i e n t of f r i c t i o n is g i v e n f r o m t b e measured value j u s t before fallure.

.._...

Y

..,..I.

.

a-.

I..*

. . I

-1.. YI

Fig.10.: C o o r d l n a t e s of roller In t w o - roller t e s t

._.

-..-

-3

c : 2J-stribut;m of stress

Fig.11.: S u b s u r f a c e s h e a r s t r e s s e s a n d d e f o r m a t l o n

In o u r test c o n d l t i o n s t h e m a x i m u m value of t h e h e a t I n t e n s i t y is qo 25 W / m m s . W h e n t h e rates of t h e q u a n t i t y h e a t f l o w i n g f r o m e a c h point of t h e c o n t a c t a r e a I n t o t h e upper a n d l o w e r rollers a r e e x p r e s s e d by r and I - r r e s p e c t l v e l y , t h e s u r f a c e t e m p e r a t u r e at t h e point of t h e c o n t a c t a r e a of t h e upper r o l l e r is e q u l v a l e n t t o t h a t of t h e l o w e r roller. Multiplylng t h e c a l c u a l t e d v a l u e of t h e t h e r m a l stress by r a n d I-r t h e n o r m a l a n d s h e a r i n g s t r e s s a c t l n g on t h e upper a n d l o w e r rollers c a n b e obtained. In o u r test c o n d i t i o n s r = 0,513 a n d 1-7 = 0,487. T h e f r i c t i o n a l f o r c e a c t s on t h e

J Z ~

Fig.12.: D i s t r i b u t i o n of r e s u l t a n t s t r e s s a c t i n g on t h e upper roller at t h e Incipient stage of f a i l u r e ; c o e f f i c i e n t of f r l c t l o n 0,065 In Fig 12 a n d 13 t h e o r d i n a t e and a b s c i s s a i n d i c a t e t h e p o s i t i o n of t h e e v a l u a t e d s t r e s s In t e r m s of t h e p a r a m e t e r s y a n d z. The m a x l m u m v a l u e of t h e stresses (lk, 5 45' a n d csZy o c c u r s below t h e c o n t a c t i n g s u r f a c e , a n d t h e p r o f i l e of d i s t r i b u t i o n of t h e stresses is approximately symmetrical t o t h e origin for t h e roller p a i r s w h o s e v a l u e of t h e c o e f f l c i e n t of f r l c t l o n w a s u n d e r 0 , l . On t h e c o n t r a r y , t h e p r o f i l e of d i s t r i b u t i o n of t h e stresses I S n o t s y m m e t r i c a l t o t h e o r i g i n f o r t h e roller w h o s e value of t h e c o e f f i c i e n t of f r i c t i o n was l a r g e r

423

&....,.." ( a ) Dtstribution of stress

2.

I I

A".-

( b ) Distribution of stress ZI,?

I

I I 111 I 1 I

I I I

trr

Fig.14.: Distribution of equivalent s t r e s s on and below the surface for different coefficient of friction

typical element passes through a cycle of reversed shearing and shearing s t r a i n as shown in Fig.11. Rolling resistance arising in t h i s way has been studied by Tabor 171. Fig 15 and 16 show t h e distribution of t h e maximum value of t h e positive and negative components of t h e reversed shearing s t r e s s and of t h e shearing s t r e s s acting on t h e upper rollers. The same figures present also the values of t h e flow shearing s t r e s s for lubricated and d r y friction conditions calculated from t h e micro hardness on t h e basis of equations published in t h e reference 181. The reversed shearing s t r e s s acting at 5-10 p below t h e contact surface of t h e roller type A and C is equal t o t h e flow shearing stress with lubrication before t h e t e s t . A

- ...ICI

I-,

Distribution of stress

Try

Fig.13.: Distribution of resultant s t r e s s acting on t h e upper roller a t t h e incipient stage of failure coefficient of failure 0.5

than 0,l. The maximum value of t h e s t r e s s e s occurs on or below t h e surface, as shown Fig. 13. Figures 14. 15 and 16 show t h e distribution of t h e maximum value of t h e equivalent s t r e s s e s ok, the positive and negative components of t h e reversed shear s t r e s s o z y and shear s t r e s s o 45" for different values of friction coefficient. of the Figure 13 shows the distribution equivalent s t r e s s e s . The maximum value occurs at a depth "z" beneath the contact surface upto a coefficient of friction of 0,2. When t h e value of t h e coefficient of friction is larger than 00,2 t h e maximum value of t h e equivalent s t r e s s occurs on t h e contact surface, Fig. 14. The reversed shear s t r e s s e s acting parallel to t h e plane of t h e contact surface and its maximum value occur at a depth "z" beneath t h e contact surface and a r e dependent on t h e coefficient of friction (F1g.16). The maxlmum shear s t r e s s value occurs at a constant depth "z" below t h e contact surface 22 at an angle of 45" to t h e plane a t t h e surface and is independent of t h e coefficient of friction, Fig.15 and 16.

Therefore, t h e surface layer of t h e roller type A and C is work-hardened and t h e mechanical properties of t h e layer increased. The surface layer of a thickness of about 15 p cannot be fractured due t o t h e shearing force acting on t h e surface of t h e roller. The reversed shearing s t r e s s in t h e same surface layer of the rollers type B and D is considerably higher than t h e flow shearing s t r e s s before and a f t e r t h e t e s t with lubricatfon. Therefore, t h e layer which w a s deeper than 2-4 p below t h e surface can be fractured due t o t h e action of t h e shearing force on t h e contact surface of t h e roller w i t h lubrication. In dry friction conditions t h e reversed shearing s t r e s s Selow t h e TIN- layer of t h e roller pairs type A , B , C and D was considerably higher than t h e flow shearing s t r e s s before and a f t e r t h e t e s t s . Therefore, t h e s t r u c t u r e below t h e TIN layer can be fractured due t o t h e action of t h e shearing force on t h e surface of t h e roller. As shown i n Fig.6-9 t h e depth of t h e work-hardened layer and of t h e plastic deformation of t h e upper

424

I I I I I I

I

Fig.15.: Distribution of reversed shearing s t r e s s and flow shearing s t r e s s on and below t h e s u r f ace at t h e Incipient stage of failure

roller pairs a f t e r t h e failure w a s approximately equal t o t h e depth wh er e t h e modification of t h e s t r u c t u r e occurs due t o t h e action of t h e orthogonal shearing s t r e s s .

6 CONCLUSIONS

The failure resistance and frictional c h a r a c t e r i st i c s of t h e roller pairs of which one w a s TiN coated and t h e other heat treated w e r e examined using a t wo - r o l l er machine. On t h e basis of m i c ro s t r u ct u r e observations of t h e failure, measurements of hardness of t h i s pa rt and t h e calculation of t h e s t r e s s resulting from t h e combination of contact s t r e s s field and t h e friction force the following results were obtai ned. The ratio of film thickness t o combined s urfa c e te x t u r e w a s from 0,095 t o 0,248. This means th a t t h e t e s t s wer e run under almost metallic contact. The coefficient of friction of t h e TIN coated roller pairs was higher than t h a t of t h e heat t r e a t e d roller pairs by about 17-28 % . The wear t r a c k in t h e direction of frlctional force w a s smoother than t h a t before t h e t e s t s .

i6-3G-flou

IF - - - - f l o w

shearing stress before t e s t s s h e a r i n g stress after t e s t s

Flg.16.: Distribution of reversed shearing s t r e s s , shearing s t r e s s and flow shearing s t r e s s on and below t h e surfa c e at t h e incipient stage of fa ilure

The surfa c e fatigue damage stage on all types of roller pairs w a s dependent on t h e value of t h e coefficient of friction and distribution of microhardness in t h e vicinity of t h e contact surface. By te sting under dry friction conditions t h e lifetime of t h e TIN coated roller pa irs w a s longer than t h a t of the heat tre a te d roller pairs by about 40 %. A t t h e incipent stage of failure t h e s u m of t h e bulk and flash te m pe ra ture w a s higher than t h e AC, te m pe ra ture . This confirm t h a t a n approx 1. p thichk layer of a uste nite w a s formed on roller pairs along t h e tested surface on t h e heat tre a te d. The surfa c e fatigue damage of the TIN coated roller pa irs w a s independent of t h e te m pe ra ture rise on t h e contact surface directly. Terauchiss results show that the failure resistance of t h e TIN-and Tic - coated roller pairs w a s higher than t h a t of t h e he a t-treated roller pairs. According to thim and considering t h e r e s u l t s of t h i s investlgatlon I t Is clear that a beneficial effect of TIN coatings on t h e failure re sista nc e and wear c ha ra c te ristic can be

425

expected o n l y w h e n t h e b a s e m a t e r i a l is h e a t t r e a t e d a n d t h e c o n t a c t s u r f a c e is v e r y s m o o t h b e f o r e t h e coating is applied. T h e depth w h e r e f r a c t u r e of t h e roller o c c u r s d u e t o t h e a c t i o n of t h e r e v e r s e d s h e a r i n g arid s h e a r i n g s t r e s s agrees w e l l w l t h t h e c a l c u l a t e d value.

7 ACKNO WLEDCEMENTS T h e a u t h o r would l i k e t o t h a n k dr.A.H.Ruhh of the National Institute for Standards and Technology ( N I S T / N B S ) f o r c o - o p e r a t i o n , a n d t h e U.S.-Jugoslav J o i n t Board on S c i e n t i f i c a n d Technological Cooperation f o r a s s i s t a n c e .

REFERENCES (1) TERAUCHI, Y., NADANO, H., KOHNO, M.. NAKAMOTO, Y., S c o r i n g r e s i s t a n c e of TiC - a n d International, TIN - Coated Gears,-Tribology O c t o b e r , 1987. V01.20, No.5 (2) NADANO. H., TERAUCHI, Y., T h e M e c h a n i s m of S e l z u r e in Two-Roller T e s t s - JSME I n t e r n a t i o n a l J o u r n a , 1978, Vol. 30, No. 265

(3) CZICHOS, H., Tribology s e r i e s 1, ELSEVIER, 1978 (41 DOWSON, D., Proc.Inst.Mech.Eng., A(1967-681, V01.182, Pt.3,p.151 (5) WELLAUER, E,I.. HOLLWAY, T r a n s . A S M E , a n S e r . B . 1976, Vo1.98, No.2

G.A.,

( 6 ) VIZINTIN, J., Annual R e p o r t f o r t h e S e c o n d Year, 1987, R e s e a r c h p r o j e c t No. JFP-597/NBS

(7) TABOR, D., Rolling f r i c t i o n , Proc.Roy. SOC. A.1955, 229, 198 (8) HABIG, K.H., V e r s c h l e i s s W e r k s t o f f e n , H a n s e r , 1980,p.140

und

Hhrte

von


SESSION XIX DEFORMATION Chairman:

Dr. B.J. Briscoe

PAPER XIX (i)

Measurements of thin films adhesion and mechanical properties with indentation curves

PAPER XIX (ii)

Soft metallic coatings in metal forming processes

PAPER XIX (iii)

Deformation and fracture of hard coatings during plastic indentation


429

Paper XIX (i)

Measurements of thin films adhesion and mechanical properties with indentation curves J.L. Loubet, J.M. Georges and Ph. Kapsa

Measuring c o n t i n u o u s l y t h e a p p l i e d d e p r e s s i o n d e p t h and t h e c a r r i e d l o a d d u r i n g a n i n d e n t a t i o n test i s v e r y i n t e r e s t i n g t o c h a r a c t e r i z e n o t o n l y t h e p l a s t i c p r o p e r t i e s o f a material b u t a l s o t h e e l a s t i c p r o p e r t i e s . I n more f o r t h i n l a y e r s , t h i s approach can allow a n e s t i m a t i o n o f t h e a d h e s i o n . T h i s paper d e a l s w i t h some r e s u l t s o b t a i n e d on t h i n c o a t i n g s w i t h an e x p e r i m e n t a l i n d e n t a t i o n d e v i c e developped i n o u r l a b o r a t o r y . 1 INTRODUCTION it is said that bulk Generally, mechanical p r o p e r t i e s o f t h i n l a y e r s are c o r r e c t l y measured by an h a r d n e s s test i f t h e maximum i n d e n t a t i o n d e p t h i s i n f e r i o r t o t h e t h i c k n e s s d i v i d e d by 1 0 [l]. T h i s r u l e h a s t o b e a s s o c i a t e d w i t h a l i m i t a t i o n due t o t h e s u r f a c e roughness. So, t h e p e n e t r a t i o n h a s a l s o t o b e s u p e r i o r t o 1 0 times t h e roughness a m p l i t u d e . Then t o i n v e s t i g a t e t h e p r o p e r t i e s o f a l a y e r , t h e s u r f a c e roughness must b e i n f e r i o r t o t h e t h i c k n e s s d i v i d e d by 100. I n t h e s e c o n d i t i o n s , i n d e n t a t i o n c u r v e s are v e r y helpful to give elastic and plastic c h a r a c t e r i s t i c s even a t low l o a d s [2] and adhesion est i mat i o n o f t h i n l a y e r s . After a brief reminder on the m i c r o i n d e n t a t i o n t e c h n i q u e , some r e s u l t s on a Titanium Nitride (TiN) layer (thickness e = 8 pm o b t a i n e d by C.V.D. on AISI 304 L s t a i n l e s s s t e e l ) and Boron C a r b i d e l a y e r (B13C2) (e = 50 pm d e p o s i t e d by C . V . D . on g r a p h i t e ) are p r e s e n t e d , A d i s c u s s i o n a b o u t t h e s e r e s u l t s i s proposed.

the diamond i n d e n t e r i s o b t a i n e d through t h e r m a l e x p a n s i o n o f a metal c y l i n d e r , A , h e a t e d w i t h an electrical c u r r e n t .

2 EXPERIMENTAL TECHNIQUE

The e x p e r i m e n t a l s e t - u p used f o r t h e m i c r o i n d e n t a t i o n tests i n t h e p r e s e n t s t u d y h a s been a l r e a d y d e s c r i b e d by LOUBET e t a l . [ 3 , 41. I t i s s c h e m a t i c a l l y shown i n f i g . 1. I n i t s p r i n c i p l e , t h e experiment c o n s i s t s i n measuring simultaneously t h e load P a p p l i e d t o a Vickers diamond i n d e n t e r and t h e p e n e t r a t i o n o f t h e i n d e n t e r , h , i n t h e sample C . The p e n e t r a t i o n d e p t h o f t h e V i c k e r s indenter i n t h e sample i s measured and c o n t r o l l e d with a displacement transducer D (maximum a c h i e v a b l e d i s p l a c e m e n t : 200 pm ; resolution : pm). The i n d e n t a t i o n tests are performed a t a c o n s t a n t p e n e t r a t i o n rate o f 0.1 pm.s-1. The sample i s s e t on a p i e z o - e l e c t r i c t r a n s d u c e r E used t o measure t h e l o a d P a p p l i e d t o t h e i n d e n t e r . The l o a d c a p a c i t y o f t h e c e l l i s 0 < P < 50 N w i t h a r e s o l u t i o n o f lod4 N. The c e l l assembly i s m a i n t a i n e d w i t h a r i g i d h o l d e r F i n s u c h a way t h a t t h e a-p d i s t a n c e remains c o n s t a n t d u r i n g t h e experiment. A s a matter o f f a c t , t h e d i s p l a c e m e n t o f t h e V i c k e r s

F i g . 1 Schematic diagram of t h e equipment : ( A ) d i l a t i o n system ; (B) V i c k e r s i n d e n t e r ; ( C ) specimen ; (D) d i s p l a c e m e n t t r a n s d u c e r ; (E) l o a d t r a n s d u c e r .

3 VICKERS INDENTATION CURVES An example o f l o a d i n g - u n l o a d i n g c y c l e i s s c h e m a t i c a l l y shown i n f i g . 2. Point B c o r r e s p o n d s t o t h e maximum p e n e t r a t i o n hT a c h i e v e d d u r i n g t h e test u n d e r t h e l o a d PM whereas hR i s t h e d e p t h of t h e remanent p r i n t o f t h e i n d e n t e r i n t h e material and hRt t h e i n t e r s e c t i o n between t h e h axis and t h e t a n g e n t drawn t o t h e u n l o a d i n g c u r v e a t p o i n t B. A s a matter o f f a c t , f o r an e l a s t o p l a s t i c m a t e r i a l , t h e p e n e t r a t i o n o f t h e V i c k e r s i n d e n t e r makes a

430

p r i n t whose diagonal i s D, r e v e a l i n g thus t h a t a p l a s t i f i c a t i o n o f t h e material occurs d u r i n g the t e s t .

P

As a p i l e up e f f e c t i s not n e g l i g i b l e i n p r a c t i c e semi-emperical r e l a t i o n s are proposed [ 4 , 51. For i n s t a n c e :

HV = 1.854

f

PM Kg2 (hR'

(3) +

ho)2

where Kg and ho are geometric parameters t a k i n g i n t o account t h e shape d e f e c t s of t h e diamond pyramid (ho) and t h e occurence o f a p l a s t i c a l l y deformed zone surrounding t h e imprint (Kg). The values of t h e s e two parameters are determined experimentally from a comparaison between t h e o p t i c a l observations ( D ) and t h e i n d e n t a t i o n curves ( h R i ) . 4 . 2 Young modulus One o f t h e advantages of i n d e n t a t i o n curves (on c l a s s i c a l hardness t e s t s ) is t o g i v e a l o c a l s t i f f n e s s of t h e t e s t m a t e r i a l . This one could be derived from t h e tangent BC' of t h e unloading curve ( f i g . 2 ) . The s t i f f n e s s i s expressed by : Fig. 2 Loading-unloading c y c l e recorded during a microindentation t e s t , f o r an e l a s t o p l a s t i c material. As shown below, several important material parameters, i . e . t h e Young modulus E and t h e Vickers hardness Hv,can be derived from t h e loading-unloading c y c l e recorded during a microindentation test performed with a Vickers diamond pyramid ; t h e stress i n t e n s i t y f a c t o r Klc can be obtained with complementary observations of t h e i n d e n t a t i o n p r i n t s [5].

4. DETERMINATION

OF THE MECHANICAL PROPERTIES

A l o t of work was done about t h e determination of t h e mechanical p r o p e r t i e s with t h e h e l p of i n d e n t a t i o n curves [6, 71. Our aim h e r e i s n o t t o review i t but j u s t t o give few reminders on t h i s s u b j e c t .

4 . 1 Vickers hardness Hy It is well known t h a t t h e l o c a l Vickers hardness of t h e sample can be derived from t h e geometric f e a t u r e s of t h e Vickers i n d e n t a t i o n print. From t h e o p t i c a l measurement of t h e imprint diagonal l e n g t h , D. t h e hardness, HV is :

K =

PM

&

2D (hT

-

(4)

hR')

For m a t e r i a l of low Young modulus ( e g : L ) Where aluminium) K i s equal t o E s / ( l ES and s , are r e s p e c t i v e l y t h e Young modulus and t h e Poisson r a t i o of t h e sample. On t h e c o n t r a r y , f o r m a t e r i a l o f high Young modulus t h e e l a s t i c modulus of t h e diamond i n d e n t e r i s no l o n g e r i n f i n i t e with r e s p e c t t o t h a t of t h e sample. W e have proposed [8] t h a t :

'3

3

+ -

- =

K

.

(5) Ed

ES

where t h e s u b c r i p t d s t a n d s f o r diamond.

4 1 - 3 d

= 10-12 pa-1 a t y p i c a l value f o r Ed diamond, w e have found a good agreement between t h e Young modulus value of S i l i c o n Carbide ( S i c ) obtained by a c o u s t i c techniques and obtained by i n d e n t a t i o n curves [8].

With

5 RESULTS AND DISCUSSION A Titanium N i t r i d e (TiN) l a y e r ( t h i c k n e s s e = 8 pm) deposited by CVD on a s t a i n l e s s s t e e l

where PM i n t h e maximum load applied t o t h e indenter. From t h e i n d e n t a t i o n curve, hardness number, i f p i l e - u p eft'ect i s n e g l i g i b l e , is given by :

where hR' i s d e f i n i t e d by t h e tangent ( B C ' ) t o t h e unloading curve (BC), i n f i g . 2.

(AISI 304 L ) and a Boron Carbide (B13C2) l a y e r ( e = 50 pro) deposited by CVD on g r a p h i t e are characterized. Both samples have been previously polished with diamond p a s t e t o have a roughness i n f e r i o r t o 0.1 pm. Analysis of obtained i n d e n t a t i o n curves d l o w s t o d e f i n e two d i f f e r e n t behaviors : ( i )a t low l o a d s , corresponding t o low i n d e n t a t i o n depth, t h e i n d e n t a t i o n curves are r e p r e s e n t a t i v e of t h e mechanical p r o p e r t i e s of t h e c o a t i n g s ( f i g . 3 ) . The hardness and t h e l o c a l s t i f f n e s s a r e evaluated ( t a b l e 1 ) . A more d e t a i l e d s t u d y of B13C2 l a y e r s was done [g]. I t c l e a r l y shows t h a t Young modulus i s s t r o n g l y dependant on t h e stochiometry ( i . e . carbon c o n c e n t r a t i o n ) of t h e l a y e r [lo],

43 I

1

TiN-CVD

T h i c k n e s s pm

8

Hardness GPa

20

46-48

3

GPa

300

350-475

c r i t i c a l load N

1.1

5

E/1 -

c r i t i c a l d e p t h pm critical depth

0.5

thickness

1

1

0.12

s u b s t r a t e n a t u r e IAISI 304 L

c

/y/

c

B13Cz-CVD

Coating n a t u r e

h a r d n e s s GPa

E/1-

3

GPa

I 1

1.95 200

50

1 I I 1

3.5-4 0.07-0.08 graphite 0.1-0.3 30

T a b l e 1 : Mechanical and geometrical c h a r a c t e r i s t i c s o f TiN and B13C2 c o a t e d samples

F i g . 3 Low l o a d i n d e n t a t i o n c u r v e s f o r TiN ( A ) and B13C2 (B).

( i i )f o r e x p e r i m e n t s a t h i g h e r l o a d s , corresponding t o higher i n d en t at i o n depth, a d i f f e r e n t behavior is noticed. After a critical p o i n t , some d i s c o n t i n u i t i e s are n o t i c e d on t h e curves ( f i g . 4 ) . Observations o f i n d e n t a t i o n p r i n t s show t h e p r e s e n c e o f numerous c r a c k s (fig. 5). W e c a l l them a n n u l a r c r a c k s . The d i s c o n t i n u i t i e s correspond, for u s , t o t h e f o r m a t i o n o f t h e a n n u l a r c r a c k s i n and around t h e i n d e n t a t i o n p r i n t . T h i s i d e a is confirmed by the fact that the critical point c o r r e s p o n d s , on b o t h c o a t i n g s , t o t h e f o r m a t i o n of t h e f i r s t a n n u l a r c r a c k a t t h e p e r i p h e r y o f the indentation p r i n t .

