Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T04:12:04.613Z Has data issue: false hasContentIssue false
  • English
  • Français

A Macromechanical Constitutive Model of Shape Memory Alloys Under Uniaxial Cyclic Loading

Published online by Cambridge University Press:  09 August 2012

H. Lei ,
B. Zhou ,
Z. Wang  and
Y. Wang
H. Lei*
Affiliation:
College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China
B. Zhou
Affiliation:
College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China
Z. Wang
Affiliation:
College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China
Y. Wang
Affiliation:
College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China
*
*Corresponding author ([email protected])
Get access

Abstract

In this paper, the thermomechanical behavior of shape memory alloys (SMAs) subjected to uniaxial cyclic loading is investigated. To obtain experimental data, the strain-controlled cyclic loading-unloading tests are conducted at various strain-rates and temperatures. Dislocations slip and deformation twins are considered to be the main reason that causes the unique cyclic mechanical behavior of SMAs. A new variable of shape memory residual factor was introduced, which will tend to zero with the increasing of the number of cycles. Exponential form equations are established to describe the evolution of shape memory residual factor, elastic modulus and critical stress, in which the influence of strain-rate, number of cycles and temperature are taken into account. The relationship between critical stresses and temperature is modified by considering the cycling effect. A macromechanical constitutive model was constructed to predict the cyclic mechanical behavior at constant temperature. Based on the material parameters obtained from test results, the hysteretic behavior of SMAs subjected to isothermal uniaxial cyclic loading is simulated. It is shown that the numerical results of the modified model match well with the test results.

