On the Hardness of Stressed Bodies
Abstract Generated abstract
This paper examines how the measured hardness of steel changes under different stressed and deformed states, addressing conflicting earlier results on tension, bending, compression, and torsion. Using Rockwell hardness measurements on steel specimens subjected to tensile, compressive, and torsional loading, both after unloading and in some torsion tests under sustained load, the study compares hardness changes with deformation level, torque, rest time, and position within compressed specimens. The experiments indicate little change in the elastic range, decreased hardness after tensile deformation and at small compressive deformation, increased hardness with larger compression and torsion, and time-dependent changes after torsional deformation. Additional sectioning of compressed specimens suggests a nonuniform hardness distribution, including relatively undeformed conical zones and higher hardness near central regions.
Full Text
ON THE HARDNESS OF STRESSED BODIES
V. P. Shubin
As is known, in solid-state physics and in metal science there is no term more indeterminate than hardness. Indeed, hardness is not a physical constant characterizing a given body and independent of the method used to determine it; on the contrary, hardness is a quantity that depends on the method by which it is measured. Thus, the hardnesses of one and the same body, measured by different methods, may prove to be very different. Nevertheless, hardness is the mechanical characteristic of a material that is most often and most easily measured. The question of changes in hardness in connection with the stressed state of a material is of extremely great importance, since the solution of this question, and even more the establishment of a dependence between changes in hardness and the working capacity of a stressed material, determines the solution of the problem of wear of a number of machine parts.
All machine parts in the course of operation are stressed, and their behavior in service differs in many respects from that assumed in calculations and design.
It seems to us that the study of the hardness of stressed bodies is of great practical and theoretical interest.
The hardness of a body in a stressed state was apparently first tested by Fink and Van Horn [1], in connection with the verification of Rosenhain’s views, according to which the main cause of the high hardness of metals after heat treatment or cold deformation is distortion of the crystal lattice. Fink and Van Horn tested the Rockwell hardness of the most stretched fibers under bending in specimens of duralumin and α-brass (30% Zn). The results of the experiments showed a lowering of hardness.
Engineer D. M. Zagorodskikh [2] carried out a series of experiments to determine the hardness of stressed bodies under tensile deformation, using a portable Brinell press with a ball of \(d = 5\) mm, under a load of 750 kg and with a holding time of 30 sec. He obtained results showing that, under tension of a body, the hardness decreases insignificantly up to the yield point, considerably at the yield point, and beyond the yield point the hardness also remains lower than the initial hardness, but increases in comparison with the hardness at the yield point. We give below Table 1, showing the results obtained by engineer D. M. Zagorodskikh.
Table 1
| Specimen No. | Stress \(\sigma\), kg/mm² | Hardness \(HB\), initial | Hardness \(HB\), under stress | Decrease in hardness, % | Note |
|---|---|---|---|---|---|
| 1 | 16.5 | 154.3 | 151.5 | 1.82 | |
| 2 | 26.3 | 155.7 | 144.7 | 7.07 | |
| 3 | 35.8 | 156.6 | 128.2 | 18.13 | Yield point |
| 4 | 48.8 | 157.1 | 138.5 | 11.84 |
Material—a plain carbon steel having the chemical composition: 0.28% C; 0.12% Si; 0.59% Mn; 0.04% P; 0.02% S.
Our work [3], devoted to the study of the hardness of stressed bodies under torsion, showed that within the limits of proportionality the Shore hardness changes almost not at all; the hardness begins to increase from the moment the metal passes into the plastic zone. The hardness increases with increasing stress according to the linear law
\[ y = ax + B \tag{1} \]
Engineer M. P. Markovets [4] shows that steel containing 0.25% C increases its hardness after bending by 44%, and steel containing 0.35% C by 34%. However, Engineer Markovets did not indicate the degree of bending deformation, and the hardness itself was determined after removal of the load and deformation.
