Effect of hydrogen on the rate-dependent deformation of superelastic NiTi shape memory alloy springs: Experimental observation and thermo-diffusional-mechanically coupled model

•The influence of hydrogen on the rate-dependent deformation of NiTi SMA springs is revealed.•A thermo-diffusional-mechanically coupled constitutive model of NiTi SMA is constructed.•A semi-analytical model for helical spring is developed by simultaneously considering the torsion and bending deformation modes as well as the thermo-diffusional-mechanical coupling effect.•Deformation behaviors of NiTi SMA springs with and without hydrogen charging are well reproduced by the proposed model. In practical applications, NiTi shape memory alloy (SMA) devices are often serviced in hydrogen-rich environments, leading to a significant change in their service performance. In this paper, the influence of hydrogen on the rate-dependent deformation of superelastic NiTi SMA helical springs is investigated. In the experimental aspect, electrochemical hydrogen charging is performed for the NiTi SMA springs with two different spring indexes (8.5 and 11.7). Then, multi-step tension-unloading tests with the range of loading rate from 0.1 mm/s to 10 mm/s are performed for the springs with and without hydrogen charging. Experimental results show that hydrogen charging can significantly affect the rate-dependent deformation and temperature evolution of the springs. In the theoretical aspect, a thermo-diffusional-mechanically coupled constitutive model is constructed in the framework of irreversible thermodynamics. In the proposed model, the strains associated with the elasticity, martensite transformation (MT), thermal expansion, hydrogen expansion and plasticity are taken into account. The contributions of lattice and trapped hydrogens to the total hydrogen concentration are considered. The thermodynamic driving forces of MT and plastic deformation are derived by the newly established Helmholtz free energy. The evolution of temperature is derived from the energy conservation equation and Fourier’s law. The evolution of hydrogen concentration is obtained by combining the mass conservation equation and Fick’s law. To accurately describe the deformation behavior of helical springs, a new semi-analytical model is established by addressing the thermo-diffusional-mechanical coupling effect and both the torsion and bending deformation modes. By comparing the predictions with the experimental results, the proposed model's capability to reproduce the rate-dependent deformation of NiTi SMA springs with and without hydrogen charging is validated. Moreover, the deformation behavior of the