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The Effect of Non-Constant Young's Modulus in Modelling of Tension and Compression of Superelastic NI-TI Shape Memory Alloys

Published online by Cambridge University Press:  03 October 2011

Andrej Puksic*
Affiliation:
Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, 1000 Ljubljana, Slovenia
Janez Kunavar*
Affiliation:
Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, 1000 Ljubljana, Slovenia
Miha Brojan*
Affiliation:
Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, 1000 Ljubljana, Slovenia
Franc Kosel*
Affiliation:
Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, 1000 Ljubljana, Slovenia
*
* Corresponding author
** Graduate student
*** Assistant Professor
**** Professor
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Abstract

Many unresolved issues remain in the field of modelling of shape memory alloys. In this paper the problem of unequal elastic properties of austenite and martensite is addressed. We propose a modification of the micromechanical material model that enables the application of different Young's modulus for austenite and martensite. The corresponding computational model for the application of the micromechanical approach to modeling of superelasticity in shape memory alloys is demonstrated. Material properties for Ni-Ti alloy (50.8 at.% Ni) obtained from literature and from our own experiments were applied to the model and a sample calculation of a 3D model subjected to uniaxial loading was performed. The results were compared to experimental results obtained from tensile and compressive tests. In general the presented model predicts well the level of the superelastic stress plateau and maximum transformation strain in tension. The agreement in compression is worse but the overall characteristics of the tension-compression asymmetry are predicted correctly.

Type
Research Article
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2010

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References

REFERENCES

1. Brinson, L. C., “One Dimensional Constitutive Behavior of Shape Memory Alloys: Thermo-Mechanical Derivation with Non-Constant Material Functions,” Journal of Intelligent Material Systems and Structures, 4, pp. 229242 (1993).CrossRefGoogle Scholar
2. Hwang, S. F. and Tsai, F. M., “One-Dimensional Finite Element Analysis of the Behavior of Shape Memory Alloys,” Journal of Mechanics, 22, pp. 5965 (2006).Google Scholar
3. Patoor, E., Lagoudas, D. C., Entchev, P. B., Brinson, L. C. and Gao, X., “Shape Memory Alloys, Part I: General Properties and Modeling of Single Crystals,” Mechanics of Materials, 38, pp. 391429 (2006).CrossRefGoogle Scholar
4. Bhattacharya, K., Microstructure of Martensite, Oxford University Press, New York (2003).CrossRefGoogle Scholar
5. Wang, X. and Yue, Z., “Three-Dimensional Thermomechanical Modeling of Pseudoelasticity in Shape Memory Alloys with Different Elastic Properties Between Austenite and Martensite,” Materials Science and Engineering: A—Structures, 425, pp. 8393 (2006).CrossRefGoogle Scholar
6. Thamburaja, P. and Anand, L., “Polycrystalline Shape-Memory Materials: Effect of Crystallographic Texture,” Journal of the Mechanics and Physics of Solids, 49, pp. 709737 (2001).CrossRefGoogle Scholar
7. Anand, L. and Kothari, M., “A Computational Procedure for Rate-Independent Crystal Plasticity,” Journal of the Mechanics and Physics of Solids, 44, pp. 525558 1996.CrossRefGoogle Scholar
8. Gall, K. and Sehitoglu, H., “The Role of Texture in Tension-Compression Asymmetry in Polycrystalline NiTi,” International Journal of Plasticity, 15, pp. 6992 1999.CrossRefGoogle Scholar
9. Musienko, A., Tatschl, A., Schmidegg, K., Kolednik, O., Pippan, R. and Cailletaud, G., “Three-Dimensional Finite Element Simulation of a Polycrystalline Copper Specimen,” Acta Materialia, 55, pp. 41214136 (2007).CrossRefGoogle Scholar
10. Mura, T., Micromechanics of Defects in Solids, second edition, Martinus Nijhoff Publishers, Dordrecht (1987).CrossRefGoogle Scholar
11. Lemaitre, J. and Chaboche, J. L., Mechanics of Solid Materials, Cambridge University Press, Cambridge (1990).CrossRefGoogle Scholar
12. Holzapfel, G., Nonlinear Solid Mechanics, John Wiley & Sons, Chichester (2000).Google Scholar
13. Siredey, N., Patoor, E., Berveiller, M. and Eberhardt, A., “ Constitutive Equations for Polycrystalline Thermoelastic Shape Memory Alloys.: Part I. Intragranular Interactions and Behavior of the Grain,” International Journal of Solids and Structures, 36, pp. 42894315 (1999).CrossRefGoogle Scholar
14. Bo, Z. and Lagoudas, D. C., “Thermomechanical Modeling of Polycrystalline Smas Under Cyclic Loading, Part I: Theoretical Derivations,” International Journal of Engineering Science, 37, pp. 10891140 (1999).CrossRefGoogle Scholar
15. Otsuka, K. and Wayman, C. M., Shape Memory Materials, Cambridge University Press, Cambridge (1998).Google Scholar
16. Simo, J. C. and Hughes, T. J. R., Computational Inelasticity, Springer, New York (1998).Google Scholar
17. Suiker, A. S. J. and Turteltaub, S., “Computational Modelling of Plasticity Induced by Martensitic Phase Transformations,” International Journal for Numerical Methods in Engineering, 63, pp. 16551693 (2005).CrossRefGoogle Scholar
18. Weisstein, E. W., Euler Angles, From Math World–A Wolfram Web Resource, http://mathworld.wolfram.com/EulerAngles.html.Google Scholar
19. Liu, Y. and Xiang, H., “Apparent Modulus of Elasticity of Near-Equiatomic NiTi,” Journal of Alloys and Compounds, 270, pp. 154159 (1998).CrossRefGoogle Scholar
20. Jung, Y., Papadopoulos, P. and Ritchie, R. O., “Constitutive Modelling and Numerical Simulation of Multivariant Phase Transformation in Superelastic Shape-Memory Alloys,” International Journal for Numerical Methods in Engineering, 60, pp. 429460 (2004).CrossRefGoogle Scholar
21. Stupkiewicz, S. and Petryk, H., “Modelling of Laminated Microstructures in Stress-Induced Martensitic Transformations,” Journal of the Mechanics and Physics of Solids, 50, pp. 23032331 (2002).CrossRefGoogle Scholar
22. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P., Numerical Recipes in Fortran 77, second edition, Cambridge University Press, Cambridge (1992).Google Scholar
23. Niclaeys, C., Ben Zineb, T., Arbab-Chirani, S. and Patoor, E., “Determination of the Interaction Energy in the Martensitic State,” International Journal of Plasticity, 18, pp. 16191647 (2002).CrossRefGoogle Scholar
24. Smith, I. M. and Griffiths, D. V., Programming the Finite Element Method, second edition, John Wiley & Sons, Chichester (1988).Google Scholar