F i g . 4 High l o a d i n d e n t a t i o n c u r v e s f o r TiN ( A ) and B13C2 ( B ) showing d i s c o n t i n u i t i e s .

432

w e can write i t , w i t h t h e h e l p o f ( 7 ) , d u r i n g t h e a n n u l a r b r e a k i n g b e h a v i o r u n d e r t h e form :

o r more s i m p l y : a H = - + h

b(e) h2

where ( a ) and ( b ) h a v e t o b e e x p r e s s e d i n f u n c t i o n of t h e mechanical and geometrical p r o p e r t i e s o f t h e l a y e r and t h e s u b s t r a t e . T h i s e x p r e s s i o n is v e r y similar t o t h e one proposed by JONSSON e t a l . [ll] :

2 c e (H,

H = H s +

-

H,)

-

c2e2 ( H ~ H,)

+

D

(11) D*

where H, i s t h e h a r d n e s s o f t h e s u b s t r a t e , Hc i s t h e h a r d n e s s of t h e l a y e r , e is t h e thickness of t h e layer, C a numerical c o n s t a n t . and The d i f f e r e n c e i s i n t h e f i r s t term which does n o t a p p e a r e x p l i c i t e l y i n o u r e q u a t i o n .

6 COATING-SUBSTRATE ADHESION

F i g . 5 Scanning Electronic Microscopy observations of indentation p r i n t of TiN l a y e r ( P = 10 N ) .

a review o f the methods Recently, including the indentation test, for the measurement of c o a t i n g s u b s t r a t e a d h e s i o n was done [12]. I n t h e indentation t e s t , the coatingsubstrate adhesion is measured by the resistance t o p r o p a g a t i o n o f a c r a c k a l o n g t h e interface. Different modelisations where proposed. I n t h e case of V i c k e r s i n d e n t a t i o n and h a r d l a y e r s , most of t h e work i s due t o EVANS and coworkers [l3, 161. O t h e r works, on o t h e r s i t u a t i o n s were d o n e , i n p a r t i c u l a r f o r l a y e r s softer than t h e s u b s t r a t e l i k e polymeric f i l m s d e p o s i t e d o n steels [17, 181. I n t h i s p a p e r we are i n t e r e s t e d i n h a r d l a y e r - s u b s t r a t e a d h e s i o n and w e p r o p o s e a n o t h e r p o i n t o f view on t h e i n t e r f a c e f r a c t u r a t i o n . I n t h e m o d e l i s a t i o n proposed by CHIANG e t a l . [l7], t h e i n t e r f a c e f r a c t u r e i s c o n s i d e r e d t o b e similar t o a l a t e r a l f r a c t u r e as s e e n f o r b u l k b r i t t l e materials. The thoughness (KIc) o f the interface can b e e s t i m a t e d if the mechanical p r o p e r t i e s of t h e l a y e r and o f t h e s u b s t r a t e and t h e r a d i u s o f t h e debounding area (C,) are known.

The law between t h e l o a d ( P ) and t h e penetration depth (h) during t h e annular b r e a k i n g b e h a v i o r i s roughly o f t h e form :

P

-

Pc =

so

B ( h - hc)

P = P h + Pc

(6)

- B

h,

(7)

where Pc and hc c h a r a c t e r i z e t h e c r i t i c a l p o i n t and B a c o n s t a n t o f p r o p o r t i o n a l i t y . A s t h e h a r d n e s s i s d e f i n i t e d by :

a P H=h2

where H i s t h e h a r d n e s s o f t h e l a y e r and Pp i s t h e minus i n d e n t a t i o n l o a d f o r t h e propagation of t h e crack. T h i s approach s u p p o s e s , as t h e a u t h o r s s a i d , t h a t t h e f i l m and t h e s u b s t r a t e have similar mechanical D r o D e r t i e s .

433

Uncracked

Fig. 6 Schematic representation of the " c i r c u l a r crack" propagation during loading. I n our proposed modelisation w e consider t h a t two phenomena p l a y t h e major r o l e . They are : - t h e annular f r a c t u r e s c r e a t e d around the indentation p r i n t , - t h e e l a s t i c d e f l e c t i o n of t h e s u b s t r a t e caused by t h e applied load. Then t o e x p l a i n t h e debounding of t h e l a y e r , we have t o consider t h e succession of t h e following events ( f i g . 6 ) . a t a c r i t i c a l l o a d , a f i r s t annular breaking around t h e i n d e n t a t i o n p r i n t occurs. A s t h e r e i s an e l a s t i c d e f l e c t i o n of t h e s u r f a c e around t h e contact a r e a , tensile stresses appear a t t h e i n t e r f a c e . The l a y e r is now bounded on t h e s u r f a c e only by adhesive forces. - a t t h i s p o i n t , i f t h e e l a s t i c energy s t o r e d i n t h e f i l m i s g r e a t e r than t h e energy o f cohesion of t h e i n t e r f a c e , a f r a c t u r e of r a d i u s Co is c r e a t e d . I f not, a g r e a t e r l o a d must be applied, so a g r e a t e r elastic deflection, t o create the interfacial fracture. T h i s l e a d s t o a s i d e e f f e c t , t h e formation of numerous annular fractures before the debounding of t h e l a y e r . I n t h i s p o i n t of view, t h e mechanism involved i s completely d i f f e r e n t from t h e one of lateral crack of bulk materials. I t is s p e c i f i c t o t h i s kind of f r a c t u r a t i o n . To avoid confusion w e c a l l t h i s i n t e r f a c i a l crack " c i r c u l a r crack'?, and n o t "lateral crack". The s t r a i n energy rate o f t h e system can be estimated [5]. It i s roughly o f t h e form :

-

The s u r f a c e energy of cohesion of t h e i n t e r f a c e (Winter) can be then estimated by t h e measurement o f t h e r a d i u s Co of t h e c i r c u l a r crack and t h e mechanical p r o p e r t i e s of t h e

materials.

In this proposed modelisation, the adequate q u a n t i f i c a t i o n of t h e method i s n o t achieved. It i s j u s t a proposal of an o t h e r mechanism t o e x p l a i n i n t e r f a c i a l breaking d u r i n g i n d e n t a t i o n t e s t . I n p a r t i c u l a r , no account was taken of t h e i n f l u e n c e of r e s i d u a l stresses generated d u r i n g t h e d e p o s i t i o n of t h e layer. Residual compressive stresses are thought t o i n f l u e n c e i n t e r f a c e cracking by inducing buckling of t h e f i l m above t h e crack and t h e r e a f t e r , by providing and a d d i t i o n a l d r i v i n g f r o c e f o r crack growth [l5].

7 CONCLUSIONS The method of continuous depth r e c o r d i n g may be used t o g i v e a q u a n t i t a t i v e mechanical c h a r a c t e r i z a t i o n o f t h e material over a wide range o f d e p t h s within t h e l a y e r . - A t small load o r low i n d e n t a t i o n depth ( h e/5 o r l o ) , more s p e c i f i c behavior can be n o t i c e d . For hard f i l m s , f o r a c r i t i c a l load o r a c r i t i c a l i n d e n t a t i o n depth, an annular breaking around t h e i n d e n t a t i o n p r i n t occurs. This annular breaking o f t h e f i l m g i v e s a d i s c o n t i n u i t y on t h e i n d e n t a t i o n curve. If t h e i n d e n t a t i o n depth i n c r e a s e s o t h e r annular breakings occur. The e f f e c t of t h e mechanical p r o p e r t i e s o f t h e s u b s t r a t e is f e l t d u r i n g t h i s behavior. Measurement of adherence o f t h i n f i l m s r e q u i r e s t h e c o n t r o l l e d propagation o f a w e l l defined crack along t h e i n t e r f a c e . I n d e n t a t i o n techniques provide a means o f g e n e r a t i n g such c r a c k s on a s u f f i c i e n t l y small s c a l e t o investigate thin f i l m s . W e have proposed a schematic d e s c r i p t i o n of t h e propagation of such f r a c t u r e . However f u r t h e r work i s needed t o understand and recommend as a technique t h e i n d e n t a t i o n adhesion t e s t .

-

434

Acknowledgments The authors are indebted to the French Direction des Recherches, Etude et Techniques. They wish to thank Drs MAUGIS D. and SURRY C. for helpful discussions and advice. References [l] PEGGS, G.N., LEIGH, I.C., "Recommended €or micro-indentation Vickers procedure hardness test", Report MOM 62, U.K. National Physical Laboratory, England, 1983. [2] ROSS, J.D.J., POLLOCK, H.M., PIVIN, J.C. and TAKADOUM, J., Thin Solid Films, 148. 1987, p. 171. [3] LOUBET, J.L., GEORGES, J.M., MARCHESINI. O., MEILLE, G., J. of Tribology, 106, 1984, P. 43. 141 LOUBET, J.L., GEORGES, J.M., MEILLE, G., "Microindentation techniques in materials science and engineering", ASTM S.T.P 889, BLAU P.J. and LAWN B.R. (Eds), 1986, p. 72. [5] LOUBET, J.L., "Courbes d'indentation et effet d'kchelle : quelques cas expkrimentaux", These d'Etat, Universitk Claude Bernard, Lyon, 1986. [ 61 See for example : "Microindentation techniques in materials science and engineering", ASTM S.T.P. 889, BLAU, P.J. and LAWN, B.R., (Eds), 1986. "71 BHATTACHARYA, A.K., NIX, W.D., Int. J. Solids Structures, Vol 24, n o 9, 1988, p. 881. [8] DUGNE, O . , GUETTE, A., NASLAIN, R., LOUBET, J.L., GEORGES, J.M., KAPSA, Ph., SAUREL, J.M., ALAMI, K., AMAUDRIC DU CHAUFFAUT C., "Mechanical characterization of Sic CVD thin films by acoustic and micro-indentation techniques", submitted to Thin Solid Films. [9] REY, J., "Dkpots par LPCVD de carbures de Bore s u r cermets WC-CO", These, Universite de Limoges , 1988. [lo] REY, J., MALE, G., KAPSA, Ph., LOUBET, J.L., Proceedings of EUROCVD 7, 19-23 Juin 1989, Perpignan. France. [ll] JONSSON, B. and HOGMARK, S., Thin Solid Films, 114, 1984, p . 257. [12] RICKERBY, D.S., Surface and Coatings Technology, 36, 1988, p. 541. ~ 1 3 1LOH, R.L., ROSSINGTON, c., EVANS, A.G., J. Am. Ceram. Soc., 69, 1986, p. 139. [14] CHIANG, S . S . , MARSHALL, D.B., EVANS, A.G., "Surfaces and interfaces in ceramic and ceramic-metal systems", PASK, J. and EVANS, A.G. (Eds) Plenum, New York, 1981, p. 603. [l5] MARSHALL, D.B., EVANS, A.G., J. Appl. Phys., 56, 1984, p. 2632. [16] ROSSINGTON. C.. MARSHALL, D.B., EVANS, A.G., KHURI-YAKUB, B.T., J. Appl. Phys.. 56, 1984, p. 2639. [l7] ENGEL, P.A., ROSHON, D.D., Journal of Adhesion, 10, 1979, p . 237. [18] CONWAY, H.D., THOMSIN, J.P.R., J. Adhesion Sci. Technol., 2, 1988, p. 227.

.

435

Paper XIX (ii)

Soft metallic coatings in metal forming processes P. Montmitonnet, F. Delamare, E. Darque-Ceretti and J. Mstowski

Soft metallic coatings play an important part in many forming processes. Two cases are investigated hereafter: * forging of anti-friction alloy coated plain bearing. Application of a mechanical model shows how it is possible to design the process so that a constant coating thickness in the final bearing wall is obtained. Computation of interfacial strain explains the improved adherence of the coating. * co-extrusion or co-drawing of coated bar or wire. A mechanical model explains coating losses during wire-drawing; in the case of brass coated steel cord, these losses lead to an evolution of surface composition.

1 INTRODUCTION

Metallic coatings are used in a number of circumstances. They vary in nature, thickness, mechanical or tribological properties, ... , so as to fulfill quite diverse missions: - improving surface aspect, with generally very smooth, bright coatings: *gold or silver coatings in jewellery (the former now often replaced by TiN!) * composite coins, either legal (the french 5F coin is Cu-Ni alloy coated with Ni) or illegal, forged coins

Ill. -gold coatings are used for enhanced electrical conductibility, for instance in electric connections, or for examination of non conducting samples in SEM. - corrosion-protective coatings are widely used: zinc coatings (galvanised steel wire; zinc coated deep drawn steel sheets for car body, ...); brass coating of steel cord wire; stainless steel coating of steel strip. - tribological coatings include both hard coatings (chromium plating of gun stock, of rolls in rolling mills for improved wear resistance) and soft coatings, generally low melting point alloys containing Pb or Sn; an application to plain bearings will be detailed hereafter. - soiiie coatings are a surface treatment making adhesion to some counterpart possible. The most important case is wirelrubber adhesion in tyres, where adhesion is prompted by the brass coating, the surface composition

of which is of primary importance for the strength and fatigue resistance of the wirelrubber joint /2,3/. - in all previous examples, the necessity of the coating appeared after forming: the coating plays a major part only in the life of the formed piece. In metal forming however, quite a few operations would be impossible without a proper coating, because of too hard contact conditions. Such operations include extrusion of hard, refractory alloys performed at very high temperature /4/, where a soft metallic coating (copper, steel or even molybdenum depending on the extrusion temperature) acts as a lubricant, with anti-friction, anti-seizure and anti-wear effects. Although receding in front of more specific and efficient coatings (phosphates and other minerals), these metallic coatings are still in coninion use in extrusion. In this case, the coating has to be eliminated after foiiiiing. The ease of removal (by etching or machining) is one of the criteria for the choice of the coating metal. - the same is true in powder forming, where preforms are often canned in a metallic envelope which ensures compacity of the workpiece in extrusion, forging or hot isostatic pressing, even if some parts of it undergo tensile stresses. A number of coating techniques are used, depending mainly on desired thickness and required final properties: immersion in molten metal bath, electrochemical deposition, or plastic bonding.

436

Even if it is not chosen as the technique used to obtain the composite material, plastic deformation may be used i n some cases to improve the properties of the coating by work hardening, improving bonding, smoothing the coating surface, homogenizing its thickness. Deposition may also be easier on a semi-finite product of simpler shape than on the final part, and plastic deformation has to be applied to the composite after deposition. This will be the case of brass-coated steel cord. Furthermore, the soft metal coating can be considered as a solid lubricant, as it decreases the friction stress. This property is used in steel cord wire drawing, which would practically be impossible without the brass coating.

\

001

\

\ \

I

I

002

Figure 1 : anti friction effect of a soft coating.Yield criterion (VON MISES) states that z S o d d , where z is the friction stress and 00 the yield stress. How can plastic co-deformation improve coating adherence? the mechanism is two-stepped (figure 2, /5,6/): - elongation of the interface breaks the oxide layers if they are brittle enough. - contact pressure "micro extrudes" metal chips between the oxide plates. When contacting, these microchips immediately weld /7/.

This property makes plastic co-working an attractive possibility, as in all cases, good adherence of coating is a prerequisite for an efficient action of the coating. However, some difficulties may arise, due to the simultaneous flow of two metals with sometimes quite different mechanical properties. First, the coating metal and potential interphases must be ductile enough to withstand the plastic strain. Secondly, a flow competition will exist if two metals of very different yield stresses are co-deformed; the final geometry of the composite (coating thickness, interface position) may be quite difficult to predict. Examples of this situation, and remedies thereto, are discussed in the following. Finally, a difference in elastic moduli may cause high residual stresses in the vicinity of the interface. These general features will now be illustrated by two examples: - forming of an anti-friction coated plain bearing by backward extrusion. - evolution of coating in wire drawing of steel cord.

2 CO-EXTRUSION OF A PLAIN BEARING

2.1 description of the process In order to survive a lubrication breakdown, some bearings are coated on their internal surface with antifriction alloys. A process including co-extrusion has been proposed 181; the high strains imposed by backward extrusion are expected to promote a strong bonding between coating and substrate. Figure 3 illustrates the main steps of the process. The complete forming would consist of

die

figure 2 : metals partially bonded by plastic deformation. Note the curvature of metal fibres in the gap between oxide plates, indicating micro-extrusion. Hence, bonding will be all the more efficient as: - strain along and pressure normal to the interface are higher. - oxide layers are thinner and more brittle.

figure 3 : schematic view of bearing forming by backward co-extrusion

431

- cutting a cylindrical sample from a bar of the substrate

metal. - punching a cavity into it, to receive the coating metal. - filling the cavity by upsetting, after surface treatment of both parts (brushing) to improve adherence. - backward extrusion - cutting the top of the composite bearing, as it is both geometrically defective and weakly bonded. To minimize the quantity of the soft, expensive coating metal, we have to achieve a constant, given thickness all along the bearing wall. This thickness must be sufficient to be efficient throughout the bearing life, but excessive thickness would result in increased cost and weakened bearing wall resistance. So the thickness is fixed at design time, and iiiirst be respected during extrusion. 2.2 Flow comDetition durine backward co-extrusion Figure 4 /8/ illustrates two kinds of defects due to different yield stresses of the two metals (experiments on plasticine; yield stress ratio S=0.37 ; the initial substratehoating interface is a cylinder). Let us compare the case of a homogeneous sample to that of a composite sample. In the homogeneous case, deformation proceeds in three steps: (i) formation of a plastic zone ABCDE, limited by (r); it

takes on the shape pictured as a broken line. (ii) then this plastic zone moves downwards in a quasisteady state flow. (iii) finally, the bottom of the plastic zone reaches the bottom of the sample; from now on, the thickness of the plastic zone decreases. Let us call "interface" (I) the surface represented by the bold line, for comparison with the composite part. As long the "layer as point C has not reached the lateral part of (r), thickness" increases (a point of (I) has more and more time to move outwards before it reaches (r)). Then, real steady state is achieved until step (iii), after which the outward velocity increases, and so does the "layer thickness". For the softer coating however, things may be different. Take for instance the geometry of figure 4b. Extending plastic deformation down into the substrate would spend more energy. Hence, the plastic zone is confined in the soft layer; the outward flow is then such that it may pierce the harder envelope. Moreover, in order to achieve constant thickness, even at the wall top, it would be wise to have an initial coating metal radius greater than the punch radius by the desired coating thickness. Figure 4c shows that for a soft coating with S=0.37 , some troubles result: plastic zone is then totally confined in the soft metal, and only soft metal extrusion takes place. Then nothing remains to coat the bottom of the wall.

figure 4 : flow during backward extrusion. Coating material has initially a cylindrical shape. a - homogeneous sample (S=l) - - - limit (r)of plastic zone - virtual interface (I)

b - yield stress ratio S=0.37; initial stage of extrusion c - yield stress ratio S=0.37 initial radius of coating metal > punch radius From these first experiments, some conclusions can be drawn: - the depth of the initial coating must be of the same order as the total punch stroke. - its shape should not be kept cylindrical: the interface must "shrink" as depth increases; its ideal shape will be determined in 2.3 . - for the top of the bearing wall, a special set-up must be used, where an outer annulus, compressed by a spring, keeps the top flat (figure 5). This allows (I) to overlap the punch bottom without pre-extrusion of coating as in figure 4c. This device will be used hereafter.

438

z = 0 is taken at the bottom of the plastic zone. From the conservation of normal velocity component, the is derived: equation of the lateral part of (r)

From (eqn. l), the equation of the trajectory of a point inside (r)is easily found -1 _1 -= -1 _1 Z Y ) h h o r z = ro zo (hyperbola) (4) if ro and zo are the initial coordinates of the material point. Reporting into (eqn. 3) gives the coordinates of point (Mr)

at which a point leaves plastic zone (r).In fact, only the radial coordinate Rr is of any importance:

2.3 Optimisation of initial interface We have built a model of the process (upper bound type). Based on the observation of deformed grids 191, two velocity fields have been chosen /lo/:

* in the wall (rigid): Ll

=0

U w = -= CSt Ro ($2-1

2.3.1 Model 1 (figure 6)

* under the plastic zone (rigid) 11 = 0

+ r

figure 6 : "model 1" of co-extrusion. The plastic zone thickness decreases. left : evolution of the geometry right : schematic velocity field

w=O (7) A material point in the final interface comes from a material point on the initial interface. Hence, what is needed to obtain a constant wall thickness e is that points Mg(ro,zg) of (lo) leave the plastic zone at a constant R r = Rc

+ e (figure 6). From (eqn. 5 ) , it is easy to deduce that Mo should lie on a hyperbola. Hence, from this model, the optimal shape of (10) is easily and explicitly calculated. = Rf

2.3.2 Model 2 (figure 7) The bottom of the plastic zone is supposed fixed; hence, its thickness decreases as the punch goes down. This is valid for:

- beginning of extrusion with very soft coating of low initial depth ho (figure 4b). - end of extrusion (step (iii) of 2.2, fig. 4a) in all cases. The following velocity fields are assumed for the three blocks; they satisfy incompressibility and boundary conditions: * plastic zone (inside (r)): Urz u =h 7 uz2 w = -h 7 dh and -dt --'

r

figure 7 : model 2 of co-extrusion. The plastic zone thickness is constant. left : evolution of geometry right : schematic velocity field.

