Adhesion theories of transfer and wear during sliding of metals

Adhesion theories of transfer and wear during sliding of metals

Wear, 136 (1990) 223 223 - 235 ADHESION ~EORIES SLIDING OF METALS OF TR~SFER AND WEAR DURING L. H. CHEN Department (Tai~an~ of material Engine...

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Wear, 136 (1990)

223

223 - 235

ADHESION ~EORIES SLIDING OF METALS

OF TR~SFER

AND WEAR DURING

L. H. CHEN Department (Tai~an~

of material

Enginee~ng,

National Cheng-Kung

University, Tainan 70101

D. A. RIGNEY Department of Materials Science and Engineering, 19th Avenue, Columbus, OH 43210 (U.S.A.) (Received May 18,1989;

The Ohio State University, 116 West

accepted August 3,1989)

A regular solution model based on newest-ne~hbor pair bonding is applied in this paper to predict the effect of adhesion on transfer and wear during the dry sliding of metals. A transfer event is treated as depending on interface separation and junction adhesion. The energies of a free surface and of a large-angle grain boundary are incorporated. The results indicate that transfer is favored over direct generation of wear debris particles. To predict relative transfer trends during early stages of sliding it is sufficient to concentrate on interface separation. After continued sliding, transfer material normally consists of contributions from both sliding components, and transfer trends will also be affected by junction adhesion. Based on an ideal solution model, transfer from the component with smaller surface energy is preferred. In addition, the transfer tendency of a single-phase binary alloy, and hence its wear rate, is suppressed if the alloying element has a larger surface energy. Although the adhesion models presented in this paper are rather simplified, reviews of published experimental data show that the above surface energy criteria can serve as a crude guide for predicting transfer tendencies for simple metal-metal and metal-binary alloy combinations.

1. Introduction Transfer of material between sliding components, which affects and wear dramatically, has been reported in many tribological [l - 15). Studies on selected metal systems indicate that initial events occur as discrete fragments during early stages of sliding 9 - 111. Mutual transfer is quite commonly observed [9 - 131, 0043-1648190/$3.50

0 Elsevier Sequoial~inted

friction systems transfer [l, 2, 5, although

in The Netherlands

224

exceptions have been reported [3,10,14,15]. During continued sliding, the initial transferred fragments are deformed, fractured and blended, leading to formation of mechanically mixed material on the sliding surfaces [9 - 11, 131. Typical sliding wear debris particles come from this modified material [3,9 - 131. The debris may be generated when local conditions are suitable, e.g. when a critical layer thickness is reached [ 16 - 181. There have been several efforts to correlate adhesion and transfer processes [l, 7,19 - 221. Bowden et al. proposed that a transferred fragment occurs only when the adhesion strength of an asperity junction is large enough to shear and fracture the soft metal [l]. Various authors have proposed that transfer is favorable when the interfacial energy of the asperity junction is less than the total surface energy of the two asperities [ 19 - 211. Also, Buckley [7] and Gerkema and Miedema [22] postulated that transfer is from the cohesively weaker material to the cohesively stronger material. Recently, Chen [23] has described adhesion models which include as special cases the approaches of Seah [24], Miedema and den Broeder 1251 and Gerkema and Miedema [22]. A brief review of these adhesion models is presented in the next section. This is followed by a discussion of the application of these ideas to understanding transfer and sliding wear in simple metal-metal and metal-single-phase binary alloy systems.

