 | | 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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| S.E. Aleksandrov and R.V. Goldstein, "Generalization of the Prandtl Solution to the Case of Axisymmetric Deformation of Materials Obeying the Double Shear Model," Mech. Solids. 47 (6), 654-664 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
6 |
Pages |
654-664 |
| DOI |
10.3103/S0025654412060076 |
| Title |
Generalization of the Prandtl Solution to the Case of Axisymmetric Deformation of Materials Obeying the Double Shear Model |
| 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 |
A semianalytic solution of the problem on the compression of an annular layer of a plastic material obeying the double shear model on a cylindrical mandrel is obtained. The approximate statement of boundary conditions, which cannot be satisfied exactly in the framework of the constructed solution, is based on the same assumptions as the statement of the classical plasticity problem of compression of a material layer between rough plates (Prandtl's problem). It is assumed that the maximum friction law is satisfied on the inner surface of the layer. The solution is singular near this surface. The strain rate intensity factor is calculated, and its dependence on the process and material parameters is shown. |
| Keywords |
strain rate intensity factor, singular velocity field, semianalytic solution, double shear model |
| References |
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| 15. | S. E. Aleksandrov and Y.-R. Jeng,
"A Generalization of Prandtl's and Spencer's Solutions on Axisymmetric Viscous Flow,"
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| 16. | S. E. Aleksandrov and E. A. Lyamina,
"Singular Solutions for Plane Plastic Flow of Pressure-Dependent Materials,"
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| 17. | S. E. Aleksandrov,
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| 18. | T. A. Trunina and E. A. Kokovkin,
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with Hydraulic Forging,"
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No. 2, 71-74 (2008). |
| 19. | S. E. Aleksandrov, D. Z. Grabko, and O. A. Shikimaka,
"To the Determination of Intensive Strain Layer Thickness near the Friction
Surface in Metal Forming Processes,"
Probl. Mashinostr. Nadezh. Mashin,
No. 3, 72-78 (2009). |
| 20. | S. E. Aleksandrov and E. A. Lyamina,
"Prediction of Fracture in the Vicinity of Friction Surfaces in
Metal Forming Processes,"
Zh. Prikl. Mekh. Tekhn. Fiz.
47 (5), 169-174 (2006)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
47 (5), 757-761 (2006)]. |
| 21. | E. A. Lyamina and S. E. Aleksandrov,
"Application of the Strain Rate Intensity Factor to Modeling Material Behavior
in the Vicinity of Frictional Interfaces,"
in Lecture Notes in Applied and Computational Mechanics,
Vol. 58: Trends in Computational Contact Mechanics,
Ed. by Giorgio Zavarise and Peter Wriggers
(Springer, 2011),
pp. 291-320. |
| 22. | S. E. Aleksandrov and E. A. Lyamina,
"On Constructing the Theory of Ductile Fracture near Friction Surfaces,"
Zh. Prikl. Mekh. Tekhn. Fiz.
52 (4), 183-190 (2011)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
52 (4), 657-663 (2011)]. |
| 23. | S. E. Aleksandrov,
"The Strain Rate Intensity Factor and Its Applications: A Review,"
Mater. Sci. Forum
623, 1-20 (2009). |
| 24. | S. E. Aleksandrov and E. A. Lyamina,
Strain Rate Intensity Factor in Double Shear Model
(LAP Lambert Academic Publishing GmbH&Co, Saarbrücken, 2011). |
| 25. | S. E. Aleksandrov and O. Richmond,
"Singular Plastic Flow Fields near Surfaces of Maximum Friction Stress,"
Int. J. Nonlin. Mech.
36 (1), 1-11 (2001). |
| 26. | R. Z. Valiev, R. K. Islamgaliev, and I. V. Aleksandrov,
"Bulk Nanostructured Materials from Severe Plastic Deformation,"
Prog. Mater. Sci.
45, 103-189 (2000). |
| 27. | S. E. Aleksandrov and R. V. Goldstein,
"Kinetic Equation for the Grain Size in Processes of Intense Plastic Deformation,"
Dokl. Ross. Akad. Nauk
429 (6), 754-757 (2009)
[Dokl. Phys. (Engl. Transl.)
54 (12), 553-556 (2009)]. |
|
| Received |
05 August 2012 |
| Link to Fulltext |
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