Effect of the Type of Stress State on the Plasticity of Metals
Abstract Generated abstract
This paper investigates how the plasticity of metals depends on the rigidity of the stress state, expressed through a coefficient relating hydrostatic pressure to stress intensity. Experiments were performed under simple loading in biaxial stress states on low-plasticity LS-59 brass and D-1 duralumin, using tubular specimens under axial load and internal pressure, solid cylinders under combined tension and torsion, and compression tests with lubrication. The results compare alternative procedures for determining the stress-state coefficient and indicate that a simplified single-specimen method gives close results for brass. The study also shows that rankings of material plasticity can change with stress state, so standard axial-tension tests alone are insufficient for predicting plasticity in deformation processes.
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INFLUENCE OF THE TYPE OF STRESS STATE ON THE PLASTICITY OF METALS
G. D. Del, L. K. Spiridonov
(Presented by the scientific seminar of the Laboratory of Plastic Deformations)
With a change in the type of stress state, the plasticity of a metal changes [2, 3]. By plasticity we shall understand the magnitude of the intensity of plastic strain that, under a given stress state, the metal can undergo in the deformation zone without failing.
Until now, the plasticity expected in one process or another cannot be predicted from the results of simple mechanical tests.
The aim of the present work is to investigate the dependence of plasticity on the rigidity of the stress state, characterized by the coefficient [2]
\[ \eta=\frac{3\sigma}{\sigma_i} =\frac{\sigma_1+\sigma_2+\sigma_3}{\sigma_i}, \tag{1} \]
where \(\sigma\) is the hydrostatic pressure, \(\sigma_i\) is the stress intensity, and \(\sigma_1, \sigma_2, \sigma_3\) are the principal stresses.
The investigation was carried out under conditions of simple loading in a biaxial stress state. Low-plasticity materials were studied: LS-59 brass and D-1 duralumin.
In the range \(+1\leq \eta \leq +2\), tubular specimens loaded by an axial force and internal pressure were tested:
\[ \eta= \frac{\sigma_z+\sigma_\varphi} {\sqrt{\sigma_z^2+\sigma_\varphi^2-\sigma_z\sigma_\varphi}}, \tag{2} \]
here
\[ \sigma_z=\frac{q\cdot D_{\text{in}}}{4s} +\frac{p}{\pi D_{\text{av}}s}; \qquad \sigma_\varphi=\frac{q\cdot D_{\text{in}}}{2s}, \]
where \(q\) is the internal pressure, \(D_{\text{in}}\) is the inner diameter of the tube, \(S\) is the wall thickness, \(P\) is the axial load, and \(D_{\text{av}}\) is the mean diameter of the tube.
In the range \(-1<\eta\leq +1\), solid cylindrical specimens were tested, subjected to the combined action of an axial force and a twisting moment. In this case, the brass specimens were tested according to the procedure proposed in works [4], [5]. According to this procedure, two solid cylindrical specimens of different diameters are subjected to the combined action of tension and torsion. In this case, for both specimens the force and moment vary according to the same law. The differences in the axial loads and twisting moments applied to the specimens at the same elongation are attributed to a fictitious tube supplementing the smaller specimen.
…of the smaller diameter to the larger specimen. The stresses on the surface are determined in the same way as in testing tubes; then
\[ \eta = \frac{2R_0^{2}} {\sqrt{4R_0^{2}+3\left(\frac{M}{P}\right)^2 (R_{\mathrm{b}}+R_{\mathrm{m}})^2}}, \tag{3} \]
where \(P\) is the axial force, \(M\) is the twisting moment, \(R_0\) is the mean radius of the “tube,” \(R_{\mathrm{b}}\) is the radius of the larger specimen, and \(R_{\mathrm{m}}\) is the radius of the smaller specimen.
According to the theorem on simple loading [1], when the loads vary proportionally, the loading is close to simple. On this basis, the quantity \(\eta\), as in the elastic range, may be calculated approximately from the ratio of the deforming force to the twisting moment
\[ \eta = \frac{1} {\sqrt{1+\frac{48}{D^{2}}\left(\frac{M}{P}\right)^2}}, \tag{4} \]
where \(D\) is the specimen diameter. With this definition of \(\eta\), there is no need to test two specimens of different diameter. In Fig. 1 are compared
Fig. 1. Dependence of the plasticity of LS-59 brass on the rigidity coefficient of the stress state
Fig. 2. Dependence of the plasticity of D-1 duralumin on the rigidity coefficient of the stress state
the results obtained when determining \(\eta\) by formulas (3) and (4). As can be seen, their discrepancy is not significant. This makes it possible—
would make it possible to greatly simplify the procedure for determining the plasticity of duralumin at a given \(\eta\), limiting oneself to the testing of a single specimen.
In addition to these tests, axial compression with lubrication of cylindrical specimens made of the materials under investigation was also carried out (in this case \(\eta = -1\)).
The duralumin specimen (Fig. 2), subjected to axial compression, failed at a larger \(e\) than the brass specimen. Under axial tension, the plasticity of the duralumin specimen was lower than that of the brass one. This again indicates that the plasticity of a material cannot be judged solely from the results of standard axial-tension tests.
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