Elastic Properties of the Surface of a Solid Manifested during Microdisplacement
Abstract Generated abstract
This paper investigates elastic recovery at the contact surface of solid bodies after small tangential displacements, focusing on how the reverse motion depends on shear force, normal pressure, surface condition, and material. Experiments on pairs including hardened steel, zinc, cast iron, bronze, and pobedit contacts show that recovery increases with the applied tensile force and decreases with normal load, with hysteresis appearing more strongly in softer or low melting metals. For harder refractory materials the recovery and repeated displacement are described by a linear relation, allowing definition of a contact recovery coefficient. The study proposes that, for sufficiently clean surfaces, the elastic return is proportional to the tangential force and inversely proportional to normal pressure, and it reports material constants of about 1.0 to 1.3 microns for the tested materials.
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Proceedings of the Tomsk Order of the Red Banner of Labor Polytechnic Institute named after S. M. Kirov
Vol. 96 — 1961
Elastic Properties of the Surface of a Solid Body Manifested under Microdisplacements
I. R. Konyakhin
(Presented by the scientific seminar of the Department of Strength of Materials)
As was shown earlier by A. V. Verkhovsky [1], after a preliminary microdisplacement of one body over another and the subsequent removal of the pulling force, the displaced body returns back by some amount.
As shown by the numerous experiments we have carried out over a number of recent years, the distance traveled in the reverse motion of the specimen depends both on the magnitude of the shearing force and on the normal pressure under which the displacement was produced. The greater the applied displacing force, the greater also is the magnitude of the return path traveled by the specimen in the subsequent process. The normal load has the opposite effect: the greater its magnitude, the smaller the distance traveled by the specimen in the process of the indicated elastic return.
Let us show, using one of the experiments as an example, the process of microdisplacement and the subsequent motion of the specimen in the reverse direction upon removal of the pulling force.
The experiment was carried out on specimens: hardened steel against hardened steel, with working surfaces possessing slight roughness.
Before the experiment, the indicated surfaces were washed with alcohol and rubbed against one another in order to destroy, to some extent, the film of adsorbed substances located between the surfaces of the specimens. As a result of this, the coefficient of friction was increased from 0.12 to 0.53.
The specimens, placed one upon the other, were loaded with a normal pressure of 45 kg.
After this, displacement was produced by a tensile force $P$, increasing it from 0 to 24 kg. The displacement amounted to 0.54 micron. The subsequent removal of the pulling force was accompanied by reverse motion of the specimen by 0.26 micron; that is, the return was incomplete, with a residual displacement equal to 0.28 micron.
The results of this experiment are presented in Fig. 1, where the curve $OA$ shows the course of the microdisplacement occurring with an increase in the tensile force. The curve approaches, at the top, the limit determined by the magnitude of the friction force. The curve $AB$ represents the elastic return occurring as a result of the removal of the shearing force. The horizon-
the horizontal segment on the abscissa axis \(CB\) is the magnitude of the elastic recovery \(S\); \(BO\) is the residual displacement.
The sometimes observed curvature of the recovery graph is explained by the elastic hysteresis of the adsorbed film, which can always remain on the working surface of the specimen. When testing a material of low hardness, hysteresis manifests itself more strongly, since the given material itself possesses the indicated hysteresis properties.
What has been said can be confirmed by an experiment carried out on a specimen made of zinc. The experiment with it was conducted in the same way as in the preceding case, but only the displacement was made a second time after the first shift, during which the surface material underwent work hardening.
Fig. 1. Graph of microdisplacement and elastic recovery: hardened steel on hardened steel.
The graph of the experiment described is shown in Fig. 2. In the graph the influence of hysteresis is shown rather strongly in the form of a wide loop. Hysteresis in fusible metals manifests itself to a greater degree than in refractory metals possessing greater hardness.
The hysteresis loop has an axis of symmetry; this shows that the repeated displacement and recovery take place according to one and the same law. The slope of the axis of the diagram may to some extent serve as an indicator of the elastic properties of the given contact.
When testing the surfaces of refractory metals, hysteresis was not observed; the elastic recovery upon removal of the pulling force, as well as the subsequent repeated displacement, occur along the same inclined straight line of the graph; therefore
\[ P = KS, \]
where \(K\) is the recovery coefficient of the given contact.
In our experiments the deforming body is the upper specimen, made of pobedit, with a smooth, one may assume non-rough working surface; therefore it should be assumed that the displacement and recovery occur only at the expense of the lower specimen being tested.
Fig. 2. Graph of the manifestation of hysteresis on a zinc surface under tangential displacement within the limits of elasticity.
The dependence of the magnitude of the elastic recovery on the normal pressure was determined by carrying out several experiments, at several values of the normal load pressing the specimens against each other: \(N = 5, 15, 25, 35\), and \(45\) kg.
In each of these cases the coefficient of recovery was determined as
\[ K=\frac{P}{S}. \]
From the values of the indicated coefficient obtained in this way, a graph was constructed (Fig. 3).
From the graph presented it follows that
Fig. 3. Linear dependence between the coefficient of recovery and normal pressure.
\[ \frac{N}{K-K_{0}}=C, \]
where \(C\) is a certain constant quantity.
If we put \(K_{0}=0\), then
\[ C=\frac{N}{K}=\frac{NS}{P}; \]
then, for \(N=P\),
\[ C=S. \]
Consequently, \(C\) is that value of the elastic return which will be obtained in the case where the acting normal pressure is equal to the tensile force.
For \(K=K_{0}\), \(S=C=\infty\), but then
\[ K=\frac{P}{S}=0. \]
In the present case this means the absence at the contact of resistance caused by the process of hardening of the material. Such conclusions speak only of the presence of contamination on the working surfaces of the specimens. In the absence of the latter, the coefficient of friction would be equal to 1, and \(K_{0}\) would be equal to 0. In this case
\[ C=\frac{N}{K}=\frac{NS}{P}, \]
whence
\[ S = C \frac{P}{N}, \]
that is, the magnitude of the elastic return after the preliminary micro-displacement is proportional to the tensile force and inversely proportional to the normal pressure.
Calculations of the value \(C\) from a set of experimental data gave the following results.
| Material | zinc | hardened steel | cast iron | bronze |
|---|---|---|---|---|
| Value \(C\) | 1.0 | 1.1 | 1.2 | 1.3 microns |
Let us present one of the graphs for determining the value \(C\), constructed from the results of experiments carried out on a bronze specimen (Fig. 4); we attribute the scatter of points on this graph to insufficient surface cleanliness. In the expression
\[ C = \frac{N}{K - K_0} \]
there is a quantity \(K_0\), which depends on contamination.
The graph was constructed without taking the value \(K_0\) into account. Therefore, the greater the contamination, the farther the experimental point lies from the straight line.
Contaminating substances are always present on the surfaces of a solid body. When the latter are cleaned, the contaminating film gradually decreases; in this case, the thinner the remaining film, the more difficult it becomes to remove it.
With a decrease in the film thickness, the coefficient of friction increases. As experiments show, such an increase is the more difficult, the greater the value of the coefficient of friction.
Fig. 4. Dependence of the elastic return on the coefficient of static friction.
By lapping the surfaces against each other, it is rarely possible to raise it to a value of 0.8. However, in order to determine the material characteristic \(C\), it is not necessary to attain large values of the coefficient of static friction. This conclusion follows from the experiment presented in Fig. 4.
LITERATURE
- A. V. Verkhovsky, The phenomenon of preliminary displacements when unsmeared surfaces are set in motion from rest. Journal of Applied Physics, Vol. III, issue 3—4, 1926.