Engineer D. M. Zagorodskikh [5] arrived at conclusions opposite to those obtained by Engineer M. P. Markovets; namely, he showed that the hardness of steel under bending stress in the region of elastic deformations remains unchanged. In the case of plastic deformations, at the moment of bending there occurs a decrease in hardness, which, as the stress increases, falls still further. This conclusion would seem to confirm the conclusions from Engineer D. M. Zagorodskikh’s work on the hardness of stressed bodies under tension.
Thus, the question of the hardness of stressed bodies, despite its importance, has not been resolved. This gives us grounds to set up experiments on the determination of the hardness of stressed bodies. We carried out these investigations under tensile, compressive, and torsional deformations. In carrying out the experimental part of the work, I was greatly assisted by the students Granin and Vedenkin, members of the scientific-technical student circle. In passing, when determining hardness under compression, we carried out an investigation similar to the investigation of Academician Gubkin and Skugarev [6] on the nonuniformity of deformation of steel under compression. The hardness was determined with a Rockwell durometer, with a ball \(d = 1.53\) mm, under a load \(P = 100\) kg, on the hardness scale \(B\) of the indicating instrument.
I. Hardness of Stressed Bodies under Tension
The test was carried out on two specimens made of steel 4. The specimen diagrams are shown in Figs. 1 and 2. Along its length the specimen is divided by divisions spaced 5 mm apart. The specimens were
Fig. 1
loaded: the first to \(P = 6000\) kg; the second to \(P = 7000\) kg, after which the load was removed and hardness measurements were made. Preliminarily
we established that the hardness within the elastic range did not change. The results of the experiment are presented in Table 2. The second specimen was brought to the formation of a neck. Figs. 1 and 2 show diagrams of the change in hardness along the length of the specimens after their deformation.
Fig. 2
Table 2
| Specimen dimensions, mm | Specimen dimensions, mm | Specimen dimensions, mm | Specimen dimensions, mm | Hardness before the experiment | Section No. | Hardness at individual points after deformation, $R_B$ | Hardness at individual points after deformation, $R_B$ | Hardness at individual points after deformation, $R_B$ | Mean hardness, $R_B$ |
|---|---|---|---|---|---|---|---|---|---|
| $h$ | $b$ | $F$ | $l$ | $R_B$ | |||||
| 11 | 15 | 165 mm² | 75 | 57; 58; 57.8; 59.5; 60.8; 59; 56.7; 53; 54; 52.5 | 1 | 49.7 | 45.7 | 50 | 48.4 |
| 11 | 15 | 165 mm² | 75 | 57; 58; 57.8; 59.5; 60.8; 59; 56.7; 53; 54; 52.5 | 2 | 42.5 | 45 | 44 | 44.5 |
| 11 | 15 | 165 mm² | 75 | 57; 58; 57.8; 59.5; 60.8; 59; 56.7; 53; 54; 52.5 | 3 | 40.5 | 45.2 | 45.5 | 43.7 |