439

Here, the thickness h of the plastic zone is constant; the plastic zone goes down at the same velocity U as the Dunch. Hence:

(7) h is calculated by minimising the dissipated power /lo/. The velocity field is: * plastic zone: Ur(z-h,) u= h2

z = 0 is now taken at the bottom of the sample. * in the wall (rigid): 11 = 0 w=

2.3.3 Comparison with experiments Experiments have been carried out with: - S = 0.4 (annealed Al on work hardened Cu) - S = 0.7 (work-hardened A1 on work-hardened Cu) - S = 1.26 (AU4G [2017] on Cu) Aluminium surfaces have been lubricated by Zn stearate, copper surfaces with emulsions. Figure 8 /11/ shows the computed initial shapes (eqns. 5 , 11-14) of samples, and the computed and experimental final workpieces. Comparison shows that the technique used to compute (10) is quite efficient for optimising this process

U = CSt

( p - 1

* under the plastic zone (rigid) 0 w=O By the same manipulations as above, the lateral part of (r) can be determined, together with the trajectory of a material point; including in the analysis the points initially below the plastic zone, the whole optimal (10) can be determined /11/: 11 =

-theo.

for points initially inside (ro). Let us define point Q, which is the point of (10) which

S : 1.26

will leave the plastic zone just when its bottom will reach the sample bottom (for instance point 8 in figure 4a); coordinates of Q are:

If P is the point of (10) at the bottom of the plastic zone (point 6 in figure 4a), points between P and Q form a cylindrical part of (10)with: r = roQ Finally for points below Q:

(13)

figure 8 : optimised bearings: comparison of experimental and computed shapes. above: S=0.4 below left : S = 0.7; below right : S = 1.26 2.4 Adherence of the coating As seen in the introduction, adherence will be closely related to the strain experienced by the interface. From the velocity field, it is easy to deduce a strain map in the formed bearing. Figure 9 shows such a strain map calculated in the case of model 2 /12/ :

440

figure 10 : apparatus used to measure interface strength. highest strain show the best adherence. Extrapolation seems to show that, in agreement with literature 161, a threshold exists under which no measurable adherence is found. Hence, whatever is done to impose a good geometry at the bearing top, this part will have to be cut anyway because i? is small and will give poor or no adherence.

figure 9 : calculated strain map in a co-extruded bearing. Dotted zone represents a coating, with (10) cylindrical. Under the hypothesis used (model 2 throughout), the presence of the coating has no influence on the strain map.

- about half the strain comes when the metal is sheared at exit of plastic zone. - a zone at the top undergoes zero strain (points which were initially above the plastic zone. More generally, strain at the top of the wall is much smaller than at the bottom. - as a whole, strains are very high and, except at the top of the wall, occur under high compressive stresses, which constitutes the basis for a good adherence of coating, provided oxides are brittle enough. These conclusions on strain maps have been qualitatively confirmed by observation of grain shapes at various locations 18,121. Experiments have been carried out to measure adherence force: an annulus is cut at various elevations in the wall, and the force necessary to shear the interface is measured (figure 10, /12/). It is observed that this adherence force is greater for annuli cut near the bottom of the bearing. Average strains experienced by annuli from diverse samples have been calculated. Correlation between strain Z and adherence stress CJi is reported in figure 11. Clearly, the regions with

figure 11 : correlation between adherence and strain for several bearings.

3 WIRE DRAWING OF BRASS COATED STEEL CORD Steel cord is used in the reinforcement of tyres. The brass coating has several duties: - promote adhesion to rubber, through a series of interphases with sulfur coming from vulcanised rubber /2,3/. - protect the wire against corrosion by water diffusion through rubber. - lubricate wire-drawing, which would be practically impossible otherwise for such a hard material (yield stress reaches 3 GPa in final passes). Coating (= 1.5 pm) is deposited electrochemically before final wire drawing (15 to 18 passes). During the last part of the process, the coating may undergo severe evolution (see figure 12, /13/): -the coating becomes thinner and thinner because: * the external surface of the wire increases proportionnally to the decrease in radius (from about

44 1

1.2 nim to 0.25 mm).

* a part of the brass is lost by mechanical or chemical action and may be found in the lubricant boxes. - pre-existing scratches evolve into a transversal

"plateaux and valleys" pattern. - in extreme cases, some plateaux are practically deprived of brass. We will now illustrate these phenomena and their consequences.

i ",L

",-

0

(radians)

figure 14 : comparison of experimental 1151and computed relative passing thickness H = hf/ho. Yield stress ratio S=8 experiments by I151 - present model, with rounding radius r taken

from 1151(for extrusion)

_ _ _ _ _ present model, with r = 0 (for drawing)

figure 12 : evolution of brass coating with wire drawing (brass appears dark, steel clear). above :just after deposition; below : after 15 passes

3.1 Scalping of coating 1141 This effect is perfectly evidenced in figure 13 1151: the superficial part of a soft coating, pinched between harder materials (die and substrate), flows back as a "micro-chip'' and is rejected. Extrusion experiments by WILSON and coworkers I151 have shown that the proportion of coating which passes this obstacle mainly depends on the yield stress ratio S (substrate /coating) and the die semi-angle (figure 14).

The same model can apply to both extrusion experiments of 1151 and wire drawing, as the states of stress only differ by a hydrostatic pressure, and velocity fields are similar. Also note on figure 13 that plastic deformation of the substrate begins gradually through a rounded zone of radius r. This effect is found in extrusion, but was not observed in wire drawing 1141. The coating first contacts the die. The two shear stresses (friction on the die, shearing of interface) increase the pressure according to (eqn. 15), obtained by the slab method (stresses independent on radial coordinate r):

(see notations in figure 15). Tresca's ["friction layer"] model for friction has been assumed: ~

=- OOM m

d3

In the substrate (submitted to peripheral shear stress 71):

Far from entry, ( J ~ M= C Y ~=D0. Then pressure builds figure 13 : longitudinal section of a coated billett after interrupted extrusion. Note backflow resulting in chip formation, and progressive rounding of substrate entering plastic deformation 1151.

up more rapidly in the very thin coating than in the thick substrate. At point C (figure 15): OxD - OrD = GOD (18) and plastic deformation of substrate begins.

442

With these data, computed H is 0.99, and quite sensitive to friction (if E = 0.45, H = 0.93). Brass losses have been measured by coulometry, and correspond to an average H = 0.98 . 3.2 Roughening of the coating/substrate interface.

In hydrodynamic lubrication, roughening of a plastically deformed surface is a well known and understood phenomenon, although its modelling is in its infancy /16/, In fact, quite the same effect exists for a substrate under a much softer coating acting as a lubricant. Figure 12 /13/ compares initial and final cross sections of coated wire. On just coated wire, some scratches from previous drawing exist. Coating thickness is practically homogeneous. After 15 passes however, a "plateaux and valleys" regime appears: brass is trapped under high thickness in small areas (valleys), whereas large zones are practically devoid of brass. As drawing proceeds, the proportion of valleys regularly increases (figure 16).

1

+--

I wire

I

I

c

pressure build-up

0

x2

-'-

-

L

I

plastic defomiation of substrate

I

I

I

'-

:

___t

XO

entry zone

. X

figure 15: geometry and mechanics of drawing or extrusion of coated products. This set of equations and boundary conditions, together with the functions R(x) and h(x), permits numerical computation of hi as a function of h,. There remains to establish a relation between hi and ho . As in hydrodynamic lubrication, a parabolic velocity profile is assumed. Backflow exists between xo and point C . After C, the coating is trapped, and its thickness is computed from volume constancy, so that hf is easily calculated. h Writing the global volume constancy results in hi- f(L) ,

ho-

gOr

volume of valleys total volume of coating

80 60 70

50

40

30 20

hi

and l o0

r H is a function H(S,O,E)of yield stress ratio, die semiangle and relative rounding radius. Note that this last parameter cannot be predicted. In figure 14, we have taken for our computations the experimental values of r in /15/ corresponding to the experimental results pictured. The agreement on relative passing thickness is quite satisfactory. For application to wire drawing, we must set r=O, i.e. follow the broken line of figure 14. The following data have been used: - m = 0.5 is calculated from the experimental wire drawing force by inverting a model . - S = 3.5 as an average along 15 passes. -8~6'.

% 1

2

3

4

5

6

7

8 passnr

figure 16 : evolution of the proportion of valleys with wire drawing pass number. Cumulated surface of valleys is measured on micrographs. As this phenomenon is at present very difficult to model, we have simulated it with plasticine at large magnification, in order to observe the flow of coating and substrate around the scratch (figure 17). Rolling was selected instead of wire drawing for practical reasons. However, conclusions are quite similar: - the width of the scratch increases (just as the proportion of valleys does). - its depth decreases, faster than the overall thickness of the sample. - two ridges form on each side of the valley, tending to pierce the coating.

443

- the metal of the substrate tends to flow into the region of less resistance (the scratch full of soft metal). - the volume of an individual scratch decreases (figure 17).

However, in wire drawing, the number of valleys increases and globally, the proportidn of brass trapped in the valleys increases along the sequence (figure16). cross section of defect (cm*)

After pass 11, the global friction stress becomes greater than the maximum admissible shear stress of brass (measured by torsion). At the same stage, surface analyses reveal that uncoated steel zones appear on the surface, which explains the paradox.

07

f

/

m 2

I =

=. ' -

t

'.

+

I

Q31/

ll

/'

/'

/

+ +

0.1

1

I 0

1

-

2

\

3

P

4

pass nr

-

+

+

+

+

0

0

------+

c _ _ _ _ _ _

//--

l 1

l 1 2 3

I

I

1

2

B I 3

I 4

pass nr 1

1

I

I

4

5

7

9

I

1

I

111213

I

t

15

18

figure 18 : evolution of the friction stress z with increasing pass number. + measured average values of friction stress - - - shear yield stress of brass measured by torsion.

3.3.2 Evolution of brass surface composition

figure 17 : flow of soft coating and hard substrate (yield stress ratio S = 0.35) around a model scratch. Deformation is by rolling (4passes of 15% reduction each).

Due to the deposition technique, a gradient of composition exists initially in the brass coating (figure 19, /13/).

[cl at OHe---

/

70

As a conclusion, if the initial wire does not have a very smooth surface and if lubrication is not very efficient, the process may evolve towards a situation where most of the coating is useless because trapped in too deep valleys, whereas it is absent on large areas of the wire.

50

0c

---

/'

/

1

3.3 Tribological consequences

.-------

3.3.1 friction stress in wire drawing

t,Yl As brass is also a lubricant, any place from where it is absent will be submitted to increased friction stress. This is illustrated in figure 18, where the average friction stress has been calculated by measuring the drawing force and inverting a mechanical model of wire drawing /17/.

6

I

I

60

'a'

-'\*360 6oo Depth

(nn:

figure 19 : composition gradients in brass just after deposition. AES coupled with ion beam etching. Depth was calibrated by stylus profilometry.

444

As the surface of brass is scalped by the mechanism described in 3.1, the surface moves towards zones with higher Cu concentration. Surface composition evolves, and eventually reaches the nominal 70/30 composition in the case studied /13/. It should be remembered that this final surface composition is of tremendous importance in view of the adhesion to rubber. It has been shown that at least part of the observed evolution of brass surface composition could be attributed to the combination of scalping and the existence of an initial gradient of composition. 4 CONCLUSION Forming of coated pieces by plastic co-deformation involves severe difficulties, as the flow of two materials with very different mechanical properties is hard to foresee. However, as it generally induces good adherence of coatings, such processes are in common use and should be optimized. We have shown how mechanical models can predict the geometrical evolution and finally allow to control it. But they moreover can help understanding the evolution of the properties of the coating. In this paper, only simple modelling techniques have been used. They have proved efficient to understand the major features of the processes investigated. In particular, the analytical character of the model of bearing extrusion allowed to directly design the optimal initial shape, which would have required a very long and tedious procedure otherwise. However, some problems remain unsolved (think of the rounding of the substrate in bar extrusion), for which more sophisticated techniques such as finite elements are required. REFERENCES

/1/ DELAMARE, F. "Etude du monnayage d u n faux louis d o r d'Cpoque 1775". Mem. Et. Sci. Rev. Met. , JulyAugust 1983,385-390 /2/ VAN OOIJ, W.J. "Fundamental aspects of rubber adhesion to brass-plated steel cord." Rubber Chem. Tech. 1979,52,3,605-67 1 /3/ BOURRAIN, P. in "tire reinforcement and tire performance", ASTM STP 694. FLEMING, R.A. and LIVINGSTON, D.1, eds, 1979,Publ. ASTM, Philadelphia /4/ SCHEY, J.A., ed. "Metal deformation processes: friction and lubrication" , 1970 (Marcel DEKKER, NEW YORK)

/5/ CAVE, J.A., WILLIAMS, J.D. "the mechanism of cold pressure welding by rolling", J. Inst. Met.,1973, 101,203 /6/ BAY, N. "cold pressure welding: the mechanisms governing bonding", J. Eng. Ind. ,1974,101, 121 /7/ SIKORSKI, M.E. "The adhesion of metals and factors that influence it", Wear, 1964,1, 144 /8/ MSTOWSKI, J. "Etude thCorique et expkrimentale de la dCformation plastique d u n solide bimCtallique", Thkse de docteur-IngCnieur ENSMP, 1983 /9/ MONTMITONNET, P., MSTOWSKI, J. "Manufacturing of bi-layered plain bearings by bimetallic cold backward extrusion. 1- experimental study: simulation by plasticine", J. Mech. Working Tech. , 1983,8, 327-336 /lo/ MONTMITONNET, P., MSTOWSKI, J. "Manufacturing of bi-layered plain bearings by bimetallic cold backward extrusion. 2- Mechanical modelling", J. Mech. Working Tech. , 1983, 8, 337347 /11/ MSTOWSKI, J., MONTMITONNET, P., DELAMARE, F. "Geometrical optimisation of bilayered plain bearings manufactured by cold backward co-extrusion", J. Mech. Working Tech. , 1986, 13, 291-302 /12/ MONTMITONNET, P., MSTOWSKI, J., DELAMARE, F. "Interface adherence after cold backward extrusion of a bilayered plain bearing", J. Mech. Working Tech. , 1985, ll,23-26 /13/ DARQUE-CERETTI, E. "De la composition superficielle des laitons a, et d e son Cvolution sous bonibardement ionique. Application 2 I'ktude des surfaces de fil d'acier IaitonnC.", Thesis, 1986, UniversitC de Besancon, Nr 209 /14/ MONTMITONNET, P., DELAMARE, F. "calcul de 1'Cpaisseur passante d u n revstement mktallique au cours d u n formage multipasse", Mem. Et. Sci. Rev. Met. , July-August 1986, 347-354 /15/ WILSON, W.R.D., WHITE, D.R. "Solid lubricant entrain men t in hydrostatic ex t r u s io n " , A S LE Trans., 1980,2,3,305-314 /16/ YAMAGUCHI,K., TAKAKURA,N., FUKUDA,M. "FEM simulation of surface roughening and its effect on forming limit in stretching of A1 sheets", Proc. Conf. Adv. Tech. Plasticity, 1987, STUTTGART, Vol. I1 /I 7/ E L D E R , E. "evaluation of the influence of redundant work and friction in wire drawing", Annals CIRP, 1 9 7 6 , a , 1, 51

445

Paper XIX (iii)

Deformation and fracture of hard coatings during plastic indentation D.M. Elliott and I.M. Hutchings

The aim of this work was to investigate by means of model experiments with electroplated nickel coatings on copper substrates, the deformation and fracture of hard coatings on softer substrates. Whilst some confirmation of current theoretical models is found, the use of small loading increments in the Vickers hardness test has permitted a more detailed analysis of the deformation of the coating and substrate. An interesting feature of the results is an apparent discontinuity in the variation of indentation hardness with load observed for several coating / substrate combinations. Examination of the indents in crosssection revealed a possible connection between these discontinuities and changes in the geometry of deformation in the substrate.

Notation

the load over an area around the square perimeter of the indentation. From geometrical considerations they thus proposed the following equation:

Ho Apparent hardness Hs Substrate hardness Hc Coating hardness t

Coating thickness

d

Indent depth

L

Applied load

1.

INTRODUCTION

In many technological applications hard materials are employed as protective coatings: e.g. titanium nitride on steel. The need to be able to predict the tribological characteristics of the ever increasing number of materials used for such purposes has prompted many researchers to investigate the deformation of these coatings. One common method of investigation is to make an indentation in the coating as in a conventional hardness test, (Vickers, Knoop, or Brinell). Analysis of such tests has led to several theoretical explanations for the behaviour of the coating and substrate during indentation. Several recent models for the apparent hardness, ( Ho = normal load per unit area ), of a composite sample consisting of a coating layer on a softer substrate take the form suggested by Bucklel: Ho = Hs

[24- ~*(:)2] 4

Ho = Hs

+ b[Hc - Hs]

where Hs and Hc are the indentation hardness values for the bulk substrate and coating materials respectively. During the Vickers hardness test, which uses a pyramidal diamond indenter, Jonsson and Hogmark2 have suggested that the coating supports

+

4

[Hc - Hs]

Here c is a geometrically determined constant which depends on the relative hardness Hc/Hs, and varies from sin222" (=0.140) for high hardness ratios to 2sin21 l o (=0.073) for low hardness ratios. The thickness of the coating is denoted by t and the depth of the indentation by d. This model is valid only for indents which penetrate more than half the thickness of the coating, and when the latter behaves in a relatively brittle manner compared with the substrate. For these reasons it has a useful though limited applicability in the study of protective coating failure. Other models such as that of Haddow and Johnson3, fit cases where the volume of material displaced by the indenter produces pile-up around the indent. Burnett and Rickerby4 used a model (after Sargents ) which relies on a knowledge of the deforming volumes of the coating and the substrate and of several constants all of which have to be estimated. The mechanical behaviour of many of the materials used as tribological coatings is not yet fully understood, and many have properties which depend critically on the conditions employed in the deposition process; they may also be of variable composition. The present work was therefore carried out on coatings of nickel electrodeposited on copper substrates, in order to investigate the applicability of the various theories of indentation behaviour to a model system, with substrate and coatings of well characterized and reproducible materials, the hardness of which could be varied independently. The indent depths ranged from less than one tenth of

446

the coating thickness to about one and one half times the coating thickness; in all cases little or no pile-up occurred.

650

4

2. EXPERIMENTAL METHOD

Nickel was deposited by electroplating with small compressive residual stress, on to polished copper (B.S. no. c105) and copper-beryllium ( B.S. no. cblOl 1.7% Be) substrates 2 cm2 in area. The electroplating bath was operated with vigorous agitation at a temperature of 55"C, a pH of 5.5, and a current density of 3 A dm-2. The electrolyte consisted of 300 g of nickel sulphate, 28 g of sodium chloride and 40 g of boric acid dissolved in 1 litre of distilled water. By varying the amounts of organic additives in the plating bath, ( 3-5 g/l of saccharin and 0-0.08g/l of thiourea), by heat treatment, and annealing, the hardness of the nickel, of the copperberyllium and the copper respectively were controlled. Samples were produced with nickel coating hardness from 300 to 800 kgf mrn-2 (VPH), and copper substrate hardness from 30 to 370 kgf mm-2, giving ratios of coating to substrate hardness ranging from 1:1 to about 20:l. In this work two distinct types of nickel coatings were produced. The first was a relatively homogeneous coating similar to that produced in commercial electroplating, with hardness between 300 and 600 Kgf mm-2. The second type of coating was designed to be particularly resistant to wear, and combined high hardness with a certain amount of ductility. The increase in ductility over that of a commercially produced hard nickel electrodeposit was achieved by close control of the surface active additives in the bath, leading to the formation of a stratified structure ( with layers about l p m thick) parallel to the substrate surface. The hardness of some coatings of this type was as high as 800 kgf mm-2. Vickers indentation normal to the coatings (with thicknesses between 5 and 40 pm) was carried out with a Leitz Miniload microhardness tester using twenty-five loads ranging from 5 to 500 g force (0.049 to 4.9 N). Vickers hardness values were calculated from the measured indent diagonals ( six at each load) and plotted against load for each sample. 3. RESULTS AND DISCUSSION Figures 1, 2, 3a, and 3b show typical examples of the variation of composite hardness with load. The thickness of the coating was determined in each case in the first instance by profilometry of a step produced by a mask during electrodeposition of the coating. The thickness was subsequently measured again by optical microscopy after the coating had been sectioned. The results of these measurements suggested that the coating was thicker close to the perimeter of each specimen. The indents were all made close to the centre of the plated area on each, ensuring a similar value for the coating thickness at all loads. Care was taken to ensure that the deformation introduced by earlier indentations did not influence subsequent indentations, by spacing

0

100

500

400

200 300 Load (g force)

Figure 1. Variation of hardness with load for a 57 pm coating of nickel (VHN 588 kgf mm-2) on copper (VHN 50 kgf mm-2). 800

9

600-

E E L

0)

E. 400-

z I >

200

-

0

*-. I

0

100

.

I

.

I

. '


I

.

400

500

Figure 2. Variation of hardness with load for a 5 pm coating of nickel (VHN 670 kgf mm-2) on copper (VHN 45 kgf mm-2).

N

500 6oo

400

k -

L

2 z

300-

I

> 200100

0

100


400

500

Figure 3a. Variation of hardness with load for an 8pm coating of nickel (VHN 574 kgf mm-2) on copper (VHN 76 kgf mrn-2). """ I 4

200 0

100


400

Figure 3b. Variation of hardness with load for a 5 pm coating of nickel (VHN 683 kgf mm-2) on copper (VHN 280 kgf mm-2).

500

447

Figure 4. Forms of indent (not to scale).

Figure 4.1. Examples of indent shape produced at 65 g, 91 g (a), and 395 g (b) loads corresponding to the three linear regions of the hardness/load plot in Figure 3ba.

Figure 4.2 (a,b) Examples of indents exhibiting similar square shapes at all loads with cracking of the uppermost layers. The indents were produced by a 454 g load (a) and 1 kg load (b) in a 5pm coating of nickel (VHN 597 kgf mm-2) on copper (VHN 140 kgf mm-2). the indentation sites at least three indentation diagonal lengths apart. From the experimental results, various trends can be identified. The decrease in composite hardness as the load is increased can be categorized in three ways, depending on the relative hardness Hc/Hs, and the coating thickness. Hard coatings thicker than 30 pm, and all coatings where the hardness ratio was small, displayed an almost linear decrease of hardness with increasing load, with some minor deviations due to cracking of the coating as shown in Fig. 1. Samples with coatings thinner than about 10 pm and with very soft

substrates (30cHsc80 kgf mm-z), exhibited a much sharper decrease of hardness with load as shown in Fig. 2. The third category of coatings were in general from 5 to 15 pm thick on substrates with hardness between 7 0 and 370 kgf mm-2. In this category the decrease in hardness with load could be divided into three linear regimes, (Fig. 3a). In the case of the homogeneous (non-stratified) nickel coatings these corresponded t o three different geometries of indentation. The first (formed at the lowest loads) appeared as a normal square impression. The second (at intermediate loads) had slightly concave sides, but with no deformation of the surface

448

Figure 4.2 (c,d) Examples of indents exhibiting similar square shapes at all loads without cracking. The indents were produced by 454 g and 1 kg loads (c)(optical microscopy) and a 1 kg load (d)(SEM) in a 5 pm coating of nickel (VHN 683 kgf mm-2) on copper (VHN 280 kgf m171-2). apparent outside an area bounded by a square defined by the measured Vickers diagonal. The third (formed at the highest loads) was similar to the second but with increased curvature of the indent sides, and deformation of the surrounding surface bounded by a circle that intersected the indent corners. These three indentation shapes are shown in Fig. 4, with examples given in Figures 4.1 and 4.2. Although the nickel coatings produced with a layered structure did not exhibit these changes in indentation geometry (the indents being almost square for all loads), the discontinuities in the hardness / load plot were still evident, as seen in Fig. 3b. Cross sections through the indents (parallel to the square edge and through the deepest point) revealed that the layers in the nickel had allowed a gradual change in the form of deformation throughout the coating. The layer in contact with the indenter followed the shape of it closely, whilst the layer closest to the substrate showed deformation at high loads which followed a much smoother profile than that of the indenter. This effect is shown by the coating in Fig. 5. For the purpose of this photograph the indent was made near the edge of the coating, as the thicker layers found there show up more clearly after etching. The discontinuities in the hardness / load plot were again found to correspond to changes in the deformation geometry, but this time they were discernible only in the lower layers of the coating. The first linear region of the plot in Fig. 3b corresponded to the case where there was little or no deformation of the substrate, (Fig.6a). The second linear region appeared to correspond to a smooth bowl-like deformation of the substrate such as might have resulted from indenting the substrate with a sphere, (Fig.6b). The third linear region of the hardness plot (at high loads) was associated with indents large enough to cause pyramid - shaped deformation ( with some rounding) of the substrate (Fig.6~).

