H-phase precipitation and its effects on martensitic transformation in NiTi-Hf high-temperature shape memory alloys

Precipitate microstructure in the B2 parent phase is known to have profound impacts on the properties of NiTi-based high temperature shape memory alloys (HTSMAs), including the martensitic transformation (MT) start temperature $M_s$, temperature- and stress-hysteresis, work output, dimensional stability and functional fatigue resistance. In order to understand the underlying mechanisms and hence to optimize aging heat treatments to achieve desired properties, we systematically investigate both the mechanical and chemical effects associated with nanoscale coherent precipitates on the behavior of MT. Using NiTi-Hf HTSMA as an example, we first study the equilibrium shape and stress and strain fields of an H-phase precipitate as a function of its size. We then determine quantitatively the elastic interaction energy between a precipitate and a nucleating martensitic particle consisting of either a single variant or multiple self-accommodating variants. In the meantime, we calculate the variation of concentration field around an H-phase precipitate during its growth. Finally, we quantify and compare the effects of the spatially inhomogeneous stress and concentration fields around an H-phase precipitate on $M_s$. The results indicate that the former is the dominant factor for long aging times while latter is the dominant factor for short aging times. Since the model predicts $M_s$ as a function of aging temperature and time, it can aid the design of aging heat treatment schedule to achieve desired $M_s$.