Scaling relationship on macroscopic helical domains in NiTi tubes

Macroscopic helix-shaped deformation domains were observed in NiTi polycrystalline shape memory alloy tubes during the stress-induced martensitic phase transition of the material under uniaxial quasi-static isothermal stretching. Further experiments showed that the shape and size of the helical domain not only varied with the external applied nominal strain but also depended on the tube geometry. In this paper, we analyze and quantify the free energy of the tube system in the presence of the helical domain by the procedures of the elementary mechanics method. We prove that the shape of the helix is determined by the competition between the domain front energy and the elastic-misfit bending strain energy of the tube system. The former favors a short helical domain and promotes the domain merging into a cylindrical domain, while the latter favors a long slim helical domain. Based on the principle of minimization of free energy, the equilibrium shape of the helical domain is predicted and its dependence on the material properties, the tube geometry and the applied strain is expressed by a power-law scaling relationship. Clear physical understandings of the experimentally observed helical domain patterns are obtained and the results agree well quantitatively with the available experimental data.