Non-local modeling on macroscopic domain patterns in phase transformation of NiTi tubes

Recent experiments^[1] revealed many new phenomena of the macroscopic domain patterns in the stress-induced phase transformation of a superelastic polycrystalline NiTi tube during tensile loading. The new phenomena include deformation instability with the formation of a helical domain, domain topology transition from helix to cylinder, domain-front branching and loading-path dependence of domain patterns. In this paper, we model the polycrystal as an elastic continuum with nonconvex strain energy^[2] and adopt the non-local strain gradient energy to account for the energy of the diffusive domain front. We simulate the equilibrium domain patterns and their evolution in the tubes under tensile loading by a non-local Finite Element Method (FEM). It is revealed that the observed loading-path dependence and topology transition of domain patterns are due to the thermodynamic metastability of the tube system. The computation also shows that the tube-wall thickness has a significant effect on the domain patterns: with fixed material properties and interfacial energy density, a large tube-wall thickness leads to a long and slim helical domain and a severe branching of the cylindrical-domain front.