Figure 5. An etched cross section of a 1 kg indent in a 14 pm coating of nickel (VHN 683 kgf mm-2) on copper (VHN 280 kgf mm-2) showing the gradual change from the sharply deformed top layer of the nickel to the smoothly deformed surface of the copper.

The first and third of the regimes and deformation patterns described above are common to most indentation experiments over a range of loads from those small enough to ensure that the plastic zone is confined to the coating alone, to those where the calculated hardness value approaches that of the substrate. Often there is no distinct transition between the two. It is the second regime, which appears with some coating/substrate combinations, which is of particular interest. In this regime the substrate is smoothly profiled, with its size increasing in line with that of the indent in the coating above. The fall in the rate of increase of indent size in the coating with increasing load during regime two can be accounted for by the smooth spread of deformation (good load bearing characteristics) of the substrate. The same loads would cause a gradual increase in size of a pyramidshaped deformation (poorer load bearing characteristics) in a coatingkubstrate combination that exhibited regimes one and three only.

449

5. CONCLUSIONS A previously unreported phenomenon has been observed during the indentation of hard coatings on soft substrates.The variation of the overall indentation hardness with load, for coatings satisfying certain conditions, exhibits three linear regimes which, for homogeneous electroplated nickel coatings, correlate with a change in form of the indentation. Cross sections through the indents reveal that whilst for stratified nickel coatings deformation of the free surface takes the same form at all loads, the deformation pattern of the underlying substrate changes from one form to another, corresponding to the different linear regions of the hardness / load plot. Work is in progress to produce a theoretical model to explain these observations and to correlate the results with those obtained from scratch tests at continuously increasing load. References

1. Buckle, H., "The Science of Hardness Testing and its Research Applications", 1973, A.S.M., Metals Park, Ohio, 453. Editors: J.H. Westbrook and H. Conrad. 2. Jonsson, B. and Hogmark, S . , Thin Solid Films, 114, (1984), 257. 3. Haddow, J.B. and Johnson, W., "Indenting with Pyramids", Int. J. Mech. Sci. 3,(1961), 229-238. 4. Burnett, P.J. and Rickerby, D.S., Thin Solid Films, 148, (1987), 51-66. 5. Sargent, P.M., PhD Thesis, "Factors Affecting the Microhardness of Solids", University of Cambridge, 1979.

Figure 6. Cross sections of indents showing the three regimes (a at 50 g, b at 100 g, and c at 1 kg) corresponding to the three linear regions of the hardnesslload plot in Figure 3b.

Experiments have shown that occurrence of this second regime is dependent on several conditions. The ratio of coating / substrate hardness must lie within certain limits, namely between about 1.5:l and 6:l and the thickness of the coating should be between 4 and 12 prn.


SESSION XX COATING EVALUATION Chairman:

Professor G. Dalmaz

PAPER XX (i)

Coating evaluation methods: a round robin study

PAPER XX (ii)

The effect of dynamic loads in tribometers analysis and experiments

-


453

Paper XX (i)

Coating evaluation methods: a round robin study H. Ronkainen, S. Varjus, K. Holmberg, K.S. Fancey, A.R. Pace, A. Matthews, 6.Matthes and E. Broszeit

This paper reports work carried out at three laboratories, aimed at assessing the repeatability of various test methods used in the study of tribological coatings. The test methods were the ball crater technique for coating thickness, the Vickers microhardness test, the scratch test for adhesion and the pin on disc test for friction and wear. Three different coatings were studied, based on various compounds of titanium, boron, nitrogen and aluminium. A l s o different novel ionisation assisted PVD methods were used to produce the coatings The paper demonstrates the spread of results obtained by each of the tests on each of the coatings, both within each laboratory and also between laboratories. The results show that assessment of properties such as thickness and hardness can be made with reasonable repeatablity; greater care must be taken however in ascribing quantitive measures to adhesion levels. In particular it is necessary to define the criteria to be used for failure. In the case of friction and wear assessment the laboratories involved demonstrated that considerable variability can be seen, both in friction coefficients and wear rates. Nevertheless we demonstrate that the tests described provide a good basis for the assessment of coating properties and for the investigation of tribological behaviour, permitting further coating development. 1.

I~ODUCl'ION

With t h e increasing widespread use of surface engineering techniques in industry, there is an urgent need to develop standard coating evaluation techniques which will permit meaningful comparison of the relative performance of existing and newly developed coatings. Furthermore, the identification of standardised specifications will enable design engineers to specify coatings with confidence in more applications, thereby ahancing the triblogical performance of a wider range of engineering components. The main coating parameters which need to be assessed are thickness, hardness, adhesion and triblogical (friction and wear) performance. Over recent years, many efforts have been made to understand these properties more fully, with the development (for example) of adhesion test methods based on scratch testing, and the identification of preferred triblogical test procedures (eg the VANAS standard). The laboratories involved in the research reported here have been working for many years both independently and jointly in the evaluation of these properties. Under the aegis of a recently awarded EC EURAM grant they resolved to try to establish the consistency of tests carried out in different laboratories and to understand more fully the factors influencing relative coating performance. The designations used for the laboratories involved are: Technical Research Centre of Finland(V'IT), University of Hull ( W ) and Technische Hmhschule

Darmstadt (THD). Technologically important new coating materials, based on nitrides and brides of titanium and aluminium were chosen, representing the latest developments in plasma assisted PVD technology. 2.

EXPERIiYENTAL PRO3DLJRE

2.1

Deposition Details

basic deposition methods were used: ionisation assisted electron beam (EB) PVD and radio frequency (RF) magnetron sputtering. The former method was used at V" and UH whilst the latter was performed at THD. In addition, different coating ccmpositions were prduced by changing the source material. The combinations can be summarised as follows: Two

Source Material

Partner (Coating Designation)

Deposition --Method -__

TiB2 + RN

UH(A)

DC Ionisation ass isted EB PVD

TiB2 + N

THD(B)

RF Magnetron Sputtering

Ti A 1 N

VTT(C)

DC Ionisation ass isted EB PVD

454

Several coating thicknesses were included in the range 2 to 8Nm, representing typical values currently used for PVD deposits. The substrate material in each case was polished ASP 23 tool steel, hardmed to 64 Rc, with a surface roughness of 0.4,Um Ra. 2.2

ABRASIVE SOLUTION

k-

Gvaluation Methods

The techniques shown below were used to assess coating properties: Test Method

Property Evaluate3

Ball Crater

Coating Thickness

Vickers Microhardness

Coating Hardness

Scratch Test

Coating Adhesion

Pin on Disc

Friction and wear Performance

Test details:

t COATING

Ball Crater

+SUBSTRATE

A schematic of the test is shown in Figure 1. The b a l l diameters used were: UH 25.4 mm; THD 25.4 mm; VlT 30.0 mm.

Figure 1

A kerosene diamond suspension was used as the abrasive medium.

Schematic Views of the Ball Crater Apparatus and the Crater Profile.

Scratch Test The following expression was used to assess the thickness: Thickness =

x. y Ball Diameter

Measurement of x and y were made at UH using a Shinko profile projector, at W using an Olyrnpus BH-2 microscope and at THD using the measurement facility on a Leitz Miniload microhardness tester. Each laboratory produced one crater from which four determinations of thickness were made to obtain a mean and standard deviation value. All craters were located within a 4mm x 5mm area on each sample. Further details of the ball crater technique are given in Ref 1. Vickers Microhardness VTT used a PMT 3

machine, UH and THD used Leitz Miniload microhardness testers. In all cases loads of 15,25,50 and 100 gms were used. The indentation dwell time was 10 seconds. Each laboratory made five indentations per load within the same specified rectangular area (20mm x 5mm) on all coatings. The mean and standard deviation of the hardness n m k r was determined from each group of five indentations by one person in each laboratory.

VTT and UH used scratch testers manufactured by VTT Tech (see figures 2 and 3). THD used a CSEM (LSRH)Revetest machine. All t - e e

machines were equipped with acoustic emission and friction force measurement. The loading rate was 100N/min and the table s+ed was Ih/min. The nominal maximum load was 100N. Each machine used a Rockwell 'C' diamond indenter geometry (radius 200Jlm). The indenter was cleared of residues by manually polishing against a hard titanium nitride coating (on a high speed steel substrate), and subsequently examined in an optical microscope to confirm removal of debris. As for hardness testing, the tests were carried out at ambient laboratory temgerature and humidity conditions (typically 20 C, 5070% relative humidity). Three scratch tests per coating (one near each end and one near the centre) were performed at each laboratory. The mean and standard deviation of designated critical loads was evaluated from each group of three scratches.

Pin on Disc Test Pin on disc tests were carried out using a fixed lorn diameter polished ball as the pin. The disc was horizontal on the VTT and UH machines, and vertical on the THD machine. The pin material was M50 steel (80 Mo Cr V42 16), nominal hardness 62R The discs were coated, being ASP 23 mategial (nominal hardness 64Rc). The tests were performed

.

455

~

unlubricated at a sliding speed of O.lm/sec, and a normal force of ION; they were run for a sliding distance of 250m. The relative humidity during testing was controlled to 50 + 2% at VTT and UH; at THD the ambient hmidity was 68 4%. The temperature for the VTT and UH tests was 21 5 2OC, whilst for THD it was 23 5 IoC.

Pm

COATING A

COATING

COATING

B

C

10

€I.

8

6

II 4

2

x

UH T H D W

UH T H D W

Figure 4

3.2 Figure 2

The V l T Tech Scratch Tester

1

l n

I

Acoustic emission detector

application

Indenter Coated sample

Friction force transducer

UH T H D W

Coating Thickness Measurements

Vickers Microhardness

Figures 5 a, b and c summarise the hardness results as a function of load for each coating. The error bars represent standard deviations. In general, measurements performed at UH give the highest readings; those from VTT tend to be the lowest. Results from all three laboratories show a comparable hardness-load trend for coating C (Figure 5c) but this is less apparent for coating A and B as shown in Figures 5a and b. In the case of coating A, indentation sizes were more difficult to discern, due to the existence of other marks on the surface. Prabably the most interesting aspect is the considerable difference in absolute values from each institution. This can be most clearly seen in Figure 5c, where standard deviations for individual results are relctively small.

Driven sample-holder

Figure 3

table

Schematic view of a Scratch Tester

3.

RESULTS

3.1

Ball Crater

Figure 4 shows the mean thickness values for each coating, the error bars represent standard deviations. In all cases, the VTT measurements have the lowest standard deviation values and this is attributed to the ball crater scars being more symmetrical than those from THD and UH. Nevertheless, agreement between the mean thickness values from all laboratories was god.

3.3

Scratch Tests

In scratch testing the normal load can be applied incrementally or continuously. In our tests the latter route was followed. The detection of 'failure' events can be by acoustic means, by monitoring of tangential force or by optical means. We utilised all of these in our tests. To some extent we found that the interpretation of results was highly subjective. In particular, the definition of critical loads initially differed from laboratory to laboratory. Many writers have referred to the existence of "lower" and "upper1'critical loads, representing cohesive and adhesive failure respectively, ie a failure within the coating or at the coating to substrate interface.

456

TANGENTIAL FORCE HV

a)

6000

r;-u"l THD

COATING A

0

50001

T

4000 '

3000

2000

T +

I

T

3 8, I

I

A

1000

k2T

20

60

40

80

100

LOAD /q

El

6000

T 71-t

5000

4000

'OAYNG I T

SLIDING DISTANCE Figure 6

3000

2000

'Oo0

-

I

P'

B

t 20

40

60

80

100

LOAD /q HV

C)

COATING C 4000t

30001 looot

T

f z

2000

I

if

€ I

I: I

20

40

S

60

80

100

LOAD /g

Figure 5

A Typical Tangential Force Trace from a Scratch Test

Coating Hardness 'iiesults

Figure 6 is an example of a scratch test trace. After discussion between the laboratories we defined the criteria for two critical loac'ls, L and LCzT: L corresponds to thg' Tirst signific%T change in the tangential force, L is the first substantial change in the FGgential force gradient. The results, utilising these criteria (Figure 71, show a gsneral agreement between laboratories within the standard deviation limits for both critical loads. No systematic correlation was found between results derived frcm acoustic emission traces from any of the laboratories. Representative scratches from the three coatings are shown in Figure 8. Direct inspection of these scratches allows the definition of two further critical loads: LCID and Lc2 L is the first point of cohesive fai!?ure:'E is the first point of adhesive failure. fgDcan be seen from Figure 8 that Lc2D occurs within the scratch channel for the coatings A and B whereas coating C first shows adhesive failure outside of the channel.

.

Figure 9 summarises the L and L values. There is general agreemeng' !&tweenc%e results of all the 3 laboratories within standard deviation limits. However the L C1 D values of coating A show larger variations. Figure 10 shows the appearance of three scratches frcm this group. Although the nature of the failure is similar, it occurred sooner on the UH machine, for this coating.

457

NORMAL FORCE

COATING

COATING

COATING

NORMAL FORCE

B

C

N

A

N

COATING B

COATING C

f

100

100

II

80

80

I

1 III$ 1

60

40

COATING

1%

60

i:

40

20

20

uuu UH THD VTT

Figure 7a

UH THD VTT

UH THD VTT

Lmer Critical Loads, Assessed from the Friction Force Trace ( Lc, T)

Figure 8

UH THD VTT

Figure 7b

Scratches frcm Coatings A, B and C

UH THD VTT

I I UH THDVTT

Upper Critical Loads, Assessed from the Friction Force Trace (LCzT)

458

NORMAL

FORCE

N

COATING C

COATING A

NORMAL

FORCE

N

100

100

80

80

60

60

PI

40

20

COATING A

COATING B

w

II I

40

20

u

& I UH THD VTT

Figure 9a

UH THD VTT

UH THD VTT

Lower Critical Loads, Assessed by Direct Observation (Lp,n)

Figure 1 0

COATING C

UH THD VTT

Figure 9 b

Three scratches on Coating A. (Top carried out at UH, middle at THD and bottom at VTT)

UH THD VTT

UH THD V l T

Upper Critical Loads, Assessed by Direct Observation (L-.,,.,)

459

During the tests, formation of white pwderlike wear debris was observed for all the coatings. The debris formation was found to be related to the friction behaviour of the coatings. For example, for the A coating (Figure 12) visible onset of wear debris formation happened after the first peak (/ct= 0.77) of the friction curve.

The results derived from the friction output can be compared with those derived from direct observation. The Lc2 results for coatings A and B show good agreement. However for coating C the results are not comparable, the failure mechanism being very different, as shown in Figure 8. In the case of the lower critical load values (Lc1 ) , the agreement between the friction force derived values and those by observation was less consistent, ie for coating B agreement was good, but not for coatings A and C. The probable reason for this was a greater amount of 'noise' on the tangential force trace, making determination difficult. 3.4

,.

UH

100 -

1.

THO

VTI

COATING A

UH

THO

COATING A

Figure 1 1

COATING B

COATING C

Figure 13

VTI

COATING B

DISC WEAR

I

P

"t

x10i5m3

/

Nm

Pin on Disc Tests

The pin on disc tests were carried out twice in each laboratory for each coating. Figure 1 1 shows the value of the steady state coefficient of friction for the coatings in pin on disc tests. For coating A the correlation of the friction values is god, whereas for coating B the variation in coefficient of friction ranges from 0.59 to 0.91. Results show that the lowest values were measured in UH and the highest in W. This may be an indication of differences in the measurement equipment or the apparatus characteristics. However the variation of the results show better agreement than those from "a UK interlaboratory project" (Ref 2) and about the same magnitude of variation as in "multilaboratory tribotesting" (Ref 3) , which were carried out with bulk materials.

1.o

PIN WEAR

10

'

UH

THO

VIT

COATING C

x10i5 m3 / Nm

The Mean Values of the Wear Rates

The mean values for the wear rates with the pin on disc system are sumnarized in Figure 13. The wear rates for steel pins and coated discs are in good agreement for coatings A and B whereas for the tests carried out at THD on coating C the values are higher. This is probably due to the influence of the higher relative humidity at THD, on this particular coating. If it were due to the different mounting arrangement (ie the vertical disc) then we would have expected differences also for the other coatings.

Steady State Coefficients of Friction

I

If 0.5

S

I

I

250m

0

Figure 12

Friction Behaviour of Coating A

Microscopic examination of the wear surfaces showed formation of transfer layers on the wear surface of the pin in all cases, as shown in Figures 1 4a, 1 5a and 16a. The wear scars o€ the discs were usually covered with scratches and some formation of the transfer layer was also detected (Figures 14b, 15b and 16b). In 15b a layer of wear debris can be seen beside the wear track.

460

Figure 14

Wear surface of the pin (a) and the disc (h) in pin on disc test for coating A (VTT test 2 ) . The arrow indicates the sliding direction of the counter face.

Figure 15 Wear surface of the pin (a) and the disc (b) in pin on disc test for coating B (VTT test 2 ) . The arrow indicates the sliding direction of the counter face.

46 I

It is worth mentioning that tests were also conducted at UH using an SAE 52100 (1OOCr6) ball as the pin, rather than M50 material. The difference in contact behaviour with coating C in this case was remarkable. Considerable pick-up or transfer of ball material to the disc was observed, and the friction coefficient was similar to that for steel to steel contacts. The transfer can be seen in 3D profilometer traces obtained at THD, in Figure 17. We believe that this effect is probably due to the higher hot hardness of the M50 material, compared to the SAE 52100, and the possible surface thermal softening of the latter during sliding, particularly at asperities where high flash temperatures occur. It is also possible that the effect is influenced by the different alloy constituents within M50 and the changes induced in interfacial tribochemistry. This would explain why the effect was not observed with coatings A and B. We also believe that our other results pint to a wear mechanism which is dominated by contact chemistry. A s evident in Table 1 , in order to have nominally similar sliding speeds and distances in all laboratories, it was necessary to use different wear track diameters. This meant that the number of wear passes differed; UH being the greatest, followed by THD then VTI'. There was certainly no systematic increase in wear rate when comparing laboratories using increasing numkrs of passes. In fact, if anything, there was a decrease. This seems to confirm the importance of tribochemical processes cmpred to ones based on fatigue alone. 4.

DISCUSSION ANTI CONCLUSIONS

Ball cratering for coating thickness measurements, microVickers testing for hardness, scratch testing for adhesion and pin on disc testing for wear and friction characterization have all been shown to provide useful information on the mechanical and tribological properties of coatings, ad should form the basis of standardised coating evaluation methods.

Figure 16

Wear surface of the pin (a) and the disc (b) in pin on disc test for coating C (VTT test 2). The arrow indicates the sliding direction of the counter face.

The ball crater test is quick to carry out; its only real disadvantage is that it requires the removal of the coating in a small (typically < 2 m diameter) flat area of the surface. Our tests show that the accuracy of the test is good, being independant of factors such as hardness and thickness, in the range we studied. Also surface roughness variations did not effect the accuracy, although if the roughness is too great this can make measurement more difficult. In other work we have satisfactorily used the method to measure thicknesses well over 100,Um. In Vickers microhardness testing the influence of the coating thickness is critical. For example coating C, which is the thinnest (approx 2.5&m), shaws typical load -hardness dependance, where higher loads give lower measured hardnesses. The influence of substrate hardness is clear.

462

a ) After t e s t i n g with an M50 ball. as t h e pin. Figure 17

b) After t e s t i n g with a SAE 52100 ball as the pin.

3-D Profilometer Traces of W e a r Tracks on c o a t i n g c .

testl

test2

THD testl

COATING A s l i d i n g t r a c k d i a m e t e r 18.7 wear volume o f p i n 0.97 wear r a t e of p i n 0.39 wear volume of d i s c 21.99 wear r a t e of d i s c 8.8 steady s t a t e p 0.65

18.8 1.45 0.58 25.05 10.02 0.66

23.6 1.7 0.68 34.14 13.65 0.70

UH

test2

VTT testl

test2

23.6 1.6 0.64 37.83 15.13 0.72

36.6 2.16 0.86 36.1 14.5 0.74

36.6 3.01 1 .2 41.8 16.7 0.75

23.5 0.94 0.37 23.26 9.3 0.70

23.5 1.01 0.4 47.06 18.82 0.75

35.5 2.03 0.81 44.3 17.7 0.90

35.5 2.49 1 56.5 22.6 0.91

Imm - 1 2 1 x 1 0 15m3 1x1 011 2 n 3 / N m /x10-15m3 1x10 m /Nm

COATING C s l i d i n g t r a c k d i a m e t e r 1 8 . 8 32.1 23.5 wear volume of p i n 5.37 9 . 4 3 7.26 wear r a t e of p i n 2.15 3.77 2.9 wear volume o f d i s c 60.06 64.1 151.78 wear r a t e o f d i s c 24.02 23.6 60.71 steady s t a t e p 0.66 0.75 0.91

23.5 14 5.6 135.6 54.24 0.70

34 7.75 3.1 89.5 35.8 0.89

35.5 9.32 3.73 93.7 37.5 0.85

/mm 1 2 1x1 0-1 5m3 /XI Om1 2n3/Nm 1x1 0 I 1 5m3 1x10 m /Nm

COATING B s l i d i n g t r a c k diameter 18.8 18.8 wear volume of p i n 2.36 1.19 wear r a t e of p i n 0.94 0.48 wear volume of d i s c 21.74 25.69 wear r a t e of d i s c 8.7 10.28 steady s t a t e p 0.54 0.63

Table 1

A summary o f t h e P i n o n D i s c T e s t Data.