2. Adhesion

equations

The adhesion energy is defined here as the energy required per unit area to break an interface into two free surfaces. With this definition, the adhesion energy has the same meaning as the fracture energy described by Seah in his consideration of grain boundary decohesion [24 J, and it is equivalent to the device work described by Hirth and Rice in some limiting cases [ 261. Gerkema and Miedema [ 221 and Miedema and den Broeder [ 251 have defined adhesion energy in the opposite sense, i.e. the energy decrease per contact area when two free surfaces are replaced by an interface. By this definition, the sign of the adhesion energy is reversed. The following simplifying assumption is used: all interfaces prior to separation may be treated as large-angle grain boundaries [22,23,25, 27, 281. Then the adhesion energies of various simple metal and single-phase binary alloy systems can be expressed mathematically by applying the empirical approximation that grain boundary energy is one third of the surface energy [28 - 301. For a simple metal A, one obtains directly the adhesion energy 5 AEA,A,

= xYA,S

(1)

where YA,Sis the surface energy of metal A,. By using a regular solution model [31] with a correlation of grain boundary structure with the bulk structure as postulated by Seah [24],

225

one can derive the adhesion phase binary alloy [23] AE A,A,(XA2gb) = z7.4:

energy

+ ;(tX,db)(y,:

aEA,A,(XA2gb) for an Al-A2

-Y/J

-

& ~‘VX*,gb)

single-

(2)

where XAzgb is the equilibrium solute fraction on a grain boundary, AiPX( tx*y ) is the enthalpy of mixing of (1 - tXAzb) of A, with tXqzb of AZ per unit area. As discussed in ref. 23, t is a segregation factor which is between 0.5 and 1. The first extreme is for the case of monolayer (submonolayer) segregation with a large enrichment ratio if one assumes that each newly formed free surface possesses a solute fraction of XAzgb/2. The second extreme is for the case of at least two layers of grain boundary segregation and with the same solute enrichment after boundary separation. In deriving eqn. 2 it has been assumed that there is no solute redistribution, i.e. fast fracture and low temperature. Equation (2) reduces to eqn. (1) for pure metal systems. In a sliding process, if one assumes that the asperity junctions are like large-angle gram boundaries [22,32], then the energy involved in junction adhesion is the negative value of the adhesion energy. A general form of the adhesion energy for an asperity junction between two single-phase binary alloys Al-A2 and B,-B2 is given by eqn. (10) of ref. 23. Its limiting case, that of pure metals A, and B, in contact, is expressed by AE A,% =

;(Y*,’ + %$

5 z - - 24 S

aA,B,

(3)

where wA,B, is an interaction parameter. 2 and S are the coordination number and the cross-section area of an atom respectively, assuming that Ai and B, have the same crystal structure and lattice parameter. Another limiting case, that of Al-A2 in contact with Bi , is expressed by AE A,B,(XA;nt)

= aEA,B,+XA,int I (4)

where XA*i”t is the solute fraction at the asperity surface of the Al-A2 alloy before junction adhesion. It is assumed here that there is no interdiffusion across the interface after junction formation. 3. Simple metal/metal

sliding systems

3.1. Transfer during early stages of sliding To simplify the discussion, it will be assumed that no blending is involved in the transfer events which occur during early stages of sliding. In this case the initial transferred fragments are unmixed chemically. There is support for this assumption from experiments on sliding for short distances. In an Al/B, sliding combination, AEA,A, is the energy required for the is the energy decrease associated with fragmentation of Ai, and mA,a,

226

junction adhesion. Then the energy change in a transfer event of Ai to B,, If A&A1 + B,) is negative, the energy WA1 -+ Bi), is AG,A, -- A&+,. decrease in junction adhesion is greater than the energy required for fragmentation of A,, which implies that forward transfer of A, to Bi is favorable. If AE(A, + Bi) is positive and, for some reason, e.g. failure of a weak boundary, fragmentation of A, does occur, back transfer is preferable since the energy difference between back transfer and forward transfer of a loose A, piece, (-AJ~,,,~) - (-AEA,n,), is negative, i.e. --A&A, -+ Br). According to eqns. (I) and (3)

~WAI -+ Bd = ~=A,A, - @A,B, = Similarly,

with transfer

;(Y*:- YFg + $ &,B,

from B, to Ai 52

W&

-+ A,) = A&,B,-

~A,B,

= ;(YB;-YA,p)

