The contact of rough surfaces carrying pressure sensitive boundary layers

Thinning Films and Tribological Interfaces / D. Dowson et al. (Editors) © 2000 Elsevier Science B.V. All rights reserved.

45

The contact of rough surfaces carrying pressure sensitive boundary layers K A B lencoe, J A Williams

Department of Engineering, Cambridge University, Trumpington Street, Cambridge, CB2 1PZ, UK

When two rough surfaces are loaded together it is well known that the area of true contact is very much smaller then the geometric area and that, consequently, local contact pressures are very much greater than the nominal value. If the asperities on each surface can be thought of as possessing smooth summits and each of the solids is elastically isotropic then the pressure distribution will consist of a series of small, but severe, Hertzian patches. However, if one of both of the surfaces in question is protected by a boundary layer then both the number and dimensions of these patches, and the form of the pressure distribution within them, will be modified. Recent experimental evidence from studies using both Atomic Force Microscopy and micro-tribometry suggests that boundary films produced by the action of commercial anti-wear additives, such as ZDTP, exhibit mechanical properties, which are affected by local values of pressure. These changes bring about further modifications to local conditions. These effects have been explored in a numerical model of rough surface contact and the implications for the mechanisms of surface distress and wear are discussed.

NOTATION A P P R #

area of true contact normal load on asperity line contact normal pressure at the asperity contact radius of curvature of asperity tips coefficient of friction

1.

INTRODUCTION

A common starting point for the modelling of many contact situations involving engineering surfaces is the analysis of the conditions pertinent to the contact of a single, representative asperity. Consideration is then given to the topography within the

v Y h E N

Poisson's ratio uniaxial yield stress film thickness elastic modulus number of asperities in contact

macro-contact summing up the contribution to the global values of load support at all such individual asperity contacts. The conclusions of the Greenwood and Williamson analysis of the interaction of nominally flat surfaces which carry a

46

random distribution of asperity heights, of characteristic tip radius R, are well known [1]. As the surfaces are pressed together, the number of true asperity contacts N increases in direct proportion to the applied normal load P. The total area of real or true contact A, which consists of the summation of all the individual contact spots also increases in proportion to the number of asperities in contact and thus also depends linearly on P. As the load on the contact is raised, existing asperity contacts experience more severe pressures and grow in area, while newly formed, smaller points of contact are much more modestly loaded. However, both the average size of asperity contacts (i.e. A/N) and the average contact pressure (P/A) stay essentially constant. It is straightforward to demonstrate that these relations can be strictly true under idealised (but not unrealistic) circumstances; a case in point being a surface which consists of elastic, spherically-tipped asperities with heights that possess an exponential probability density function. Greenwood and Williamson showed that this invariance of average asperity pressure with load is substantially true for surfaces generated by a number of manufacturing processes such as grinding or lapping- provided that the applied loads are such that the real area of contact is only a small proportional of the nominal area. Of course, although the average pressure across the contact under these circumstances may be comparatively modest, individual, prominent asperities can see very large pressures and this has important consequences for both the frictional sliding resistance offered by the contact and the rate of degradation or wear of the surfaces. The force of friction under sliding conditions is generated at these small islands of true contact and so, if this is to be minimised, every effort is made to ensure that the surfaces are coated with a boundary layer of low shear strength. From the point of view of surface degradation or wear, what matters is the

extent of any regions of surface (or subsurface) material plasticity. Provided the surface slopes of the asperities are small, there are unlikely to be any elements of surface ploughing and this, if combined with a friction regime in which local friction coefficients are less than about 0.3, implies that the transition from elasticity to plasticity is likely to occur a little below the contact surface. Under situations of repetitive contact, in which the loads are such that some asperities generate sub-surface stresses that are consistently above the elastic or shakedown limit, an element of plastic deformation may be introduced into the weaker surface on each cycle of loading. There is much experimental evidence that these increments eventually, by some process of strain accumulation, contribute to the loss of material, i.e. to wear [2]. The presence of a softer, lower modulus, surface layer can help alleviate these conditions by attenuating the values of the pressures at the local asperity maxima; if these can be brought down to values below the material shakedown limit then longer surface (and thus component) lives will be anticipated. It is this cushioning effect of b o u n d a r y lubricant surface layers that we explore in this contribution; in particular, attempting to model the circumstances of steel surfaces lubricated by softer boundary films.

2.

