A general macroscopic description of the thermomechanical behavior of shape memory alloys

Abstract

The paper presents a macroscopic description that allows the simulation of the global thermomechanical behavior of shape memory alloys (SMA). Use is made of the thermodynamics of irreversible processes framework. Two internal variables are taken into account: the volume fraction of self-accommodating (pure thermal effect) and oriented (stress-induced) product phase. A specific free energy, valid in the total range of phase transition, is defined with particular attention paid to the interaction term. A study of the thermodynamic absolute equilibrium during phase transition proves its instability, and hence explains the hysteretic behavior of SMA. The kinetic equations for the internal variables are written in such a general way that the model could comply with the second law of thermodynamics. The postulate of five yield functions (each of them being related to one process) permits the phase transition criteria to be defined and the kinetic equations related to each process through consistency equations to be derived. The parameters of the model have been identified for three particular SMA, and the simulated results show good agreement with experiments.