A crystal plasticity based constitutive model accounting for R phase and two-step phase transition of polycrystalline NiTi shape memory alloys

Experimental observations show that the phase transition (PT) between austenite (A) and martensite (M) phases in NiTi shape memory alloys (SMAs) often occurs as a two-step process involving an intermediate phase, i.e., rhombohedral (R) phase (Helbert et al., 2014). In this work, a constitutive model is constructed to predict the phase transitions (PTs) among three phases (i.e., A, R and M ones) based on crystal plasticity theory. At single crystal scale, austenite, 4 variants in R phase and 24 variants in martensite one are introduced through certain relationships of crystallographic orientation. The constitutive model is developed in the framework of irreversible thermodynamics with considering various inelastic deformation mechanisms, i.e., the PT between austenite and R phases, the one between mixed A+R and martensite phases, and the reorientation/detwinning of R phase. At polycrystalline scale, to estimate the interactions among grains and obtain the overall response of polycrystalline aggregates, the developed single crystal constitutive model is linearized and implemented into an incremental self-consistent homogenization scheme. The capability of the newly developed constitutive model to describe the stress-induced PTs among three phases of polycrystalline NiTi SMAs is validated by comparing the predictions with the experimental data over a wide range of temperature. Furthermore, the effect of texture on the asymmetric tension-compression response of NiTi SMAs undergoing two-step PT is discussed.