THE INFLUENCE OF THE MECHANICAL PROPERTIES OF MATERIALS ON THE DEFORMED STATE OF CYLINDRICAL SPECIMENS UNDER RADIAL COMPRESSION

Yu. S. Bogomolov

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

Studies [1, 2, 3] make it possible to establish the character of the development and distribution of strains, for different degrees of compression of cylindrical specimens, along the radius. However, the experiments were carried out on lead and aluminum specimens [1, 2], or on models made of optically active materials [3]. Meanwhile, of practical interest is the study of the deformed state under radial compression of steel blanks, which are quite often subjected to transverse forging and rolling, as well as of specimens made of brass, bronze, duralumin, etc.

The aim of the present work is an attempt to evaluate the influence of the mechanical properties of materials on the deformed state under radial compression of cylindrical specimens between the flat plates of a press.

The study of the deformed state was performed by the method of coordinate grids rolled on. The technology of applying the grid with the aid of typographic ink was carried out according to the method of Ya. B. Fridman, T. K. Zilova, and N. I. Demina [4]. The grid consists of a system of tangent circles with a diameter of one millimeter. The choice of such a grid is due to a number of its advantages in comparison with other types of grids: a) the directions of greatest elongations (the principal axes of the ellipse) are easily determined; b) simplicity of processing the measurement results.

The calculation formulas for determining the logarithmic principal strains are:

\[ e_1 = \ln \frac{a}{d}, \]

\[ e_2 = \ln \frac{b}{d}, \]

where \(d\) is the diameter of the initial circle of the measuring grid;
\(a, b\) are the axes of the ellipses (deformed circles) of the measuring grid.

The third component of strain may be determined from the condition of constancy of volume:

\[ e_1 + e_2 + e_3 = 0. \]

Parallel experiments on compression of cylindrical specimens along the radius made of structural steel and steel Kh18N9T, bronze, brass LS-59, and du-

duralumin made it possible to compare the deformed state of these materials at different degrees of compression. The experiments were performed on specimens 40 mm in diameter and 20 mm long. Coordinate grids were rolled onto the end faces of the specimens. Before deformation of the specimens, the average diameter of the grid circles was refined by measuring, under an instrumental microscope, the diameters of 10 circles along the horizontal of the specimen and 10 in the vertical direction.

The experiments show that the magnitude and character of the distribution of strain for Kh18N9T steel and structural steel, as well as for bronze and brass, are approximately the same at the corresponding degrees of upsetting. Figures 1 and 2 show photographs of the dividing grids on steel specimens at degrees of upsetting of 7.5 and 39%.

Initially (Fig. 1), the vertical rows of circles of the dividing grid remain almost straight, acquiring a very slight curvature in the vicinity of the contact areas. The horizontal rows of circles curve more noticeably, turning into curved lines with their convexity directed toward the center of the specimen; moreover, their greatest curvature occurs in the zones adjoining the contact areas. In these regions, individual circles of the dividing grid are also deformed, becoming ellipses. In the central part of the specimen the horizontal rows of circles are practically arranged along horizontal straight lines. The pattern of the dividing grid does not change on the lateral peripheral parts of the specimens.

With an increase in the degree of upsetting (Fig. 2), the curvature of the rows of circles becomes more noticeable. The pattern of the dividing grid is also distorted on the lateral peripheral parts of the specimens; the vertical rows of circles are curved, with the convexity of the curves directed toward the lateral peripheral parts of the specimen.

The horizontal rows of circles appear as curves not only in the contact zones, but also in the central part of the specimen. The exception is the rows of circles of the dividing grid located along the axes of symmetry; they remain practically straight lines.

Such is the qualitative picture of the change in the pattern of the dividing grid of steel specimens as a function of the degree of deformation. It looks the same for brass and bronze specimens. A substantial difference is found in the character of the distribution and in the magnitude of the principal strains of duralumin at degrees of upsetting \(\delta \leq 15\%\).

Figure 3 shows the dividing grid on the end face of a duralumin specimen at 21% upsetting. On it, a zone of increased deformation is clearly visible, consisting of two bands of strongly deformed circles passing as diagonals from one end of the upper contact area through the center to the other end of the lower contact area.

Figure 4 gives the diagrams of the principal strains along the axes of symmetry at 21% upsetting. The solid line shows the diagrams for Kh18N9T steel, the dashed line for lead, and the dash-dotted line for duralumin. A comparison of the diagrams of the principal strains of duralumin specimens with steel specimens of grade Kh18N9T shows that at the contact area the principal strains of these materials are approximately equal; then, in duralumin, they are smaller by 10–20%. This phenomenon is observed at a distance from 0.05 to 0.4 of the height of the compressed specimen from the point of contact. In the central part of the duralumin cylinder, the principal strains increase sharply, reaching a maximum at the center of the specimen, and exceed the strain of the steel specimen by 50–70%. Such intensive growth of the principal strains of duralumin specimens in the cent-

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

of the central part at reductions of more than 15% is explained by the appearance of cracks that arise as the reduction increases to 22–25%.

A special series of experiments on specimens made of the highly strain-hardening steel Kh18N9T and of lead, which practically does not harden under static loading, made it possible to determine the influence of material hardening on the deformed state. Steel and lead specimens, with coordinate grids rolled onto their end faces, were subjected to radial compression to various degrees of reduction. The magnitude of the load \(P\), the width of the contact area \(a\), the corresponding central angles \(\alpha\), the section height \(H\), and the conventional degree of deformation

\[ \delta = \frac{D-H}{D}\cdot 100\% \]

are given in the table.

Table

Comparison of the plots of the principal strains of the highly strain-hardening steel Kh18N9T with lead (Fig. 4) shows that the hardenability of materials has only a slight effect on the deformed state under radial compression of cylindrical specimens. The character of the distribution of the principal strains is practically the same, while the magnitude of the strain in the non-hardening material is lower by 10–15%.

Conclusions

1. The method of rolled coordinate grids made it possible to establish that the increase in plastic strains proceeds from the contact areas toward the center of the specimen. At small degrees of reduction the maximum of the principal strains is located between the contact area and the central part of the specimen; at large reductions it shifts to the center of the specimen.

2. The deformed state under radial compression in materials occupying an intermediate position between brittle and plastic materials (duralumin) differs very substantially from the deformed state of plastic materials.

3. The influence of material hardening on the magnitude and field of distribution of plastic strain under radial compression of cylinders is small. In highly strain-hardening materials, the principal strains along the axes of symmetry of the specimens are greater than in non-hardening materials by 10–15%.

References

1. G. V. Boguslavskii. Deformation of round bodies under radial compression between flat plates. Problems in the Theory and Practice of Metal Forming. Mashgiz, 1959.

2. I. A. Efimov. Deformation in transverse forging. Proceedings of LPI, No. 185. Metal Forming, 1956.

3. V. V. Shveikin, V. B. Skornyakov. Fundamentals of the modern theory of deformation and stresses in transverse forging and screw rolling. Collection of Scientific Works of the Ural Polytechnic Institute, issue 122, Sverdlovsk, 1961.

4. Ya. B. Fridman, T. K. Zilova, N. I. Demina. Study of plastic deformation and fracture by the method of rolled grids. Oborongiz, 1962.