 | | 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
|
| In English (Mech. Solids): | | 3212 |
|
| << Previous article | Volume 49, Issue 1 / 2014 | Next article >> |
| I.V. Mishustin and A.A. Movchan, "Modeling of Phase and Structure Transformations Occurring in Shape Memory Alloys under Nonmonotonically Varying Stresses," Mech. Solids. 49 (1), 27-39 (2014) |
| Year |
2014 |
Volume |
49 |
Number |
1 |
Pages |
27-39 |
| DOI |
10.3103/S002565441401004X |
| Title |
Modeling of Phase and Structure Transformations Occurring in Shape Memory Alloys under Nonmonotonically Varying Stresses |
| Author(s) |
I.V. Mishustin (Institute of Applied Mechanics, Russian Academy of Sciences, Leninskii pr-t 32A, Moscow, 117334 Russia, lewis@nm.ru)
A.A. Movchan (Institute of Applied Mechanics, Russian Academy of Sciences, Leninskii pr-t 32A, Moscow, 117334 Russia, movchan47@mail.ru) |
| Abstract |
A model of deformation of shape memory alloys (SMA) under nonmonotone loading is proposed. The model takes into account the fact that there is no strain hardening in the process of accumulation of the first phase transformation strains and describes both the usual hardening and the cross-hardening observed in martensite inelasticity experiments. Several examples illustrate the process of solving the model one-dimensional deformation problem with a given law of variation of the stress and the phase composition parameter and the problem on the direct transformation that occurs when cooling an SMA rod subjected to a constant bending moment. |
| Keywords |
shape memory alloy, phase and structure transformations, nonmonotone loading |
| References |
| 1. | A. A. Movchan and S. A. Kazarina,
"Shape Memory Materials as an Object of Deformable Solid Mechanics:
Experimental Studies, Constitutive Relations, Solution of Boundary-Value Problems,"
Fiz. Mesomekh.,
15 (1), 105-116 (2012). |
| 2. | E. Z. Vitaikin, D. F. Litvin, S. Yu. Makushev, and V. A. Udovenko,
"Structure Mechanism of Shape Memory Effect in Alloys,"
Dokl. Akad. Nauk SSSR
229 (3), 597-600 (1976). |
| 3. | A. A. Movchan, S. A. Kazarina, and Tant Zin Aung,
"Analog of Theory of Plasticity for Describing Deformations of Shape Memory Alloys
under Phase and Structure Transformations,"
Deform. Razrush. Mat.,
No. 9, 2-7 (2009). |
| 4. | M. Achenbach,
"A Model for an Alloy with Shape Memory,"
Int. J. Plasticity
5 (4), 371-395 (1989). |
| 5. | K. Tanaka,
"A Phenomenological Description of Thermomechanical Behavior of Shape Memory Alloys,"
J. Pressure Vessel Technol. Trans. ASME
112 (2), 158-163 (1990). |
| 6. | C. Liang and C. A. Rogers,
"One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials,"
J. Intell. Mater. Syst. Struct.
1 (2), 207-234 (1990). |
| 7. | E. J. Graesser and E. A. Cozzarelli,
"A Proposed Three-Dimensional Constitutive Model for Shape Memory Alloy,"
J. Intell. Mater. Syst. Struct.
5 (1), 78-89 (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. Tekhn. Fiz.
36 (2), 173-181 (1995)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
36 (2), 300-307 (1995)]. |
| 10. | L. S. Brinson and M. S. Huang,
"Simplification and Comparisons of Shape Memory Alloys Constitutive Models,"
J. Intell. Mater. Syst. Struct.
7 (1), 108-114 (1996). |
| 11. | J. G. Boyd and D. C. Lagoudas,
"A Thermodynamic Constitutive Model for Shape Memory Materials. Part 1:
The Monolithic Shape Memory Alloy,"
Int. J. Plasticity
12 (6), 805-842 (1996). |
| 12. | J. Lubliner and F. Auricchio,
"Generalize Plasticity and Shape-Memory Alloys,"
Int. J. Solids Struct.
33 (7), 991-1003 (1996). |
| 13. | W. Huang,
"Yield Surface of Shape Memory Alloys and Their Applications,"
Acta Meterialia
47 (9), 2769-2776 (1999). |
| 14. | A. E. Volkov and V. Yu. Sakharov,
"Thermomechanical Macromodel of Shape Memory Alloys,"
Izv. Ross. Akad. Nauk. Ser. Fiz.
67 (6), 845-851 (2003)
[Bull. Russ. Acad. Sci. Phys. (Engl. Transl.)]. |
| 15. | C. Lexcellent, M. L. Boubaker, C. Bouvet, and S. Calloch,
"About Modeling the Shape Memory Alloy Behavior Based on
the Phase Transformation Surface Identification
under Proportional Loading and Anisothermal Conditions,"
Int. J. Solids Struct.
43 (3-4), 613-626 (2006). |
| 16. | J. Arghavani, F. Auricchio, R. Naghdabadi, et al.,
"A 3-D Phenomenological Constitutive Model for Shape Memory Alloys under Multiaxial Loading,"
Int. J. Plasticity
26, 976-991 (2010). |
| 17. | A. A. Movchan, I. A. Movchan, and L. G. Sil'chenko,
"Micromechanical Model of Nonlinear Deformation of Shape Memory Alloys
in Phase and Structure Transformations,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 118-130 (2010)
[Mech. Solids (Engl. Transl.)
45 (3), 406-416 (2010)]. |
| 18. | A. A. Movchan, I. A. Movchan, and L. G. Sil'chenko,
"Effect of Structural Transformation and Deformation Nonlinearity on the Stability
of a Shape Memory Alloy Rod,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 137-147 (2010)
[Mech. Solids (Engl. Transl.)
45 (6), 876-884 (2010)]. |
| 19. | A. A. Movchan, L. G. Sil'chenko, and T. L. Sil'chenko,
"Taking Account of the Martensite Inelasticity in the Reverse
Phase Transformation in Shape Memory Alloys,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 44-56 (2011)
[Mech. Solids (Engl. Transl.)
46 (2), 194-203 (2010)]. |
| 20. | V. A. Likhachev (Editor),
Materials with Shape Memory Effect. A Handbook
(Izd-vo NIIKh SPbGU, St. Petersburg, 1998)
[in Russian]. |
| 21. | 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)]. |
| 22. | A. A. Movchan and I. A. Movchan,
"One-Dimensional Micromechanical Model of Nonlinear Deformation of Shape Memory Alloys
under Direct and Inverse Thermoelastic Transformations,"
Mekh. Komp. Mater. Konstr.
13 (3), 297-322 (2007)
[J. Comp. Mech. Design (Engl. Transl.)]. |
| 23. | A. A. Movchan, S. A. Kazarina, I. V. Mishustin, and I. A. Movchan,
"Thermodynamical Justification of the Model of Nonlinear Deformation
of Shape Memory Alloys in Phase and Structure Transformations,"
Deform. Razrush. Mater.,
No. 8, 2-9 (2009). |
|
| Received |
07 September 2013 |
| Link to Fulltext |
|
| << Previous article | Volume 49, Issue 1 / 2014 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English