N A T U R E OF B O U N D A R Y F I L M S

A boundary lubricant can be thought of as a surface layer deposited or formed on either one or both of the harder substrates which offers a reduced resistance to shear of the junction. In dry sliding contacts, soft or low shear solids (typified by soft metals such as lead or lamellar solids such as molybdenum disulphide) can be employed. However, these are inappropriate in lubricated systems. In internal combustion engines, for example, the complex contact conditions within the valve train impose severe performance requirements on the lubricant [3]. The occurrence of regions of near-zero oil-entrainment velocity leads to

47 very low oil film thicknesses at some points in the operating cycle. In these regions the lubricant itself cannot prevent contact between the rubbing surfaces and protection is obtained by using lubricant additives which are able to produce solid-like films which then act as boundary lubricants. Good boundary lubricants are those which achieve a successful compromise between being sufficiently robust to maintain their integrity under these arduous sliding conditions and having a sufficiently low shear strength to ensure that the shear plane is located within the protective film. The efficiency of the film then results from the equilibrium between film wear and film formation rates. oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.---'-'-'-

< 900 n m

" . ' . ' . ' . ' . ' . ' . ' . ' . a l k y l phosphate .'. . . . . . . . . . . .

tnm

E (GPa)

J

40

1

2

p (GPa)

Fig. 1 (a) Simplified structure of the full anti-wear film formed by a simple ZDTP solution on a ferrous substrate which is covered by a thin inorganic sulphide/oxide layer. Some deposits of inorganic phosphates are formed which are assumed to be smeared out over the surface. The elastic moduli of the layers are taken as: steel 210 GPa, inorganic oxide layer 90 GPa; phosphate layer 15
The chemical family of zinc dialkyl dithiophosphates (ZDTP' s) have been extensively used for many years as lubricant additives because of both their anti-oxidant and anti-wear properties. The composition and formation mechanisms of the films that they produce have been extensively studied [4-10] and it is now accepted that these grow from decomposition products via degradation mechanisms, which may involve oil oxidation [11] thermal decomposition [12] or hydrolysis [13]. Analytical techniques have been used to determine the nature of the ZDTP films after solvent washing which shows them to be mainly composed of amorphous phosphates [14] though they may also contain sulphides and oxides [15]. Cryogenic studies without solvent washing of the films have extended the analysis to the outer composite organic layers and have demonstrated that the overall film thickness can be as much as several hundred nano-metres [ 16-18]. As a result of both their inhomogeneous nature and their small scale, it is extremely difficult to measure the corresponding mechanical properties of these layers. However, elegant experimental work, using a form of the Surface Force Apparatus designed and built at the Ecole Centrale de Lyon, is leading to a great improvement in our understanding [19]. In some of the most recent of this work, ZDTP films were generated at the Thornton Research Centre of Shell Research on small steel blocks using a reciprocating Amsler machine which had been modified to simulate the contact conditions of the cam/follower system in the valve train of an internal combustion engine [20]. The blocks were stored in the base oil (containing predominantly paraffinic hydrocarbons, with very low concentration of polar compounds) immediately after production of the films and were kept immersed when not subsequently being measured. Mechanical test measurements of the films in the central area of the wear track indicated that the ferrous substrate was coated with 3 distinct

48 layers, as shown diagrammatically in Fig. 1 [21,221.

3. C O N T A C T S ON L A Y E R E D ROUGH SURFACES

A thin layer of sulphides and oxides (-20 nm thick)is formed on the immediate surface of the steel substrate, which is rapidly covered by a protective polyphosphate film (-40 nm thick). A much thicker discontinuous layer of alkyl phosphate precipitates (up to perhaps 900 nm thick) is located between the inorganic phosphates and the bulk of the lubricant. This outer layer exhibits visco-elastic properties and appears relatively mobile, i.e. it is capable of large strains or plastic flow. The intermediate polyphosphate layer which may be discontinuous and occur as relatively discrete patches or pads is much more robust and appears to accommodate the applied pressure through an increase in the values of its mechanical strength properties. The sulphide/oxide layer, immediately adjacent to the metal surface, was found to have an elastic modulus of ca. 90 GPa and a hardness of between 4 and 5 GPa (i.e. comparable to the steel substrate) while both the modulus and the hardness of the polyphosphate layer increased with pressure p. In particular, the elastic modulus was observed to grow more or less linearly from an initial value of ca. 15 GPa (which was maintained up to a critical pressure Pc of ca. 1 GPa) to approximately 40 GPa at a pressure of 2 GPa. This relationship can be thus written simply as:

