Plastic Deformation of Copper and Duralumin under Complex Loading
Abstract Generated abstract
Experiments are reported on plastic deformation of annealed copper and duralumin D16 tubular specimens subjected to complex combined loading at constant Huber-Mises stress intensity. The loading programs varied the magnitudes, ratios, and directions of the principal stresses, and the resulting plastic strain increments were related to the arc length of the loading path in stress space. For all 13 specimens tested under complex loading, the intensity of plastic strain increased despite constant stress intensity, and the plotted dependence on path arc length was approximately linear. The results support earlier findings for brass and suggest that strain intensity increment depends mainly on loading-path length and only weakly, if at all, on the form of the loading curve.
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PLASTIC DEFORMATION OF COPPER AND DURALUMIN UNDER COMPLEX LOADING
V. I. Maksak, G. A. Doshchinskii
(Presented by the scientific seminar of the Department of Strength of Materials)
Earlier [1], the plastic deformation of brass under complex loading characterized by constancy of the stress intensity $\sigma_i$ was investigated. Analysis of the experimental results showed that loading along the surface of the Huber–Mises cylinder causes an increment of plastic strains.
Below are presented the results of experiments on complex loading at constant stress intensity for copper and duralumin D16. The specimens were sections of tubes 200 mm long. The outside diameter and wall thickness of the copper specimens were 30 mm and $2^{\pm 0.08}$ mm, and for the D16 specimens, respectively, 40 mm and $1.5^{\pm 0.04}$ mm. All specimens were annealed with subsequent cooling in the furnace: the copper specimens at a temperature of 600°C for one hour, and those of D16 at a temperature of 360°C for 5 hours. In all, 10 copper and 7 duralumin specimens were tested. To check the isotropy of the material, from each batch one specimen was tested in tension in the axial direction and one in the transverse direction. The maximum discrepancy of the tension diagrams for both materials was 4–5%.
The equipment, instruments for measuring strains, and the investigation procedure are described in [2].
Two series of experiments were carried out with the copper specimens. Specimens No. 3 and No. 4 were tested in such a way that, under complex loading, the principal stresses remained constant in magnitude but changed their direction relative to the particles of the specimen; moreover, the ratio $\sigma_2/\sigma_1$ for these specimens was respectively 0 and 0.5. Specimen No. 5 was loaded in such a way that the magnitude of the principal stresses and their ratio changed, while the direction remained constant. Specimen No. 6 was tested in tension with torsion; in this case the principal stresses, their ratio, and their directions changed. In the first series the stress intensity was $\sigma_i = 10\ \text{kg}/\text{mm}^2$.
In the second series, specimens No. 7, 8, 9, and 10 were loaded, respectively, in the same way as specimens No. 3, 4, 5, and 6 in the first series, and $\sigma_i = 13\ \text{kg}/\text{mm}^2$.
The D16 specimens were tested at $\sigma_i = 17\ \text{kg}/\text{mm}^2$; moreover, Nos. 3, 4, 5 were loaded so that the principal stresses remained constant but rotated, and the ratio $\sigma_2/\sigma_1$ was, respectively: 0; 0.25; 0.5. Specimens No. 6, 7 were tested according to the same program as the copper specimens No. 5, 6, only the stress intensity was $\sigma_i = 17\ \text{kg}/\text{mm}^2$.
Thus, under complex loading, 13 specimens were tested. In all cases, in the segment of complex loading with \(\sigma_i = \mathrm{const}\), an increment of plastic strains was observed.
Fig. 1.
Fig. 2.
Taking as a parameter the length of the arc of the loading path
\[ dS=\sqrt{dS_1^2+dS_2^2+dS_3^2}, \]
where
\[ S_1=\sqrt{\frac{2}{3}}\left(\sigma_z-\frac{\sigma_\theta}{2}\right), \]
\[ S_2=\frac{\sqrt{2}}{2}\sigma_\theta;\qquad S_3=\sqrt{2}\tau_{\theta z}, \]
the increment of the intensity of plastic strains can be represented as a function of the arc. This dependence is shown in Fig. 1 for copper and in Fig. 2 for D16. From these graphs it is evident that all the experimental points lie close to a straight line. For copper at \(\sigma_i = 10\ \mathrm{kg/mm^2}\) there is a considerable scatter of the experimental points, which can probably be attributed to experimental error.
The results of tests of copper and duralumin under complex loading, presented here, also confirm the conclusions drawn on the basis of experiments with brass in [1].
Under complex loading characterized by constancy of the stress intensity, the strain intensity increases.
The increment of the strain intensity is a function of the arc length of the loading path, independent of, or only weakly dependent on, the form of the loading curve.
REFERENCES
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V. I. Maksak, G. A. Doshchinskii. Plastic deformation of brass under complex loading. Izv. TPI, vol. 147, 1965.
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V. I. Maksak, G. A. Doshchinskii. On a method for investigating plastic deformation under complex loading, Izv. TPI, vol. 147, 1965.