A multi-scale modeling of complex thermomechanical loading paths in high-temperature shape memory alloys using a crystal-plasticity framework

A crystal-plasticity approach with a mean-field framework using a self-consistent approach was developed for complex thermo-mechanical loading in high-temperature shape memory alloys (HTSMAs). More specifically, an implicit scale transition rule called β -transition rule was employed. A grain-size-dependent martensitic transformation activation criterion was implemented to offer a smooth transformation hardening behavior as well as a saturating transformation strain magnitude function of the local von Mises stress. Two complex loadings were considered: out-of-phase (OP), consisting of a simultaneous increase of stress and decrease of temperature, and in-phase (IP), consisting of a simultaneous increase of stress and temperature. The material parameters were calibrated using isobaric experiments at different stress levels. This calibration was then used to model complex loading paths to evaluate the relevance of using isobaric parameters for the description of complex paths. Computational results are evaluated based on their capability to reproduce the transformation, actuation, and residual strains experimentally observed for the different loading paths considered. Results show a robustness to predict different loading paths using a set of isobaric calibrated parameters. In-phase paths are described on a purely qualitative basis due to the lack of quantitative experimental data. The model developed can capture the first cycle response shape explained by an initial loading in the self-accommodated martensitic state. • Crystal plasticity is used to model proportional/non-proportional loading in HTSMA. • An implicit mean-field transition is implemented for rate-dependent effects. • A grain size dependent transformation criterion is used for transformation behavior. • Model is robust to isobaric, proportional/non-proportional thermomechanical loads. • Initial transformation of self-accommodated martensite is captured and explained.