+ -

-WA,B,

24 S

Equations (5) and (6) indicate that @A$, has the same effect on transfer of Ai to Bi and B, to Ai. A positive wA,B, retards transfer whereas a negative OA,a, promotes transfer. By subtracting eqn. (6) from eqn. (5), one obtains

AJWI + JV - WBI -+ A,) = mA,A, - &,B,

=%(m,'-YB,O

(7)

Equation (7) does not contain the ~teraction term since ~~,a, has the same effect on transfer in both directions. Therefore, with the absence of a junction adhesion term, eqn. (7) shows that the preferred transfer direction is from the cohesively weaker side to the cohesively stronger side if one uses as indications of the cohesive strengths. By taking a largeAE A,A, and &QB, angle grain boundary and the free surface as two reference states, one can obtain a simple rule of thumb from eqn. (7) that the preferred transfer direction is from the metal with the smaller surface energy to the metal with the larger surface energy.

3.2. Prolonged abiding A loose fragment is more likely to transfer (forward or back) than to form loose wear debris directly, because transfer is always associated with an energy decrease via junction adhesion, This statement is in agreement with the experimental observations cited in Section 1. In the following discussion, the assumption is made that all loose fragments transfer to and are incorporated in the mixed material which develops on the surface during continued sliding. Suppose that a steady state is reached with XAIMM and XBIMMas the volume fractions of Ai and B 1, respectively, in the mixed material. Then the energy change for a transfer event of A, to the mixed material, hE( A, --f MM),

227

can be expressed

by

AE(Ai + MM) = AEA IA1- XA,MMAEA1A1- XB,MMAEA,B, = XBIMM(& =

X,,MMAE(A,

A

-

UA

IB I)

f, B,)

Similarly, the energy change for a transfer AE(B1 + MM), is WBi

+ MM) =

XAIMM(&l,B,

= XA

(8)

-

event of Bi to the mixed material,

mA,B,)

(9)

1M”AE(B, + A,)

By subtracting eqn. (9) from eqn. (8) and using the relations (6) and (7), one obtains AE(A, + MM) - AE(B, + MM) = f (YAIS- Y$) + (XB,~~ 52 x - -aA,B, 24 s

given in eqns.

-XAIMM)

(10)

Since XAIMM and XBIMMare usually not equal, it is obvious from eqn. (10) that the interaction parameter wA,B, has different effects for the two transfer directions. A positive wA,~, enhances the transfer probability from the smaller surface energy component and vice versa. For example, if the transfer layers are rich in Ai (i.e. if transfer is preferably from the Ai side), . . a positive oA,B, causes the energy difference in eqn. (10) to be more negative relative to the ideal solution case, which gives rise to a further increase of the transfer tendency from Ai. However, if the surface energy difference term is fairly large compared with the chemical interaction term, one can simply use the relative surface energies of the sliding materials to predict the transfer tendencies. In this case, the one with the smaller surface energy has a larger transfer tendency compared with its sliding counterpart. Furthermore, since wear debris are normally generated from the mixed material, the component with the smaller surface energy has a larger wear rate, provided that the chemical interaction term can be neglected. 4. Metal/single-phase

binary alloy sliding systems

4.1. Transfer during early stages of sliding Next we consider an AI-AZ single-phase binary alloy in sliding contact with a pure Bi metal. By using the same approach as in Section 3, i.e. regarding a transfer event as consisting of subsurface fracture and junction adhesion, one obtains the following two equations to describe the energy changes involved in initial transfer of an Al-A2 fragment to a surface of Bi and of a Bi fragment to AI-AZ, respectively WAC-AZ

-+ B,) =

aEA,A,(XA,gb)

-

mA,B,(XAzint)

(11)

228 -+ A,-A,) = A-%,,, - AEA,a,(X,li”t) Therefore, the energy difference between expressed by the following equation

(12)

WB,

WA,-Az

.+ B,) - m(B,

the two transfer

events can be

-+ AI-AZ) = A-G,A,(XA,~~) - maIaI

(13)

