A phase-field study of martensite formation in Fe–Mn–Al–Ni shape memory alloys as caused by nanoscale B2-ordered precipitate and matrix phase interplay

This work is motivated by a new generation of iron-based shape memory alloys that have the potential to serve as an enabling technology in civil engineering applications, such as novel pre-stressing mechanisms and high fiber content reinforced high performance concrete.

With the aim of better understanding the underlying microstructural mechanisms that cause the unique macroscopic behavior of these alloys, we present a multidisciplinary effort between mechanics and materials science oriented thermodynamics to carefully study the martensitic phase transformation in the quaternary Fe–Mn–Al–Ni alloy system. More specifically, an Allen–Cahn type phase-field model is used to describe the martensite formation in this shape memory alloy, which is based on the nanoscale interplay of $B2$-ordered precipitates and the matrix material. The underlying multiphase approach is transformed into a homogenized dual phase description with the aim of approximating the martensite start temperature. The calibration of all phase-field related model parameters is performed by means of temperature-dependent data provided through Calphad computations.

Three-dimensional, spatially and temporally resolved finite element simulations are performed on topologically varied unit cells, in order to assess the model. It is found that $B2$-ordered precipitates stabilize the austenite state due to additional mechanical driving force contributions that build up in the vicinity of the inclusions, which is also observed in experiments. Moreover, the results confirm that our hypothesis regarding the key microstructural mechanisms yield $M_s$ temperature predictions, that are in good agreement with experimental data. In addition, extensions of the current approach towards multi-variant systems as well as rate-independent dissipation formulations are discussed. The latter aspect will, for instance, be essential to capture sigmoidal-type hysteresis behavior of iron-based SMA systems at larger length scales, which will be addressed in future investigations. In this regard, the modeling framework proposed in this work is shown to serve as a substantial basis for studying characteristic transformation phenomena that are observed in the Fe–Mn–Al–Ni alloy.