A Multiscale Model of First and Second Order Phase Transformations with Application to SMA Single Crystals

This work aims to connect an atomistic model with continuum theory of phase transformations in shape memory alloys (SMAs). A formulation of the Helmholtz free energy potential based on Einstein potential has been developed. The atomic potential was used to describe the interatomic interactions in a biatomic crystal of NiTi. The microscopic expressions of the instantaneous mechanical (continuum) variables of mass, momentum, internal energy, and temperature have been derived in terms of the atomic variables. The developed Helmholtz thermodynamic potential is used in the context of the sharp phase front-based continuum framework proposed by Stoilov and Bhattacharyya [Acta Mater., 50 (2002), pp. 4939–4952] to study the micro-macro transition during the thermomechanical response of NiTi crystals. The developed model has been successfully used to predict the response of a one-dimensional single crystal system.