/mm

,2 /XI 5m3 1x10 2n3/Nm 1x101x1 0-I 5:3/Nm

oI1

463

For coating A (approx. 4.5,Um) the correlation is not so apparent, the trend only being evident in the V" tests. Also the measurement of the indentation sizes was made more difficult due to coating structural effects. For coating B (approx 8.3pm) a combination of effects are clearly occurring, possibly relating to growth morphological changes through the coating thickness. Even on this coating though, the hardness test results from the three laboratories show similar trends. In the scratch test, the Lcl (lower value) and Lcg (higher value) are suitable prame ers to be used for cohesion and adhesion evaluation. Depending on the coating and substrate properties, the Lc values determined from friction traces may differ from values detennined by direct (opticalmicroscope) examination. Determination of L from friction traces would be suitable For practical quality assurance of the coatings, whereas direct examination is useful for analysing the physical phenomena in the contact. It seems that the thicker the coating, the better is the agreement between the values determined from the traces and by direct observation. The pin on dis'c test results emphasise the need to ensure identical test conditions, and the wide variability which can occur both in wear rates and friction coefficients. In practice we are dealing with complex interactions and failure mechanisms which produce variability in performance. This should be taken into account when assessing new surface engineering developments and designing and optimising tribological contacts. For the particular sliding pairs evaluated in this work, it was evident that the tribochemistry was a critical factor in determining the behaviour. Indeed, even when a relatively small change was made, such as moving from one steel to another for the pin, the performance characteristics changed completely. Further work at our laboratories will examine the influence of environmental changes, such as humidity; and different contact pressures, sliding speeds etc will be used to further assess the mechanisms occurring. It is also intended to carry out tests under extreme conditions, such as those in metal cutting at the tool tip. For optimal tribological design it is necessary to carry out comprehensive studies of this kind under the real contact conditions. However for initial comparative studies on newly developed coatings, our work has shown that the pin on disc test can provide a useful indication of relative performance, and an insight into the effects which control the performance. This gives the possibility to further optimise coating properties. In order

that the coatings from different laboratories can be compared, we recommend that a series of standard tests are devised building upon the work reported here. Acknowledgements Financial support for this work was provided at UEI and THD by the European Camunity €TIRAM scheme. At V'IT the work was supported by the Technology Developent Centre of Finland. We are indebted to several colleagues for helping in the practical work, in particular Peter Holiday (UH)and Werner Herr (THD)for pin on disc testing and Gary Robinson for SEM work. Special thanks go to Mandy Allen for typing the manuscript. References

1.

J VALLI, J POLOJARVI and U MAKELA, V'IT Research Notes 435, Technical Research Centre of Finland.

2.

A

3.

E AMOND and MG GEE, Wear, 120 (1987), 101.

H C CZICHOS, S BEand J LEXOW, Wear, 114 1987) 100.


465

Paper XX (ii)

The effect of dynamic loads in tribometers analysis and experiments

-

H. Heshmat

The analyses was carried out for dry contact tribosystems to elucidate the notorious uncharacterized relationship between the coefficient of friction, wear, and sliding velocity as functions of the tribotesters global dynamic properties: its mass, imbalance, stiffness, frequency, etc. Since the presence and level of dynamic loads are elevated by an order of magnitude in the modern tribotesters, dry contact, high speed rolLing/sliding and low resilient tribomaterials are the subject of study. Two types of tribometers, pin-on disk and disk-on-disk, have been considered for evaluation in order to determine: 1) dynamic forces due to runout of the spinning disc specimen; 2 ) load wear and coefficient of friction measurements and their interlocking relationship with item 1. The significance of the anal-yses lies in the prediction of dynamic loads in the contact surfaces of the tribomaterials due to the runout (static, dynamic and transient) of the specimens; where the coefficients of friction and wear values cbntain a certain degree of error in a complex form. The results of analyses and theoretical models backed by experiments offers a guide towards the correction, measurement and design methodology of such tribotesters.

1

INTRODUCTION

The subject of evaluation of coatings and tribomaterials based on their frictional characteristics and wear between sliding surfaces has been studied extensively for many years in terms of their controlling factors and parameters such as materials, surface conditions, sliding directions, well-defined crystallographic directions, load, speed, temperature, environment, lubricants, and many others. Various theories have been proposed concerning the mechanisms of friction and wear, and numerous attempts have been made to establish quantitative relationships between the many parameters involved. However, little or no attention has been paid in the past to tribotesters and test specimens' dynamic characteristics and their effect on the measured friction and wear. Refs.[l through 61 are both sparse and dated, and the findings contained therein are in need of supplemental work. In these early papers, some of the features of vibrations induced by friction and dynamic characteristics of the test facility have been studied. Ref. [ 6 1 provides preliminary experimental scattered plots of raw data (in its appendix), indicating detected mechanical vibration frequencies relevant to a pinion disk tester, and it was concluded that "these vibrations are difficult to determine and to describe and are not often reported in the t r i bo 1 og i ca 1 1i t e ra t u re " The purpose of the present theoretical and experimental investigation was to assess dynamic responses attributed to undesirable characteristics of tribometers and test specimens that unduly influence the validity of the friction and wear data. This is often hindered by the complexity of the friction and wear processes and the lack of standardized methods of tribotesting, and by the lack of reliabLe data. In this context, the vibrations of tribotesters

.

are an important characteristic which influences measured friction and wear values. The measured data are yet to be corrected for the test system characteristics. The findings of this investigation unveil many salient but undesirable influences of dynamic behavior on the validity of tribological data. When the rotating test specimens are not perfectly circular, higher harmonics will be present. The strength of each harmonic depends on the profile of the rotating specimen. Separation at the contact could occur if the dynamic forces are larger than the applied static load. The dynamic force may be synchronous or non-synchronous relative to the spin speed depending on the shape of the rotating specimen. The magnitude of the dynamic force depends on the amplitude as well as frequency of the vibrating test specimen. This paper describes the results of experimental investigations of the effects of runout of the specimens and rotational frequencies on the measured frictional and traction forces. Experiments were conducted on two types of tribometers, high speed, high temperature, solid lubricated, pin-on disk and disk-on-disk. When friction and slip/roll tests were conducted on the tribometer, any runout in disk motion produced an additional load due to the inertia of the static pin or rotating disk sample holder. The range of fluctuating dynamic frictional and tractive forces for various loads and speeds are presented and discussed. It is concluded that friction and wear data attributable solely to material properties/environment are not accurately determined or given, because the actual values of contact forces contain a certain degree of error in a complex form. However, careful calculations will permit them to be taken into account when data are interpreted.

466

2

PIN-ON DISK

-

SLIDING WEAR TRIBOMETER

spindle is driven by a 30 hp vari-drive motor (it can also be driven by an air turbine) located at the left end.

The most critical first step in tribological simulator testing under extreme conditions is to design a reliable tester. This requires careful integration of materials selection, thermal analysis, and system dynamic analysis. One of the major trade-offs in the design of a surface system is between rotor dynamics and thermal isolation. The designer is driven simultaneously toward short hot-section overhangs (to maintain high critical speeds), and toward large overhangs (to minimize the support bearing temperatures). The thermal and dynamic analyses can be executed using finite element techniques. These analyses usually require several iterations before a balance satisfying all design criteria is achieved. In general, the test specimen should be separated as much as possible from the nearest rotor support bearing; this is desirable in order to minimize the cooling required to maintain manageable support bearing temperatures and acceptable rotor-dynamic behavior. In the case of elevated Fig. 1 High Temperature Pin-on-Disk Tribometer temperatures, if acceptable dynamics cannot be achieved by using the shaft as a heat dam to isolate the test area, external cooling--a water jacket--must be added to protect the support KQ Rotor Beanngs Stillness bearing thermally. K Contan Hen2 Stiffness Once the materials have been selected, and KdQ Loading Arm Beanng Stillness KL = Pivot IGimbal) Beanngs Stlnness thermal effects, such as temperature distribution and differential thermal expansion issues resolved, the following factors must be carefully considered. Stresses due to static loads and friction-induced vibrations; Contact geometry, including stresses, relative surface motions, and local contact geometry; Operating speeds, including drive system power and speed control; Environmental issues. , The sliding wear tribometer shown in Fig. 1 was built and used for tests up to 1500'F. The detailed description of the test rig has been Fig. 2 Schematic of Pin-on-Disk Tribometer given elsewhere [ 7 1 . The rig has a water-cooled support spindle to minimize the length of the test disk overhang. The purpose of this design is to allow the rotor to operate at speeds up to TraCtion Rig -Pin on Disk 50,000 rpm. Friction and wear studies have been conducted on this tester at shaft speeds up to 0 10 20 30 40 50 60 30,000 rpm (equivalent surface speed of 110 m/sec ( c m ) l I I I I I I ( 4 3 3 0 in/sec)). Next to rotor dynamics and ( I n ) ? 30 60 90 120 150 160 210 240 2

--

"'$

thermal isolation, the most important part of simulator design is ensuring that dynamic loads at the interface contacts are minimized. When friction and wear tests are conducted on such a tribometer, any runout in disk motion will produce an additional load due to the inertia of the pin holder, loading arm, etc. 3

MATHEMATICAL MODEL OF THE PIN-ON DISK TRIBOMETER

The dynamic force assessment was performed for two models used in the friction and wear test and in the traction test. The first model is the pin-on disk rig as shown in Figure 1 and its schematic is shown in Figure 2. The mathematical model, as shown in Figure 3 , includes a spindle which may rotate u p to 30,000 rpm and a non-rotating arm connected to a universal joint (gimbal bearing). The test specimen fixed at one end of the arm is riding on a disk which is attached to the spindle. The

Station No

SI

62

S H

Pivot Arm

, 8PM)t

Fig. 3 Mathematical Model of the Pin-on-Disk Tribometer As seen in the model (Figures 2 and 3 ) , the loader arm is coupled with the rotating specimen via Hertzian contact stiffnesses, K. The range of contact stiffness K was evaluated based on pin and rotating specimen (disk) geometries and physical properties of the specimens. Thus, average values of the K (which is a stiff spring) are used to model the contact between the pin and the disk.

467

When the pin is loaded on the disk through static weight, frictional forces, f, are measured at the contact while the disk is rotating. Under the ideal situation, f is easily assessed when there is no vibration at the pin and disk interface. A small amplitude at the disk, due to runout or unbalance, will generate a dynamic harmonic force superimposed on the applied static load. The magnitude of the dynamic force depends on the amplitude as well as frequency of the vibrating disk. The amplitude, whether coming from runout or imbalance, determines the magnitude of the dynamic force under a constant spin speed. Separation at the contact will occur if the dynamic force is larger than the static load. The dynamic force may be synchronous or non-synchronous to the spin speed depending on the shape of the disk. For a pure circular disk, the dynamic force is synchronous with respect to the rotational speed. When the disk is not perfectly circular, higher harmonics will be present. The strength of each harmonic depends on the profile of the disk. The spindle is supported by two ball bearings. The stiffness values of these bearings as a function of speed is listed in Table 1. A harmonic response multi-level finite element computer program [ 8 ] for the rotor bearing system was used to perform the calculation. An undamped natural frequency solution reveals that the first three critical speeds of the system are at 29,780; 66,600 and 147,300 rpm. Their TABLE 1 CALCULATED VALUES OF TRIBOMETERS BALL BEARINGS STIFFNESS COEFFICIENTS Upper S p i n d l e Bearings Speed > 75,000 r p m

ID, R1 (Sl05) and R3 (P106)

Lower

Spindle Bearings

ID, Rl (bl05) and Rg (1107)

Speed

> 35,000 rpm

R1 (P105)

major frequency component of interest. The dynamic force, as a function of rotational speed and amplitude can be plotted as shown in Figure 7 under synchronous excitation. Note that the sharp increase of the force when the system operates around the first natural frequency (29,000 rpm). Critical Speeds Pin-on-Disk Rig-KB

= 8.96E5 (#105) 6 73E5 (#107) at 30.000 rprn

System Condmn' Made Number. Natural Frequency:

Spin Speed Level Ratio

1 1

29,780 rpm

-1.01 -4.0

KXX

KXY

KYX

KYY

15000 30000 50000 75000

1.0170E+06 8.9606E+05 6.0688E+05 4.6708E+05

3.7621E-02 3.02936-02 2.40408-02 1.3384E-02

1.8106E-02 2.20031-02 1.5297E-02 1.16078-02

1.0170E+06 8.9606E+05 6.0688Ec05 4.6708E+05

Drive Spindle 0 Pivol Arm

1.00

0.00

1 2

8.0

120

16.0 I

20.0(in.) I

0I

4.0

I

I

I

I

I

I

I

.10

0

10

20

30

40

50

Fig. 4

First Mode of the Pin-on-Cislt Model

Critical Speeas Pin-on-Disk Rig-KB Syslem Condition. Mode Number: Natural Frequency:

= 8.96E5 (#105) 6.73E5 (#lo71 at 30,000 rpm 1

2 66,000 rprn

' OI

Spin Speed Level Ratio 1 1.00 2 0.00

Level 1 2

UDrive Spindle 0 Pivol Arm

0.5

OIzZ'I2r \ /

-1.o.4.0 .4.0

0 0

4.0 4.0

I

I

0

10

I

-10

8.0 8.0

12.0 12.0

16.0 16.0

I

I

I

20

30

40

R2 (8107)

1.1482E+06 6.7271E+05 5.1675Et05 5.7906E+05

Fig. 5 8.2633E-02 3.1202E-02 2.1957E-02 3.8672E-02

5.1899E-02 4.4891E-02 2.2007E-02 2.8892E-02

1.1482E+06 6.7271E+05 5.1675E+05 5.7906E+05

R3 (8106) 15000 30000 50000 75000

1.0842E+06 7.6423E+05 4.8830E+05 4.7501E+05

-1.8389E-03 4.5273E-03 -5.3595E-02 -6.79798-03

-3.07826-02 -1.0832E-02 -7.6289E-03 -7.2274E-03

(cm)

89188

Second Mode of the Pin-on-Disk model^

Critical Speeds Pin-on-Disk Rig-KB System Condition: Mode Number: Nalural Frequency:

20 20 .O (in.) . .

I

50

Axial Location

15000 30000 50000 75000

(cm)

Axial Location (in.)

-0.5

SPEED

Level

1

2

= 8.96E5 (#lo51 6.73E5 (#107) at 30.000 rpm 1

3 147,300 rprn

Spin Speed Level Rail0 1 1 .OO 2 0.00

Level 1 2

13Drive Spindle Q

Pivol A n

1.0842E+06 7.6423E+05 4.8830E+05 4.75018+05

corresponding mode shapes are plotted as shown in Figures 4 to 6 respectively. Operating near or at critical speeds should always be avoided. The dynamic force calculation is accomplished by inducting vibration at the disk through externally applied harmonic force. Using the harmonic response computer code, the force between the pin and the disk is then computed at every speed of interest. The relationship between disk amplitude and dynamic force in the contact can be established at various speeds and excitation frequencies. The synchronous excitation frequency (once per revolution) is the

-1.0

'

I

1

0

4.0

8.0

I

4

I

I

I

I

I

0

10

20

30

40

50

-10

12.0

16.0

20.0 (in.]

.4.0

(cm)

Axial Location

Fig. 6

Third Mode of the P i n - o n - D i s k

Model BBSsr

468

If the disk has an out-of-roundness profile, higher harmonics may be generated. The most common one may be coming from a disk with elliptical shape. This type of disk profile will generate an excitation frequency at twice the rotational speed. The same approach was taken to calculate the dynamic force when this 'twice-per-rev' excitation is introduced. As shown in Figure 8 the dynamic force is plotted as a function of the rotational speed. Of course, the out-of-roundness of the disk should be much smaller than the first harmonic amplitude generated by the runout o r imbalance.

2+1 358

2w

-

180

-

80

Pin on Disk-Synchronous Excitation

the listing o f tribological components under extreme conditions. Such programs as the Air Force's high performance turbine engine technology involve temperatures well beyond the capability of liquid lubricants. The temperatures of interest range from sub room temperature to at least 1500-2000°F. Photos of the rolling-contact simulator setup are shown in Figures 9(a) and 9(b). A schematic drawing is shown in Figure 10. This tester is capable of simulating lubrication effects in rolling contact at surface speeds as high as 200 m/sec (78,750 in/sec) and slip/roll well above +loo%. It is intended for studies of the rolling-contact traction and wear properties of solid lubricant combinations under conditions closely approximating those encountered by high DN rolling-element bearings. Changing the configuration of the contact specimens enables

M

Ilr-1n 80-

Fig. 9(a)

40 -10

Photograph of High Temperature Solid Lubrication Rolling Contact S l i p / R o l l Traction Test Rig

0- 0

When all these amplitudes are present, the forces are superimposed in the form Fd = F, sin Wt + Fu sin ( W t + 0 ) + Fs sin (2Wt + 6 ) + higher order terms where Fd is the total dynamic force and Fr, Fu and Fs are dynamic forces due to runout, imbalance and 'two-per-revolution' respectively. 4 and $ are phase angles of these forces. It is obvious that the largest total force will occur when all the three component forces are in phase.

4

DISK-ON-DISK TRACTION TRIBOMETER

The multitude of advanced systems now under development that will have to operate in hostile environments has led to heightened interest in

Fig. 9 ( b )

Closeup Photograph of Disk-on-Disk Tribometer

469

given in Table 1. The mode shapes of the first two modes are shown in Figures 12 and 13. Critical Speeds Disk on Oisk-Model

with No Pedestal spin Speed Level Ratio 1 1.00 2 -1.OO

1 1

System Condition: Mode Number:

Natural Frequency:

32.750 Qm

Level 1 GlLower Spindle 2 0 Upper Spindle

r 8

0.5

e

P

2

H 0 .-

E Fig. 10

Schematic Drawing of Disk-on-Disk Rolling Friction Simulator

-1.0

MATHEMATICAL MODEL OF THE DISK-ON-DISK TRIBOMETER

M

10

3.0

30 9.0

6.0

40

12.0

--

5;

18.0

15.0

21.0

60 1

24.0 I

0

StaoonNo.

1

4

4,

7

8

51

11

60 6 4

57

66

67

72

19 StationNo

15 Ton

I

I

4 !I t r w h ,

4

1

Lower Spindle ma2

Fig. 11

12.0

16.0

20.0

I

,

I

I

I

I

I

-1.0

0

10

20

30

40

50

(cm)

Axial Location (in.) agm

Fig. 12

First Mode Shape of the Disk-on-Disk Model

Critical Speeds Disk on Disk Model with

-

System Conddion: Mode Number: Natural Frequemy:

No Pedestal 1

2 108,100 rpm

I

spin Speed Level Ratio 1 1.00 2 -1.00

Level 1 mLowerSpindle 2 mUpper Spindle

-4.0 I

'

0 I

a

I

I

I

I

-10

0

10

20

30

40

50

-1.0

I

I

4.0

8.0

12.0

16.0

20.0 (in.) (cm)

Axial Location amm

Fig. 13

Second Mode o f the Disk-on-Disk Model

-Model wlth NO Pedestal

9

(cm) (in.) 0

8.0

4.0

-0.5

The mathematical model for this case now includes two spindles, the lower one drives the other up or down to 30,000 rpm. The lower spindle is driven by a vari-drive motor (identical to the pin-on disk spindle) located at the left end. The upper spindle is designed such that it is dynamically identical to the lower one except it is driven by the air turbine. The complete model is shown in Figure 11. Again, a stiff spring is Dlsk on Disk

(in.)

0

.4.0

different component geometries, such as the ball/race or roller/race contact to be simulated. When testing at elevated temperatures for a solid lubrication condition, traction data are taken in a transient mode and the test procedure was devised as follows: the lower spindle (cylindrical disk) speed was maintained constant, the upper spindle speed (disk with crowned profile) which is driven by the air turbine was set different than that of the lower one. Then, test load was applied to the upper spindle (see Fig. 10) while test disks were separated from each other by a distance of a few mils (typically 90 to 100 pm). The traction was then begun by bringing two disks into contact and shutting off the air to the upper spindle turbine. Consequently the upper spindle gradually coasted down to a speed lower than that of the lower spindle speed, thus obtaining traction data for various slip/roll ratios. 5

-0.5

Mathematical Model o f the Disk-on-Disk Tract !Lon Tribometer

used to model the contact between the two disks. A critical speed calculation is performed for this model using undamped bearing stiffness and

When the upper disk is loaded on the lower one through a static force, the upper spindle will be driven via traction force. The tractive (frictional) force is measured continuously at the contact. A small amplitude at the disks due to runout, imbalance, etc. will generate a dynamic harmonic force superimposed to the applied static load. Unlike the pin-on-disk model presented earlier, both spindles rotate. The runout or imbalance on the two disks will have a relative phase angle when they rotate. This phase angle may also vary in time since the traction between the two disks are not constant. For the same reason, a constant speed ratio between the two spindles may not be maintained. Since the purpose of this study is to assess the dynamic forces generated in the contact based on certain excitation amplitudes at the disk, where the magnitude of the dynamic force depends

470 470

on the the amplitude amplitude as as well well as as the the frequency frequency of of the the on vibrating disk, disk, the the following following assumptions assumptions were were vibrating made for for computation: computation: made The displacements displacements due due to to disk disk runout runout occur occur The at the lower disk. at the lower disk. The two spindles are rotating approximately at the same speed. A rotor dynamics computer program that handles multi-rotor bearing system [ 8 ] is used to analyze the dynamic behavior of this system. Given the forcing functions, synchronous or non-synchronous, the computer program computes displacements and reaction forces. In order to simulate the dynamics of the disk-on-disk model with the existing analytical tools, a constant synchronous force is applied at the lower disk and displacement is evaluated at the contact. Since the two spindles are rotating in the opposite direction (from the viewpoint of the coordinate system), the speed ratio of the two rotors are 1.0 and -1.0 respectively. Hence, a zero speed ratio indicates a non-rotating shaft. The steady state response of both spindles was calculated and the reaction force in the contact was evaluated based on the relative displacement between the two disks. The reaction force in the contact, due to an applied synchronous force of 445 N (100 lbs) at the lower disk, is shown in Figure 1 4 . The displacement at the disks under the same condition is shown in Figure 15.

resPectiVelY. This force will be present even if the rotor is not rotating.

