INFLUENCE OF CERTAIN FACTORS ON THE PLASTICITY OF METALS

L. K. Spiridonov, V. A. Ogorodnikov

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

The plasticity of metals depends on the type of stress state, the loading history, the geometry of the specimen cross section, the stress gradient, temperature, deformation rate, scale factor, etc.

The dependence of plasticity on the type of stress state has been considered in a number of works [1, 3].

In the present work, the influence on the plasticity of metals of the geometry of the specimen cross section, the loading history, and the stress gradient has been investigated.

To investigate the influence of the geometry of the specimen cross section on plasticity and stability, specimens with the same cross-sectional area were made in the form of a rectangle with different aspect ratios, an equilateral triangle, a circle, and a ring. To exclude the influence of differences in the initial mechanical properties, all specimens were made from one steel bar.

The specimens were loaded by an axial tensile force up to fracture. The strain intensity at fracture was calculated as

\[ e_{ip}=\ln \frac{F_0}{F_{\text{ш}}} \]

and at loss of stability as

\[ e_{iy}=\ln \frac{F_0}{F_p}, \]

where

\(F_0, F_{\text{ш}}, F_p\) are the cross-sectional areas of the specimen, respectively, before testing, at fracture, and in the zone of uniform deformation.

For specimens with a rectangular cross section, over the range of aspect ratios studied, the strain at loss of stability and at fracture practically does not depend on changes in this ratio (Fig. 1). The specimen with a triangular cross section has the same values of these strains (\(e_{iy}=0.22;\ e_{ip}=0.74\)). The greatest plasticity was observed in solid cylindrical specimens, \(e_{ip}=0.97\), and the smallest in the tubular specimen, \(e_{ip}=0.58\). Loss of stability of the tubular specimen occurred at approximately the same degree of strain as in specimens of other cross sections, \(e_{iy}=0.24\).

The influence of the loading history was studied on specimens made in the form of a cube from LS-59-1 brass and D-16 duralumin. The specimens were upset to a prescribed degree of deformation under conditions of a linear stress state, with lubrication of the end faces. Then the specimen was again given the shape of a cube by planing under light cutting conditions, and was upset to the same degree of deformation, but now in a direction perpendicular to the original one. The sequence of operations was continued until fracture. Figure 2 shows the dependence of the total strain on the degree of deformation in one step. The results obtained made it possible to draw the following conclusions: 1) the total degree of deformation depends on the amount of deformation per step, i.e., the more often the direction of load application is changed, the higher the plasticity of the material;

Fig. 1. Dependence of plasticity (1) and stability (2) on the side ratio in specimens of steel St. 3 with a rectangular cross section

Fig. 2. Dependence of plasticity on the amount of deformation per step: ●—D16; x—LS-59-1

2) the total deformation depends on the initial properties of the material.

The magnitude of plasticity is affected by the gradient of stresses and strains. In [2] it is noted that, when a tube is flared by a conical punch, the material of the tube at the upper end is subjected to linear tension; in this case, the degree of deformation at the moment of formation of a local thinning is greater than the deformation in testing this material in uniaxial tension. The authors explain this fact by the influence of the strain gradient. In [4] it is indicated that the ultimate strength of the surface layers in bending specimens of brittle materials is higher than in tensile testing of the same material. Apparently, this fact is also explained by the presence of a stress gradient.

In the present work, the influence of the gradient of stresses and strains was studied on specimens subjected to tension and pure bending. For this purpose, a low-ductility steel R18 was selected, which in tensile testing practically does not form a neck and which can be brought to fracture under pure bending.

To calculate the strains, impressions were made on the specimens with a diamond pyramid at a spacing of 2 mm. The distances between impressions were measured on a toolmaker’s microscope before and after deformation. Figure 3 shows the distribution of strains on both sides of the fracture.

Fig. 3. Distribution of strains along the length of the specimen on both sides of the fracture: ○ — tension, △ — pure bending

In tension, the strain is localized at the site of fracture; in pure bending, the strains are distributed uniformly along the length of the specimen.

The strain in bending proved to be smaller than the strain obtained in tension. This fact requires further investigation.

Conclusions

1. It has been established that, for specimens of St. 3 steel with a rectangular cross section, plasticity is practically independent of the aspect ratio.

2. Results have been obtained showing that the plasticity of a metal increases with increasing nonmonotonicity of the process.

3. The influence of the gradient of strains and stresses on the plasticity of metals has been investigated. It has been established that the strains in bending are smaller than in tension.

References

1. V. L. Kolmogorov. Stresses, Strains, Fracture. Metallurgizdat, Moscow, 1970.

2. E. A. Popov, A. A. Shevchenko. Forging and Stamping Production. Moscow, “Mashinostroenie,” 1970, No. 3.

3. G. D. Del’, L. K. Spiridonov. Influence of the type of stress state on the plasticity of metals. VI Scientific and Technical Conference. Section OMD, abstracts of reports, Tula, 1970.

4. L. S. Burshtein. Static and Dynamic Tests of Rocks. Leningrad, “Nedra,” 1970.