Dynamics of non-isothermal martensitic phase transitions and hysteresis

We consider a non-isothermal one-dimensional model of martensitic phase transitions that incorporates a finite bar with a non-monotone temperature-dependent stress-strain law and non-zero latent heat. Two dissipation mechanisms are considered: heat conduction and the internal viscous dissipation of kinetic origin. Time-dependent displacement and ambient temperature are prescribed at the ends of the bar. Numerical simulations of this model predict both rate-independent hysteresis, which persists at slow loading, and the rate-dependent portion due to thermal effects. The loops possess serrations caused by nucleation and annihilation events and the motion of interfaces. We observe that when heat conductivity is large, or the applied loading is sufficiently slow, the results are similar to those of Vainchtein and Rosakis [Journal of Nonlinear Science 9 (6) (1999) 697] for the isothermal case, with serrated loops accompanied by nucleations and stick-slip motion of phase boundaries. At faster loading and smaller heat conductivity (or larger latent heat), the stick-slip interface motion is partially replaced by irregular slow-fast interface motion and damped temporal oscillations in both released heat and end load. We show that at higher loading rates more interfaces are formed, and the phase transition causes self-heating of the bar, in qualitative agreement with experimental observations. (C) 2002 Elsevier Science Ltd. All rights reserved.