Constitutive model for NiTi polycrystalline alloys undergoing transformation and plastic deformation processes

Recent experimental investigations have provided new insights into the interplay between martensitic transformation, reorientation and dislocation slip in NiTi SMA. Interactions of these processes give rise to complex coupled phenomena such as transformation-induced plasticity, stabilization of martensite through plastic deformation, or plasticity-induced micro-strain heterogeneity. The plastic deformation in NiTi not only generates irrecoverable strain at the macroscale, but it also induces substantial strain heterogeneity in the microstructure, which significantly affects the functional properties and allows for new technology pathways for designing smarter SMA products.

Building on ideas about how the deformation processes interact, we propose an extended constitutive model to simulate the aforementioned phenomena. The model employs conventional internal variables to describe the microstructural processes, yet expands on the associated dissipation. Additionally, it introduces a simple numerical homogenization scheme that constructs a “compound” representative volume element integrating the response of several interacting sub-elements to mimic such microstructural heterogeneities. This numerical approach enables capturing the dominant experimentally observed effects at reasonable computational costs. The model is implemented in finite element software and several computational simulations of NiTi components are performed. Comparison of simulations with experimental data confirms the excellent predictive capabilities of the model over a wide range of applied stresses and temperatures.