 | | 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
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| In English (Mech. Solids): | | 4810 |
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| A. V. Konovalov, "Torsion of cylindrical rods and pipes with large plastic strains," Mech. Solids. 36 (3), 86-94 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
3 |
Pages |
86-94 |
| Title |
Torsion of cylindrical rods and pipes with large plastic strains |
| Author(s) |
A. V. Konovalov (Ekaterinburg) |
| Abstract |
We formulate problems of torsion for cylindrical circular rods and pipes
made of an elastic-plastic material with large plastic strains
and describe the results of their solution.
In contrast to classical problems [1], our assumptions do not require
zero strains along
the coordinate axes of the cylindrical reference frame with the z-axis
along the longitudinal axis of the cylinder or pipe; and there is no requirement
that the normal stress components should vanish on coordinate
surfaces.
An explanation is given to the presence of residual axial strains
in a twisted rod or pipe (the Pointing effect).
This effect was discovered in experiments with twisting
wires and rods of steel, copper, and aluminum [2-4]. It was then observed
and studied experimentally for twisted cylindrical and tubular samples
of these and other materials [5-8]. However, the authors of these
investigations gave no explanation to the observed phenomena.
We show that the mean normal stress in an interior part of a
rod or a pipe is positive and may attain values commensurable
with those of the yield stress. |
| References |
| 1. | L. I. Sedov, Continuum Mechanics. Volume 2 [in Russian], Nauka,
Moscow, 1984. |
| 2. | J. F. Bell, Experimental Principles of the Mechanics of Solids.
Part 2. Finite Deformations [Russian Translation],
Nauka, Moscow, 1984. |
| 3. | A. Nadai, Plasticity and Fracture in Solids [Russian translation],
Izd-vo Inostr. Lit-ry, Moscow, 1954. |
| 4. | Ya. B. Fridman, Mechanical Properties of Metals.
Part 1. Deformation and Fracture [in Russian], Mashinostroenie, Moscow, 1974. |
| 5. | I. N. Andronov, N. P. Bogdanov, and V. A. Likhachev,
"Axial deformation of alloys subjected to alternating torsion,"
Problemy Prochnosti, No. 6, pp. 106-119, 1990. |
| 6. | I. N. Andronov, S. P. Belyaev, Z. P. Kamentseva, et al.,
"Torsion induced axial strains in titanium nickelide,"
Problemy Prochnosti, No. 3, pp. 117-119, 1990. |
| 7. | I. P. Andronov, N. P. Bogdanov, V. P. Vlasov, et al.,
"Alternating character of axial deformation of metals under plastic
torsion," Problemy Prochnosti, No. 9, pp. 86-88, 1990. |
| 8. | J. F. Bell, "Experiments on the kinematics of large
plastic strain in ordered solids," Int. J. Solids and Struct., Vol. 25,
No. 3, pp. 267-278, 1989. |
| 9. | A. V. Konovalov, "Constitutive relations for an elastoplastic
medium under
large plastic deformations," Izv. AN. MTT [Mechanics of Solids],
No. 5, pp. 139-147, 1997. |
| 10. | B. A. Cotter and R. S. Rivlin,
"Tensors associated with time-dependent stress,"
Quart., Appl. Math.,
Vol. 13, No. 2, pp. 177-188, 1955. |
| 11. | L. Szabo and M. Balla, "Comparison of some
stress rates," Int. J. Solids and Struct., Vol. 25, No. 3,
pp. 279-297, 1989. |
| 12. | A. A. Pozdeev, P. V. Trusov, and Yu. I. Nyashin,
Large Elastic-Plastic Deformations [in Russian],
Nauka, Moscow, 1986. |
| 13. | P. I. Polukhin, G. Ya. Gun, A. M. Galkin,
Resistance of Metals and Alloys to Plastic Deformation: a Handbook
[in Russian], Metallurgiya, Moscow, 1983. |
|
| Received |
01 July 1998 |
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