Stress and deformation analyses for the case of a rigid cylindrical indenter making contact with a half-space carrying an elastic surface layer with differing mechanical properties from the bulk have been carried out by a number of authors [23-28]. The usual method of solution is to first calculate the local surface deformations from the degree of nominal overlap of the two surfaces and then to solve, either analytically or numerically, the stressdeformation integral equation so arriving at a consistent distribution of normal pressure at the interface: this can then be integrated to give the normal load. Gupta and Walowit [29] and Kannel and Dow [30] obtained a generalised solution for elastic cylindrical indenters against layered elastic solids. Walowit and Pinkus [31] and King and O'Sullivan [32] analysed the stress field associated with an elastic cylindrical indenter sliding, with traction, over an elastic halfspace with a single surface layer and this analysis was extended to multiple layers by Elsharkaway and Hamrock [33]. O'Sullivan and King [34] examined the case of a spherical indenter loaded sliding over a single layered surface. Results from analyses of this sort can be validated and extended by finite element analyses such as those of Ihara [35], Komvopoulos [36] and Arnell [37].

E1

=

E0 when p< Pc

P and E1 = E 0 ~ c

when p > p c .

(1)

This description of a pressure sensitive boundary lubricant has been adopted in the modelling of rough surfaces lubricated by fully developed ZDTP anti-wear films.

A more compliant layer gives, as expected, enhanced penetration depths and potentially significant changes to the pressure profile. Sub-surface stress components, Crxx, O'zz and Crxz, are also much modified by the presence of both the surface layer and any surface friction or traction. Here the Ox direction lies in the plane of the surface while Oz is the surface normal. A stiffer surface layer behaves rather like a thin elastic plate bonded to the substrate, large bending stresses can develop giving a tensile Crxx at the interface which can be significant for the growth of cracks normal to this boundary. The shear stress Crxz is also enhanced by the stiffness of the surface layer

49 although its magnitude decays rapidly with depth z. Layers which are of lower modulus than the bulk generally lead to reduced stresses but, since they are also likely to be of lower hardness, provide lower resistance to wear or surface damage. To fully exploit the tribological potential properties of harder (and generally stiffer)surface coatings, the introduction of softer intermediate layers may be appropriate. Similar effects have been found in the case of nominal point rather than line contacts Kral et al. [38] and Lovell [39]. Mao et al. [40] have used a rigorous elastic-plastic FEM analysis to study the initiation and development of the plastic zone in various TiN coating-substrate systems, including TiN-A1, TiN-Ti, and TiNHSS (high speed steel)indented by a rigid ball. The results confirm that both the coating thickness and substrate strength have a significant influence on both the plastic deformation behaviour and the load bearing capacity.

hi h2

Fig. 2 Schematic representation of contact of a rough surface on a layered half-space. A rough steel surface (E=210 GPa) is loaded against a plane steel surface coated with two elastic layers which are assumed completely bonded to each other; the lower elastic layer is also bonded to the steel substrate. Layer 1 has mechanical properties which are affected by the local asperity pressures.

4. PRESSURE SENSITIVE LAYERED CONTACTS 4.1.

Calculation method

We have used essentially the same procedures as those of Mao et al. [41] to examine contacts between a hard material, with a known 2-D surface profile, and an elastic half-space carrying one or more thin coated layers. However, the software (which is based on that developed by Cole and Sayles [46]) has been modified to allow the elastic properties of one of these layers to be functions of the interface normal pressures so simulating the observed behaviour of the ZDTP derived layers. Figure 2 illustrates the physical picture and Fig. 3 shows the logic flow diagram of the modified software.

4.2.

Single asperity contact

To demonstrate the influence of a compliant surface coating, the contact between a single cylindrical asperity and a pressure insensitive layered substrate was first investigated using the numerical procedure described above; the situation is illustrated in Fig. 4(a). Figure 4(b) shows, as the solid curve, the Hertzian pressure distribution for a line contact between an asperity of radius 50~tm and uncoated steel surfaces loaded to an intensity of 3.5:5 kN/m. The dotted curve shows the effect on pressure of depositing at the interface a layer of a softer solid, in this case equivalent to molybdenum disulphide [42] with modulus 34 GPa, with a thickness h of ca. 1.8 ~m (and thus a value of h/R = 0.036). The effect of the compliant surface coating is to reduce to peak pressure (by a margin of about 37%) while bringing about a corresponding increase in the width of the contact zone, in this case by about 62%. These figures are very similar to those for corresponding conditions found by King and O'Sullivan [32].