-

2

3p 500

Fig. 1 5

Fig. 16

Fig. 1 4

Reaction Force in the Contact as a Function of Speed Due to an Applied Synchronous Force of 100 lbs at the Lower Disk

When the rotational speed is close to zero, 124 N ( 2 7 . 9 4 lbs), force will be generated in the contact if the deflection at the disks is 29 pm

(.00115 in.). This situation is illustrated in Figure 16 where at static solution is obtained and the reaction forces at the bearings are also included. Unlike the pin-on-disk model described earlier, both spindles are supported on bearings where loads are shared. The results shown in Figure 16 indicate that there is 124 N of force, Fc in the contact if the disks are displaced by 29 pm under an external force of 445 N applied at the disk. In other words, about 72% of the applied load is absorbed by the bearings while 28% is supported through the contact. What the results indicate i s that under zero rpm, a 27.94 lbs "static" force will be generated in the contact if the eccentricity of the lower in. and upper disks are 49 pm and 0.0

Displacement in the Contact as a Function of Speed Due to an Applied Synchronous Force of 100 lbs. at the Lower Disk

Static Reaction Forces Under 4 4 5 fJ (100 lbs) of Static Load Corresponding to 29 pm Eccentric ity

The force displacement relationship indicates that the force in the contact decreases as the speed increases until about 28,000 rpm. It shows that the dynamic force generated due to rotation counteracted the "statict' force s o that the net force becomes smaller. The force then increases sharply, in the opposite direction, as the spin speed moves close to the critical speed. The force/displacement relationship is plotted as shown in Figure 17 where the force is a function of sped and constant amplitude. The general trend of the displacement/force relationship is entirely different from that of the pin-on-disk model. Experimental da'ta will be examined for further confirmation of these analytical results. 6

SOME RECENT EXPERIMENTS

Two separate families of tests were conducted by the author, all reaffirming the presence of a respectable dynamic load contained in the frictional load. Runout of the rotating test specimens was kept to a minimum (usually less It is worthy of note than 5 pm ( 0 . 0 0 0 2 in.)). that static runout (out of roundness) of the test disks with 7 2 mm in diameter were about 2 p m (0.00008 in.) prior to assembly. The magnitude

47 1 Elapse Time - (sec) 80

0

(N)

Dynamic Farce Calculallon,Dlsk an Dlsk

(ib)

120 I

I

16

-200

-50

0

240

i

1

360

300 1

0 45

I

Amplitude of Fluotubling Dynamic Frtcllonnl Force

I 6 l

q

LBO

6 (in.) 5.08vm (0.0002) 12.7 pm (0.0005)

,

,

, I , ,

,

, , , , , , , , , , ,,,

,

,

,

,

25.4 pm (0.001 1 ,

,)

I ,

, , I

e l = 5 p m . RI = 36 mm Load = 3 9 N ( 0 875 lbs)

51 pm (0.002) 4

0

8 100

12

16

200

24

20 300

400

28

32 500

40 (mmx iO001

36

600

00

! 3324

500

(HZ)

4595

6080

0 05

9000

Speed - U, (rpm)

-

,

0 00

moo

Rotational Speed 8mm

Fig. 17

Fig. 18

Dynamic Forces in the Contact at Various Amplitudes 'Jnder Synchronous Excitation

of the dynamic runout is dependent upon the test rig characteristics, rotor speed, etc., and usually runout level increases as rotor speed increases.

-

These tests were run in the Group Number 1 pin-on disk test rig (Fig. 1) specifically instrumented for eliciting the characteristics of fluctuating frictional force due to the rotating eccentric disk. The utmost care was taken to produce a cylindrical sample with a lapped surface finish better than 2 pin. The friction force via the force transducer was measured continuously, without filtering the output signal. Basically data acquisition software for the test rigs consisted of test rig control, data collection, and data processing logic that allows completely automated control and monitoring of the test. Data inputs include speed signal and a force (frictional) signal. From a typical 5 to 6 second test duration, 250 to 300 data points were extracted from the 1.5 to 2 mega bytes of sampled data. The data collection was based on data translation DT2828 analog to digital converter interface for the IBM PC/AT. In addition to the computer, speed and frictional force signals were recorded by a multi-channel magnetic tape recorder. Speeds of the order of only 10,000 rpm and temperatures to 1300'F were conducted under various solid lubricants, materials and test loads. A sample fluctuating frictional force is shown in Figure 18, its trend indicating typical theoretically computed results. As can be seen from the plot of Figure 18, with its corresponding speed and constant load, the average frictional force decreases as speed increases (this phenomena has been discussed in 9). However, the peak-to-peak Reference amplitude of the dynamic frictinal force behaves opposite of the average force. The dynamic force response analysis showed that it is synchronous with respect to the rotational frequencies. Group Number 2 - Traction tests were conducted with 10 sets of nearly perfect concentric disks. Each set consisLs of a cylindrical disk and a disk with a crowned profile as shown in Figure 9 ( b ) . These tests were performed on the traction tribometer as shown in Figures 9 and 10. The cylindrical disk with 72 mm in diameter was mounted on the lower spindle running at a 9

Range of Fluctuating Frictional Force Induced by Eccentric Disk; Max. Yz Contact Pressure: 160 k s i

constant speed of U 1 with a known eccentricity of el. The crowned profile disk had the same diameter with a crown radius of 14.4 mm (0.5675 in.) mounted on the upper spindle (see Figure 9(b)). The upper spindle shown in Figure 9(a) had hydrostatically floated radial and thrust bearings to align with the lower disk and had freedom to rotate about the vertical axis. The upper spindle via the torque arm connected to a load cell in the horizontal (traction) direction for monitoring tractive force generated by loading two disks against each other while spinning at various speeds. The instrumentation and data acquisition technique which was employed here was similar to that of the pin-on-disk apparatus. A variety of materials and lubricants were tested under various test parameters and this is the subject of an upcoming paper. Sample data will be discussed here which is of significance as far as our analytical model and theoretical predictions are concerned. One is that the fluctuating dynamic tractive force superimposed upon steady state tractive force has a tendency to decrease with an increase of upper spindle speed U2 for a constant contact load W and speed Ul, as shown in the plot of Figure 19. I

Disk o n Disk Traction Data

- SilNd/a

SIC

Range of Fluctuating Dynamic Force

I FiS. 19

Typical Traction Data at Room Temperature, Hertz Max. Pressure 1.15 GPa (170 k s i )

412

The maximum amplitude of dynamic tractive force usually occurs at ~2 = ~1 (i.e. A U = O), where from the plot of Figure 1 9 the peak-to-peak amplitude of dynamic force is 50% of the average tractive force at U 1 = U2 = 83 cps. Interestingly, the dynamic tractive force response was usually synchronous with upper spindle speed U2. The typical dynamic tractive force response is plotted versus time (sample detailed data as part of data shown in Fig. 1 9 ) and is shown in Figure 20. Additional data taken at higher speeds is shown in Figure 2 1 and is indicative of an increase in the range of fluctuating dynamic tractive force after a dipping, which should be compared with Figure 17. I .4

I

f

t

,

I

DISK-ON-DISK

I

I

I

U = 83 cps -1 U2 = 175 cps Max. Hz Contact Press. 1.15 GPa (170 ksi)

0.64

Fig. 20

v'=

1

f

2.85 N ( 0 . 6 4 l b s )

Typical Dynamic Tractive Force Response in the Frictional Direction (Horizontal) with an Applied Normal Static Load of 44.5 N

IV

Disk on Disk Traction Data - Si3N4/a SIC Lub: Dry Range of Fluctuating Dynamic Force

7

CONCLUSIONS

The main noteworthy observations in the series of tests, together with the theoretical models described above, can be summarized as follows: Dynamic forces will always be present to some degree in high-speed tribotesting. When the rotating test specimens are not perfectly circular, higher harmonics will be present. The major frequency component is the synchronous one. Depending on the geometrical profile of the rotating specimen,, the dynamic forces could be synchronous or non-synchronous relative to the rotational frequency. Separation at the contact could occur if the dynamic forces are larger than the applied static load. The above leads us to conclude that the coefficients of friction and wear values obtained from high speed tribometers, in particular solid lubricated testing, contain a certain degree of error in a complex form. The friction and wear data should be interpreted with the aid of careful calculations and measurements in order to include dynamic forces. Moreover, the design of tribological testers for evaluating the performance o f materials under the extreme conditions that many advanced systems will have to withstand is a challenging task, and one that must be approached systematically. The tribologist must understand not only the tribomaterials properties and the ultimate application of the materials being studied, but also the tribometer itself. 8

ACKNOWLEDGEMENTS

The work discussed in this paper was made possible by the Hughes Aircraft company, U.S. Air Force Wright Aeronautical Laboratories (AFWAL/MLBT), REC, and Mechanical Technology Incorporated. The author wishes to express his appreciation to these organizations for their support. Acknowledgements are also due to B.D. McConnell, R. Dayton, M.N. Gardos, and J.F. Dill for their sustained interest in, and technical contributions to, this research. Special thanks to F. Gillham for preparing the computer solutions and T. Brandt for organizing and typing the manuscript. References

I

Fig. 21

1.

Brockley, C.A., Cameron, R. and Potter, A.F. I' F r iction-Induced Vibration", JOLT, Trans. ASME, Series F, Vol. 8 9 , No. 1, Jan. 1 9 6 7 , pp 101-108.

2.

Brockley, C . A . , KO, P.L. "Quasi-Harmonic Fr i c t i o11- Ind u c ed V ibra t i on" , JOLT, Trans. ASME, Paper No. 70-Lub-16, Oct. 1 9 7 0 , pp 550-556.

3.

KO, P.L. and Brockley, C.A. "The Measurement of Friction and Friction Induced Vibration", JOLT, Trans. ASME, Paper No. 70-Lub-15, Oct. 1970, p p 543-549.

4.

Aronov, V., D'Souza, A.F.; Kalpakjian, S. and Shareef, I., "Interactions Among Friction, Wear and System Stiffness Part 1: Effect of Normal Load and System Stiffness", JOT, Trans. ASME, Paper No. 83-Lub-34, Oct. 1983.

Peak to Peak Amplitude of Dynamic Tractive Forces as Function of Speed

In view of all of the above, one is led to the conclusion that dynamic forces due to runout of the spinning disk specimen have undesirable influences on the validity of tribological data. The trend of the experimental data is in good agreement with theoretical predictions, although it needs further elaborate analytical investigation to treat various cases of tribological test setup and conditions.

413

5.

Ibid, Part 2: Vibrations Induced by Dry Friction", JOT, Trans. ASME, Paper NO. 83-Lub-35, Oct. 1983.

6. Czichos, H., Becker, S . and Lexow, J. "Multi-Laboratory Tribotesting: Results from the Versailles Advanced Materials and Standards Programme on Wear Test Methods", Wear, 114, (1987), pp 109- 103. 7.

Dill, J.F. "Extreme Measures--Tribological Testing in Hostile Environments", Mechanical Engineering; 60/April 1988, pp 83-88.

8. Lee, C., Tecza, J. and Pace, S . "FEATURE/COJOUR: An Integrated Resource for of Rotor-Bearing Dynamic Analysis System", Proceedings of EPRI, Sept. 9-11, 1986, St. Louis, MO, U.S.A. 9. Heshmat, H., Pinkus, O., Godet, M., "On a Common Tribological Mechanism Between Interacting Surfaces", presented at the 43rd (May 1988) Annual STLE Meeting, STLE Transactions, Vol. 32, (19891, 1, 32-41.


WRITTEN CONTRIBUTIONS


411

Written contributions

Dr K Holmber (Technical Research Centre of

d

1 am a little confused about the comments that

the scratch test and friction tests like pinon-disc are not useful for tribological coating evaluation. 1 think it is important to make a clear distinction for what purpose you are using these tests. Firstly, we need to perform tests for the quality assurance of coatings. Secondly, we need simulating tribological tests to evaluate how suitable a coating is for a certain application. Our experience is that the scratch test method is the best available quality assurance method for evaluating the adhesion and tensile strength properties of coatings and the pin-on-disc test is very suitable for the friction and wear evaluation. With these methods it is possible for the producer of the coating to assure that the coating has the properties and the quality he is trying to produce. On the other hand 1 agree that there is no laboratory test available with which you can with a good probability predict how a coating will tribologically behave in some certain practical application. For this purpose the scratch test is generally not useful and the pin-on-disc test only gives some indications. Here we to a large extent rely on field experiments.

surface modification processes of the bulk material to provide improved surface functions. CHOICE OF THICKNESS It is surprising how frequently one finds aspects of material contacts can be represented by the results of Hertzian contacts. Category 1 The asperities on surfaces associated with machining methods may be represented by an array of spherical or ellipsoidal tipped projections of various heights as recorded by a stylus measuring machine. Such asperity contacts may be represented by a characteristic asperity of radius @ in contact with a rigid plane with an equivalent modulus E' where: -1= - 1+ @

9

1

4

1 1 -vl _ -

2

+

1 - v2*

(1)

E' El E2 where the subscripts 1 and 2 refer to the two surfaces in contact. Category 2

(Emeritus Professor, face Coating - Thick or

Thin? Soft or Has?' INTRODUCTION

The majority of engineering failures can be identified with an initiation due to an inadequacy of surface material properties. It is interesting that the first use of copper some 5% thousand years ago was as a track on wooden wheels to improve traction and reduce wear. Since that time developments such as painting, electroplating and surface modification processes have become well established. In the past 30 years we have seen major developments in surface coating so that the designer may now carry out two design processes. ( a ) 'Bulk design to provide strength, stiffness, etc... (b) Surface design to combat friction, wear, corrosion, fatigue etc.

They choose the best materials for both functions and use modern technology to stick them together with total reliability. This will be increasingly preferable to using

Machining often produces longer wavelength irregularities, usually called WAVINESS, and associated with vibrations during machining. Such deviations may also be considered as Hertzian contacts as were the micro contacts in category I, but with equivalent radii at least one order of magnitude greater than 6 . Category 3 These are the types of contact which arise in typical small ball bearings and would have radii at least one order or magnitude greater than the radius in category 2. Category 4 These are the types of contact such as occur in gears, cams and similar Hertzian contacts with typical radii at least one order of magnitude greater than category 3. It must be stressed that the rigid division of surface geometry into categories 1 and 2 is often not clearcut and that surfaces have smaller asperities which are undetected by stylus instruments and extend in size down to atomic dimensions. Thus, in all the above categories the assumed radii are for surfaces

478

covered with some degree of roughness. Fortunately, the use of Hertzian formulae derived for perfectly smooth curved surfaces may still be appropriate, particularly at higher loads. This problem has been considered and it has been shown that Hertz theory may be applied with less than 7 percent error provided [ l ] . Ru a=----=u 2

a0

r; ;,21'3

We consider four categories of material as defined by their H/Ef values and four categories of contacts as defined by their R values, Table 1.

R Value Category

___

-

.05

(2)

EDf

where u = ( u12 + u2' )' is the standard deviation of the roughness on the assumed smooth surfaces in categories 1 to 4.

Gears Category rexture Waviness ball bearing: cams .5 mm 50 ,um etc. 5 cm 5 cm 5 m

50 ,um

.5 m

m

.5 mm

5 m

50 ,um

.5 mm

5mm

5 cm

.5 mm

5mm

A

100

0.5 ,um

B

10

5w

C

1

D

.1

LIMIT OF ELASTIC BEHAVIOUR It is generally agreed that elastic behaviour in Hertzian contact ceases when the maximum pressure p, reaches 0.68. From Hertz theory it can be shown that: (3)

We now consider the Hertzian stress field in greater detail. In the absence of friction the two stress components the deviatoric (maximum shear stress) and the hydrostatic are as shown in Figure 1.

! Po

!

hydrostatic

Hertz pressure distri/bution

-

deviation

Fig. 1

The deviatoric component is zero at the surface, reaches a maximum at a depth of a/2 and becomes very small at a depth a. The hydrostatic component is a maximum at the surface and falls to small values at a depth a. It will thus be recognised that a surface coating of thickness t = a will virtually embrace the stress field so that in Hertzian contacts such a coating will behave as though it were the bulk material. This has been demonstrated theoretically in a more detailed study

.

The effect of frictional tractions is to introduce shear stresses at the surface and move the location of the maximum deviatoric stress towards the surface. Provided p 5 0.1 the foregoing arguments are still valid. We may now consider an order of magnitude study of coating thickness using the criteria in equation 3 .

Table 1

50

5 cm 50 cm

Coating thickness for various categories of materials and R values

In using Table 1, the actual values of Ef/H will depend on the properties of both contacting materials. However, for an approximate appreciation of the required coating thickness, one may consider the E/H values of various materials. We also recognise that the other major property defining load carrying capacity is the indentation hardness although a design would generally seldom employ nominal contact pressures greater than the yield stress Y. Table 2 gives some typical values of E/H and Y.

Material

E/H

!

(ma)

Aluminium

57 5

40

Mild Steel

98

650

Hard EN31

25

2400

Titanium Nitride

17

7500

Silicon Nitride

16.7

8000

Nylon

14

70

5

60

Rubber

.1

30

P.V.C.

.08

50

Polyethylene

Table 2

Some typical value of E/H and Y

Using the information from Tables 1 and 2, we can provide some justification for several current application of coatings.

(a) Consider the coating of cutting tools with ceramics such as TiN. Such contacts would fall between category A and B but nearer to B, and because of the relatively small nominal contact

419

area, a few m2, we consider the texture category with R = f3 = 50 pm. Thus, such coatings would need a thickness of 3-4 f.nn which is now established by practice as the appropriate coating thickness. It will also be noted that such materials have very large potential contact pressure, essential for such severe applications. (b) Coal Board authorities have discovered that materials such as High Density Polyethylene significantly increase the life of coal hoppers, shutes and pipes as compared with stainless steel plates used in earlier designs. Here, we are between categories B and C but with the larger values of R to represent the material being transported. Such applications then need coating thicknesses of cms rather than mm, and this is confirmed by practice. (c) For many years ball mills have been lined with rubber. Such situations are in category D with R of order .5 cm, thus requiring thicknesses of several cms. This again is confirmed by practice. In the foregoing arguments, it will be appreciated that when dealing with surface texture contact the use of equation 3 to define the limit of elastic behaviour is a simple order of magnitude statement. This problem is more accurately stated by the derivation of a relationship between the plasticity index and a non-dimensional nominal pressure p as shown in Fig. 2 where, [21:

- _ _ W_

p

=

A Httnf3o

0: being the standard deviation of the asperity height probability distribution, here assumed Gaussian with a truncation 30, A is the apparent area of contact of the load W and 0 is the asperity surface density. K is the ratio of plastic contact real area to elastic contact real area. K = 0 represents the transition from elastic to plastic/elastic contact and has been substantiated experimentally for small areas of apparent contact, Fig. 2 .

The curve K = 0 may be interpreted in an engineering sense for several material combinations by a plot of the elastic limit nominal pressure against the mean slope of the texture, Fig. 3 . These curves have been terminated at p = H/3 and are presumably indicative of the probable wear behaviour of the materials concerned.

10000

/-1t

PVC / %eel ruober / steel

c

Mild steel / @q steel

E

=

0 01 0

2

6

4

8

10

mean slope degrees

Fig. 3 : Some typical results for elastic ccntact of roush suriaces 1.e. when K = 0

FRICTION AND WEAR OF SOFT FILMS Consider the frictional characteristics of a soft film on a hard substrate arising from contacts. The load capacity arises from a combination of the properties of both the film and the substrate and is also dependent on the radius of the contacting bodies. For asperity size contacts it transpires that for film thicknesses greater than 10 pm the substrate makes a negligible contribution to load capacity. For thinner films the load capacity is increasingly dependent on the substrate as the film becomes thinner. Thus the frictional shear stresses are low being defined by the soft film whilst the load capacity increases as the film becomes thinner. This leads to a falling value of ,LI as the film thickness decreases. At very low values of film thickness, the value of L,I rises due to asperity penetration of the film and contact with the substrate. The smoother the surface the lower the value of film thickness at which this rise in fi will occur, Fig. 4. lead film on M.S

h = d / a where d is separation o i suriaces plas:ic area of contact K = elastic area o f contact

terminated at p = H/S

0.6

x

experiment

experimental K - 0

K=BO

,,h=2.95

M.S. cn b1.S.

Fig. 4

non dimensional nominal pressure

Fg. 2

W

p

=-

AHxrlRa

When we consider wear in such situations we recall that wear is generally agreed to be proportional to the real area of contact. Thus as a soft film wears away and becomes less than 10 pm thick its load capacity increases and thus produces a reduction of real area of contact which then manifests itself as an

480

In rolling contact bearings, it is found that soft metal films are a useful form of "lubrication" where such bearings are used in hostile environments such as space. Here, the load is carried by the hydrostatic component of the stress vector and provided the soft film thickness is very small with relation to the contact radius it will be subjected to very small surface shear stresses and therefore survives in such contacts, see Fig. 1.

increasing wear resistance, Fig. 5.

I ,I>

4

t\

40

30

-

I

0

0

2

4

6

initial film thickness

(W)

Fig. 5 : Wear resislance 01 soit metal films as a iunctlor, film thickness

01

Using the inverse of the foregoing arguments for hard films on soft substrates, one finds ,u increasing to a maximum as film thickness increases and the wear resistance reducing as the film is worn away thereby accelerating the wear process [3]. The foregoing theoretical arguments are based on modest friction and would be changed in scale where adhesion and junction growth become overtly significant. Indeed, it follows that one would not use soft metal films in continuous sliding contacts. Furthermore, when such films are used with thicknesses of microns it is imperative that the adhesion to the substrate is beyond reproach.

