Some features of deformation of the surface of a solid body
Abstract Generated abstract
This paper examines deformation in the surface layers of contacting solid bodies, focusing on rough surfaces whose discrete microcontacts undergo primary plastic and secondary elastic deformation under compression. Using high magnification deformation measurements on steel and tin coated specimens, the study evaluates how nominal contact area and the thickness of the deformable base beneath microroughnesses affect approach and surface deformation. The experiments show that deformation increases sharply as nominal contact area decreases, that base thickness can significantly influence primary deformation, and that secondary elastic deformation may constitute a large fraction of primary deformation. These observations are used to argue that computational models of rough surfaces should treat asperities as axisymmetric features located on a deformable base, and that the nearly constant ratio of secondary to primary deformation at low nominal pressures requires further theoretical explanation.
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SOME FEATURES OF DEFORMATION OF THE SURFACE OF A SOLID BODY
B. P. MITROFANOV
(Presented by the scientific seminar of the Department of Strength of Materials)
Let us consider certain features of deformation of the material of the surface layers of two contacting solid bodies, which we discovered in an experimental study of contact.
Below are the results of experiments carried out on an instrument with a deformation magnification of 25,000 times; the design of the instrument and the specimens are described in [1].
The contact of two contacting solid bodies usually has a discrete character, determined by the roughness of their surfaces. Under mutual compression, deformation of individual micro-irregularities occurs, as a result of which the bodies come closer together. The primary deformation of micro-irregularities usually proceeds plastically, while the secondary deformation, under the same loads, proceeds elastically.
The locus of all possible actual contact areas is commonly called [2] the nominal area. The deformation capacity of a contact depends on the magnitude of this area. Figure 1 shows a graph of the change in secondary deformation of the rough surface of a steel-3 specimen as a function of the magnitude of the nominal area. The roughness \((H_{\text{av}} = 1.0\ \mu)\) and the pressure on the specimen \((10\ \text{kg})\) were kept constant. The micro-irregularities of the specimen were compressed by the carefully polished plane of a special deformer made of hardened ShKh-15 steel.
The graph presented shows that, as the nominal contact area decreases, the deformation of the surface increases. Beginning in the region of a certain point \(A\), this increase becomes especially sharp.
In further investigations we used a nominal contact area equal to \(125\ \text{mm}^2\).
The complex geometric form of a rough surface is usually replaced in calculations by a simpler one.
As a rule, the surface is represented as a set of individual asperities located on the base material—the foundation.
I. V. Kragel’skii [3] models a rough surface in the form of rods of various lengths placed on a smooth, absolutely rigid foundation.
I. F. Archard represents a rough surface in the form of a multitude of spherical asperities; N. B. Demkin [4]—by spherical asperities—
of constant radius, specifying the distribution of asperities by height with a power function.
Analysis of the existing computational models of a rough surface leads, in particular, to the need to determine the influence of deformation of the base on the approach of the bodies.
This influence was evaluated in experiments carried out with special specimens. The specimen was a disk [1] of steel 3, onto the deformable part of which a layer of tin 0.5 mm thick was applied. Before each
Figure 1.
Vertical axis: deformation, in microns.
Horizontal axis: nominal area, in mm\(^2\).
test the thickness of the applied layer was reduced by grinding. The roughness of the tin surface remained constant (\(H_{\text{av}}=6\) microns). The maximum load in the experiments reached up to 40 kg.
The results of the experiment are presented in Fig. 2. They indicate a significant influence of the thickness of the layer of material serving as the base for the microroughnesses (beginning with a layer thickness of 0.4 mm) on the magnitude of the primary deformation. The value of the secondary deformation changed to a lesser degree.
Taking this circumstance into account requires refinement of the existing computational models of a rough surface. The latter must be represented in the form of axisymmetric asperities located on a deformable base.
One of the features of deformation of a rough surface is the fact that the magnitude of the secondary (elastic) deformation constitutes a significant part of the primary (plastic) deformation. Thus, in our experiments the secondary deformation of the rough surface of steel 3 amount-
was up to 50% of the primary; in the experiments of I. R. Konyakhin [1] for cast iron this same quantity was 70%. Similar results were obtained by P. E. Dyachenko [5] for steels 45 and 15.
The results of the experiments cited were obtained at nominal pressures up to \(0.35\ \mathrm{kg/mm^2}\) and with surface roughness of classes 1–7 of surface finish.
The ability of a rough surface to accumulate a significant amount of “elastic” energy can be explained by the volumetric stressed state of the surface material. If the spherical part of the stress tensor is significant in comparison with the deviatoric part, then, as is known,
Fig. 2.
one can obtain plastic and elastic deformation of the same order. Experimental confirmation of this can be found in work [6], in which the authors determined the penetration depths of hardened-steel balls into flat metal surfaces.
Our investigations on indentation of balls of diameter \(10\ \mathrm{mm}\), made of hardened steel, into flat surfaces of steels 20Kh, 45, and 3 showed that, as the load on the ball increases, the ratio of the elastic deformation of the material to the total deformation decreases. Obviously, this should also be expected when deforming a rough surface with high nominal pressures.
It is characteristic that, in the range of nominal pressures up to \(0.35\ \mathrm{kg/mm^2}\), for rough surfaces of a number of metals (steel, copper, cast iron, etc.), irrespective of roughness and pressure, a constancy is observed in the ratio of secondary deformation to primary deformation.
An explanation of this phenomenon is a necessary step toward refining the theory of deformation of a rough surface.
References
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I. R. Konyakhin. Method of normal microdeformation for determining the plastic characteristic of a material. Izvestiya vuzov SSSR, Mashinostroenie, No. 10, 1959.
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I. V. Kragel’skii, N. B. Demkin. Determination of the actual contact area. Friction and Wear in Machines, collection XIV, Academy of Sciences of the USSR, Institute of Machine Science, 1960.
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I. V. Kragel’skii. Static friction of two rough surfaces. Friction and Wear in Machines, collection IV, Academy of Sciences of the USSR, Institute of Machine Science, 1949.
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N. B. Demkin. Elastic contact of rough surfaces. Zh. Izvestiya vuzov SSSR, Mashinostroenie, No. 6, 1959.
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P. E. Dyachenko, N. N. Tolkacheva, K. N. Goryunov. Determination of the area of actual contact of surfaces. Study of wear of machine parts by means of radioactive isotopes. Academy of Sciences of the USSR, Institute of Machine Science, 1957.
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