A three-dimensional phenomenological model describing cyclic behavior of shape memory alloys

Nowadays, shape memory alloys, in particular Nickel–Titanium alloys (NiTi), are widely adopted in many fields (biomedical, aerospace, automotive, civil ...) for producing devices exploiting pseudo-elasticity or shape memory effect. These devices are often subjected to cyclic loadings and sometimes to large deformations that modify the material response inducing functional fatigue and/or plastic strains. Accordingly, the device effectiveness is limited or even completely compromised. In this paper, a model able to take into account both the phenomena is presented. Aiming to propose this model for the design and assessment of cyclically loaded devices by finite element simulations, a phenomenological approach was used, introducing internal variables able to describe the accumulation of inelastic strains due to fatigue and plasticity and assuming that their evolution law affects also the phase transformation domain amplitude. Two limit functions was introduced for defining the phase transformation domain and plastic region. The discrete formulation of the model is also presented. Peculiar attention is posed on the material model parameters and the procedure to calibrate them. Initially, a driver code was written in MATLAB for verifying the algorithm correctness and effectiveness; successively, the model was implemented by a user subroutine in a commercial finite element code. The results of several numerical tests are reported in order to show the model functionality and stability under different loading conditions. Finally, the model capability of reproducing 1D and 3D experimental tests is shown by comparison of numerical results with experimental tests published in the literature.