A Micromechanical Model For Textured Polycrystalline Ni-Ti Wires

The present research proposes a micromechanical model for shape memory alloy wires, taking the polycrystalline texture of the material into account. The texture is described by the list of crystalline orientations along with their volume fraction. Each crystalline orientation is characterized by two internal state variables: the volume fraction of self-accommodated martensite, and the volume fraction of the most favorably oriented martensitic variant (with respect to the loading direction). The influence of the 3-dimensional texture is thus considered in the one-dimensional mechanical response of the wire in traction.

This model can describe the specific thermomechanical behavior of shape memory alloy wires, such as superelasticity, self-accommodation and reorientation of martensite, as well as the one-way shape memory effect. Most crucially, the model is able to capture the nonlinear hardening that is often observed in the stress-strain response, both in the superelastic, high temperature regime, and in the low temperature regime.

The model has been implemented numerically in an efficient computational tool. A user-material subroutine (UMAT) resorting to numerical optimization tools has been developed for the finite element software ABAQUS, allowing one to simulate the response of 3-dimensional structures embedding shape memory alloy wires (such as actuators).

Several experiments on Nickel-Titanium wires have been carried out in order to calibrate and validate the model (superelastic traction tests as well as thermal cycles at fixed strain).