| 11 | 15 | 165 mm² | 75 | 57; 58; 57.8; 59.5; 60.8; 59; 56.7; 53; 54; 52.5 | 5 | 42.3 | 47.8 | 45.2 | 45.2 |
| 11 | 15 | 165 mm² | 75 | 57; 58; 57.8; 59.5; 60.8; 59; 56.7; 53; 54; 52.5 | 7 | 41.8 | 45.3 | 47.3 | 44.8 |
| 11 | 15 | 165 mm² | 75 | 57; 58; 57.8; 59.5; 60.8; 59; 56.7; 53; 54; 52.5 | 9 | 41.5 | 42.5 | 48.0 | 44.0 |
| 11 | 15 | 165 mm² | 75 | 57; 58; 57.8; 59.5; 60.8; 59; 56.7; 53; 54; 52.5 | 10 | 38.2 | 42.0 | 43.8 | 41.3 |
| 11 | 15 | 165 mm² | 75 | Mean hardness 56.83 | |||||
| 11 | 15.8 | 174 mm² | 75 | 52; 53.6; 54; 50.7; 51.2; 55; 55.5; 53.2; 49; 50 | 1 | 49.2 | 49.0 | 47 | 48.4 |
| 11 | 15.8 | 174 mm² | 75 | 52; 53.6; 54; 50.7; 51.2; 55; 55.5; 53.2; 49; 50 | 2 | 52.0 | 48.8 | 51 | 50.6 |
| 11 | 15.8 | 174 mm² | 75 | 52; 53.6; 54; 50.7; 51.2; 55; 55.5; 53.2; 49; 50 | 3 | 50.5 | 50.0 | 48.2 | 49.6 |
| 11 | 15.8 | 174 mm² | 75 | 52; 53.6; 54; 50.7; 51.2; 55; 55.5; 53.2; 49; 50 | 5 | 49.0 | 49.0 | 47.5 | 48.5 |
| 11 | 15.8 | 174 mm² | 75 | 52; 53.6; 54; 50.7; 51.2; 55; 55.5; 53.2; 49; 50 | 7 | [[unclear: first number]] | 49.6 | 48.8 | 44.9 |
| 11 | 15.8 | 174 mm² | 75 | 52; 53.6; 54; 50.7; 51.2; 55; 55.5; 53.2; 49; 50 | 9 | 49.9 | 49.2 | 48.8 | 49.3 |
| 11 | 15.8 | 174 mm² | 75 | 52; 53.6; 54; 50.7; 51.2; 55; 55.5; 53.2; 49; 50 | 10 | 50.0 | 54.2 | 52.4 | 51.2 |
| 11 | 15.8 | 174 mm² | 75 | 52; 53.6; 54; 50.7; 51.2; 55; 55.5; 53.2; 49; 50 | 11 | 50.8 | 51.2 | 50.9 | 50.9 |
| 11 | 15.8 | 174 mm² | 75 | 52; 53.6; 54; 50.7; 51.2; 55; 55.5; 53.2; 49; 50 | 12 | 48.7 | 50.8 | 51.5 | 50.3 |
| 11 | 15.8 | 174 mm² | 75 | Mean hardness 52.44 |
Considering the results of these experiments, we note a decrease in hardness after deformation. In the neck the hardness also decreased, but somewhat less in comparison with the hardness in the other sections.
2. Hardness of stressed bodies under compression
For the tests, 3 cylindrical specimens were made of steel 4. The layout of the specimens is shown in Fig. 3. The hardness before the experiment was measured along the generatrix of the cylinder, and also on the end face. The results are summarized in Table 3.
After the hardness measurement, the specimens were subjected to compressive deformation; specimen No. 1 was loaded with a force $P = 28000$ kg; specimen No. 2 with a force $P_2 = 40000$ kg; specimen No. 3 with a force $P_3 = 50000$ kg. Compression
was carried out on a press with a capacity of 60,000 kg. The compressed specimens, after removal of the load, were again tested for hardness along the generatrix of the cylinder and on the end face. The results are shown in Table 4. From the results of the experiments it may be concluded that, under small compressive deformations, when the specimen only began to acquire a barrel-shaped form (which, evidently, corresponds to the yield point), the hardness decreased.