50

Start

Rigid body Movement no

....

Calculate influence coefficients

Start next solution attempt

yes

Solve fo! pressure distribution ,,

No

g /no

load supported > applied load? yes

Calculate nodal moduli

Pressure sensitive? rio

Write pressure distribution to file Fig. 3 Flow chart showing calculation steps in the computer model. The influence of a pressure sensitive layer can be illustrated by considering a similar single cylindrical asperity in contact with a plane surface now coated with an antiwear film derived from ZDTP of a similar form to that shown in Fig. 1. As the load on the contact is increased the oil solution and alkylphosphate layer are squeezed out of the contact and, under conditions characteristic of the boundary lubrication regime, the system can be modelled as a polyphosphateoxide/sulphide bi-layer, this situation is illustrated in Fig. 5(a): the thickness

dimensions of its two constituents have been set at I00 nm and 80 nm respectively. At pressures above a gigapascal the mechanical properties of the phosphate layer are assumed to be a linear function of contact pressure i.e. to follow eqn (1) with the values given in Table I. The resulting pressure distribution is illustrated in Figure 5(b). Once again the compliant bi-layer attenuates the peak pressure (in this case by about 18%) at the cost of extending the width of the contact.

51 Table I" Summary of material properties used in the contact simulations

modulus E (GPa)

Poisson's ratio

steel substrate

210

0.3

steel indenter

210

0.3

molybdenum disulphide

34

0.13

0.036

anti-wear film: polyphosphate

15 to 40

0.3

0.002

anti-wear film: sulphide/oxide

90

0.3

0.0012

h/R

V

load

J load

hi

h2

2 2

1.8

1.8

1.6

1.6

1.4 A

1.4

g. z.~

,~ 1.2

I d~ 0.8 0.6 0.4 t 0.2[

/'

4'.;;

//

r

/

•

,,,

%.

%

,~- 0.8

%

0.6

i I

\

0.4 0.2 0 Distance from centre of contact (x/R)

0.05

Fig. 4 Cylindrical line contacts on an elastic half-space carrying (a) a single boundary layer (b) Dashed curve, influence of a molybdenum disulphide coating on the contact pressure distribution for single asperity contact h/R=O.036, load intensity 3.55 kN/m. Solid curve uncoated contact.

-~.;5

0 Distance from centre of contact (x/R)

0.05

Fig. 5 (a) Cylindrical line contacts on elastic half-spaces carrying a surface bi-layer. (b) Dashed curve, influence of a duplex ZDTP anti-wear film on the contact pressure distribution for single line asperity contact at a load intensity of 3.55 kN/m. Asperity radius 50 l.tm and film thicknesses 100 and 80 nm. Solid curve uncoated contact.

52

4.3

Multiple asperity contact

The surface profile shown in Fig. 6 was obtained from a steel specimen that had undergone a process of mild wear, characteristic of running-in, on the Amsler rig referred to in §3: it has a mean Ra value of 0.13 ~tm and (at a digitisation interval of 4.2 ~tm) a measured tip radius of 76.4~tm. There are 1016 points in the sample. When this is loaded against a plane counterface under unlubricated conditions, i.e. steel on steel, peak pressures will be generated at the points of contact corresponding to the tips of the asperities while there will be zero pressures in the valleys. This is illustrated in the plots of Fig. 7 (a) to (d) which correspond to overall load intensities of 62, 100, 332 and 660 kPa respectively; these cover the range typical of those encountered between cams and followers [5].

0"511t

~.-O.51 I 0

500 1000Distance 1500 2000 3000 3500 4000 through2500 profile(I.tm)

Fig. 6 Surface profile of a 'run-in' steel surface generated on the Shell Amsler rig: Ra = 0.13 l.tm. The asterisks indicate pressure maxima; for clarity, the minima at zero are not shown. As a result of the small n u m b e r of actual contact points, even at modest overall load intensities, contact stresses are high, more than 1.5 GPa in (a) rising to greater than 2.5 GPa in (d). The cushioning effect of the compliant lubricant layer is evident from a comparison of these points with those of Figs. 7(e) to (h) which are for the same

profile and the same load conditions but with a ZDTP-sulphide/oxide bi-layer on the surface which has the dimensions and properties used in the single asperity case. Although the thickness of the ZDTP derived layer (--180 nm) may be small compared to the radius of the asperity tip, it is comparable with the standard deviation of the surface profile since this has an Ra value of 130 nm. It is clear that, at a given load, the presence of the softer surface layer leads to a m u c h greater number of points of contact but correspondingly much attenuated levels of contact pressures. Even at a peak load of 660 kPa the m a x i m u m asperity pressure is only about 800 MPa. 5.

