Frictional shear strength

However, some theoretical treatment considers only the special case of friction sliding of a single fiber along a mechanically bonded interface, particularly for some ceramic matrix composites, where the Coulomb friction law applies. See for example Zhou and Mai (1995) and Shetty (1988). Assuming a constant friction at the fiber-matrix interface and neglecting the Poisson effects, Shetty (1988) reported a simple force balance equation for the frictional shear strength, Tfr... 

In using Eq. (6.10) to predict / , of a given composite system it is important that the said failure mechanisms all exist. If any one mechanism is apparently absent the corresponding toughness term must be excluded from the / t equation. It is also worth emphasizing that / , varies linearly with reciprocal of the frictional shear strength of the interface, i.e. l/tf, with the lower limit of (1 — Ff)/fm when if approaches infinity. This relationship has been shown to apply to many carbon fiber polymer matrix composites (CFRPs) (Harris et al., 1971 Beaumont and Phillips,... 

Fig. 6.4. Relationship between composite strength, etc, and total fracture toughness, f i, or equivalently the inverse of frictional shear strength, Tf. After Marston et al. (1974).

A number of substances such as graphite, talc, and molybdenum disulfide have sheetlike crystal structures, and it might be supposed that the shear strength along such layers would be small and hence the coefficient of friction. It is true... 

The radioautographic work suggests another model illustrated in Fig. XII-11. The load is supported over area A, with metal contacts of shear strength s over a portion of the area ctA and film-film contacts of shear strength Sf over the rest of the area. In analogy to Eq. XII-9, one can write the total frictional force, F as... 

Friction during dry sliding primarily involves a force F required to displace interlocking asperities of the softer material with shear strength s. 

Wear. Ceramics generally exhibit excellent wear properties. Wear is deterrnined by a ceramic s friction and adhesion behavior, and occurs by two mechanisms adhesive wear and abrasive wear (43). Adhesive wear occurs when interfacial adhesion produces a localized Kj when the body on one side of the interface is moved relative to the other. If the strength of either of the materials is lower than the interfacial shear strength, fracture occurs. Lubricants (see Lubricants and lubrication) minimize adhesion between adj acent surfaces by providing an interlayer that shears easily. Abrasive wear occurs when one material is softer than the other. Particles originating in the harder material are introduced into the interface between the two materials and plow into and remove material from the softer material (52). Hard particles from extrinsic sources can also cause abrasive wear, and wear may occur in both of the materials depending on the hardness of the particle. 

Here, [L is the coefficient of internal friction, ( ) is the internal angle of friction, andc is the shear strength of the powder in the absence of any applied normal load. The yield locus of a powder may be determined from a shear cell, which typically consists of a cell composed of an upper and lower ring. The normal load is applied to the powder vertically while shear stresses are measured while the lower half of the cell is either translated or rotated [Carson Marinelli, loc. cit.]. Over-... 

Carpick, R.W., Ogletree, D.F. and Salmeron, M., Lateral stiffness A new nanomechanical measurement for the determination of shear strengths with friction force microscopy. Appl. Phys. Lc//., 70(12), 1548-1550(1997). 

One of the major themes of boundary lubrication is to transfer the shear stress at the interface of direct solid contact to somewhere inside the lubricating layer, to achieve low friction and high wear resistance. In this sense, materials with low shear strength, such as liquid films, soft metals, and lamella solids, can be employed as candidate lubricants. 

Soft metals such as In, Ag, Sn, Pb, and Au can lead to reasonably low friction coefficients, when used as solid lubricants, due to their low shear strength. The metals were generally applied as thin films prepared by the vacuum deposition process. Especially, in applications to the high temperature conditions where liquid lubricants fail due to the evaporation, the thin films of soft metals can provide effective protection to the surfaces in sliding. 

On concluding this chapter, it is worthwhile to address a few issues that associate in particular with the boundary friction, i.e., the friction originated from the shear of surface films. The emphasis is given to the discussion of the shear strength and two parallel models that describe the boundary friction in terms of different mechanisms. 

In both models, the magnitude of friction can be determined in terms of the shear strength of boundary films, i.e., the critical shear stress when slip occurs, regardless of how the films are formed, by adsorption, reaction, or solidification. The existence of a critical shear stress, independent of ap-... 

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. 

For Au film, because it is soft and has lower shear strength than silicon, it is normal that Au film has a higher micro friction coefficient factor than silicon, and can be easily worn under the current experimental condition. 

To show clearly how and to what extent the parameter, Zmax. varies with the properties of the interface and the composite constituents, a simple fiber pull-out model by Karbhari and Wilkins (1990) is chosen here. This model is developed based on the assumption of a constant friction shear stress, Tfr, in the context of the shear strength criterion for interface debonding. In this model, the partial debond stress may be written as... 

Fig. 6.12. Toughness maps depicting contours of predicted fracture toughness (solid lines in kJ/m ) for (a) glass-epoxy composites as a function of fiber strength, Uf, and frictional shear stress, tf and (b) Kevlar-cpoxy composites as a function of at and clastic modulus of fiber, Ef. The dashed line and arrows in (a) indicate a change in dominant failure mechanisms from post-debonding friction, Rif, to interfacial debonding, Sj, and the effect of moisture on the changes of Of and Tf, respectively. Bundle debond length...

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