Asperity junction model

Figure 12-24. Encounter (a), deformation (b), adhesion (c), and fracture (d) of a model asperity junction. After A. P. Green [24].

The modeling of lubricant antiwear action as a competition at the asperity junctions between metal-to-metal adhesion and additive reaction, as proposed by Dorinson [9] and by Dorinson and Broman [10], was discussed in Chapter 10, Section 10.7 and Chapter 11, Section 11.2.2. The rate of wear depends on the surface concentration of asperity adhesions, denoted here by [M ], the time-dependent relation for which is... 

In developing equation (10.43) we assumed that wear causes film thinning, but not film removal. Under more severe wear conditions it is likely that the passive film is entirely destroyed at the asperity contacts. In the following, we shall consider a model where complete depassivation occurs at asperity contacts. As the asperity junctions are broken, the exposed surface areas repassivate again. We assume that a charge (C/m ) per unit area is required to repassivate the metal and we call gp the repassivation charge. The anodic current is then given by... 

The model proposed by Bowden and Tabor has been regarded as the most successful one for presenting a simple and logical theory capable of explaining the Amontons friction law. However, suspicions concerning the two fundamental assumptions in the model were gradually aroused over past years. Friction has been attributed, in Bowden and Tabor s model, to the adhesion between asperities in contact and torn-off of the adhesive junctions when the shear stress exceeds a critical value. This implies that plastic flow and surface destruction may occur at the moment of slip, and that friction is dominated by the shear strength of the adhesive conjunctions, which is material dependent. 

Consider a 3-dimensional, corrugated solid placed on a smooth substrate as a simplified model for a mechanical contact, which is a subtle case (Section III. C.5). The macroscopic contact will then consist of individual junctions where asperities from the corrugated solid touch the substrate. A microscopic point of contact p then carries a normal load Ip, and a shear force fp will be exerted from the substrate to the asperity and vice versa. These random forces fp will try to deform both solids. For the sake of simplicity, let us only consider elastic deformations in the top solid. Asperities in intimate contact with the substrate will be subject to a competition between the (elastic) coupling to the top solid and the interaction with the substrate. If the elastic stress exceeds the local critical shear stress c,p of junction p, the contact will break and asperity p will find a new mechanical equilibrium position. In order for (5 to exceed Uep, the area A = tiL- over which the random forces accumulate must be sufficiently laige. The value of L where this condition is satisfied is called the elastic... 

In Green s model it is assumed that when the sliding has attained a steady-state condition the number and the size of the junctions remain constant on the average. All motion is tangential there is no normal movement of one surface relative to the other. As the surfaces move past each other, asperities engage to form new junctions as fast as old ones are ruptured, so that the load W is continuously supported and the tan-... 

The most general modern model used to describe frictional phenomena assumes that the friction between two unlubricated surfaces arises from two sources. The first and generally most important is that of adhesion between points of actual contact between the surfaces. We have seen on various occasions that real solid surfaces are almost never smooth. A very smooth surface will normally have asperities of between 5 and 10 nm so that the true area of contact between surfaces will be less that the apparent area (Fig. 18.1). At those areas of contact, the two surfaces will be bound by a certain adhesion force arising from the interaction between the materials at the molecular level—the same basic forces we have encountered before plus, in some cases, more physical interactions due to mixing, interpenetration, or locking. For the two surfaces to move tangentially, the points or areas of adhesion, welds, or junctions must be sheared or broken. If the real area of contact is A and the shear strength of the weld or bond is s, then the frictional force due to adhesion will be... 

Adhesive wear can be explained by a model first proposed by Archard [6]. The two surfaces in relative motion only touch at the asperities. When the normal force Fn is applied, the contact zones undergo plastic deformation and micro-welds, referred to as adhesive junctions, are formed. This is the same mechanism as that governing adhesive friction, but here we are interested not primarily in energy dissipation, but in the rate at which material is torn off from the adhesive junctions. If j is the number of adhesive junctions, the contact area is given by ... 

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