Macroscopic energy barrier and rate-independent hysteresis in martensitic transformations

A thermodynamic theory for the lower-bound hysteresis in martensitic transformations is developed. It is shown that the elastic energy generated by the transformation-induced crystal lattice misfit makes the system free energy a nonlinear function of the volume fractions of the phases, lifts the additivity principle and ergodicity hypothesis of the conventional Gibbsian thermodynamics, and produces a macroscopic energy barrier between the parent and product phases. Since the energy barrier is proportional to the macroscopic volume of the system and thus cannot be surmounted by the thermally assisted nucleation of the new phase, a rate-independent hysteresis of thermodynamic nature is produced, which sets the lower bound for the total transformation hysteresis. This lower-bound hysteresis is characterized by two critical temperatures of the martensitic and reverse transformations, one during cooling and another during heating, with their difference defining the corresponding transformation hysteresis. The necessary undercooling and overheating are intrinsic material properties determined by the transformation elastic energy. The theory is tested against experimental observations, explains the ubiquitous temperature hysteresis in the martensitic transformations, and correlates the hysteresis with the volumetric misfit strain of the transformations. The proposed theory is generic and is applicable to any displacive (diffusionless and martensitic) phase transformations.