Since junction adhesion has the same effect on both transfer directions, eqn. (13) does not contain the junction adhesion term. Accordingly, the preferred transfer direction is from the cohesively weaker side to the cohesively stronger side, as concluded in Section 3.1. It is assumed that the adhesion energies AEAIA, (XAlgb) and &!&a, may be used as indications of the cohesive strengths. Equations (1) and (2) can be applied to determine the effect of the A2 alloying element on the cohesive strength of Al. The larger the yAJS value, the higher the cohesive strength. The situation becomes more comphcated if one takes into account the chemical interaction between A, and A,. For example, if TA1’ is greater than yA,S and if the interaction gives a negative departure from ideality, then the equilibrium adsorption value XAlgb will be smaller than the ideal solution case and the strengthening effect of the surface energy difference term in eqn. (2) is reduced. However, this reduction is at least partly compensated by the positive -5/12AP’“(tXA,gb) term, since the enthalpy of mixing is negative. Furthermore, the parameter t in eqn. (2) is a function of grain boundary enrichment, which affects the magnitudes of both the surface energy difference term and the enthalpy of mixing term. 4.2. Prolonged sliding As in Section 3.2 we assume that all freshly transferred fragments blended into the mixed material during prolonged sliding. To simplify discussion, consider the case of mixed material consisting of Ai and to eqns. (8) and (i.e. XA,m + X, m -1). Equations which correspond in Section 3.2 can then be expressed as follows ~(AI-AZ WBI

-+ MM) = XB,~~WA,A,(XA,~~)

-+ MM) = XA,MMWa,a,

- &,s,(XA~~?)

- LLEA,B,(XA~~~~))

are the Br (9) (14) (15)

Imagine that junction adhesion occurs between a freshly fractured surface and the mixed material. According to the assumption made in Section 2, the fracture occurs at a large-angle grain boundary. It is therefore proper to assume that XAgint is tXAzgb, provided that no solute redistribution occurs during fracture and junction adhesion. By taking the difference between eqns. (14) and (15), and using the relations given in Section 2. one obtains AE(AI-Az

-+ MM) - AE(BI += MM) = ; (?AzS +;

YB,?

~XA~‘~(YA~~ - YA,?

(16)

229

In the derivation of eqn. (161, all the interaction terms are neglected. As mentioned in the last paragraph of Section 4.1 the effect of chemical interaction is rather complex. If the surface energy difference terms in eqn. (16) are fairly large, the ideal solution model is applicable. In comparison with eqn. (lo), which is for a simple metal system, eqn. (16) indicates that alloying of A, with an element of larger surface energy tends to suppress the transfer tendency from Al. This is the same result mentioned in Section 4.1. 5. Discussion The results in this paper are based on an adhesion point of view. Mechanical and geometric effects have been neglected. For example, a loose fragment from the larger surface energy component may, rather than backtransfer, indent the smaller surface energy component if the hardness difference is sufficient. Geometric effects have been reported by many investigators [6,8,10, 33,341. They have shown that, for a rider sliding on a flat surface as in a typical pin-ondisk system, transfer is preferentially from the flat surface to the rider. In a series of pin-on-disk tests in high vacuum, Pepper and Buckley [8] reported that transfer of iron and nickel pin materials to tantalum, molybdenum and niobium disks did not occur, whereas transfer would be expected from the cohesive strength criterion. Chen and Rigney concluded that transfer and wear can be reduced by selecting the cohesively weaker material as the pin and the cohesively stronger material as thedisk [lo]. Strictly, the adhesion models in this paper should apply only to brittle solids since plastic deformation work has not been considered. Fracture mechanics offers an alternative approach for treating subsurface fracture of tough materials [35,36]. Also, to regard an asperity junction as a largeangle gram boundary may not be correct. As indicated by Ferrante et al. from a quantum mechanics calculation [37 ], the junction adhesion energy is a function of separation between the two surfaces and a function of the surface orientations. Gerkema and Miedema f22] regarded the asperity junction as an interface which is between two extremes, an epitaxial interface and a large-angle grain boundary. The regular solution model applied in this paper does not consider differences in crystal structures and lattice parameters. Buckley [ 381 reported that transformation of cobalt from hexagonal to cubic structure increased sliding wear and led to complete welding in vacuum. Atomic size difference is another factor which affects the adhesion energies. Seah [24] estimated the ratio of the critical fracture stress of the segregated grain boundary o(A,-A*) to that of the pure metal boundary o(A,) as (17)

