A micromechanically consistent energy estimate for polycrystalline shape-memory alloys, II: Application to Lüders-type strain localization

Abstract

We make use of a micromechanical energy estimate proposed in the companion paper (Peigney, 2023) to study strain Lüders-like localization in polycrystalline NiTi specimen under tension. Under the assumption that only the most favorably oriented martensitic variant is active in each grain, it is shown that the homogeneous equilibrium problem can be solved analytically for fiber textures (as commonly found in drawn wires or tubes) and more generally for transversely isotropic textures. This leads to an analytical condition for strain localization that admits an explicit expression in terms of the elastic moduli, the lattice parameters and simple statistical information on the texture. The obtained condition allows one to understand what is distinctive about NiTi compared to other shape memory alloys and why strain localization does not appear in compression. In the cases when strain localization is predicted, several quantities of interest such as the strain gap between initiation of phase transformation and localization, the stress drop at the onset of localization and the inclination of the bands can be derived. The results obtained from the presented analytical solution are compared with numerical simulations performed by taking several active variants in each grain into account and considering imperfect transversely isotropic textures. It is found that the presented analytical solution gives a fairly accurate estimate of the response of 100 (and more)-grain aggregates. Taking several active variants per crystalline orientation does not impact the localization condition significantly but gives values of the strain gaps between initiation and localization that are closer to the experimental values reported in the literature.