DETERMINATION OF CONTACT STRESSES DURING PLANE UPSETTING FROM HARDNESS DISTRIBUTION

E. S. Vaksman, G. D. Del

(Recommended for publication by the scientific conference of the Mechanical Faculty)

For an analytical study of plastic deformation in metal forming by pressure, and for calculating the working tool for strength, it is necessary to know the stresses arising in the contact between the metal being worked and the tool. At present, the determination of specific frictional forces and specific pressures is carried out by the tensometry method [1]. Below a method is set forth for determining contact stresses from the hardness distribution in the metal being worked. By this method the distribution of normal stresses in the contact was studied in certain cases of plane upsetting.

In [2] a method is presented for determining stresses in the plastic region from the hardness distribution. For this purpose, by testing in axial compression with lubrication and subsequently measuring the hardness of specimens compressed to different degrees of deformation, a calibration graph is constructed that relates the intensity of tangential stresses \(K\) to hardness. Then, measuring the hardness at various points of the deformed body, the function \(K(x, y)\) is determined with the aid of the calibration graph.

The stresses are calculated by numerical integration of the differential equilibrium equations, taking into account the established distribution of \(K\). In some cases this method also makes it possible to determine the contact stresses. The contact conditions were studied for radial compression of a cylinder and upsetting of strips of a number of materials with different dimensional ratios. The length of the specimens was three times greater than their width; as a result, the deformation in the middle part along the length was considered plane. The hardness of the deformed specimens was measured in the plane of deformation; the tested surface was carefully polished. Measurements were made with a diamond pyramid under a load of 30 kg (when testing aluminum specimens, 10 kg). For each specimen, 100–150 measurements were made. The results of the hardness measurements were averaged by drawing isoscleres—lines of equal hardness.

For constructing calibration graphs, 8–10 specimens of the materials studied were made, with a diameter of 15 mm and a height of 23 mm. The hardness of the compressed specimens was measured at meridional-section points sufficiently distant from the ends.

The method of interpretation is discussed in detail in [2]. In Fig. 1 are shown epures of contact stresses for different upsettings of prisms made of steel Kh18N9T with an initial height \(h = 24\) mm and a cross-sectional width \(в = 16\) mm. A feature of the epures is the increase in the nonuniformity of the stress distribution with increasing upsetting. The intensi-

… increase in contact stresses near the periphery of the specimen was accompanied by only a slight increase in the stresses on the axis of symmetry.

Fig. 1. Influence of the degree of upsetting on the distribution of normal contact stresses

The epures obtained are characteristic only of narrow strips and are in qualitative agreement with the results of investigations by the authors [3], [4].

Fig. 2-a. Influence of the strain-hardening capacity of the material on the distribution of normal contact stresses

An increase in nonuniformity is also caused by an increase in the strain-hardening capacity of the material (Fig. 2a). In highly strain-hardening steels X18H9T and ShKh15 the nonuniformity is greater than in weakly strain-hardening St. 3.

In the process of plastic deformation, the strain-hardening capacity of the metal decreases. The fact that, despite this, the nonuniformity of the distribution of \(\sigma_y\) increases with increasing upsetting is apparently explained by the predominant influence of the friction that increases during the deformation process. The latter is confirmed by the results shown in Fig. 2-b. Curve 1 was obtained with lubrication of the ends of the upset specimen by a mixture of colloidal graphite and glycerin, with simultaneous use of lead-foil gaskets 0.05 mm thick. Curve 2 (as well as all the other diagrams) was obtained by compressing the specimen between ground plates without lubrication.

Fig. 2-b. Influence of contact conditions on the distribution of normal contact stresses

The results shown in Fig. 4 indicate that the magnitude of the contact stresses is higher for stronger materials; however, the character of the diagram of \(\sigma_y\) is practically the same for materials of different strength.

Figure 3 gives the distribution of contact stresses during radial upsetting by 30% of a cylinder made of Kh18N9T steel and St. 3 steel, with diameters of 30 mm and lengths of 60 and 90 mm, respectively. The calculation was performed on the assumption that there is no friction at the boundary of the contact area. In this case as well, in the middle part of the contact area the normal stresses are lower than at the periphery.

The obtained diagrams of contact stresses were checked by comparing the calculated deforming forces, determined as the product of the diagram area by the length of the specimen, with the actual value

of these forces. As can be seen from the tables, during upsetting the discrepancy between the calculated forces and the actual ones did not exceed 18%.

Fig. 3. Distribution of normal contact stresses during radial compression of a cylinder

REFERENCES

1. M. I. Poksevatkin, I. Ya. Tarnovskii, A. N. Levanov. A new method for measuring contact stresses during rolling. Izvestiya vysshikh uchebnykh zavedenii, Chernaya metallurgiya, No. 4, 1964.

2. G. D. Del. Investigation of plastic deformation by hardness measurement. Izvestiya Tomskogo politekhnicheskogo instituta, vol. 138, 1965.

3. G. A. Smirnov-Alyaev, A. P. Olekhver. Investigation of contact stresses and the deformed state during plane upsetting. Kuznechno-shtampovochnoe proizvodstvo, No. 9, 1965.

4. A. D. Tomlenov. Mechanics of Metal-Forming Processes. Mashgiz, 1963.