230

where aA, and aA ? are the lattice parameters of Al and A,, respectively. For the case of monolayer segregation, substituting eqns. (1) and (2) into eqn. (17) (with the enthalpy of mixing term neglected) yields 1 +

WI-Az) = WI)

+x,r”th,SIYA,S)-

11 (18)

{(aAZ/aAI) - 11

which indicates that A, increases the cohesive strength only when uAz is smaller than ~~~~~~‘/~~,‘. Equation (18) may not be highly accurate, but it does indicate that the smaller the segregant element the larger is the increase of the cohesive strength. Although the adhesion models in this paper are rather simplified, numerous experimental observations are consistent with the predicted preference for transfer over the direct generation of loose wear debris particles. Typical debris particles contain transfer material which is well mixed mechanically. In practice, lubrication can greatly reduce junction adhesion and transfer [ 39, 401, yet typical debris particles still consist of well-blended components which include transfer material [41, 421. The models described in this paper use the free surface and a high angle grain boundary as reference states. Despite these simpl~ications, the model is useful for qualitative predictions of transfer tendencies. Of course, real surfaces and interfaces will vary considerably in structure and energy. This probably accounts for the fact that mutual transfer is quite common. Two other predictions from these models can be checked by comparison with published experimental data. The first of these is that the component with the smaller surface energy has the larger tendency to transfer. The second is that the transfer tendency can be suppressed by alloying with an element having larger surface energy. Numerous materials combinations have been tested by Buckley [7, 32, 441 to determine transfer directions after normal contact. Special cleaning procedures and all tests were conducted under ultra-high vacuum. Although no sliding motion was involved in these experiments, the adhesion models in this paper should be applicable. Indeed, with only a few exceptions, the test results agree with predictions based on surface energy. For example, copper transfers to iron, nickel and tungsten; lead, silver and gold transfer to iron. Lead also transfers to copper, according to Upit and Manik c451. With sliding contacts in vacuum, Buckley has reported transfer of copper to iron, cobalt and nickel [7]. Gerkema and Miedema [22] tested the durability of various coatings on iron and iron-base substrates. The most durable film was copper, with gold, silver and lead next in order. Cerkema and Miedema [22] also found that the duration life of a lead coating increases greatly by alloying with a small amount of copper. For a lead coating, platinum and molybdenum have the strongest alloying effect

231 TABLE 1 Iron concentration

(at.%) in mixed material produced during pin-on-disk tests [46] Fe/Ni

Fe/MO

0.46 (0 - 1.78)

1.06 (0.47 - 2.12)

-80a

99.56 (99.48

Trace of Ni

No MO detected

Contact geometry

Fe/Cu

Fe/Ccl

Pin/disk

0.35 (0.10 - 0.81) ::I-99)

Disk/pin

5 wt.% Ni

- 99.60)

The values in parentheses are the ranges of measured values. aData were collected via energy dispersive spectroscopy (EDS) analysis, mostly on wear debris and pieces of mixed material peeled from the substrate. For the case of an Fe pin/MO disk system, no debris particles were found. For that system, eight out of ten peeled-off fragments were identified by EDS as iron while the remaining two were molybdenum.

