Simulation of grain size effects in nanocrystalline shape memory alloys

Recently, it has been demonstrated that martensitic transformation in nanocrystalline shape memory alloys can be suppressed for small grain sizes. Motivated by these results, we study the grain size dependence of martensitic transformations and stress-strain response of nanocrystalline shape memory alloys within the framework of the Ginzburg-Landau (GL) theory. A GL model for a square to rectangle transformation in polycrystals is extended to account for grain boundary effects. We propose that an inhibition of the transformation in grain boundary regions can occur, if the grain boundary energy of the martensite is higher than that of the austenite phase. We show that this inhibition of transformation in grain boundary regions has a strong influence on domain patterns inside grains. Although the transformation is inhibited only at the grain boundaries, it leads to a suppression of the transformation even inside the grains as grain size is decreased. In fact, below a critical grain size, the transformation can be completely suppressed. We explain these results in terms of the extra strain gradient cost associated with grain boundaries, when the transformation is inhibited at grain boundaries. On the other hand, no significant size effects are observed when transformation is not inhibited at grain boundaries. We also study the grain size dependence of the stress strain curve. It is found that when the transformation is inhibited at grain boundaries, a significant reduction in the hysteresis associated with stress-strain curves during the loading-unloading cycles is observed. The hysteresis for this situation reduces even further as the grain size is reduced, which is consistent with recent experiments. The simulations also demonstrate that the mechanical behavior is influenced by inter-granular interactions and the local microstructural neighbourhood of a grain has a stronger influence than the orientation of the grain itself. (C) 2015 AIP Publishing LLC.