APPLICATION OF THE HARDNESS MEASUREMENT METHOD IN STUDYING THE STRESS STATE OF PARTS OPERATING AT ELEVATED TEMPERATURES

G. D. Del, F. Kh. Tomilov, L. A. Polinovskii

(Presented by the scientific seminar of the Laboratory of Plastic Deformations)

In solving a wide range of problems associated with the study of the stress–strain state of plastically deformed metal, use is made of the relationship between hardness and stress intensity \[1, 2, 3\]. To interpret the results of hardness measurements, a calibration graph is used: strain intensity—$l_i$, hardness—$H$, stress intensity—$\sigma_i$. The graph is constructed from the results of tests of specimens of the material under investigation in uniaxial tension or compression. The independence of this relationship from the type of stress state under ordinary temperature–rate conditions of plastic deformation was established experimentally in \[4\]; however, in a number of practically important cases it becomes necessary to determine stresses in parts operating at elevated temperatures. Examples include the shells of high-pressure boiler drums, turbine disks, and the like.

High-pressure boiler drums operate at a temperature of $350^\circ\mathrm{C}$ under conditions of prolonged loading. It is not considered possible to measure the hardness of the shell material at the operating temperature; therefore, the hardness on the shell is measured after it has cooled. When determining the stress state near the openings of high-pressure boiler drums by the hardness measurement method, it becomes necessary to investigate the influence of temperature and loading duration on the calibration relationship.

Flat specimens made of steels 22K, 16GNM, and 16GNMA were tested in tension. Plates of each material were manufactured from a single sheet. The specimens underwent heat treatment together; the deviation of the initial hardness for a batch of specimens made from one material was 3 HB units. The tests were carried out at room temperature and at the operating temperature ($350^\circ\mathrm{C}$) on a DST-5000 type machine. The specimen was heated for 30 min at the operating temperature, after which it was loaded smoothly. Then the load was removed and the specimen cooled together with the furnace. The hardness of the cooled specimens was measured at two points of the working section on a portable TShP-2 hardness tester by indenting a steel ball 10 mm in diameter under a load of 1000 kg. The same instrument was used to measure hardness on boiler shells.

Each specimen was deformed to a different degree of deformation. After unloading, the stress intensity $\sigma_i$ and the strain intensity $e_i$ were determined.

Fig. 1. Relationships between strain intensity \(e_i\), Brinell hardness \(HB\), and stress intensity \(\sigma_i\) at normal and elevated temperatures.

Top plot: Steel 22K
Legend: \(\times\)—\(20^\circ\mathrm{C}\); \(\circ\)—\(350^\circ\mathrm{C}\).

Middle plot: Steel 16GNM
Legend: \(\times\)—\(20^\circ\mathrm{C}\); \(\circ\)—\(350^\circ\mathrm{C}\).

Bottom plot: Steel 16GNMA
Legend: \(\times\)—\(20^\circ\mathrm{C}\); \(\circ\)—\(350^\circ\mathrm{C}\).

![Figure 2 graph]

Fig. 2. Effect of deviations in the initial hardness on the calibration relationship
\(e_i—H—\sigma_i\) for steel 16GNM at a temperature of \(350^\circ\text{C}\)

![Figure 3 graph]

Fig. 3. Effect of loading duration on the calibration chart for steel 16GNMA
at a temperature of \(350^\circ\text{C}\)

Figure 1 presents the test results. The onset of hardening during testing at a temperature of 350°C corresponds to the reduced yield strength of the material. With further loading, in comparison with testing the material at a temperature of 20°C, a more intense increase in hardness occurs; i.e., the elevated temperature during loading shifts the calibration curve \(H — \sigma_i\) into the region of lower stresses.

We obtain a calibration curve for a material with reduced mechanical properties. The independence of the relationship \(e_i — H — \sigma_i\) from the type of stress state has been experimentally demonstrated for various materials [4]. Therefore, it should be expected that at elevated temperature this relationship will also be unique.

To determine the intensity of stresses and strains from hardness in parts operating at elevated temperature, it is necessary to use a calibration curve constructed from tests at the operating temperature.

Deviations in the heat-treatment conditions of the shell material and nonuniformity of the chemical composition lead to scatter in the initial hardness; therefore it becomes necessary to assess the influence of the initial hardness on the calibration curve. Calibration curves for steel 16GNM, having different initial hardness, are given in Fig. 2. The maximum deviation of the initial hardness was 25 \(HB\) units. Scatter in the initial hardness leads to a shift of the calibration curve. Therefore, it is necessary to construct the calibration curve from the results of tests of specimens made directly from the material of the part. If constructing such a curve is not possible, then, having a series of calibration curves for the material under study and the initial hardness of the material of the part, an approximate calibration curve can be constructed.

To establish the influence of the duration of loading on the relationship between hardness and stress in plastically deformed metal, experiments were carried out on four specimens of steel 16GNMA. Each specimen was held under load at a temperature of 350°C for 100 hours. The test results are given in Fig. 3. Long-term loading of up to 100 hours practically does not affect the dependence \(e_i — H — \sigma_i\) and may be disregarded when constructing calibration curves.

Conclusions

1. To determine the stress state from hardness in parts operating at elevated temperature, it is necessary to use a calibration curve constructed from the results of tests of specimens made from the material of the part at the operating temperature.

2. It has been established that long-term loading (up to 100 hours) does not affect the calibration dependence \(e_i — H — \sigma_i\) and may be disregarded when constructing the calibration curve.

REFERENCES

1. N. N. Zorew, G. D. De’l, G. L. Kufarew, M. G. Goldschmidt. Spannungszustand in der Schnittzone. Annals of the C.J.R.P., vol. XIV, 1967.

2. G. D. Del’, B. P. Chebaevskii. Stress concentration in the plastic region at a circular hole. Izv. vuzov, “Mashinostroenie,” No. 11, 1968.

3. G. D. Del’, E. S. Vaksman, V. A. Ogorodnikov. The stress-strain state under plane and axisymmetric upsetting. Izv. TPI, vol. 183, 1968.

4. G. D. Del’. Hardness of deformed metal. Izv. AN SSSR, “Metally,” No. 4, 1967.