on increasing duration life, while silver has the smallest. For silver coatings the data agree with predictions for solutes of platinum and molybdenum, but not for indium, aluminum, copper and palladium. For nickel sliding against a-phase Ni-BOat.%Mo under a controlled argon atmosphere, Merrick and Brooks [14] observed that nickel transfers to the alloy, with no evidence of transfer in the reverse direction. For nickel slid against Ni-33at.%Cr under a dry nitrogen atmosphere, Beaton and Brooks [15] reported that the transfer direction is from the alloy to nickel. Our own experiments involved pin-on-disk tests in vacuum (1.9 - 6.7) X lop3 Pa [lo, 461. Each pin (3.2 mm in diameter and 2 mm long) was aligned with its axis parallel to the radius of a vertical rotating disk and was placed with its center at a distance of 6 mm from the center of the disk. The contact load was 0.78N (80gf). The sliding combinations included Fe/Cu, Fe/Cu-15wt.%Ni, Fe/Ni and Fe/MO; tests with the materials interchanged were also run. Details of the materials and test conditions are given in refs. 10 and 46. During early stages of sliding the results indicated that the amount of iron transferred to molybdenum is greater than vice versa, and the amount of iron transferred to nickel is greater than to copper. After prolonged sliding (see Table 1) there is a tendency for the iron content in the mixed material to increase in the following order for both pin/disk and disk/pin configurations Fe/Cu < Fe/Cu-

15wt.%Ni < Fe/Ni < Fe/MO

Table 1 also shows that the mixed material consists mainly of material from the disk side. This geometric effect was discussed earlier in this section. 6. Conclusions The models described in this paper are based on a nearest-neighbor pair bonding approach with free surfaces and large-angle grain boundaries as reference states.

232

The results lead to the following conclusions. (1) During early stages of sliding, junction adhesion has the same effect on both transfer directions for the two sliding components. Therefore, the transfer tendency can be predicted simply by comparing the energies required for subsurface fracture, i.e. by comparing the cohesive strengths of the components. Further, the component with smaller surface energy has the larger transfer probability. If fracture occurs in the component having larger surface energy, then back transfer is favored. (2) During prolonged sliding, since the mixed material is usually composed unevenly of materials from the two sliding components, junction adhesion does not have an equal effect on the two transfer directions. Analysis of simple metal to metal systems indicates that a positive deviation of the chemical interaction parameter from ideality enhances transfer from the component with smaller surface energy. (3) Compared with direct formation of loose wear debris, a fragment of material prefers transfer since the latter process gives rise to a further decrease in free energy of the system. (4) Analysis based on an ideal solution model indicates that alloying elements of larger surface energies can raise the cohesive strength of a metal. The transfer tendency of the alloy is then suppressed. The effect of chemical interaction of the alloying element with others is complex because both positive and negative contributions may exist simultaneously.

Acknowledgments This work began at the Ohio State University with research sponsored by the Office of Naval Research (Contract N00014-82-C-0255). It has continued with support from the Chinese National Science Council (Contract Nos. NSC75-0201-E006-11, NSC75-0405-E006-14 and NSC77-0201-E00603R) and from the Office of Naval Research (Contract NOOOl4-89-J-1234).

