Describing internal subloops due to incomplete phase transformations in shape memory alloys

The hysteretic response of shape memory alloys (SMAs) is one of their essential characteristics and is related to the martensitic phase transformation. The hysteresis loop may be observed either in stress-strain or strain-temperature curves. In brief, it is possible to say that the major (or external) hysteresis loop can be defined as the envelope of all minor (or internal) hysteresis loops, usually denoted as subloops. The macroscopic description of the SMA hysteresis loops, together with their subloops due to incomplete phase transformations, is an important aspect in the phenomenological description of the thermomechanical behavior of SMAs, being of great interest in technological applications. This contribution exploits the description of these internal subloops and employs a constitutive model previously proposed by [1,20,25]. Numerical investigations of the phenomenon are carried out to show the capability of this model to describe these inner subloops. Comparisons between numerical and experimental results show that they are in close agreement. Moreover, numerical simulations are carried out to elucidate different aspects of this hysteretic behavior.