A Phenomenological Description of the Thermomechanical Coupling and the Rate-dependent Behavior of Shape Memory Alloys

Shape memory alloys (SMAs) present a rate-dependent behavior, which means that the thermomechanical response depends on the loading rate. Therefore, although martensitic transformation can be considered as a non-diffusive process, the phase transformation critical stresses are temperature dependent and, since heat transfer process is time dependent, it affects the thermomechanical behavior of SMAs. This article deals with the rate dependence of SMAs, proposing a 1D constitutive model to describe this effect. The proposed model is formulated within the framework of continuum mechanics and thermomechanical coupling terms of the energy equation are incorporated in the formulation in order to describe the rate-dependent behavior. Numerical simulations are carried out comparing results with experimental data available in literature for different loading rates and environmental media, presenting a close agreement. Afterwards, numerical tests are performed in order to evaluate the model capabilities showing that it is capable to capture the general thermomechanical behavior of SMAs.