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233 8 S. V. Pepper and 13. H. Buckley, Metallic transfer between metals in sliding contact examined by Auger emission spectroscopy, NASA, TN O-671 6,19’72. 9 D. A. Rigney, L. H. Chen, M. G. S. Naylor and A. R. Rosenfield, Wear processes in sliding systems, Wear, 100 (1984) 195 - 219. 10 L. H. Chen and D. A. Rigney, Transfer during unlubricated sliding wear of selected metal systems, Wear, 105 (1985) 47 - 61. 11 D. A. Rigney, L. H. Chen and M. Sawa, Transfer and its effects during unlubricated sliding. In H. D. Merchant and K. J. Bhansali (eds.), Met41 Transfer and Culling in Metallic Systems, TMS-AIME, (198’7) 87 - 102. 12 T. Sasada, S. Norose and Y. Shimura, Composition of Wear Particles Produced under Sliding Friction of Different Metal Combinations, Proc. 18th Japan Congr. on lateral Research, Society of Materials Science, Kyoto, 1975, pp. 77 - 81. 13 T. Sasada, S. Norose and H. Mishina, The behavior of adhered fragments interposed between sliding surfaces and the formation process of wear particles, J. Lub. Technol., 103 (1983) 195 - 202. 14 E. A. Merrick and C. R. Brooks, Interface wear reactions between nickel and nickel20 at.% molybdenum alloy in a simulated face seal, Wear, 31 (1975) 317 - 330. 15 M. S. Beaton and C. R. Brooks, Interface wear reactions between nickel and nickel-33 at.% chromium alloy in a simulated face seal, Wear, 36 (1976) 63 - 71. 16 J. Don and D. A. Rigney, Prediction of debris flake thickness, Wear, 105 (1985) 63 - 72. 17 T. F. J. Quinn and J. L. Sullivan, A review of oxidational wear. In Wear of Materials I, American Society of Mechanical Engineers, New York, 1977, pp. 110 - 115. 18 J. L. Sullivan, T. F. J. Quinn and D. M. Rowson, Developments in the Oxidational Theory of Mild Wear, Tribol. Int., August (1980) 153 - 158. 19 E. S. Machlin and W. R. Yankee, Friction of clean metals and oxides with special reference to titanium, J. Appl. Phys., 25 (1954) 576 - 581. 20 E. Rabinowicz, Influence of surface energy on friction and wear phenomena, J. Appl. Phys., 32 (1961) 1440 - 1444. 21 T. Sasada, S. Norose and H. Morohashi, Adhesive Wear in Metal/Polymer Rubbing, Proc. 19th Japan Congr. on Materials Research, Society of Materials Science, Kyoto, 1976, pp. 77 - 80. 22 J. Gerkema and A. R. Miedema, Adhesion between solid metals: observations of interfacial segregation, effects in metal film lubrication experiments, Surf. Sci., 124 (1983) 351- 371. 23 L. H. Chen, On interfacial adhesion, Ser. Metall., 19 (1985) 371 - 375. 24 M. P. Seah, Adhesion-induced interface decohesion, Acta Metall., 28 (1980) 955 962. 25 A. R. Miedema and F. J. A. den Broeder, On the interfacial energy in solid-liquid and solid-solid metal combinations, 2. ~etallhd., 70 (1978) 14 - 20. 26 J. P. Hirth and J. R. Rice, On the the~odynamics of adsorption at interfaces as it influences decohesion, Metull. Trans., September (1980) 1501 - 1511. 27 D. Tabor, Friction - the present state of our understanding, J. Lub. Technol., 103 (1981) 169 - 179. 28 A. R. Miedema and P. F. de Chatel, A semiempirical approach to the heat of formation problem. In L. H. Bennett (ed.), Theory of Alloy Phase Formation, Proc. Symp. 108th AIME Annual Meeting, New Orleans, LA, February 1979, pp, 344 - 372. 29 M. P. Seah and C. Lea, Surface segregation and its relation to grain boundary segregation, Philos. Mug., 31 (1975) 627 - 645. 30 L. E. Murr, Inferfucial Phenomena in Metals and Alloys, Addison Wesley, London, 1975, Tables 3.5 and 3.6. 31 R. A. Swalin, Thermodynamics of Solids, John Wiley and Sons, Inc., New York, 1972,2nd edn., Chapter 7. 32 D. H. Buckley, The metal-to-metal interface and its effect on adhesion and friction, J. Colloid Interface Sci., 58,l (1977) 36 - 53.