Fig. 5
Table 3
| Specimen No. | Dimensions, mm: $d$ | Dimensions, mm: $h$ | Hardness along the generatrix $R_B$ | Average hardness $R_B$ | Hardness on the end face $R_B$ | Average hardness $R_B$ |
|---|---|---|---|---|---|---|
| 1 | 25 | 26,8 | 40; 47,8; 48,2; 40,4; 44,2; 46,8; 41,8 | 44,6 | 48; 49,2; 51,2 | 49,5 |
| 2 | 25 | 28,3 | 44, [[unclear]]; 41,2; 41,5; 41,4; 42,7; 46; 43,2 | 42,9 | 51; 49,5; 51,8; 44,8; 47,5 | 48,9 |
| 3 | 25 | 27,0 | 42,7; 41,2; 38; 41; 41,2; 42; 42,8 | 41,3 | 45,5; 49; 46,5; 47,0 | 47,0 |
Table 4
| Specimen No. | Dimensions before test, mm: $d$ | Dimensions before test, mm: $h$ | Dimensions after test, mm: $d_1$ | Dimensions after test, mm: $h_1$ | Hardness along the generatrix after deformation $R_B$ | Average hardness $R_B$ | Hardness on the end face after deformation $R_B$ | Average hardness $R_B$ |
|---|---|---|---|---|---|---|---|---|
| 1 | 25 | 26,8 | 26,5 | 24,5 | 34,2; 45,8; 46; 42; 39,8; 49; 45,7 | 43,2 | 46,8; 43; 52; 52; 47,5 | 48,26 |
| 2 | 25 | 28,3 | 28,2 | 21,6 | 46; 50,8; 50; 53; 49; 43; 41 | 49,4 | 53; 49,5; 52,5; 53,5; 58; 55; 56,2 | 54 |
| 3 | 25 | 27,0 | 31,9 | 19,2 | 50,5; 49,9; 57; 54; 53 | 52,88 | 52; 58,8; 54; 52; 55,5; 53,5 | 53,9 |
With considerable deformations the hardness increases, and the more so the greater the deformation. The dependence of hardness on the degree of deformation is shown in Fig. 4.
Fig. 4
3. Hardness of stressed bodies under torsion
To determine the hardness under torsion, we made 7 specimens of steel 3 and steel 4, the diagram of which is shown in Fig. 5. The specimens, on an Amsler torsion machine with a capacity of 150 kg·m, were subjected to twisting deformation brought to a definite value of the torque.
Fig. 5
After application of the torque the specimens were again unloaded, removed from the machine, and tested for hardness. After a certain rest the specimens were again tested for hardness. The data of these tests are shown in Table 5.
The data of this table show that with an increase in the value of the torque the hardness increases, although only slightly. Within the limits of elastic deformations and flow, the hardness changes hardly at all. Interesting results are shown by the rest of the specimens after deformation. Evidently, as a result of the internal rearrangement of the structure of the material during deformation and of attempts during rest to restore this structure, complex phenomena occur that influence the increase in hardness even beyond the limits of the hardness obtained during deformation. In this case the hardness first increases, and with subsequent rest (in our case after 15 days) begins to decrease. Figure 6 gives the curves of hardness measurement during rest.
Table 5
| Steel | Specimen No. | Diameter \(d\), mm | Length \(l\), mm | Hardness before test \(R_B\) | Value of \(M_{\mathrm{cr}}\), kg·m | Mean hardness under load \(R_B\) | Mean hardness after rest, 3 days | Mean hardness after rest, 7 days | Mean hardness after rest, 15 days | Mean hardness after rest, 18 days |
|---|---|---|---|---|---|---|---|---|---|---|
| Steel No. 3 | 1 | 15.4 | 150 | 59.65 | 15.5 | 59.54 | 60.5 | 63.57 | 66.0 | 64.0 |
| Steel No. 3 | 2 | 15.1 | 150 | 57.99 | 25.0 | 57.43 | 59.0 | 59.5 | 60.57 | 58.9 |
| Steel No. 3 | 3 | 15.2 | 150 | 56.47 | 35.0 | 59.20 | 58.2 | 57.6 | 57.2 | 56.0 |
| Steel No. 4 | 4 | 14.6 | 150 | 72.8 | 15.5 yield | 76.6 | 76.5 | 75.3 | 78.2 | 77.2 |
| Steel No. 4 | 5 | 15.0 | 150 | 73.1 | 20.0 | 79.0 | 79.1 | 78.7 | 79.5 | 79.0 |
| Steel No. 4 | 6 | 15.0 | 150 | 71.8 | 25.0 | 83.1 | 83.2 | 83.3 | 84.6 | 84.4 |
| Steel No. 4 | 7 | 15.4 | 150 | 72.8 | 30.0 | 83.1 | 86.5 | 86.8 | 89.0 | 88.2 |
At the same time, 2 specimens of steel 4 were tested for repeated twisting. The experiment proceeded according to the following plan: the hardness was measured at \(M_{\mathrm{cr}}=0\), then a twisting moment of a definite value was applied to the specimen,
Fig. 6
the twisting moment was removed, and the hardness was measured. After this the same specimen was again loaded, but now with a moment of greater value, which was again removed, the new hardness was measured, and so on. The results of these investigations are summarized in Table 6.