Finally, one must briefly discuss the use of potential value of multi-layer coatings. In the early days of CVD coatings, it was found that a thin coating of Tic on cutting tools such as tungsten carbide greatly extended wear life. This led to the use of Tic coatings on steel to reduce wear. This seemed valid until it was found that in extended use the whole surface suffered microscopic brittle failure. This arose due to the diffusion of carbon, at the elevated temperature due to rubbing, producing a sub-surface embrittled layer. This is now easily avoided by interposing an appropriate intermediate layer as a diffusion barrier in such systems. Multi-layer coatings are of increasing significance since they offer a simple method of controlling the thermal and electrical properties of surfaces. In the PvD coating process, one may deposit aluminium but if one introduces a blast of oxygen at regular intervals one produces a layered coating of aluminium and aluminium oxide with thicknesses of order of few hundred angstroms. Thus, one has produced a coating with thermal and electrical properties which are markedly different in the two principle orthogonal directions. Such techniques will no doubt become increasingly important in tribology as our understanding of surface behaviour improves. TYPE OF PROCESS

Hard ceramic films are now well established in metal cutting systems. Thin soft metal films are used in dry intermittent contacts such as aircraft fasteners, e.g. nuts and bolts made from reactive metals such as titanium are coated with PVD aluminium (with 5% magnesium). This has replaced electrodeposited cadmium which as undesirable toxic effects. Soft metals films are extensively used in electrical connectors which often require intermittent sliding. Such coatings use complex nickel, silver and gold layers deposited to limit both wear and corrosion. The new PVD deposition methods offer the possibility of simple systems due to the enhanced dense crystal structure obtained by these processes. Somewhat thicker soft metal layers have long been used in hydrodynamic bearings. Here, intimate contact only occurs during the first revolution at start up. In such bearings it is found that although the volume wear is not significantly different the radial wear is much less in bearings having smaller initial clearances, i.e. the wear occurs over a longer arc but less depth with a tight bearing. Perhaps, with the development of improved engineering production and coating technology, we may be able to see significant advances in the design of hydrodynamic bearings.

It is not without interest that the type of surface film required may often define the type of coating process required. Thus, highly adhered micron thick ceramic coatings with excellent adhesion immediately suggest the CVD and PVD coating methods. In a recent data item ESDU have provided details of all the principal coating and surface modification processes and their significance in tribology (4). References Greenwood J A, Johnson K L, Matsubara E, "A surface roughness parameter in Hertz contact", Wear, 100, 47, 1984. Halling J, Arnell, R D, Nuri K A. "The elastic-plastic contact of rough surfaces and its relevance in the study of wear", Proc. Inst. Mech. Eng., 202, 81, 1988. Halling J. "The tribology of surface coatings, particularly ceramics. Proc. Inst. Mech. Eng., 200, 31, 1986. Selection of surface treatments and coatings for combating wear of load bearing surfaces. Engineering Sciences Data Item No 86040, 1986.

48 1

16th LEEDS-LYONSYMPOSIUM ON TRIBOLOGY MECHANICS OF COATING

-

5th 8th SEPTEMBER 1989 LIST OF AUTHORS

Dr.

Dr

.

Dr.

NAME

AFFILIATION/ADDRESS

M.J. ADAMS

Unilever Research Port Sunlight Laboratory UK

J. ATTAL

Laboratoire de Microacoustique de Montpellier Universitb des Sciences et TechniquesduLanguedoc Place Eugene Bataillon 34060 Montpellier Cedex France

D.D. AUGER

Dr.

P.J. BLAU

MI.

A. BOUCHOUCHA

Laboratoire E.R.M.E.S.

6, rue du Joli Coeur

54000 Nancy France

B.J. BRISCOE

Imperial College Particle Technology Group Department of Chemical Engineering Prince Consort Road South Kensington London SW7 2BY UK

Dr.

E. BROSZEIT

Universidadde Oviedo E.T.S. lngenieros lndustriales de Gijon Gijon Spain

Technische Hoschschule DarmStadt lnstitut fur Werkstoffkunde Grafestr.2 D-6100 Darmstadt FRG

Dr.

S.J. BULL

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de MBcanique deq Contacts - BBiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Materials Engineering Centre Hawell Laboratory UKAEA Oxfordshire OX11 ORA UK

Mr.

S.J. CALABRESE Rensselaer Polytechnic Institute Troy New-York 12180-3590 U.S.A.

CSEM CH 2007 Neuchatel Switzerland

Mr.

A.L. CARTER

Shell Research Ltd. Thornton Res. P.O. Box 1 Chester CHI 3SH UK

C. BlSELLl

Montreal General Hospital Montreal Canada

Dr.

J.C. BELL

Dr.

J.D. BOBYN

University of Waterloo Department of Mechanical Engineering 355 St Clair Ave East Toronto OW14 1P3 Ontario Canada

Dr.

Y. BERTHIER

Mr.

lnstitut National des Sciences Appliquees de Lyon Laboratoire de Mecanique des Contacts - Batiment 113 20, avenue Albert Einstein 69621 Villeurbanne cedex France

The Aerospace Corporation Chemistry and Physics Laboratory El Segundo, CA 90245 U.S.A.

Dr.

AFFILIATION/ADDRESS

B. BOU-SAID

R. BAUER

F.J. BELZUNCE

NAME

Dr.

Dr.

Mr.

TITLE

Metals and Ceramics Division Oak Ridge National Laboratory P.O. Box 2008 Oak Ridge, TN 37831-6063 USA

Imperial College Particle Technology Group Department of Chemical Engineering Prince Consort Road South Kensington London SW7 2BY UK

482

NAME

AFFILIATION/ADDRESS

Dr.

J.P. CHAMBARD Laboratoire E.R.M.E.S. CNRS U.A. 875 INPL Universite de Nancy I 6, rue du Joli Coeur 54000 Nancy France

Dr.

T.P. CHANG

Center for Engineering Tribology Northwestern University Evanston, IL. 60208 U.S.A.

Prof.

H.S. CHENG

Center for Engineering Tribology Northwestern University Evanston, IL. 60208 U.S.A.

Dr.

L. CHOLLET

CSEM CH 2007 Neuchatel Switzerland

Dr.

R.E. CLAUSING


Dr.

Dr.

Dr.

Dr.

Dr.

Prof.

S.J. COLE

R. DANJOUX

Imperial College Tribology Section Exhibition Road London SW7 2BX UK MECICA SARL 12, Place G. Braque 51100 Reims France

E. DARQUE-CERElTl Ecole des Mines de Paris CEMEF Sophia Antipolis 06565 Valbonne Cedex France

F. DELAMARE

K.M. DELARGY

Ecole des Mines de Paris CEMEF Sophia Antipolis 06565 Valbonne Cedex France Shell Research Ltd Thornton Res. P.O. Box 1 Chester CHI 3SH UK

Ph. DESTUYNDER Ecole Centrale de Paris Laboratoire de Mecanique des Sols et Structures Grande Voie des Vignes 92290 Chgtenay-Malabry France

TITLE

NAME

AFFILIATION/ADDRESS

Prof.

T.A. DOW

North Carolina State University Department of Mechanical and Aerospace Engineering Precision Engineering Laboratory Campus Box 7910 Raleigh, North Carolina 27695-7910 U.S.A.

Prof.

D. DOWSON

The University of Leeds Institute of Tribology Department of Mechanical Eng. Leeds LS2 9JT UK

Mr.

G. DROUIN

Ecole Polytechnique of Monteral Canada

Dr.

M.L. EDLINGER

CEMEF Ecole des Mines de Paris Sophia Antipolis 06560 Valbonne France

Prof.

M. EGEE

Service Universitaire d’Energetique B.P. 347 51062 Reims Cedex France

Dr.

P.D. EHNl

U S . Naval Research laboratory Washington DC 20375 U.S.A.

Dr.

D.M. ELLIOlT

University of Cambridge Department of Materials Science and Metallurgy Pembroke Street Cambridge CB2 2Q;Z UK

Or.

Y. ENOMOTO

Mechanical Engineering Laboratory Namiki 1-2 Tsukuba-Shi, Ibaraki-Ken 305 Japan

Dr.

K.FANCEY

University of Hull Department of Engineering Design and Manufacture Cottingham Road Hull N. Humberside HU6 7RX UK

Dr.

B. FANTINO

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de Mecanique des Contacts - Bgtiment 113 20, avenue Albert Einstein 69621 Villeurbanne Icedex France

483

NAME

AFFILIATION/ADDRESS

Mr.

A. GIROUD

D.P.C.M.-C.E.R.T.S.M. D.C.A.N. Toulon B.P. 77 83800 Toulon Naval France

Dr.

J.R. GLADSTONE

Universtiy of Waterloo Department of Mechanical Engineering 355 St Clair Ave East Toronto OM14 1P3 Ontario Canada

Prof.

M. GODET

lnstitut National des Sciences Appliquees de Lyon Laboratoire de MBcanique des Contacts - Bitiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Prof.

M. GUEURY

E.R.I.N., E.S.S.T.I.N. Parc Robert Bentz 54500 Vandoeuvre-les-Nancy France

Prof.

P. GUIRALDENQ Ecole Centrale de Lyon Departement de MBtallurgie Physique MatBriaux (CNRS URA 447) B.P. 163 69131 Ecully Cedex France

Prof.

J. HALLING

58, lrby Rd. Heswall Wirral L61 6XF UK

Dr.

H. HESHMAT

Mechanical Tribology Inc. 968 Albany Shaker Road Latham, New-York 12110 USA

Dr.

M. HEURET

Service Universitaire d’Energ8tique B.P. 347 51062 Reims Cedex France

Dr.

D.A. HILLS

Oxford University Department of Engineering Science Parks Road Oxford, OX1 3PJ UK

Dr.

M.R. HILTON

The Aerospace Corporation Chemistry and Physics Laboratory El Segundo, CA 90245 U.S.A.

Dr.

K. HIRATSUKA

Tokyo Institute of Technology 2-12-1, Ookayama, Meguro-ku Tokyo 152 Japan

AFFILIATION/ADDRESS

Dr.

S. FAYEULLE

Ecole Centrale de Lyon B.P. 163 69131 Ecully Cedex France

Dr.

E. FELDER


Mr.

J.E. FERNANDEZ Universidad de Oviedo E.T.S. lngenieros lndustriales de Gijon Gijon Spain

Dr.

J. FISHER


Dr.

L. FLAMAND

lnstitut National des Sciences AppliquBes de Lyon Laboratoire de MBcanique des Contacts - Btitiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Dr.

Dr.

Dr.

Dr.

Dr.

Prof.

P.D. FLEISCHAUER The Aerospace Corporation Chemistry and Physics Laboratory El Segundo, CA 90245 U.S.A.

J. FRANSE

A. GABELLI

Philips Research Laboratoires Postbus 80.000 5600 JA Eindhoven The Netherlands SKF Engineering & Research Centre B.V. Postbus 2350 3430 DT Nieuwegein The Netherlands

A. GANGOPADHYAY Tribology Group National Institute of Standards and Technology Gaithersburg, MD 20899 USA. M.N. GARDOS

Hughes Aircraft Company El Segundo CA 90245 U.S.A.

J.-M. GEORGES Ecole Centrale de Lyon Laboratoire de Technologie des Surfaces - URA CNRS 855 B.P. 163 69131 Ecully Cedex France

484

TlTLE NAME Dr.

K. HOLMBERG

Technical ResearchCentre of Finland Laboratory of Enginering Production Technology Metallimiehenkuja6 SF-02150 ESP00 Finland

Mr.

H-S. HONG

The Lubrizol Corporation Wickliffe, OH 44092 USA.

Dr.

L.L. HU

Tokyo Institute of Technology 2-12-1, Ookayama, meguro-ku Tokyo 152 Japan

Dr.

Prof.

Dr.

I.M. HUTCHINGS University of Cambridge Department of Materials Science and Metallurgy Pembroke Street Cambridge CB2 2QZ UK

B. JACOBSON

S. JAHANMIR

NAME

AFFILIATION/ADDRESS

SKF Engineering & Research Centre B.V. Postbus 2350 3430 DT Nieuwegein The Netherlands and Chalmers Universityof Technology Fack 5402 20 Gottenburg Sweden Tribology Group National Institute of Standards and Technology Gaithersburg, MD 20899 USA.

AFFILIATION/ADDIW

Dr.

V.W. KANNEL

Battelle Columbus Division 505 King Ave. Colombus, OH. 43201 U.S.A.

Dr.

Ph. KAPSA

Ecole Centrale de L.yOn Laboratoire de Technologie des Surfaces - URA CNRS 855 B.P. 163 69131 Ecully Cedex France

Prof.

F.E. KENNEDY

Thayer School of Engineering Dartmouth College Hanover, NH 03755 USA

Dr.

M. LABERGE

University of Waterloo Department of Civil Engineering Waterloo N2L 3G1 Ontario Canada

Mr.

E. LANZA

Laboratoire de Chimie Marine et Physico-Chimie Universitb de Toulcin et du Var 83130 La Garde France

Dr.

J. LEPAGE

Laboratoire E.R.M.E.S. CNRS U.A. 875 INPL Universitb de Nancy 1 6, rue du Joli Coeur 54000 Nancy France

Mr.

J.-M. LEROY

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de Mbcanique des Contacts - BBtiment 113 20, avenue Albert Eiinstein 69621 Villeurbanne Cedex France

Mr.

L. JIA-JUN

Tribology ResearchInstitute Tsinghua University beijing China

Dr.

X.X. JIANG

Institute of Metal Research Shenyang China

Dr.

S.Z.LI

Institute of Metal Research Shenyang China

Mr.

Z.M.JIN


Mr.

2. LIN-QING

Tribology Research Institute Tsinghua University Beijing China

Dr.

J.-C. LIU

University of New Mexico Mechanical Engineering Department Albuquerque, NM 07131 U.S.A.

Prof.

F.D. JU

University of New Mexico MechanicalEngineering Department Albuquerque, NM 87131 U.S.A.

485

NAME

AFFILIATION/ADDRESS

Mme

M.F. LlZANDlER

Laboratoirede Chimie Marine et Physico-Chimie Universite de Toulon et du Var 83130 La Garde France

Dr.

J.L. LOUBET

Ecole Centrale de Lyon Laboratoire de Technologie des Surfaces URA CNRS 855 B.P. 163 69131 Ecully Cedex France

Dr.

Dr.

B. MAITHES

A. MATTHEWS

Technische Hoschschule DarmStadt lnstitut fur Werkstoffkunde Grafestr.2 D-6100Darmstadt FRG University of Hull Department of Engineering Design and Manufacture Cottingham Road Hull N. Hurnberside H U 6 7RX UK

NAME

AFFILIATION/ADDRESS

Mr.

NlVOlT

Laboratoire E.R.M:E.S, CNRS U.A. 875 INPL Universite de Nancy I 6,rue du Joli Coeur 54000 Nancy France

Dr.

D.NOWELL

Oxford University Department of Engineering Science Parks Road Oxford, OX1 3PJ U.K.

Prof.

D. PAULMIER

Laboratoire E.R.M.E.S. 6,rue du Joli Coeur 54000 Nancy France

Mr.

M.C. PEREZ BECARES Unidad de Tribologia Madrid Spain

Dr.

M.B. PETERSON Tribology Group National Institute of Standards and Technology Gaithersburg Maryland 20899 U.S.A.

Mr.

J.I. Mc COOL

Penn State Great Valley Malvern, PA 19355 U.S.A.

Dr.

J.B. MEDLEY

University of Waterloo Department of Mechanical Engineering 355 St Clair Ave East Toronto OW14 1P3 Ontario Canada

Dr.

R. RAMOARINA

Laboratoire E.R.M.E.S. CNRS U.A. 875 INPL Universite de Nancy 1 6,rue du Joli Coeur 54000 Nancy France

Laboratoire E.R.M.E.S. CNRS U.A. 875 INPL Universite de Nancy 1 6,rue du Joli Coeur 54000 Nancy France

Dr.

K.V. RAVl

Crystallume Menlo Park, CA 94015 U.S.A.

Dr.

L. REZAKHANLOU Ecole des Mines L.S.G.2MiL.G.M. Parc de Saurupt 54042 Nancy Cedex France

Dr.

D.S. RICKERBY

Materials Engineering Centre Hawell Laboratory UKAEA Oxfordshire OX1 1 ORA UK

Mr.

A. RlCON

Unidad de Tribologia Madrid Spain

Mr.

C.H. RIVARD

Hopital Ste Justine Montreal Canada

Dr.

A. MEZlN

Dr.

P. MONTMlTOf IET Ecole des Mines de . -iris CEMEF Sophia Antipolis 06565 Valbonne Cedex France

Dr.

J. MSTOWSKI

Wyzsza Szkola lnzynierska UI. Podgorna 50 65246 Zielona Gora Poland

Dr.

Th. NEVERS

Ecole Centrale de Paris Laboratoirede Mecanique des Sols et Structures Grande Voie des Vignes 92290 Chiitenay-Malabry France

486

NAME

Ms

Dr.

Dr.

Mr.

H. RONKAINEN Technical ResearchCentre of Finland Laboratory of Enginering Production Technology Metallimiehenkuja 6 SF-02150 ESP00 FinIand

A. SACKFIELD

A. SAIED

P. SAINSOT

lnstitut National des Sciences AppliquBes de Lyon Laboratoirede MBcanique des Contacts - Batiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France


Dr.

T. SASADA

Tokyo Instituteof Technology 2-12-1, Ookayama, meguro-ku Tokyo 152 Japan

Dr.

J.M. SAUREL

Laboratoirede Microacoustiquede Montpellier UniversitB des Sciences et Techniques du Languedoc Place Eugene Bataillon 34060 Montpellier Cedex France

Mr.

Dr.

H. SIMURA

I.L. SINGER

Mr.

R. SMALLEY

S.K.F. Engineering and Research Centre Postbus 2350 3430 DT Nieuwegein The Netherlands

Dr.

W.D. SPROUL

Basic Industrial Research Laboratory Northwestern University Evanston, IL. 60208 U.S.A.

Mr.

Y. SUN

lnstitut National des Sciences AppliquBes de Lyon Laboratoire de MBcanique des Contacts Bitiment 113 20, avenue Albert Einstein 69621 Villeurbanne cedex France

Laboratoire de Microacoustique de Montpellier UniversitB des Sciences et Techniquesdu Languedoc Place Eugene Bataillon 34060 Montpellier Cedex France

V. SAMPER

A. SEBAOUN

AFFILIATION/ADDRESS

Trent Polytechnic Department of Mathematics Nottingham NG1 4BU UK

Dr.

Mr.

NAME

AFFILIATION/ADDRESS

Laboratoire de Chimie Marine et Physico-Chimie UniversitB de Toulon et du Var 83130 La Garde France Mechanical Engineering Laboratory Namiki 1-2 Tsukuba-Shi, Ibaraki-Ken 305 Japan

US. Naval Research Laboratory Washington DC 20375 U.S.A.

-

Dr.

A.G. TANGENA

Philips Research Laboratories Postbus 80.000 5600 JA Eindhoven The Netherlands

Dr.

M. THOMA

MTU Motoren- und l’urbinen-Union Munchen GmbH Munich, FRG

Dr.

P.J. TWEEDALE Imperial College Particle Technology Group Department of Chemical Engineering Prince Consort Road South Kensington London SW7 2BY UK

Dr.

E. VAN SCHEL

Service Universitaired’EnergBtique B.P. 347 51062 Reims Cedex France

Mr.

R. VIJANDE

Universidad de Oviedo E.T.S. lngenieros lndustrialesde Gijon Gijon Spain

Prof.

B. VILLECHAISE 1.U.T d’Angoulame 4, avenue de Varsovie 16021 Angouleme Cedex France

Prof.

L. VINCENT


487

TITLE

NAME

AFFILIATION/ADDRESS

Dr.

J. von STEBUT

Ecole des Mines L.S.G.2M/L.G.M. Parc de Saurupt 54042 Nancy Cedex France

Dr.

M. WATANABE

Mechanical Engineering Laboratory Namiki 1-2 Tsukuba-shi, lbaraki-Ken 305 Japan

Prof.

W.O. WlNER

Georgia Institute of Technology Atlanta, GA 30332 USA.

Mr.

J.Q. YAO


Mr.

2. YONG-WU

Tribology Research Institute Tsinghua University Beijing China

Dr.

C.S.YUST


Dr.

H.ZAIDI

Laboratoire E.R.M.E.S. 6, rue du Joli Coeur 54000 Nancy France


489

16th LEEDS-LYON SYMPOSIUM ON TRIBOLOGY MECHANICS OF COATING

-

5th 8th SEPTEMBER 1989 LIST OF DELEGATES

NAME

AFFILIATION/ADDRESS

y x

NAME

AFFILIATION/ADDRESS

Mr.

J. ALMACINHA

Research Assistant DEMecIFaculdadede Engenharia Rua dos Bragas 4099 Porto Codex Portugal

Mr.

E. BEGHlNl

SKF ENGINEERING & RESEARCH CENTRE B.V. Postbus 2350 3430 DT, Nieuwegein The Netherlands

Dr.

J.C. BELL

Dr.

L. ANDRADE FERREIRA Lecturer

Shell Research Ltd Thorton ResearchCentre (LSPI5),P.O. Box 1 Chester CH1 3SH U K.

T

E

DEMecIFaculdadede Engenharia Rua dos Bragas 4099 Porto Codex Portugal Mr

M. ARMBRUSTER

President de la Ste Franqaise de Tribologie Aerospatiale 37, Bd de Montmorency 75781 Paris Cedex 16 France

Mr.

M. BENMALEK

Centre de recherche de Voreppe S.A. B.P.27 38340 Voreppe France

Dr.

P. BERNARD

lnstitut National des Sciences Appliquees de Lyon Laboratoire de Mecanique des Contacts, Bstiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Dr.

Y. BERTHIER

lnstitut National des Sciences Appliquees de Lyon Laboratoirede Mecanique des Contacts, Bitiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Dr.

J. ATTAL

Lab, of Microacoustic Universitedes Sciences & TechniquesduLanguedoc 34060 Montpelier Cedex France

Mr.

D. AUGER

University of Waterloo ONTARIO 2L 3G1 Waterloo Canada

Dr.

D. BARKER

Tribology Section Imperial College Dept of Mechanical Engineering London SW7 2AZ UK

Dr.

C. BlSELLl

SHELL Research Ltd,PO Box 1 Chester CH1 3SH UK

Metallurgiste C.S.E.M. Case Postale 41 2007 Neuchatel C.H.

Mr.

N. BLANCHARD

THOMSON CSF Laboratoire Central de Recherche 91403 Orsay France

Dr.

P.J. BLAU

Friction & Wear Task Leader Oak Ridge National Laboratory P.O. Box 2008 Oak Ridge TN 37831-6063 U.S.A

Dr.

B. BOU-SAID

lnstitut National des Sciences Appliqubes de Lyon Laboratoirede MBcanique des Contacts - Bitiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Dr.

Ms

Prof

T.W. BATES

M. BAUER

G. BAYADA

Societe Europeenne de Produits RBfractaires 84130 Le Pontet France lnstitut National des Sciences Appliqubes de Lyon Laboratoire de Mecanique des Contacts, BPiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

490

NAME Dr.

M. BRENDLE

C.R. sur la Physico-Chimie des Surfaces Solides 24AvenueduPdtKennedy 68200 Mulhouse France

Dr.

