On Some Phenomena in a Compressed-Sheared Discrete Contact

I. R. Konyakhin, B. P. Mitrofanov

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

In the authors’ works [1, 2, 3], experimental results are presented for the investigation of the preliminary displacement of a discrete contact of two solid bodies, and a phenomenological theory is proposed for elastic preliminary displacement.

In the present work, certain new experimental facts are set forth and analyzed.

The study of phenomena occurring in a discrete contact under simultaneous variation of the compressive and shearing forces is of practical interest, since such phenomena are often observed in real contacts.

The experimental facts considered below were obtained on discrete contacts of metallic specimens [1] under conditions of elastic preliminary displacement.

It was shown earlier [1, 2] that the process of loading and unloading a compressed contact by a shearing force \(P\) can be represented as a dependence of the magnitude of the preliminary displacement \(\Delta s\) on the shearing force. In Fig. 1, a, the branch \(OA\) corresponds to loading, and the branch \(AB\) to unloading.

Among the possible methods of unloading there is one in which no mutual displacement of the specimens occurs. This method, consisting in the simultaneous variation of the compressive and shearing forces, is represented in Fig. 1, a by the straight lines \(AC\), \(1—1\), \(2—2\), \(3—3\), \(4—4\).

Of interest is the dependence, recorded in this case, of the shearing force on the compressive force. In Fig. 1, b, graphs of such dependences are shown; moreover, curves 1, 2, 3, 4 were obtained after partial removal of the shearing force, and curve 5 after complete removal.

To explain this character of the curves, one may use the model of a single asperity [3] of a compressed-sheared contact. Indeed, the diagram of tangential stresses for a single asperity at the moment of deformation corresponding to point \(B\) in Fig. 1, a will be two-valued, Fig. 1, c. The sizes of the slip zones for an individual asperity will depend on the ratio of the shear and compression forces of the corresponding asperity. When the compressive force \(N\) is reduced under conditions of absence of mutual displacement of the contacting bodies (Fig. 1, c), a special restraining force \(P\) will be required, which compensates the disturbance of equilibrium of the horizontal forces of the contact.

Fig. 1.

Let us note that, at the instant of unloading of the contact corresponding to point \(B\) (Fig. 1,a), the indicated forces are self-balanced.

The nature of curves 1, 2, 3, 4, 5 is also clear.

At the beginning and at the end of the simultaneous decrease in the compressive and shear forces, zones leave contact for which the shear force is proportional to the compressive force [3]. This explains the equality, in absolute value, of the quantities \(\dfrac{dP}{dN}\) at the beginnings and ends of curves 1, 2, 3, 4, 5 (Fig. 1,b).

The change in \(\dfrac{dP}{dN}\) between the beginnings and ends of the curves is explained, in particular, by the influence of zone \(b\) of the contact (Fig. 1,c).

The maximum value of the force \(P_0\) on curve 5 is equal to the sum of the tangential forces having the same direction at the instant corresponding to point \(B\). If, after removal of the shearing force (point \(B\), Fig. 1,a), the simultaneous change of the compressive and shearing forces for an immobile contact is carried out in steps, so that after each step the resulting force \(P\) is removed, then the total shearing force, for a large number of steps, tends to twice the value \(P_0\). In Fig. 1,c the results of such tests are given for a hardened-steel–copper contact at different unloading steps \(n\).

Let us give one more example from the experiments performed.

After an elastic preliminary displacement of a discrete contact, the shearing force was decreased in steps, after each of which the compressive force was also decreased. The latter led to a mutual displacement of the specimens (for example, 1—2 in Fig. 1,d), which, at a certain value of the compressive force, changed sign. At this instant the decrease of the compressive force was stopped. Then the changes of the shearing and compressive forces were carried out analogously, which made it possible to obtain points 3, 4, 5, 6.

The indicated points correspond to the instants when the zones of reverse slip have been eliminated and all contacting asperities have completely slipped.

This is confirmed by the fact that the ratio of the shear force of the contact to the compressive force, at the instants corresponding to points 2, 3, 4, 5, 6 (Fig. 1,d), is equal to the coefficient of friction.

It is necessary to note that if the contact possesses significant adhesive properties, then the dependences considered above change. Thus, for example, in experiments with a zinc specimen, curve 5 (Fig. 1,b) was obtained as increasing over the entire range of decrease of the compressive load.

In conclusion, let us consider a phenomenon that was observed under the following conditions. At a constant compressive force, two preliminary displacements in opposite directions were produced in succession, with the shearing effort of the first displacement being greater than that of the second. After unloading from the shearing force, the compressive load was decreased and the mutual displacement of the specimens was recorded. In Fig. 2,b graphs are shown of the dependence of specimen displacements on the compressive force.

Line 1 corresponds to a single-valued change of the shearing force—\(OAB\) (Fig. 2,a), curve 7 to a two-valued change \(OABCD\). Successively performed two-valued shears with different forces correspond to curves 2, 3, 4, 5, 6. A characteristic feature of the displacements represented by the latter curves is their two-valuedness. Thus, for example, if after two successive shears \(OAB\) and \(BEK\) (Fig. 2,a) the compressive load is decreased, then we record

first there was displacement \(KL\) in one direction, and then \(LO\) in the opposite direction. Moreover, the direction of the first displacement was opposite to the direction of the last shear. The latter is explained by the fact that, when the compressive load was reduced, the slip zones that had arisen during unloading \(EK\) were first eliminated. The resulting disturbance of equilibrium led to a mutual displacement of the specimens \(KL\). A further reduction of the compressive load led to the elimination of the slip zones that had arisen during unloading \(EK\), and to a change in the direction of displacement.

Fig. 2.

The experimental facts presented in this work on the study of elastic preliminary displacement agree with the previously proposed explanation of the nature of this phenomenon.

REFERENCES

1. I. R. Konyakhin and B. P. Mitrofanov. Determination of losses due to mechanical hysteresis. Physics of Metals and Metallography. Nauka Publishing House, vol. 17, no. 6, 1964.

2. I. R. Konyakhin and B. P. Mitrofanov. Procese disipative in cazul deplasazii prealabile in limitele elasticitatii. Studii si cercetari de Mecanica Aplicata, No. 1, vol. 15, 1964.

3. B. P. Mitrofanov. The nature of elastic preliminary displacement. Izvestia of Higher Educational Institutions, Mechanical Engineering, No. 5, 1965.