Macroscopic modeling of strain-rate dependent energy dissipation of superelastic SMA dampers considering destabilization of martensitic lattice

Superelastic shape-memory alloys (SMAs) are unique smart materials with a considerable energy dissipation potential for dynamic loadings with varying strain-rates. The energy dissipation arises from a hysteretic phase transformation of the polycrystalline atomic grid structure. In fact, the nucleation from austenite to martensite phase and vice versa exhibits a strong thermomechanical coupling. The hysteresis depends on the latent heat generated by the austenitic-martensitic transformation and the convection of that heat. Due to the thermomechanical coupling, the martensitic nucleation stress level and thus the propagation of martensitic phase fronts strongly depends on the material temperature. High strain-rate interferes with the release of the latent heat to the environment and determines quantity, position and propagation of martensitic transformation bands. Lastly, high strain-rate reduces the hysteresis surface. The propagation velocity and quantity of martensitic bands have an impact on martensitic phase stability. The degree of atomic disorder and accordingly the change in entropy influences the reverse phase transformation from martensite to austenite. In other words, the stability of the martensitic state affects the stress level of the reverse transformation. However, in phenomenological superelastic SMA models, which are used to simulate energy dissipation behavior, the effects of the rate-dependent entropy change are not considered in particular. To incorporate the rate-dependent entropy change, we improved a one-dimensional numerical model by introducing an additional control variable in the free energy formulation for solid-solid phase transformation of superelastic SMAs. In this model, the observed effects of the strain-rate on the reverse transformation are taken into account by calculating the rate-dependent entropy change. A comparison of the numerical results with the experimental data shows that the model calculates the dynamic superelastic hysteresis of SMAs more accurately.