B.J. BRISCOE

Dept. Chemical Engineering Imperial College Prince Consort Rd. South Kensington London SW7 2BY UK

Dr.

R. W. BRUCE

LaboratoriesSurface Technology Division Alcoa Center PA 15069 USA

Dr.

S. BULL

Materials Engineering Centre 8552 Harwell Laboratory United Kingdom Atomic Energy Authority Oxfordshire OX11 ORA UK

Dr.

A. BURROWS

Editor, Tribology International Butterworths PO BOX 63 Bury Street GU2 5BH Guildford Surrey UK

Dr.

Mr.

Prof

Mr.

Mr.

Ph. CANN

M. CANTAREL

J.-P. CELIS

J.-P. CHAMBARD

H.S. CHANG

AFFILIATION/LIDDRESS

AFFILIATION/ADDRESS

Tribology Section Imperial College Exhibition Road London SW7 2BX UK lngbnieur Chef du Dept. Physique des Surfaces Ets Technique Central de I'Armement 16 bis, Av. Prieur de la CBte d'Or, 94114 Arcueil Cedex France Dept. MTM - KU - LEUVEN De Croylaan 2 8-3030, Heverlee Belgium E.R.M.E.S. /I.N.P.L. C.N.R.S 6 rue du Joli Coeur 54000 Nancy France Tribology Section Imperial College Dept of Mechanical Engineering London SW7 2BX U.K

Dr.

J.-P. CHAOMLEFFEL

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de Mbcanique des Contacts - BBtiment 113 20, avenue Albert Einstein 69621 Villeurbanne cedex France

Prof

H.S.CHENG

W.P. Murphy Professor of Mechanical Engineering Center for Engineering Tribology Catalysis BLDG Northwestern University Evanston, IL 60208 U.S.A

Prof.

T. CHILDS

The University of Leeds Department of Mechanical Engineering lnstitut of Tribcilogy Leeds LS2 9JT UK

Dr.

R.J. CHllTENDEN

Industrial Unit of Tribology The Universityof Leeds Woodhouse Lane Leeds LS2 QJT' U.K.

Dr.

L. CHOLLET

C.S.E.M. Case postale 41 2007 Neuchatel C.H.

Dr.

S.J. COLE

Tribology Section Imperial College Exhibition Road London SW7 2,BX UK

Dr.

F. COLIN

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de Mbcanique des Contacts - BAtiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Mr.

B. CONSTANS

Lubrication Engineer ELF-FRANCE CRES B.P.22 69360 St Symphorien d'0zon France

Dr.

M. CONTE

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de MBcanique des Contacts - BAtiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

49 1

T

m

Dr.

NAME

AFFIU ATION/ADDRESS

R.C. COY

Shell Research Ltd Thorton ResearchCentre (LSP/5) P.O. Box 1 Chester CH13SH UK

J.-P.DHUIQUE-MAYER RVI DER 1 Etudes Moteurs Avenue 1, Les Courbaisses 69800 SAINT-PRIEST France

Dr.

Y.S. DONG

Academic Visitor Tribology Section Dept. of Mechanical Eng. Imperial College London SW7 2AZ UK

Prof

D. DOWSON

The University of Leeds lnstitut of Tribology Department of Mechanical Engineering Leeds LS2 9JT UK

Mr.

P. DRONIOU

Head of Metalworking Lab. C.F.P.I. 28 Bd Camelinat 92233 GennevilliersCedex France

Mr.

C. DRUET

SociBtB TRANSROL Groupe SKF 148, rue Felix Esclangon B.P. 908 73009 Chambery Cedex France

Mrs

M.-C. DUBOURG


Mr.

R. DWYER-JOYCE

Ecole des Mines, Centre de Mise en Forme des Materiaux Sophia Antipolis 06565 Valbonne France

Tribology Section Imperial College Exhibition Road London SW7 2BX UK

Mrs

M.-L. EDLINGER

Centre de Recherches de Voreppe Groupe TRANSFORMATION B.P.27 38340 Voreppe France

Ecole des Mines Centre de Mise en Forme des MatBriaux Sophia Antipolis 06565 Valbonne France

Prof

M. EGEE

Service Universitaire d’Energ6tique B.P.347 51062 Reims Cedex France

J.F. CRETEGNY

S.E.P. Laboratoire For& de Vernon B.P.802 27207 Vernon Cedex France

Prof

G. DALMAZ


Mr

J.DANROC

Engineer CEA-IRDI-DMECN DBpartement de Metallurgie de Grenoble CENG-85X 38041 Grenoble Cedex France

Mr.

Dr.

Mr.

Prof

J.A. DAVIDSON

P. DEIAINE

F. DELAMARE

P. DENEUVILLE

P. DESTUYNDER

AFFILIATION/ADDRESS

Mr.

Dr.

Dr.

NnME

Materials Research Director Richards Medical Company 1450 Brooks Road Memphis, TN 38611 U.S.A.

lnstitut National des Sciences Appliquees de Lyon Laboratoire de MBcanique de: Contacts - Btitiment 113 20 Avenue . Albert Einstein 69621 Villeurbanne Cedex France

Ecole Centrale de Paris Grande Voie des Vignes 92295 Chtitenay Malabry France

492

NAME

AFFILIATION/ADDRESS

TITLS Prof

Mr.

D. ELLIOTT

University of Cambridge Dept of Materials Science and Metallurgy Pembroke Street Cambridge CB2 3QZ UK

Mr.

L.H. EVANS

Senior Lecturer Department of Mathematical Sciences Chisholm Instituteof Technology Melbourne Australia

B. FANTINO

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de Mbcanique des Contacts - Bliment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Dr.

S. FAYEULLE


Dr.

E. FELDER

Ecole des Mines Centre de Mise en Forme des Matbriaux Sophia Antipolis 06565 Valbonne France

Dr.

Dr.

Dr.

Dr.

Dr.

J.E. FERNANDEZ RlCO OVIEDO UNIVERSITY E.T.S. INGENIEROSINDUSTRIALES Gijon, Spain L. FIAMAND

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de MBcanique des Contacts - BPiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

P.D. FLEISCHAUER The Aerospace Corporation Post Office Box 92957 El Segundo Los Angeles, CA 90245 U.S.A.

S.E. FRANKLIN

Philips Centre for Manufacturing Technology Building SAQ-2 PO BOX 218 5600 MD,Eindhoven The Netherlands

NAME J. FRENE

AFFILIATION/ADDRESS

Laboratoire de Mbcanique des Solides Facultb des Sciences de Poitiers 40, Avenue du Recteur Pineau 86022 Poitiers Cede)c France

Dr.

A. GABELLI

SKF Engineering and Research Centre B.V. Postbus 2350 3430 DT Nieuwegein The Netherlands

Dr.

M.N. GARDOS

Chief Scientist MaterialsTechnology Laboratory Hugues Aircraft Company P.O. Box 902 EI/F150 El Segundo CA 90245, U.S.A

Prof

J.-M. GEORGES

Ecole Centrale de Lyon Laboratoire de Technologie des Surfaces URA C.N.R.S.855 BP 163 69131 Ecully Cedex France

Mr.

J.R. GLADSTONE

Research Engineer University of Waterloo 355 St. Clair Aye East Toronto OM4 .IP3 Ontario, Canada

Prof

M. GODET

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de Mbcanique des Contacts - Bstiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Mr.

R. GOJON

Directeur Technique Socibtb Industrielle des Coussinets 4, rue de la Liberte B.P.73 74009 Annecy Cedex France

Mrs

C. GOULBORN

The Universityof Leeds Institute of Tribology Department of Mechanical Engineering Leeds LS2 9J’T UK

Dr.

GRAS

I.S.M.C.M. Laboratoire de Tribologie 3 rue Fernancl Hainaut 93407 St.Ouen Cedex France

493

NAME Prof

P. GUIRALDENQ

Ecole Centrale de LyOn B.P. 163 69131 Ecully Cedex France

Mr.

J.C. HAMER

Tribology Section Imperial College Exhibition Road London SW7 2BX UK

Mr.

Prof

R.T. HARDlNG

M. HASEGAWA

The Universityof Leeds Instituteof Tribology Department of Mechanical Engineering Leeds LS2 9JT UK Himeji Institute of Technology Department of Mechanical Engineering 2167 Shosha, Himeji, Hyogo Ken Japan

Mr.

D. HERTZ

FRAGEMA-FRAMATOME DIV. Combustible 10, rue J.RBcamier 69006 Lyon France

Dr.

H. HESHMAT

MechanicalTechnology INC 968 Albany-Shaker Road LATHAM, New-York 12110 USA

Dr.

D.A. HILLS

AFFILIATION/ADDRESS

AFFILIATION/ADDRESS

OXFORD UNIVERSITY Dept. of Engineering Science Parks Road Oxford 0x1 3PJ UK

Mr.

K. HIRATSUKA

Tokyo Institute of Technology 2-12-1, Ookayama, Meguro-ku 152 Tokyo Japan

Dr.

K. HOLMBERG

Technical ResearchCentre of Finland VTT/KOT,Metallimiehenkuja 6 SF-02150,Espoo Finland

Dr.

H.-S. HONG

ResearchAnalyst The Lubrizol Corporation 29400 Lakeland Boulevard Wickliffe,Ohio 44092-2298 U.S.A.

Dr.

C.J. HOOKE

University of Birmingham Dept of Mechanical Engineering P.O. Box 363 Birmingham 815 21T UK

Mr.

J.-L. HOUPERT

SORETRIB Ecole Centrale de Lyon B.P. 163 69131 Ecully Cedex France

Pr.

E. IOANNIDES

Visiting Professor Imperial College London SKF Engineeringand Research Centre B.V. Postbus 2350 3430 DT Nieuwegein The Netherlands

Pr.

B. JACOBSON

SKF Engineeringand ResearchCentre B.V. Postbus 2350 3430 DT Nieuwegein The Netherlands and Chalmers University Technology Fack S-402 20 Gottenburg Sweden

Dr.

S. JAHANMIR

Dr. Group leader Tribology Group National Institute of Standards and Technology Gaithersburg, Maryland 20899 U.S.A.

Dr.

Z.M. JIN

The University of Leeds Institute of Tribology Department of Mechanical Enginewing Leeds LS2 9JT UK

Mr.

B. JOBBINS

The University of Leeds Institute of Tribology Department of Mechanical Engineering Leeds LS2 9JT UK

Mr.

D.A. JONES

The University of Leeds Institute of Tribology Department of Mechanical Engineering LeedsLS29JT UK

494

TITJEE

AFFILIATION/ADDRESS

TITLE NAME -

AFFILIATION/ADDRESS

Dr.

A. JONGEJAN

Elsevier Science Publishers Sara Burgerhartstraat25 1055 KV,Amsterdam The Netherlands

Mr.

J.-M. LEROY

Dr.

F.D. JU

PresidentialProfessor Mechanical Engineering Dept. University of New Mexico Albuquerque, NM 87131 U.S.A.

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de Mecanique des Contacts - Bi3timent 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Dr.

s. LI

LONZA AG GFAPHITE BUSINESS UNIT 56043 Sins C.H.

Mrs

M.-F. LIZANDIER

Chercheur Laboratoire de Chimie Physique de Toulon Universitbde Toulon et du Var Avenue de I’lJniversit6 83130 La Garde France

Mr.

J.-J. LOPEZ

CENCENG Dept. de Metallurgie de Grenoble Lab. d’Etudes de Matbriaux Minces BP 85X 38041 Grenoble Cedex France

Dr.

J.-L. LOUBET

Laboratoire de Technologie des Surfaces Ecole Centrale de Lyon B.P.163 69131 Ecully Cedex France

Dr.

A.A. LUBRECHT

SKF Engineering and ResearchCenter B.V. Postbus 23501 3430 DT Nieuwegein The Netherlands

Prof.

K.C. LUDEMA

University of Michigan Ann Arbor, U.S.A.

Dr.

C.N. MARCH

Industrial Unit of Tribology The University Wood House Lane Leeds LS2 9JT U.K.

Mr.

H. MARGINSON

Tribology Section Imperial College London SW7 2BX U K.

Dr.

R. MARSOLAIS

Centre de Recherche de Voreppe B.P.27 38340 Voreppe France

Mrs

Dr.

A. JULLIEN

V. W. KANNEL

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de Mbcanique des Contacts - Bgtiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France Battelle 505 King avenue Colombus, OH 43201-2693 U.S.A.

Dr.

P. KAPSA

Ecole Centrale de Lyon Lab. de Technologie des Surfaces URA C.N.R.S.855 BP 163 69131 Ecully Cedex France

Prof.

F.E. KENNEDY

Dartmouth College Thayer School of Engineering Hanover, NH 03755 U.S.A.

Dr.

M. LABERGE

Department of Civil Engineering University of Waterloo Waterloo N2L 3G1 Ontario Canada

Mr.

J. LAUClRlCA

TEKNIKER C/ISASI S/N,Eibar 20600 Guipuzcoa Spain

Prof.

J. LEDOCQ

Facultb Polytechniquede Mons rue de Houdain B 7000 Mons BELGIUM

Dr.

J. LEPAGE

Laboratoire E.R.M.E.S. 6 rue du Joli Coeur 54000 Nancy France

495

NAME Dr.

J.-M. MARTIN

Lab. de Technologie des Surfaces Ecole Centrale de Lyon BP I63 69131 Ecully Cedex France

Mr.

D. MARTIN

Elf France Tour Elf 2, Place de la Coupole La DClfence 6 92400 Courbevoie France

Dr.

T. MATHIA

Lab. de Technologie des Surfaces Ecole Centrale de Lyon BP 163 69131 Ecully Cedex France Dept. of Engineering Design and Manufacture University of Hull Hull HU6 7RX U.K.

Dr.

A. MAlTHEWS

Dr.

P. MAURIN-PERRIER HYDROMECANIQUE & FROlTEMENT Z.l.sud Rue B. Fourneyron 42166 Andrezieux-Boutheon France

Dr.

Prof.

B.D. Mc.CONNELL

J.I. Mc.COOL

WRDC/MLBT Wright-PattersonAFB Dayton, OH 45433 U.S.A.

Assistant Professor Industrial& Management Systems Engineering Dept. Penn State Great Valley 30 E. Swedesford Road Malvern, PA19355 USA.

Dr.

J.B. MEDLEY

Dept. of Mechanical Eng. University of Waterloo Waterloo, Ontario N2L 3G1 Canada

Dr.

M.-H. MEURISSE

lnstitut National des Sciences Appliqubes de Lyon Laboratoire de Mecanique des Contacts - BPtiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Dr.

N. MIKKELSEN

NAME

AFFILIATIONIADDRESS

University of Aarhus Instituteof Physics DK 8000,Aarhus C Danemark

AFFILIATION/ADDRESS

Dr.

P. MONTMITONNET Ecole des Mines Centre de Mise en Forme des MatBriaux Sophia Antipolis 06565 Valbonne France

Mrs

S. MOORE


Dr.

S.L. MOORE

Sunbury Research Centre Chertsey Road Sunbury-on-Thames TWI 6 7LN Middlesex UK

Dr.

M. MOUWAKEH

lnstitut National des Sciences Appliquees de Lyon Laboratoire de MBcanique des Contacts - BPtiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Mr.

D. NELIAS

Turbomeca 64320 Bizanos France

Dr.

A.V. OLVER

Westland Helicopters Ltd Yeovil,BA20 2YB U.K.

Dr.

C. PAN

Member of Technical Staff Digital Equipment Corp. 333 South Street Shrewsbury Massachusetts01545-4112 U.S.A.

Prof.

D. PAULMIER

Laboratoire E.R.M.E.S./I.N.P.L. C.N.R.S 6 rue du Joli Coeur 54000 Nancy France

Dr.

P. PERSON

Manufacture Michelin Service EFNLADOUX 63040 Clermont-Ferrand France

Dr.

M.B. PETERSON

Tribology Group National Instituteof Standards and Technology Gaithersburg Maryland 20899 U.S.A.

496

NAME Mr.

J.C. PlVlN

C.S.N.S.M. Lab. RenB Bernas 6At 108 6P 1 91406 Orsay France

Dr.

A. PLAGGE

Dow Corning GmbH Munchen Pelkovenstrasse152 D-8000 Miinchen 50 W.GERMANY

Dr.

F. PLATON

E.N.S.C.I. 47 Av. Albert Thomas 87065 Limoges Cedex France

Mrs ,

L. RAVELOJAONA

lnstitut National des Sciences AppliquBes de Lyon Laboratoire de MBcanique des Contacts - 6Atiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Mr.

R. REZAKHANLOU

Laboratoire de GBnie MBtallurgique Ecole des Mines Parc de Saurupt 52042 Nancy France

Dr.

F. ROBBE-VALLOIRE I.S.M.C.M. Lab. de Tribologie 3 rue Fernand Hainaut 93407 St.Ouen Cedex France

Dr.

B. ROBERTS

Mrs

Prof.

H. RONKAINEN

L. ROZEANU

NAME

AFFILIATION/ADDRESS

Manager National Centre of Tribology Risley Warrington WA3 6AT Cheshire UK Research Scientist Technical Research Centre of Finland Laboratory of Engineering Production Technology Metallimiehenkuja6 SF-02150,ESpoo Finland

Technion Israel institute of Technology Department of Materials Engineering, Technion City 32000 Haifa Israel

AFFILIATION/ADDRESS

Mr.

A.A. SAAD

Tribology Sectiion Imperial Collhgie London SW7 2BX London UK

Mr.

A. SAADA

lnstitut National des Sciences AppliquBes de Lyon Laboratoire de Mbcanique des Contacts - Btiment 113 20, avenue Alb'ert Einstein 69621 Villeurbenne Cedex France

Dr.

A. SACKFIELD

Trent Polytechinic Nottingham NGl 46U UK

Mr.

P. SAINSOT

lnstitut Nationaldes Sciences Appliqubes de Lyon Laboratoire de MBcanique des Contacts - Btiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Mrs

V. SAMPER

Ecole des Mines Centre de Mise en Forme des Matbriaux Sophia Antipolis 06565 Valbonne France

Dr.

S. SAUTTER

SKF Gleitlager GmbH Mijhlenstrasse D-6625 Puttlingen 3 F.R.G.

Dr.

R.S. SAYLES

Tribology Section Imperial Collhge Exhibition Road London SW7 26X UK

Mr.

M. SCHAULE

Senior Engineer Digital Equipmlint Intl. Sudetenstrassr?5 D-8950 Kaufbeuren F.R.G.

Mr.

R. SCHMID

Materials Developm.nribology Sulzer Brothers Ltd CH-8401Wintwthur C.H.

Dr.

I.L. SINGER

Code 6170-NRL Washington DC 20325 U.S.A.

Mr.

R.J. SMALLEY

SKF Engineeringand Research Centre B.V. 3430 DT Nieuwegein The Nertherlands

491

NAME

AFFILIATION/ADDRESS

Mr.

E. STEIGER

Steiger S.A. Les Bosquets 1800 Vevey C.H.

Mr.

Y.T. SUN

lnstitut National des Sciences AppliquBes de Lyon Laboratoire de MBcanique des Contacts - Batiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Prof.

D. TABOR

Emeritus Professor Cavendish Laboratory Madingley Road Cambridge CB3 OHE UK

Dr.

A.G. TANGENA

Philips Research Laboratories POB 8000 5600 JA Eindhoven The Netherlands

Dr.

Dr.

Prof.

C.M. TAYLOR

M. THOMA

J. TlCHY

The University of Leeds lnstitue of Tribology Department of Mechanical Engineering Leeds LS2 9JT U K.

MTU Motoren und Turbinen union Munchen GmbH Dachauer Str. 665 8000 Munchen 50 F.R.G.

Rensselaer Polytechnic Institute Troy NY 12180-3590 USA.

Mr.

L. TILGNER

SKF Gleitlager GmbH Muhlenstrasse D-6625 Puttlingen 3 F.R.G.

Mr.

C. TOURNE

S.N.E.C.M.A. Service Y.L.B. Ets de Villaroche 77550 Moissy Cramayel France

Dr.

R. TRABELSI

lnstitut National des Sciences AppliquBes de Lyon Laboratoire de MBcanique des Contacts - BIirnent 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

NAME

AFFILIATION/ADDRESS

Dr.

J.H. TRlPP

SKF Engineering and Research Centre 3430 DT Nieuwegein The Netherlands

Mr.

E. VANCOILLE

Engineer DEPT. MTM - KU - LEUVEN De Croylaan 2 B-3030 Heverlee Belgium

Dr.

P. VELEX

lnstitut National des Sciences AppliquBes de Lyon Laboratoire de Mecanique des Contacts - BAtiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Dr.

F. VERGNE

SNR Roulements 1, rue des Usines B.P.17 74010 Annecy Cedex France

Dr.

P. VERGNE

lnstitut National des Sciences AppliquBes de Lyon Laboratoire de Mecanique des Contacts - Batiment 113 20, avenue Albert Einstein 69621 Villeurbanne Cedex France

Prof.

R. VIJANDE DlAZ

Oviedo University E.T.S. ingenieros lndustriales Gijon Spain

Prof.

L. VINCENT


Prof.

0. VINGSBO

Uppsala University School of Engineering Dept. of Materials Science Box 534 S-751 21 Uppsala Sweden

Mr.

J.-F. VlOT

RhGne-PoulencRecherche Centre des Carrihres 85, av. des Frbres Perret 69190 Saint-Fons France

Dr.

J. VON STEBUT

Laboratoire de GBnie MBtallurgique Ecole des Mines Parc de Saurupt 52042 Nancy France

498

AFFILI ATION/ADDRESS

Dr.

G.T.Y. WAN

SKF Engineering & Research Centre B.V. 3430 DT Nieuwegen The Netherlands

Dr.

M. WATANABE

Mechanical Eng. Laboratory Namiki 1-2,Tsukuba-shi 305 Ibaraki-ken Japan

Mr.

A.J. WlNN

The University of Leeds Institute of Tribology Department of Mechanical Engineering LeedsLS2 9JT UK

Dr.

N. WUETHRICH

Materials Develop.lTribology Sulzer Brothers Ltd Winterthur CH-8401 C.H.

Mr.

J.Q. YAO


Mr.

K. YOSHIDA

Nippon Mining Tokyo Japan

Dr.

H.ZAlDl

Lab. E.R.M.E.S. 1I.N.P.L. C.N.R.S 6 rue du Joli Coeur 54000 Nancy France

Mr.

M. ZBINDEN

EDF-Etudes et Recherches Centre des Renardieres, route de Sens BP 1 Ecuelles 77250 Moret sur Loing France

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