 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| V. L. Dil'man and A. A. Ostsemin, "On the stress-strain state of a plastic ring subjected to tension," Mech. Solids. 37 (2), 88-97 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
2 |
Pages |
88-97 |
| Title |
On the stress-strain state of a plastic ring subjected to tension |
| Author(s) |
V. L. Dil'man (Chelyabinsk)
A. A. Ostsemin (Chelyabinsk) |
| Abstract |
We investigate the stress-strain state (SSS) of an axially symmetric
plastic layer of a hollow cylinder (pipe) having a
circular ring in cross-section. We assume that the layer is symmetric
with respect to one of such cross-sections, and that the connected
components of its axial section have a
symmetry axis parallel to the axis of the pipe. The pipe or
another shell structure containing the layer is subjected to an
axial tensile load. Such a shape may be possessed by transverse welds in
pipes, cylindrical reservoirs or other
structures, for example, welds of a rectangular or X-shaped
cross-section with or without reinforcement. No limitations are imposed on
the thickness of the layer, but it is assumed that for the interior regions
of the cross-sections of the layer, whose SSS is not determined by the
shape of free surfaces, one can adopt the hypothesis of plane
cross-sections orthogonal to the axis of the pipe. We find a new
approximate solution of the complete system of equations describing the SSS
of the plastic medium in the layer. Analysis of the formulas obtained for
the stress tensor components shows that the normal stresses decay in the
direction from the center of the layer cross-section toward the contact
surfaces, i.e., ductile fracture may only occur on a surface outside the
central region of the layer. These formulas allow us to calculate the
tensile load that causes fracture.
Circular ring shape is typical of transverse welds of
cylindrical shell structures, as well as axially perforated
cylindrical workpieces subjected to upsetting. The SSS of such
workpieces was previously studied by the variational (extremal) methods
and the method of upper bounds [1, 2]. Welds were studied
experimentally [3]. A theoretical study of the SSS of a thin
ring-shaped plastic layer is undertaken in [4] on the basis of the
methods applied in [5, 6, 7] to solid cylindrical samples of
circular cross-section. It should be mentioned that the fact that
the contour of the ring-shaped plastic layer is doubly connected
substantially increases the mathematical difficulty of the problem.
We propose a new approximate method for solving the complete system
of equations describing the SSS of a plastic layer with a doubly
connected contour in the axially symmetric case. This method allows
us to find the tensile load that causes fracture of the layer and the
joint containing this layer.
One of the difficulties of the problem is that
the boundary conditions following from the
existence of free surfaces and the symmetry of the layer are
insufficient for the SSS to be uniquely defined at the interior
points of the layer, since the stress distribution at the interface
between the soft layer and the basic metal is unknown. Thus, one
cannot avoid additional hypotheses regarding the internal state of
the layer material. |
| References |
| 1. | E. P. Unksov, W. Johnson, V. L. Kolmogorov, et al.,
Theory of Plastic Deformation of Metals [in Russian], Mashinostroenie,
Moscow, 1983. |
| 2. | I. Ya. Tarnavskii, A. A. Pozdeev, O. A. Ganago, et al.,
Theory of Plastic Metal Working [in Russian], Metallurgizdat, Moscow, 1963. |
| 3. | A. V. Puiko, M. G. Zel'man, and Yu. I. Anisimov,
"Experimental analysis of
plastic deformation of soft annular layers in pipes,"
in Economy of Material, Energy, and Human Resources in Welding Industry
[in Russian], pp. 271-273, Ob-vo Znanie, Chelyabinsk, 1986. |
| 4. | A. S. Bogomolova, " On the stress state of a plastic layer
with doubly-connected boundary under axially symmetric deformation,"
in Welded Metal Structures and Their Production [in Russian], pp. 178-183,
Chelyabinsk, 1972. |
| 5. | L. M. Kachanov, "On the problem of plastic layer deformation,"
Doklady AN SSSR, Vol. 96, No. 2, pp. 249-252, 1954. |
| 6. | O. A. Bakshi and L. M. Kachanov, "On the stress state of a plastic
layer subjected to plastic deformation," Izv. AN SSSR. Mekhanika, No. 2,
pp. 134-137, 1965. |
| 7. | L. M. Kachanov, Principles of the Theory of Plastcity [in Russian],
Nauka, Moscow, 1969. |
| 8. | A. A. Ostsemin and V. L. Dil'man,
"On the compression of a plastic layer between two rough slabs,"
Probl. Prochn., No. 7, pp. 107-113, 1990. |
| 9. | P. W. Bridgman, Studies in Large Plastic Flow and
Fracture [Russian translation], Izd-vo Inostr. Lit-ry, Moscow, 1955. |
|
| Received |
05 January 2000 |
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