Table 6
| No. of specimens | Dimensions, mm: \(d\) | Dimensions, mm: \(l\) | Value of \(M_{\mathrm{cr}}\), kg·m: 0 | Value of \(M_{\mathrm{cr}}\), kg·m: 29.5, flow | Value of \(M_{\mathrm{cr}}\), kg·m: 40.0 | Value of \(M_{\mathrm{cr}}\), kg·m: 55.0 | Value of \(M_{\mathrm{cr}}\), kg·m: 65.0 | Value of \(M_{\mathrm{cr}}\), kg·m: 74.7, failure | |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 19.6 | 160 | 68.4 | 70.5 | 74.8 | 82.8 | 87.3 | 89.6 | Average hardness |
| 2 | 14.8 | 150 | \(M_{\mathrm{cr}}=0\) | 15.5 | 23.0 | 25.0 | 29.8 | — | |
| 2 | 14.8 | 150 | 69.6 | 71.8 | 87.2 | 90.5 | 94.6 | — | Average hardness |
Repeated twisting of one and the same specimen has the effect of producing a more intense increase in hardness in comparison with the hardness under the same external torque applied without repeated twisting.
4. Hardness of stressed bodies without removal of the applied torque
In Sections 1, 2, and 3 of the present work we investigated the influence of the stressed state on the hardness of stressed bodies. However, the hardness was investigated after removal of the applied load. In the present section we present the results of experiments to determine the hardness of stressed bodies under torsion without removal of the stresses. To carry out this task, an apparatus was designed, shown in Fig. 7.
Fig. 7
The torque was produced by turning a ratchet seated on a key on the specimen being tested. The forces were measured with the aid of a dynamometer. For the investigation, specimens of mild steel were made, shown in Figs. 8 and 9. The hardness was measured along the generatrix of the specimens; moreover, in the conical specimens the hardness was measured at diameters \(d_1 = 8\) mm; \(d_2 = 7.5\) mm; \(d_3 = 7\) mm; \(d_4 = 6.5\) mm. The conical specimens were intended to create different stresses along the length of the specimen under the same torque.
Fig. 8
The results of the experiments are presented by diagrams of the change in hardness as a function of \(M_{\mathrm{cr}}\), shown in Figs. 10, 11 and 11a. Analyzing these experiments,
Fig. 9
we come to the conclusion that, if one does not count the evidently accidental hardness readings for specimen No. 2 at \(M_{kr}=1705\ \text{kg·cm}\) and for specimen No. 3 at
Fig. 10
\(M_{kr}^{n}=1890\ \text{kg·cm}\), then, with an increase in the twisting moment, the hardness falls to a certain value and then begins to increase.