234 33 M. Antler, Tribological properties of gold for electric contacts, IEEE Trans. Parts, Hybrids, and Packag., PHP 9 (1) (1973) 4 - 14. 34 M. Cocks, Interaction of sliding metal surfaces, J. Appl. Phys., 33 (1962) 2152 2161. 35 A. R. Rosenfield, A shear instability model of sliding wear, Wear, 116 (1987) 319 328. 36 A. R. Rosenfield, Shear instabilities in sliding wear. In P. S. Godavarti, A. T. Santhanam and K. L. Murty (eds.), Tribological Mechanisms and Wear Problems in Materials, ASM International, 1987, 53 - 59. 37 J. Ferrante, J. R. Smith and J. H. Rose, Universal Binding Energy Relations in Metallic Adhesion. In J. M. Georges (ed.), Microscopic Aspects of Adhesion and Lubrication, Elsevier, 1982, pp. 19 - 30. 38 D. H. Buckley, Adhesion and wear of cobalt and cobalt-base alloys, Cobalt (Engl. Ed.), 38 March (1968) 20 - 28. 39 B. W. Sakmann, T. J. Burwell, Jr. and J. W. Irvine, Jr., Measurements of the adhesion component in friction by means of radioactive indicators, J. Appl. Phys., 15 (1944) 459 - 473. 40 E. Rabinowicz and D. Tabor, Metallic transfer between sliding metals: an autoradiographic study, Proc. R. Sot. London, Ser. A, 208 (1951) 455 - 475. 41 W. A. Glaeser, Wear properties of heavily loaded copper-base bearing alloys, J. Met., October (1983) 50 - 54. 42 P. Heilmann, J. Don, T. C. Sun, W. A. Glaeser and D. A. Righney, Sliding wear and transfer. In K. C. Ludema (ed.), Wear of Materials, 1983, American Society of Mechanical Engineers, 1983,414 - 425; Wear, 91 (1983) 171 - 190. 43 D. H. Buckley, Adhesion of metals to a clean iron surface studied with LEED and Auger emission spectroscopy, Wear, 20 (1972) 89 - 103. 44 D. H. Buckley, Surface effects in adhesion, friction, wear and lubrication, Elsevier Tribol. Ser., 5 (1981) Chapter 5. 45 G. P. Upit and J. J. Manik, Cohesion of juvenileous surfaces of plastic metals, Wear, I1 (1968) 333 - 340. 46 L. H. Chen, Transfer during sliding wear of selected metal systems, Ph.D. Thesis, Metall. Engr. Dept., The Ohio State University, March 1984 (available from University Microfilms, 300 N. Zeeb Road, Ann Arbor, MI 48106).

Appendix : Nomenclature aA,r

aA,

Al, B, AI-A, S

t

&,MM ’ x,Tj 1MM X ‘4,int XAzgb

z

parameters of AI and A2 species pure metals a single-phase binary alloy with A2 as the solute cross-section area of an atom a segregation factor to allow for cases of grain boundary segregation ranging from the case of monolayer decohesion with large enrichment (t = l/2) to the case with at least two layers of segregation (t = 1) volume fractions of A, and B1, respectively, in the mechanically mixed material fraction of AZ in an AI-A2/B1 interface equilibrium solute fraction on a large-angle grain boundary in an AI-AZ single-phase binary alloy coordination number

lattice

235

YAP,YAzS, YB,S Wj

0 m

AlA,,

AE

A,A,tXAzgb)

&BIB,

~‘4 I% ‘!=A,B,(XA,int)

AE(i+j) AE(i + MM) Lylmix

surface energies of A,, A, and B1 metals, respectively interaction parameter of nearest-neighbor atoms i and j based on a regular solution model critical fracture stress of a grain boundary adhesion energies of pure metals A, and B1, respectively adhesion energy of AI-A2 single-phase binary alloy, with grain boundary decohesion as reference adhesion energy of an interface between A, and B1 metals adhesion energy of an interface between AI-A2 alloy and B1 metal energy change involved in transfer of a fragment from the i component to the surface of the j component energy change involved in transfer of a fragment from the i component to the mixed material enthalpy of mixing per unit area