ON THE CONTACT AREA DURING SHEAR

I. R. Konyakhin, B. P. Mitrofanov, M. S. Gorb’enko, V. I. Kolosov

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

The interaction of contacting bodies during shear consists in the successive course of two processes: first, compression of the contact by a normal load, and second, shear by a tangential load.

At present, the magnitude of the actual contact area formed when contacting bodies are pressed together is determined with sufficiently good approximation [1]. On the question of the magnitude of the area of actual contact between bodies subjected to shear, various opinions have been expressed.

The application of a tangential load changes the stressed state of the deformed asperities of the surface layer. An approximate calculation by M. M. Saverin [2] showed that the application of a tangential load to the contact of a disk with a plate causes the point of maximum shear stress to move toward the contact surface. It is known that, in the absence of a tangential load, this point is located at some distance from the contact surface [3].

Experiments show that plastic deformation of a rough surface begins at stresses over the contact area of the order of \(3\sigma_t\). If the point with maximum shear stress emerges onto the contact surface, then, consequently, plastic deformation of the surface will begin at stresses smaller than \(3\sigma_t\).

S. B. Aibinder [4], on the basis of the above considerations, assumes that plastic deformation of the surface, when the point with maximum shear stress emerges onto the contact surface, will occur at the stress \(\sigma_t\); consequently, the contact area under the application of tangential loads may increase by three or more times. According to work [5], however, the magnitude of the contact area at a friction coefficient \(\mu = 0.5\) should increase only by a factor of 1.35. N. B. Demkin [6] did not find any change in the area of actual contact under conditions of a low coefficient of friction.

In order to obtain additional experimental results on the question under consideration, the authors of the present article carried out two series of experiments.

In the first series of experiments, steel and copper models of individual asperities in the form of cones with apex angles of \(120^\circ\) and \(150^\circ\) were tested. In a special device (Fig. 1), two asperities were simultaneously compressed, and then the contact formed during compression was sheared. The increase in the contact area in this case reached 35% (Fig. 1).

![diagram and graph: vertical load \(P\); plot of \(F_0/F,\%\) versus \(P,\mathrm{kgf}\), with curves labeled “steel 3” and “copper”]

Fig. 1.

![graph: \(N,\mathrm{kgf}\) versus \(\delta,\mu\mathrm{m}\), with curves labeled 1, 2, 3]

Fig. 2. Dependence of approach on load. The dashed line denotes contact with a copper specimen of surface cleanliness class 5; the solid line denotes contact with the planed surface of a specimen made of steel 5.

1 — approach under the first loading,
2 — approach under repeated loadings,
3 — approach after 100 cyclic shears.

The ratio of the tangential force to the normal force—the coefficient of friction—had a value of 0.4.

The second series of experiments was carried out on an apparatus for investigating microdeformation [7]. In this case, shear deformation of the polished surface of the specimen was produced by alternating displacement of the upper specimen, made of hard alloy, over the tested specimen. The contact plane of the upper specimen was polished. The amplitude of the displacements reached 0.03 mm.

The experiments showed that, with an increase in the number of shears (Fig. 2), the stiffness of the contact increases. This indicates that, during shear, the specimens approach one another and, consequently, that the area of actual contact increases. For the copper specimen, after a certain increase in the contact stiffness, a decrease was then observed. It should be noted that, in this case, copper was smeared onto the upper specimen.

Analysis of the results obtained shows that the area of actual contact during shear increases, in the cases considered, by approximately a factor of 1.5.

Similar results were obtained when comparing the bearing surfaces for rough planes, some of which had been compressed by a smooth hard punch, while others had been treated by burnishing under the same contour pressures [8].

REFERENCES

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

2. M. M. Saverin. Contact Strength of Materials. Mashgiz, 1946.

3. N. M. Belyaev. Calculation of the greatest design stresses in the compression of contacting bodies. Collection 102, 1929.

4. S. B. Aibinder. On the area of contact between rubbing bodies.

5. Farlane J. Mc. and Tabor D. Adhesion of solids and the effect of surface film. Relation between friction and adhesion. Proceedings of the Royal Society, 1950, ser. A, v. 202.

6. N. B. Demkin. The actual area of contact under static loading and at the onset of motion. Izvestiya VUZov, Mashinostroenie, No. 4, 1962.

7. I. R. Konyakhin. A method of normal microdeformation for determining the plastic characteristic of a material. Izvestiya VUZov, Mashinostroenie, No. 10, 1959.

8. Yu. G. Proskuryakov, V. M. Menshakov. Microgeometry of the surface in certain methods of strengthening-calibrating treatment of metals. Izvestiya VUZov, Mashinostroenie, No. 7, 1961.