 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 48, Issue 5 / 2013 | Next article >> |
| S.E. Aleksandrov and R.V. Goldstein, "Stress-Strain State in an Elastoplastic Cylindrical Tube with Free Ends. I. General Solution," Mech. Solids. 48 (5), 537-545 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
5 |
Pages |
537-545 |
| DOI |
10.3103/S0025654413050099 |
| Title |
Stress-Strain State in an Elastoplastic Cylindrical Tube with Free Ends. I. General Solution |
| Author(s) |
S.E. Aleksandrov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, sergei_alexandrov@yahoo.com)
R.V. Goldstein (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, goldst@ipmnet.ru) |
| Abstract |
We obtain a general solution for the stress-strain state in an elastoplastic tube whose ends are stress-free. The tube is subjected to internal and external pressures which can vary in time rather arbitrarily. But it is assumed that the radius of the elastoplastic boundary does not decrease during the entire deformation process. The tube material obeys a yield condition depending on the mean stress. The corresponding yield surface has the shape of a cone in the space of principal stresses. The theory of plastic flow is used. The plastic potential is taken in the form of the von Mises condition. Thus, the associated plastic flow law is not satisfied, and the material is plastically incompressible. Numerical methods are only needed for successively solving several transcendental equations and calculating ordinary integrals. |
| Keywords |
cylindrical tube, elastoplastic deformation, yield condition, mean stress |
| References |
| 1. | R. Hill,
The Mathematical Theory of Plasticity
(Clarendon, Oxford, 1950; Gostekhizdat, Moscow, 1956). |
| 2. | A. Mendelson,
Plasticity Theory and Application
(Macmillan, New York, 1968). |
| 3. | V. V. Sokolovskii,
The Theory of Plasticity
(Vysshaya Shkola, Moscow, 1969)
[in Russian]. |
| 4. | J. Chakrabarty,
Theory of Plasticity
(McGraw-Hill, New York, 1987). |
| 5. | S. E. Aleksandrov and R. V. Goldstein,
"Calculation of the Pipeline Wall Thickness under Internal
Pressure at an Arbitrary Law of Hardening,"
Deform. Razrush. Mat.,
No. 9, 15-20 (2011)
[Russ. Metallurgy (Metally) (Engl. Transl.)
2012 (10), 873-878 (2012)]. |
| 6. | D. W. A. Rees,
"Autofrettage Theory and Fatigue Life of Open-Ended Cylinders,"
J. Strain Anal. Engng Des.
25 (2), 109-165 (1990). |
| 7. | D. C. Drucker and W. Prager,
"Soil Mechanics and Plastic Analysis for Limit Design,"
Quart. Appl. Math.
10 (2), 157-165 (1952). |
| 8. | W. A. Spitzig, R. J. Sober, and O. Richmond, "The Effect of
Hydrostatic Pressure on the Deformation Behavior of Maraging and
HY-80 Steels and Its Implications for Plasticity Theory,"
Metallurg. Trans. 7A (11), 1703-1710 (1976). |
| 9. | A. S. Kao, H. A. Kuhn, W. A. Spitzig, and O. Richmond, "Influence
of Superimposed Hydrostatic Pressure on Bending Fracture and
Formability of a Low Carbon Steel Containing Globular Sulfides,"
Trans. ASME. J. Engng Mater. Technol. 112 (1), 26-30
(1990). |
| 10. | C. D. Wilson,
"A Critical Reexamination of Classical Metal Plasticity,"
Trans. ASME. J. Appl. Mech.
69, 63-68 (2002). |
| 11. | P. S. Liu,
"Mechanical Behavior of Porous Metals under Biaxial Tensile Loads,"
Mater. Sci. Engng
A422, 176-183 (2006). |
| 12. | V. N. Nikolaevskii,
Mechanical Properties of Soils and Plasticity
in Mechanics of Deformable Solids,
Itogi Nauki i Tekhniki [Progress in Science and Technology]
(VINITI, Moscow, 1972),
[in Russian], |
| 13. | A. Yu. Ishlinskii,
"On Plane Motion of Sand,"
Ukrain. Mat. Zh.
6 (4), 430-441 (1954)
[Ukrain. Math. J. (Engl. Transl.)]. |
| 14. | D. W. A. Rees,
Basic Engineering Plasticity
(Elsevier, Amsterdam, 2006). |
| 15. | O. A. Kilikovskaya and N. V. Ovchinnikova, "Influence of Material
Hardening and Compressibility on the Solution of Elastoplastic
Deformation Problems for a Space with a Cylindrical Cavity," Izv.
Akad. Nauk. Mekh. Tverd. Tela, No. 1, 75-91 (2012) [Mech. Solids
(Engl. Transl.) 47 (1), 57-70 (2012)]. |
| 16. | S. E. Aleksandrov and R. V. Goldstein,
"Effect of the Mean-Stress Dependence of Yield Conditions
on Residual Stresses and Strains,"
Dokl. Ross. Akad. Nauk
438 (2), 185-188 (2011)
[Dokl. Phys. (Engl. Transl.)
56 (5), 279-282 (2011)]. |
| 17. | S. Alexandrov, Y.-R. Jeng, and E. Lyamina,
"Influence of Pressure-Dependency of the Yield Criterion
and Temperature on Residual Stresses and Strains in a Thin Disk,"
Struct. Engng Mech.
44, 289-303 (2012). |
|
| Received |
06 April 2013 |
| Link to Fulltext |
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