Keywords

SuperelasticCyclic loadingResidual strain
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 3 , September 2012 , pp. 469 - 477
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Brinson, L. C., “One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-Constant Material Functions and Redefined Martensite Internal Variable,” Journal of Intelligent Material Systems and Structures, 4, pp. 229–242 (1993).CrossRefGoogle Scholar
2. Sun, Q. P. and Hwang, K. C., “Micromechanics Modeling for the Constitutive Behaviors of Polycrystalline Shape Memory Alloys,” Journal of Mechanics and Physics of Solids, 41, pp. 1–33 (1993).CrossRefGoogle Scholar
3. Boyd, J. G. and Lagoudas, D. C., “A Thermodynamic Constitutive Model for the Shape Memory Materials Part II: The SMA Composite Material,” International Journal of Plasticity, 12, pp. 843–873 (1996).CrossRefGoogle Scholar
4. Brocca, M., Brinson, L. C. and Bazant, Z. P., “Three-Dimension Constitutive Model for Shape Memory Alloys Based on Microplane Model,” Journal of Mechanics and Physics of Solids, 50, pp. 1051–1077 (2002).CrossRefGoogle Scholar
5. Peng, X., Pi, W. and Fan, J., “A Microstructure-Based Constitutive Model for the Pseudoelastic Behavior of Niti SMAs,” International Journal of Plasticity, 24, pp. 966–990 (2008).CrossRefGoogle Scholar
6. Zhou, B., Liu, Y. J., Leng, J. S. and Zou, G. P., “A Macro-Mechanical Constitutive Model of Shape Memory Alloys,” Science in China Series G: Physics, Mechanics & Astronomy, 52, pp. 1382–1391 (2009).CrossRefGoogle Scholar
7. Feng, X. Q. and Sun, Q. P., “Shakedown Analysis of Shape Memory Alloy Structures,” International Journal of Plasticity, 23, pp. 183–206 (2007).CrossRefGoogle Scholar
8. Lubliner, J. and Auricchio, F., “Generalized Plasticity and Shape Memory Alloys,” International Journal of Solids and Structures, 33, pp. 991–1003 (1996).CrossRefGoogle Scholar
9. Gong, J. M., Tobushi, H., Takata, K. and Okumura, K., “Analysis and Simulation on Cyclic Superelastical Deformation Behavior of Tini Shape Memory Alloy Subjected to Loading And Unloading,” International Journal of Aeronautical Materialia, 4, pp. 6–12 (2002).Google Scholar
10. Malécot, P., Lexcellent, C., Foltête, E. and Collet, M., “Shape Memory Alloys Cyclic Behavior: Experimental Study and Modeling,” International Journal of Engineering Materials Technology, 1–28, pp. 335–45 (2006).CrossRefGoogle Scholar
11. Wael, Z. and Ziad, M., “A 3D Model of the Cyclic Thermomechanical Behavior of Shape Memory Alloys,” Journal of Mechanics and Physics of Solids, 55, pp. 2427–2454 (2007).Google Scholar
12. Saint-Sulpice, L., Chirani, S. A. and Calloch, S., “A 3D Super-Elastic Model for Shape Memory Alloys Taking Into Account Progressive Strain Under Cyclic Loadings,” Mechanical Materials, 41, pp. 12–26 (2009).CrossRefGoogle Scholar
13. Auricchio, F., Reali, A. and Stefanelli, U., “A Three-Dimensional Model Describing Stress-Induced Solid Phase Transformation with Permanent Inelasticity,” International Journal of Plasticity, 23, pp. 207–226 (2007).CrossRefGoogle Scholar
14. Kang, G. Z., Kan, Q. H., Qian, L. M. and Liu, Y. J., “Ratchetting Deformation of Superelastic and Shape Memory Niti Alloys,” Mechanical Materials, 41, pp. 139–153 (2009).CrossRefGoogle Scholar
15. Kan, Q. H. and Kang, G. Z., “Constitutive Model for Uniaxial Transformation Ratchetting of Super-Elastic Niti Shape Memory Alloy at Room Temperature,” International Journal of Plasticity, 26, pp. 441–465 (2010).CrossRefGoogle Scholar
16. Delville, R., Malard, B., Pilch, J., Sittner, P. and Schryvers., D., “Transmission Electron Microscopy Investigation of Dislocation Slip During Superelastic Cycling of Ni-Ti Wires,” International Journal of Plasticity, 27, pp. 282–297 (2011).CrossRefGoogle Scholar
17. Ren, W. J., Li, H. N. and Song, G. B., “Phenomenological Modeling of the Cyclic Behavior of Superelastic Shape Memory Alloys,” Smart Materials and Structures, 16, pp. 1083–1089 (2007).CrossRefGoogle Scholar
18. Lagoudas, D. C., Mayes, J. J. and Khan, M. M., “Simplified Shape Memory Alloy (SMA) Material Model for Vibration Isolation,” Proceedings of SPIE, 4326, pp. 452–461 (2001).Google Scholar
19. Tobushi, H., Shimeno, Y., Hachisuka, T. and Tanaka, K., “Influence of Strain Rate on Superelastic Properties of Tini Shape Memory Alloy,” Mechanical Materials, 30, pp. 141–150 (1998).CrossRefGoogle Scholar
20. Nemat-Nasser, S. and Choi, J. Y., “Strain Rate Dependence of Deformation Mechanisms in a Ni–Ti–Cr Shape-Memory Alloy,” Acta Materialia, 53, pp. 449–454 (2005).CrossRefGoogle Scholar
21. Nemat-Nasser, S. and Guo, W.-G., “Superelastic and Cyclic Response of Niti SMA at Various Strain Rates and Temperatures,” Mechanical Materials, 38, pp. 463–474 (2006).CrossRefGoogle Scholar
22. Lee, W. S., Lin, C. F., Chen, T. H. and Hwang, H. H., “Effects of Strain Rate and Temperature on Mechanical Behaviour of Ti– 15Mo–5Zr–3Al Alloy,” Journal of Mechanical Biomedical Materials, 1, pp. 336–44 (2008).CrossRefGoogle Scholar
23. Wang, Z. Q., Lei, H. S, Zhou, B. and Wang, Y. L., “Influence of Strain Rate on Mechanical Properties of Shape Memory Alloy,” Key Engineering Materials, 467–469, pp. 585–588 (2011).Google Scholar
24. Tanaka, K., “A Thermomechanical Sketch of Shape Memory Effects: One-Dimension Tensile Behavior,” Research Mechanical, 18, pp. 251–263 (1986).Google Scholar
25. Auricchio, F. and Sacco, E., “A One-Dimensional Model for Superelastic Shape Memory Alloys with Different Elastic Properties Between Austenite and Martensite,” International Journal of Non-linear Mechanical, 32, pp. 1101–1114 (1997).CrossRefGoogle Scholar