Elastic Preliminary Displacement in the Presence of an Intermediate Layer

B. P. Mitrofanov, V. I. Maksak

(Presented by the scientific seminar of the Department of Strength of Materials)

In the interaction of rough bodies, as is known, deformation of the surface layer is observed in the zone of discrete contact. Depending on the character of the acting forces, the displacements observed in this case are called approach or preliminary displacement [1, 2].

Usually the surfaces of contacting bodies are separated by thin adsorption layers of various nature and origin; they contain particles of the base material, traces of oil remaining after surface treatment, etc. In experimental studies of deformations of surface layers, various methods of cleaning the surfaces are used [1, 3].

On the other hand, the study of deformations of discrete contact in the presence of a thin intermediate layer is of theoretical interest and practical importance, since this layer substantially affects the development of many phenomena and technological processes.

A substance distributed as a thin layer on the surface of a solid body acquires properties different from those usually observed in the bulk. Thus, for example, a liquid in a thin layer on the surface of a solid body possesses elasticity of form, passing into another aggregate state—quasi-solid [3].

In order to clarify the influence of a thin intermediate layer on the character of deformation of discrete contact, a series of experiments was carried out with contacts of the following pairs of materials: hardened steel—hardened steel, copper—copper, hardened steel—lead.

The specimens and the device for measuring displacements are described in [4]. The following materials were used as intermediate layers: solidol, water, machine oil, dispersed chalk, rosin, and graphite. The contacting surfaces of the specimens were treated with abrasive paper. In the experiments, approach and elastic preliminary displacement were measured.

Analysis of the experimental results makes it possible to make the following statement:

1. Liquid intermediate layers have a very weak effect on the magnitude of the approach of the contacting bodies (Fig. 1).

2. The presence of an intermediate layer does not change the character of the dependence of shear force on displacement, but it strongly affects the magnitude of the limiting shear force, i.e., the coefficient of static friction (Fig. 2).

Fig. 1. Dependence between approach \(\delta\) and compressive force \(N\) for contact of hardened specimens of steel 45. 1 — without an intermediate layer; 2 — rosin layer; 3 — solidol layer; 4 — water layer; 5 — chalk layer; 6 — graphite layer; 7 — oil layer.

Fig. 2. Dependences between preliminary displacements \(\Delta\) and shearing forces \(P\) for contact of hardened specimens of steel 45. Compressive force 45 kg. The specimens were in contact over an annular area 2 mm wide and with a mean diameter of 20 mm. 1 — without an intermediate layer; 2 — rosin layer; 3 — solidol layer; 4 — water layer; 5 — copper layer; 6 — graphite layer; 7 — oil layer.

It is characteristic that, at small shear forces, the magnitude of the displacement does not depend on the presence of an intermediate layer.

The assertions listed here make it possible to represent the features of elastic preliminary displacement with intermediate layers in the following way.

The magnitude of the deformation of thin intermediate layers of liquid materials in a quasi-solid state is small in comparison with the deformation of the surface of the contacting bodies. However, the influence of these layers on the deformation of the surface is large and apparently manifests itself through the plasticizing action [5] on volumes of metal undergoing local plastic deformation [6]. In the experiments this was recorded as a decrease in the coefficient of friction. Then, for the analysis of elastic preliminary displacement in the presence of an intermediate layer, one may use the relations set forth in [6], taking into account the influence of the intermediate layer through a change in the coefficient of friction.

Let us analyze certain theoretical relations, using the shear formula for a unit asperity [6]

\[ \Delta=\frac{3(2-\mu)}{8Ga}\,fN\left\{1-\left[1-\frac{P}{fN}\right]^{2/3}\right\}, \]

where \(\Delta\) is the relative tangential displacement of a unit asperity of the contacting bodies,
\(\mu\) is Poisson’s ratio,
\(G\) is the shear modulus,
\(a\) is the radius of the pressure circle,
\(f\) is the coefficient of friction,
\(N\) is the compressive force,
\(P\) is the shearing force.

Hence the compliance \(d\Delta/dP\) will be

\[ \frac{d\Delta}{dP}=\frac{2-\mu}{4Ga}\left[1-\frac{P}{fN}\right]^{-1/3}. \]

Consequently, the initial compliance, equal to

\[ S_0=\frac{2-\mu}{4Ga}, \]

does not depend on the coefficient of friction, i.e., on the presence of an intermediate layer, which is confirmed by the experiments (Fig. 2).

The magnitude of the limiting preliminary displacement will be proportional to the coefficient of friction:

\[ \Delta_{\mathrm{pr}}=\frac{3(2-\mu)}{8Ga}\,fN. \]

This fact also agrees with the experiments.

In conclusion, we note that the effects of intermediate layers made of materials such as graphite, chalk, rosin, etc., on preliminary displacement and approach may be different from those considered above. This is explained by the fact that in this case the thickness of the layers may be greater. The magnitude of the deformation of such layers will also be greater, comparable with the deformation of the metal surface or even exceeding it.

REFERENCES

1. N. B. Demkin. The Actual Contact Area of Solid Surfaces. Publishing House of the Academy of Sciences of the USSR, 1962.

2. I. V. Kragel’skii, V. S. Shchedrov. The Development of the Science of Friction. Publishing House of the Academy of Sciences of the USSR, 1956.

3. A. S. Akhmatov. Molecular Physics of Boundary Friction. Fizmatgiz, 1963.

4. I. R. Khaikin. Theory of Preliminary Displacements as Applied to Problems of Contacting Machine Parts. Tomsk University Press, 1965.

5. V. I. Likhtman, P. A. Rebinder, G. V. Karpenko. The Influence of a Surface-Active Medium on the Processes of Deformation of Metals. Publishing House of the Academy of Sciences of the USSR, 1954.

6. B. P. Mitrofanov. Elastic preliminary displacement. Izv. vuzov; Mashinostroenie, No. 5, 1965.