A three-dimensional phenomenological model for shape memory alloys including two-way shape memory effect and plasticity

The one-way and two-way shape memory effects (SMEs) as well as the thermal hysteresis represent fundamental properties when dealing with the design of detachable and thermally-stable connection systems based on shape memory alloys (SMAs). Such properties can be induced and tuned by thermo-mechanical processes that include thermal treatments and severe pre-deformation in martensitic state, causing the onset of plastic strains. In such complex conditions, material modeling is of great importance to support the design. This paper proposes a generalization of the three-dimensional phenomenological constitutive model by Souza et al. (1998), in order to describe the behavior of severely pre-strained NiTi-based SMAs. The proposed model allows to describe pseudoelasticity, one-way and two-way SMEs, as well as additional physical phenomena evidenced experimentally, such as transformation temperatures' evolution, thermal hysteresis, phase transformations at low stresses, thermal strains, and phase-dependent elastic properties. Several numerical simulations, ranging from uniaxial tests to the finite element analysis of two case-studies, are performed. Model results are in good agreement with the results of a performed experimental campaign and allow to discuss SMA behavior under such complex loading conditions.