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Published December 2016 | Published
Journal Article Open

A micromechanics-inspired constitutive model for shape-memory alloys that accounts for initiation and saturation of phase transformation


A constitutive model to describe macroscopic elastic and transformation behaviors of polycrystalline shape-memory alloys is formulated using an internal variable thermodynamic framework. In a departure from prior phenomenological models, the proposed model treats initiation, growth kinetics, and saturation of transformation distinctly, consistent with physics revealed by recent multi-scale experiments and theoretical studies. Specifically, the proposed approach captures the macroscopic manifestations of three micromechanial facts, even though microstructures are not explicitly modeled: (1) Individual grains with favorable orientations and stresses for transformation are the first to nucleate martensite, and the local nucleation strain is relatively large. (2) Then, transformation interfaces propagate according to growth kinetics to traverse networks of grains, while previously formed martensite may reorient. (3) Ultimately, transformation saturates prior to 100% completion as some unfavorably-oriented grains do not transform; thus the total transformation strain of a polycrystal is modest relative to the initial, local nucleation strain. The proposed formulation also accounts for tension–compression asymmetry, processing anisotropy, and the distinction between stress-induced and temperature-induced transformations. Consequently, the model describes thermoelastic responses of shape-memory alloys subject to complex, multi-axial thermo-mechanical loadings. These abilities are demonstrated through detailed comparisons of simulations with experiments.

Additional Information

© 2016 Elsevier. Received 29 May 2015, Revised 2 February 2016, Accepted 17 February 2016, Available online 18 February 2016. SI:Pierre Suquet Symposium. This work draws from the doctoral thesis of AK at the California Institute of Technology. AK and KB gratefully acknowledge the financial support of the US Army Research Office (W911NF-07-1-0410) and US Department of Energy (DE-FC52-08NA28613). AS acknowledges support from US Department of Energy - National Nuclear Security Administration (DE-NA0001805) that supported his post-doctoral studies at California Institute of Technology, where he began his efforts on this project, and thanks the Colorado School of Mines for support that enabled its completion.

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