A Robust Macroscopic Finite Element Model Implementation for Coupled Phase Transformation and Plastic Deformation in Shape Memory Alloys

Commercial applications of Shape Memory Alloys (SMAs) typically involve cyclic thermo-mechanical loading, during which the response evolves due to combined deformation from phase transformation and plasticity. Such response is complex to predict due to tension/compression asymmetry in phase transformation and plasticity, as well as anisotropy inherent to the phase transformation. However the ability to predict the ratcheting response is beneficial to select appropriate training procedures for specific components.

We present a robust finite element method (FEM) based implementation of a coupled phase transformation, cyclic plasticity constitutive laws for simulating macro-scale response in SMAs. This phenomenological model is unique in explicitly incorporating the mechanisms of martensite initiation, interaction between growing martensite plates that can lead to varying levels of hardening and gradual saturation of phase transformation at larger strains. The plastic constitutive law is able to simulate the Bauschinger effect and ratcheting behavior. The interaction between plasticity and phase transformation is explicitly accounted. The FEM formulation enables simulation of the structural mechanics of components such as tubes, including the effects of geometry and grips.

We demonstrate the strengths of the model through simulations of actuation response of NiTi tubes subjected to tension and torsion. This micro-mechanics inspired FEM-based model provides an efficient tool for predicting macro-scale, multi-deformation mode and multi-axial loading response in SMA structures, expediting the component design process.