Abstract
Shape memory alloys (SMAs) exhibit hysteresis behaviors upon stress- and temperature-induced loadings. In this chapter, we focus on numerical simulations of microstructure evolution of cubic-to-tetragonal martensitic phase transformations in SMAs in 3D settings under the dynamic loading conditions. A phase-field (PF) model has been developed to capture coupled dynamic thermo-mechanical behavior of such SMA structures and the system of governing equations have been solved numerically using the isogeometric analysis. Temperature induced reverse and forward transformations have been applied to a cubic SMA specimen, starting with evolved accommodated martensitic microstructure. We have observed that during the forward transformation, the martensitic variants nucleate abruptly. The transient microstructures are aligned along \(\left[ 110 \right]\) planes, which is in accordance with the crystallographic theory and experimental results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bhattacharya, K.: Microstructure of Martensite: Why it Forms and How it Gives Rise to the Shape-Memory Effect. Oxford University Press, ISBN: 9780198509349 (2003)
Otsuka, K., Wayman, C.: Shape Memory Materials. Cambridge University Press, ISBN: 052144487 (1999)
Lagoudas, D.: Shape Memory Alloys: Modeling and Engineering Applications. Springer, ISBN: 9780387476858 (2008)
Barsch, G., Krumhansl, J.: Twin boundaries in ferroelastic media without interface dislocations. Phys. Rev. Lett. 53(11), 1069–1072 (1984)
Ahluwalia, R., Lookman, T., Saxena, A.: Dynamic strain loading of cubic to tetragonal martensites. Acta Materialia 54(8), 2109–2120 (2006)
Dhote, R., Gomez, H., Melnik, R., Zu, J.: Isogeometric analysis of coupled thermo-mechanical phase-field models for shape memory alloys using distributed computing. Procedia Comput. Sci. 18, 1068–1076 (2013)
Melnik, R., Roberts, A., Thomas, K.: Computing dynamics of copper-based SMA via centre manifold reduction of 3D models. Comput. Mater. Sci. 18(3), 255–268 (2002)
Cottrell, J., Hughes, T., Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CAD and FEA. John Wiley & Sons, ISBN: 9780470748732 (2009)
Sapriel, J.: Domain-wall orientations in ferroelastics. Phys. Rev. B 12(11), 5128 (1975)
Acknowledgments
This work was made possible with the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca) and Compute/Calcul Canada. Support of NSERC and CRC program is also gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Dhote, R., Gomez, H., Melnik, R., Zu, J. (2015). Temperature Induced Cubic-to-Tetragonal Transformations in Shape Memory Alloys Using a Phase-Field Model. In: Cojocaru, M., Kotsireas, I., Makarov, R., Melnik, R., Shodiev, H. (eds) Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science. Springer Proceedings in Mathematics & Statistics, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-12307-3_26
Download citation
DOI: https://doi.org/10.1007/978-3-319-12307-3_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12306-6
Online ISBN: 978-3-319-12307-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)