Determination of the interaction energy in the martensitic state

This study deals with the problem of interactions between martensite Habit Plane Variants (HPV) in Shape Memory Alloys (SMA). A new approach to this problem, based on the definition of “clusters of variants“, allows a better description of observed phenomena. This method is applied in two situations where the results obtained using classical formulations did not correspond to the observations. In Cu-based SMA, the classical interaction matrix shows limitations for the simulation of cooling at low stress level. This matrix does not make it possible to take into account the large number of HPVs which are activated during such a cooling and leads to compute a very large interaction energy. The new formulation uses a description closer to the actual martensitic microstructure developed during this kind of loading, and leads to a more realistic determination of the interaction energy. The definition of a new interaction matrix is derived from this approach. The classical calculation of the interaction matrix does not make it possible to obtain the self-accommodating groups experimentally observed for NiTi SMA. This is related to the morphology of martensite HPVs in these alloys which are composed of two Correspondence Variants (CV). The new approach is applied at the CV scale and the obtained interaction matrix fully agrees with observations.