On the modeling of shape memory alloys using tensorial internal variables

In the literature, some experimental results of polycrystalline NiTi shape memory alloys reveal a strong change in temperature occurring already in a strain range which is commonly regarded as linear elastic. This is rather surprising, since it may be an indication for an evolution of martensite in the linear elastic region. To consider this effect in material models, a tensorial internal variable for the description of the phase transformation along with a suitable approach for the inelastic strain rates resulting from the formation of martensite may be used. Stress-induced phase transformations within shape memory alloys can be regarded as straightened transformations, i.e. during a forward transformation, martensite variants which fit best to the current stress state are favored. Due to this, an appropriate description for the evolution of phase transformations should provide two information: first, the scalar mass fraction of martensite, and second, the orientation of the martensite variants. The internal tensorial variable which is introduced in this article is based on the growth of one single martensite variant. From this variable the information about the mass fraction of martensite and about the average direction of the martensite variants can be extracted. Exemplarily, the embedded tensorial variable within the material model developed by Raniecki et al. [B. Raniecki, C. Lexcellent, K. Tanaka, Arch. Mech. 44 (3) (1992) 261–284] and extended by Müller [C. Müller, Thermodynamic Modeling of Polycrystalline Shape Memory Alloys at Finite Strains, Mitteilungen aus dem Institut für Mechanik, Ruhr-Universität Bochum, 2003] is discussed.