Constitutive models for shape memory alloys: A two-phase mixture model and a microstructure-based model, pp. 1-47
Authors: Xianghe Peng, Wenli Pi and Xuesong Long
Abstract: 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 response.