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Constitutive models for shape memory alloys: A two-phase mixture model and a microstructure-based model, pp. 1-47 $100.00
Authors:  Xianghe Peng, Wenli Pi and Xuesong Long
Two models for the constitutive behavior of polycrystalline shape memory alloys
(SMAs) are presented. One is a two-phase mixture model, and the other is a
microstructure-based two-phase model, accounting for the typical constitutive behavior of
Ni-Ti SMAs under different stress states. In both models, it is assumed that in the
interested ranges of stress and temperature, the austenite phase is linearly elastic while the
martensite phase is elastoplastic.
In the first model, an SMA is considered to be composed of austenite and martensite
phases, and its constitutive behavior is the combination of the individual behavior of each
of the two phases. Making use of the simple Tanaka‘s phase-transformation rule, the main
features of SMAs, such as shape memory effect and pseudoelasticity, can be successfully
described. The constitutive behavior of SMA Au–47.5 at.% Cd subjected to uniaxial
tension/compression and the pseudoelasticity of a polycrystalline Cu–Al–Zn–Mn SMA
subjected to proportional and nonproportional complex stress/strain histories were
simulated and compared with experimental results.
Experiments showed that the pseudoelastic behavior of NiTi SMAs under pure
tension and that under pure torsion were distinctly different, due to the different
deformation-induced-transformation microstructures. SEM observation showed parallel
texture on the surface of the NiTi SMA microtubes subjected to pure torsion, indicating
alternatively arranged parallel fine lamellas of austenite and martensite phases. During
pure tension, it was observed that martensite initiated from the parent phase and grew to
macroscopic bands, and, correspondingly, a typical stress drop or macroscopic instability
was observed in the tensile stress–strain curve. FE analyses based on these microstructures
replicated the experimental results under pure tension and under pure torsion, respectively,
indicating the important role of the microstructure in the macroscopic constitutive

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Constitutive models for shape memory alloys: A two-phase mixture model and a microstructure-based model, pp. 1-47