Fig. 11
Fig. 11-a
Table 7
| Specimen No. | Value of $M_{\mathrm{cr}}$, kg·cm | Average hardness in sections | Average hardness in sections | Average hardness in sections | Average hardness in sections |
|---|---|---|---|---|---|
| Specimen No. | Value of $M_{\mathrm{cr}}$, kg·cm | $d_1 = 8$ mm | $d_2 = 7.5$ mm | $d_3 = 7.0$ mm | $d_4 = 6.5$ mm |
| 1 | 0 | 30.95 | 33.25 | 32.7 | 35.8 |
| 1 | 1220 | 42.3 | 37.0 | 36.0 | 34.3 |
| 1 | 1525 | 30.9 | 28.7 | 26.4 | 29.3 |
| 1 | 1775 | 27.3 | 23.7 | 22.8 | 23.7 |
| 1 | 1885 | 26.3 | 23.6 | 25.2 | 26.4 |
| 2 | 0 | 30.3 | 31.7 | 30.4 | 31.1 |
| 2 | 1285 | 27.6 | 24.6 | 21.2 | 24.5 |
| 2 | 1465 | 20.7 | 21.2 | 21.5 | 21.4 |
| 2 | 1705 | 23.3 | 23.9 | 22.1 | 28.8 |
| 2 | 1890 | 21.9 | 20.9 | 19.2 | 28.9 |
| 3 | 0 | 37.25 | |||
| 3 | 1220 | 28.7 | |||
| 3 | 1465 | 26.6 | |||
| 3 | 1645 | 26.4 | |||
| 3 | 1890 | 30.2 |
5. Distribution of hardness over the diametral section of specimens
In work [6], Academician S. I. Gubkin and N. G. Skucharev, in studying the nonuniformity of deformation in a dynamically compressed cylinder made of alloy T4, found that the greatest hardness is observed in the middle part of the specimen, and that, near one end surface and the other, two cones are clearly distinguished which have almost not undergone plastic deformation.
[Diagram of hardness distribution over the diametral section of a specimen. Inscription below the diagram: “Average hardness on the generatrix 43; before deformation: at the end 47.”]
Fig. 12
We set up analogous experiments for the static compression of a steel specimen. For this purpose, specimens deformed in compression were sawed along the plane of the diametral section. The cut surface was carefully ground, and on it a grid of mutually perpendicular lines was drawn. The hardness around these lines was measured with a Rockwell hardness tester. We tested three specimens with different degrees of deformation and made about 400 hardness measurements. Figure 12 shows a specimen with the hardness values indicated on it at the points considered. It follows from this figure that two cones, having almost identical hardness, are clearly distinguished, which indicates the absence of plastic deformations in this zone. An increase in hardness along the middle lines, both horizontally and vertically, is clearly expressed. A decrease in hardness is observed at the points farthest from the center of the specimen. It is also possible to distinguish two more cones, encompassing part of the material already in the plastic zone; moreover, within these cones the hardness changed little in comparison with the hardness before the experiment.
As was already indicated above, the question of the hardness of stressed bodies is of undoubted interest. The tests we have carried out have shown the full necessity of a more careful study of the hardness of bodies under stress. Our experiments have touched upon only a small set of questions; however, even here a certain definiteness and functional dependence of hardness on the forces applied to the material is already noticeable. We intend in the future to consider a number of still more general questions connected with the problem under consideration—the hardness of stressed bodies.
REFERENCES
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D. M. Zagorodskikh. On the question of hardness in the stressed state of a body. Vestnik metallopromyshlennosti No. 10, 1937—reference to the works of Fink and Van Horn.
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D. M. Zagorodskikh. On the question of hardness in the stressed state of a body. Vestnik metallopromyshlennosti No. 10, 1937.
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V. P. Shubin. Hardness of stressed bodies. Vestnik metallopromyshlennosti No. 1, 1939.
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M. P. Markovets. Investigation of steel in bending. Sel’skokhozyaystvennaya mashina No. 4, 1932.
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D. V. Zagorodskikh. On the hardness of stressed bodies. Vestnik metallopromyshlennosti No. 10–11, 1939.
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S. I. Gubkin and N. G. Skucharev. Experimental Questions of the Plastic Deformation of Metals. ONTI, p. 31, 1934.