| | 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
|
In English (Mech. Solids): | | 4760 |
|
<< Previous article | Volume 50, Issue 2 / 2015 | Next article >> |
I.V. Mishustin and A.A. Movchan, "Analog of the Plastic Flow Theory for Describing Martensitic Inelastic Strains in Shape Memory Alloys," Mech. Solids. 50 (2), 176-190 (2015) |
Year |
2015 |
Volume |
50 |
Number |
2 |
Pages |
176-190 |
DOI |
10.3103/S0025654415020077 |
Title |
Analog of the Plastic Flow Theory for Describing Martensitic Inelastic Strains in Shape Memory Alloys |
Author(s) |
I.V. Mishustin (Institute of Applied Mechanics, Russian Academy of Sciences, Leningradskii pr. 7, Moscow, 125040 Russia, lewis@nm.ru)
A.A. Movchan (Institute of Applied Mechanics, Russian Academy of Sciences, Leningradskii pr. 7, Moscow, 125040 Russia, movchan47@mail.ru) |
Abstract |
Martensitic inelasticity effects in shape memory alloys are described by a version of the plastic flow theory with isotropic and translational hardening, where the maximum value of the phase-structure strain intensity is taken for the isotropic hardening parameter. We show that, in the framework of this model, the entire inelastic deformation process is generally divided into the stages of purely translational and combined hardening and the tangent modulus is discontinuous on the interface between these stages. |
Keywords |
shape memory alloy, martensitic inelasticity, plastic flow theory, isotropic hardening, translational hardening, tangent modulus |
References |
1. | G. B. Kurdyumov and L. G. Khandros,
"On the "Thermoelastic" Equilibrium on Martensitic Transformations,"
Dokl. Akad. Nauk SSSR
66 (2), 211-214 (1949)
[Ukr. J. Phys. (Engl. Transl.)
53 Spec. Issue, 89-92 (2008)]. |
2. | V. A. Likhachev, S. L. Kuz'min, and Z. P. Kamentseva,
Shape Memory Effect
(Izd-vo LGU, Leningrad, 1987)
[in Russian]. |
3. | Y. Liu, Z. Xie, J. van Humbeeck, and L. Delaey,
"Some Results on the Detwinning Process in NiTi Shape Memory Alloys,"
Scripta Mater.
41 (12), 1273-1281 (1999). |
4. | P. Thamburaja,
"Constitutive Equations for Martensitic Reorientation and Detwinning in
Shape-Memory Alloys,"
J. Mech. Phys. Solids
53, 825-856 (2005). |
5. | Y. Liu and H. Xiang,
"Apparent Modulus of Elasticity of Near-Equiatomic NiTi,"
J. Alloys Compounds
270, 154-159 (1998). |
6. | S. A. Abdrakhmanov and K. D. Dyushkeev,
Laws of Behavior of Shape-Memory Alloys under Thermal Force Action
(Ilim, Bishkek, 1992)
[in Russian]. |
7. | Y. Liu, J. van Humbeeck, R. Stalmans, and L. Delaey,
"Some Aspects of the Properties of TiNi Shape Memory Alloy,"
J. Alloys Compounds
247, 115-121 (1997). |
8. | Y. Liu, Z. Xie, J. van Humbeeck, and L. Delaey,
"Asymmetry of Stress-Strain State Curves under Tension and Compression
for NiTi Shape Memory Alloys,"
Acta Mater.
46 (12), 4325-4338 (1998). |
9. | V. A. Lomakin,
"Mechanics of Media with Stress-State-Dependent Properties,"
Fiz. Mezomekh.
10 (5), 41-52 (2007). |
10. | V. A. Lomakin,
"Constitutive Models of Mechanical Behavior of Media
with Stress-State-Dependent Material Properties,"
Adv. Struct. Mater.
7, 339-350 (2011). |
11. | J. A. Shaw and S. Kyriakides,
"Thermomechanical Aspect of TiNi,"
J. Mech. Phys. Solids
43 (8), 1243-1281 (1995). |
12. | G. Airoldi, T. Ranucci, G. Riva, and A. Sciacca,
"The Two-Way Memory Effect by the Pre-Strain Training Method in a 50Ti40Ni10Cu (at %) Alloy,"
Scripta Mater.
34 (2), 287-292 (1996). |
13. | 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,"
Deform. Razrush. Mater.,
No. 9, 2-6 (2009). |
14. | 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. Mezomekh.
15 (1), 105-116 (2012). |
15. | 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)]. |
16. | Z. P. Kamentseva, S. L. Kuz'min, and V. A. Likhachev,
"Strain Hardening of Titanium Nickelide,"
Probl. Prochn.,
No. 9, 87-91 (1980)
[Strength of Materials (Engl. Transl.)
12 (9), 1151-1155 (1980)]. |
17. | A. Bertram,
"Thermo-Mechanical Constitutive Equations for the Description of Shape Memory Effect in Alloys,"
Nuclear Engng Des.
74 (2), 173-182 (1982). |
18. | A. E. Volkov, V. A. Likhachev, and A. I. Rozov,
"Mechanics of Plastic Materials with Phase Transitions,"
Vestnik Leningrad. Univ. Mat. Mekh. Astronom.,
No. 19 (4), 30-37 (1984)
[Vestnik Leningrad Univ. Math. (Engl. Transl.)]. |
19. | M. A. Savi, A. Paiva, A. P. Baeta-Neves, and P. M. C. L. Pacheco,
"Phenomenological Modeling and Numerical Simulation of Shape Memory Alloys:
A Thermo-Plastic-Phase Transformation Coupled Model,"
J. Int. Mater. Syst. Struct.
13 (5), 261-273 (2002). |
20. | A. F. Saleeb, S. A. Pabudala, and A. Kumar,
"A Multi-Axial, Multi-Mechanism Based Constitutive Model
for the Comprehensive Representation of the Evolutionary Response
of SMA's under General Thermomechanical Loading Condition."
Int. J. Plasticity
27 (5), 655-687 (2011). |
21. | J. Arghavani, F. Auricchio, and R. Naghdabasi,
"A Finite Strain Kinematic Hardening Constitutive Model
Based on Hencky Strain: General Framework, Solution Algorithm,
and Application to Shape Memory Alloys,"
Int. J. Plasticity
27 (6), 940-961 (2011). |
22. | Yu. I. Kadashevich and V. V. Novozhilov,
"The Theory of Plasticity which Takes into Account the Bauschinger Effect,"
Dokl. Akad. Nauk SSSR
117 (4), 586-588 (1957). |
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)]. |
24. | R. A. Aratyunyan and A. A. Vakylenko,
"On Multiple Loading of Elastoplastic Medium,"
Izv. Akad. Nauk SSSR. Mekh.,
No. 4, 53-61 (1965). |
25. | 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). |
26. | A. A. Movchan, L. G. Silchenko, and T. L. Silchenko,
"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 (2011)]. |
27. | R. J. Wasilevski,
"Martensitic Transformation and Fatigue Strength in TiNi,"
Scripta Metal.
5 (3), 207-211 (1974). |
28. | K. N. Melton and O. Mercier,
"Fatigue of TiNi Thermoelastic Martensites,"
Acta Metall.
27 (1), 137-144 (1979). |
|
Received |
29 September 2014 |
Link to Fulltext |
|
<< Previous article | Volume 50, Issue 2 / 2015 | Next article >> |
|
If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|