  Titanium-based shape memory alloys, such as Ti2448, have attracted enormous
attention owing to their unique thermomechanical properties and potential
biomedical applications. In this study, we develop a polycrystalline phase
field to investigate the grain size dependence of the martensitic
transformation and associated mechanical properties of nanograined Ti-Nb
alloys. It is shown that a reduction of the average grain size strengthens the
suppression of the martensitic transformation (MT), leading to an increase of
the transformation stress, shrinkage of the stress hysteresis, and elimination
of residual strain. The time-temperature-transformation curves of nano-grained
Ti-Nb alloys with different average grain sizes are obtained and the validity
of Hall-Petch relation is also confirmed in all studied grain sizes.
Furthermore, when the average grain size becomes ultrasmall, both the
temperature- and stress-induced MTs show the continuous second-order phase
transition behavior. These superior transformation characteristics are
attributed to the high density of grain boundaries and the related dominant
role of the gradient energy at the nanoscale. Our results have profound
implications for the design and control of the properties in nano-grained shape
memory alloys.
