Mechanics of Twin Boundaries and Elastic Anisotropy in NiTi

NiTi shape memory alloys exhibit their well-known thermo-mechanical behavior because of the reversible martensitic phase transformation between B2 austenite and B19’ martensite. In this study, we discuss how elastic anisotropy affects the stress-state in twinned martensitic microstructures. Using elastic constants for B19’ martensite derived from ab initio calculations, we demonstrate that the special symmetry of martensite twins in NiTi can be used to directly calculate the complete stress state, which can be described as a superposition of externally applied stresses and compatibility stresses that arise at the twin boundaries. Moreover, we adapt and extend a well-known micromechanical model developed by Gall and Sehitoglu for the selection of twin variants during the stress-induced martensitic transformation in single crystalline NiTi, and we provide an in-depth analysis of compatibility stresses and uniaxial elastic stiffness as a function of crystal orientation. Using these results, we (i) discuss why the macroscopic Young’s modulus of B19’ NiTi is considerably lower than what is conventionally expected from the elastic constants (taking different typical textures into account), and (ii) present experimental results from nanoindentation experiments as well as numerical results from complementary Finite Element simulations that demonstrate how elastic anisotropy affects the small-scale micromechanical response of NiTi. Combining theoretical information and micromechanical models that consider the elastic anisotropy of B2 and B19’ with experimental techniques provides the tools for an in-depth and more realistic analysis of the mechanical behavior of twinned martensitic structures in NiTi, ultimately offering the potential to improve small-scale devices and components.