 | | 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 |
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| Total articles in the database: | | 12854 |
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| In English (Mech. Solids): | | 4810 |
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| A.A. Movchan, I.A. Movchan, and L.G. Sil'chenko, "Micromechanical Model of Nonlinear Deformation of Shape Memory Alloys under Phase and Structure Transitions," Mech. Solids. 45 (3), 406-416 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
3 |
Pages |
406-416 |
| DOI |
10.3103/S0025654410030118 |
| Title |
Micromechanical Model of Nonlinear Deformation of Shape Memory Alloys under Phase and Structure Transitions |
| Author(s) |
A.A. Movchan (Institute of Applied Mechanics, Russian Academy of Sciences, GSP-1, V-334, Leninskii pr-t 32A, Moscow, 117334 Russia, movchan47@mail.ru)
I.A. Movchan (Institute of Applied Mechanics, Russian Academy of Sciences, GSP-1, V-334, Leninskii pr-t 32A, Moscow, 117334 Russia)
L.G. Sil'chenko (Institute of Applied Mechanics, Russian Academy of Sciences, GSP-1, V-334, Leninskii pr-t 32A, Moscow, 117334 Russia) |
| Abstract |
We propose a model of nonlinear deformation of shape memory alloys (SMA) under phase and structure transitions which reflects the basic characteristics of the phenomena that occur in these materials at the microlevel. The model takes account of the influence on the processes in SMA not only of the applied external macroscopic stresses but also of the microstresses randomly distributed in the material volume under study, with the characteristics of these distributions (mathematical expectation and root mean square deviation) treated as material constants. We also demonstrate that the results predicted by the model agree well with the experimental data for nickel titanium alloy samples. |
| Keywords |
shape memory alloys, elementary volume, martensite mesoelement, phase and structure transitions |
| References |
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| 2. | A. A. Il'in,
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| 3. | R. J. Comstock, Jr., T. F. Buchheit, M. Somerday, and J. A. Wert,
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| 5. | T. Waitz, V. Kazykhanov, and H. P. Karnthaler,
"Martensitic Phase Transformations in Nanocrystalline NiTi Studied by TEM,"
Acta Mater.
52, 137-147 (2004). |
| 6. | A. A. Movchan, S. A. Kazarina, Tant Zin Aung,
"Analog of Theory of Plasticity for Describing Deformations of Shape Memory Alloys under Phase and Structure Transformations,"
Deformats. Razrush. Mat.,
No. 9, 2-7 (2009). |
| 7. | A. A. Movchan,
"Micromechanical Constitutive Equations for Shape Memory Allows,"
Probl. Mashinostr. Nadezhn. Mashin,
No. 6, 47-53 (1994). |
| 8. | A. A. Movchan,
"Micromechanical Description of the Deformation due to Martensite Transformations in
Shape-Memory Alloys,"
Izv. Akad. Nauk, Mekh. Tverd. Tela,
No. 1, 197-205 (1995)
[Mech. Solids (Engl. Transl.)
30 (1), 186-192 (1995)]. |
| 9. | A. A. Movchan,
"Selecting a Phase-Diagram Approximation and a Model of the Disappearance of Martensite Crystals for Shape Memory Alloys,"
Zh. Prikl. Mekh. Tekh. Fiz.
36 (2), 173-181 (1995)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
36 (2), 300-307 (1995)]. |
| 10. | A. A. Movchan,
"Analytical Solution of Problems on the Direct and Inverse
Transformations in Shape Memory Alloys,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 136-144 (1996)
[Mech. Solids (Engl. Transl.)
31 (4), 116-123 (1996)]. |
| 11. | A. A. Movchan,
"Some Manifestations of Oriented Transform Ability of Shape-Memory Alloys,"
Zh. Prikl. Mekh. Tekh. Fiz.
37 (6), 181-189 (1996)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
37 (6), 926-933 (1996)]. |
| 12. | A. A. Movchan,
"Consideration of the Elastic Modulus Variability and the Effect of Stresses on the Phase Composition in Shape Memory Alloys,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 79-90 (1998)
[Mech. Solids (Engl. Transl.)
33 (1), 64-72 (1998)]. |
| 13. | A. A. Movchan,
"Coupling Effects in Bending Problems for Beams of a Shape Memory Alloy,"
Zh. Prikl. Mekh. Tekh. Fiz.
39 (1), 164-173 (1998)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
39 (1), 143-151 (1998)]. |
| 14. | A. A. Movchan,
"Torsion of Shape Memory Alloy Prismatic Rods,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 143-154 (2000)
[Mech. Solids (Engl. Transl.)
35 (6), 119-128 (2000)]. |
| 15. | A. A. Movchan and L. G. Sil'chenko,
"Buckling of a Rod Undergoing Direct or Reverse Martensite
Transformation under Compressive Stresses,"
Zh. Prikl. Mekh. Tekh. Fiz.
44 (3), 169-178 (2003)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
44 (3), 442-449 (2003)]. |
| 16. | A. A. Movchan and L. G. Sil'chenko,
"The Stability of a Plate of Shape-Memory Alloy in a Direct Thermoelastic Phase Transition,"
Prikl. Mat. Mekh.
68 (1), 60-72 (2004)
[J. Appl. Math. Mech. (Engl. Transl.)
68 (1), 53-64 (2004)]. |
| 17. | A. A. Movchan and L. G. Sil'chenko,
"Analysis of Buckling Induced by the Direct Thermoelastic Transformation under the Action of Compression Stresses,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 132-144 (2004)
[Mech. Solids (Engl. Transl.)
39 (2), 104-114 (2004)]. |
| 18. | A. A. Movchan and L. G. Sil'chenko,
"Analytical Solution of the Coupled Buckling Problem for a Plate from a Shape Memory Alloy Subjected to Inverse Martensite Transformation,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 164-178 (2004)
[Mech. Solids (Engl. Transl.)
39 (5), 134-145 (2004)]. |
| 19. | A. A. Movchan and L. G. Sil'chenko,
"The Stability of a Circular Plate of Shape Memory Alloy
during a Direct Martensite Transformation,"
Prikl. Mat. Mekh.
70 (5), 871-883 (2006)
[J. Appl. Math. Mech. (Engl. Transl.)
70 (5), 785-795 (2006)]. |
| 20. | A. A. Movchan and L. G. Sil'chenko,
"Buckling of a Circular Plate Made of a Shape Memory Alloy due to a Reverse Thermoelastic Martensite Transformation,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 117-130 (2008)
[Mech. Solids (Engl. Transl.)
43 (1), 100-111 (2008)]. |
| 21. | I. G. Petrovskii,
Lectures in Theory of Ordinary Differential Equations
(Gostekhizdat, Moscow-Leningrad, 1952)
[in Russian]. |
| 22. | S. D. Prokoshin, L. M. Kaputkina, T. V. Morozova, and I. Yu. Khmelevskaya,
"Dilatometric Anomalies and Shape Memory Effect in Titanium Nickelide Alloy after Low-Temperature Thermo-Mechanical Treatment,"
Fiz. Metal. Metalloved.
80 (3), 70-77 (1995)
[Phys. Met. Metallography (Engl. Transl.)]. |
| 23. | Yu. I. Kadashevich and V. V. Novozhilov,
"The Theory of Plasticity which Takes into Account Residual Microstresses,"
Prikl. Mat. Mekh.
22 (1), 78-89 (1958)
[J. Appl. Math. Mech. (Engl. Transl.)
22 (1), 104-118 (1958)]. |
|
| Received |
11 January 2010 |
| Link to Fulltext |
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