DISCUSSION

ZDTP was originally formulated as an anti-oxidant additive but it soon became apparent that chemicals of this sort also significantly reduced the friction between sliding steel surfaces and enhanced their capacity to withstand repeated contacts without the onset of scuffing. Their success as effective anti-wear additives is dependent on the formation of effective tribo-chemical films at locations of particularly arduous contact. The principal requirement of these films is to be sufficiently robust to survive in situations of repeated sliding and yet to offer a comparatively low resistance to shear. Examination of such films formed under conditions mimicking those of real operation, indicate that certain of the zinc dialkyl dithiophosphates are capable of producing relatively large patches of solid material within the overall contact area, somewhat elongated in the direction of sliding, and that these are capable of sustaining pressures of more than a gigapascal [44]. Evidence that it is this ability that is associated with their success as anti-wear additives can be inferred from the fact that a chemically similar diaryl dithiophosphates additives which, under the same loading conditions, fail to produce such burnished planar areas and are very much less successful in postponing surface failure [44,45]. Furthermore, it appears from

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(h) (d) Fig. 7 Influence of surface layers on distribution of peak asperity pressures for the geometry of Fig. 6" (a) to (d) dry contact and (e) to (h) with duplex ZDTP compliant anti-wear films. Load intensities (a)and (e) 62 kPa; (b) and (f) 100 kPa; (c) and (g) 332 kPa; (d) and (h) 660 kPa. Note the difference in scales between (a) to (d) and (e) to (h).

54

the work at Lyon, that the material within these patches exhibits an effective elastic modulus which increases with the application of greater local pressures so further enhancing their mechanical integrity and ability to sustain the imposed sliding velocity. Notwithstanding this increase, the achieved values of the film elastic modulus are very much less than those either of the underlying steel substrate, or indeed of the mixed sulphide/oxide layer with which the metal is inevitably covered. Provided the thickness of this softer layer is comparable with asperity heights it can act as a cushion, reducing the magnitudes of the loads carried by the most heavily loaded asperities albeit at the cost of increasing the number of individual points of contact. If this results in a reduction in the number of asperities at which the elastic or shakedown limit of the substrate material is exceeded it will be reflected in a significant increase in the overall life of the contact.

6.

CONCLUSIONS

• The introduction of a boundary layer with a reduced elastic modulus at the interface of a single Hertzian contact reduces the peak pressure at the cost of a corresponding increase in the breadth of the contact zone. • ZDTP additives in mineral oils form complex layered surface films of comparatively low strength on ferrous surfaces. The mechanical properties of these surface films can be influenced by the magnitude of the locally generated contact pressures. • If two rough surfaces, each carrying such boundary layers are brought into contact then, provided that the magnitudes of the film thicknesses are comparable with those of the surface topographies, the number of individual points of contact can be greatly increased with a corresponding dramatic reduction in the value of the peak

asperity pressures. Such reductions in asperity pressure would be expected to lead to extensions in surface, and thus component, lives. • Boundary layers derived from ZDTP films can be sufficiently compliant to provide the benefits of asperity pressure attenuation but can also possess an enhanced degree of robustness because of the beneficial effect of local pressures on their mechanical properties. ACKNOWLEDGEMENTS We are grateful to Dr R. C. Coy and Dr G. W. Roper at Shell Research Ltd., Thornton Research Centre, Chester, and to Professor J. M. Georges, Dr A. Tonck and Dr S. Bec at Ecole Centrale de Lyon for numerical data on the ZDTP films. We also should like to thank Professor T. Bell and Dr K. Mao of the University of Birmingham for advice and assistance on the use of the contact software and Shell Research and EPSRC for financial support to one of us (KAB).

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55 6 Gunsel, S. and Spikes, H . A . In-situ measurement of ZDDP films in concentrated contacts. Trib. Trans. 36(2) (1993) 276-282 7 Tonck, A., Martin, J. M., Kapsa, P and Georges, J-M. Boundary lubrication with anti-wear additives: study of interface formation by electrical contact resistance. Tribol. Inter. 12 (1979) 209-213 8 Cann, P., Spikes, H. A. and Cameron, A. Thick film formation by ZDDP's. Trans ASLE 26(1) (1983) 48-52

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