Constitutive Model for Ni-Ti-Fe Shape Memory Alloys Exhibiting Pronounced R-Phase Transformation

Specific heat treatment or addition of a ternary element may induce a two-stage transformation sequence in NiTi shape memory alloys (SMA). A typical example of intermediating phases is so-called R-phase, a rhombohedral distortion of the cubic austenitic phase, which exhibits much lower transformation strain and thermal hysteresis than the subsequent transition to monoclinic martensite. In specific alloys, e.g., in NiTi slightly enriched by iron, the temperature and stress intervals in which R-phase is stable are quite broad. Hence, the influence of R-phase on the macroscopic (thermo)mechanical response should be considered when developing and designing products from these alloys. Within this context, tailored constitutive models allowing to reproduce the response in complex loading scenarios without additional experimental effort can be extremely beneficial. This paper presents an enhanced constitutive model for NiTi SMA featuring the R-phase transition. The model recognizes R-phase as a distinct phase, respects the coupled influence of stress and temperature on any phase transformation, and covers reorientation (reconfiguration) of both martensite and R-phase with applied stress. The core of the model consists of two material functions: one captures the energy stored in the material at a given thermodynamic state, the other defines the energy released during dissipative processes, which are considered rate-independent. The model was validated through a direct comparison of experimental tests (isothermal tensile tests, isobaric thermal tests, recovery stress tests) with simulated counterparts.