A micromechanical modelling of the hysteretic behaviour in thermally induced martensitic phase transitions: application to Cu–Zn–Al shape memory alloys

Abstract

The hysteretic behaviour of Cu–Zn–Al shape memory alloys (SMAs) in thermally induced martensitic phase transition is dealt with. The problem is studied by means of a kinematic analysis where the internal variables describing the material's microstructure are regarded as implicit functions of the applied thermomechanical loading parameters (Σ ij , T). On the other hand, a thermodynamic approach is used in which the local balance formalism is based on the thermoelastic equilibrium concept. Considering that thermoelastic equilibrium temperatures between phases, in the forward and reverse transformation, are dependent on the location in the transformation path enables the hysteretic behaviour to be determined. Hence, a set of non-linear equations is deduced simulating the complete and partial cycles. Results obtained in this way, in the thermally induced phase transition with no applied stress, are in good agreement with experimental observations performed on Cu-based SMAs.