Dynamic Models of Martensitic Phase Transitions

Anna Vainchtein
Post-doctoral Research Associate
Division of Mechanics and Computation
Department of Mechanical Engineering
Stanford University

Sponsored by the Dept. of Engineering Mechanics

Date:  Monday, March 6, 2000
Time:  3:30 p.m.
Place:  W131 Nebraska Hall


Shape memory alloys (e.g. NiTi, CuAlNi) have a wide range of existing and potential applications, such as development of smart materials and structures. Under applied cyclic loading, these materials undergo martensitic phase transformations and exhibit a markedly hysteretic behavior. The hysteresis loops on the load-elongation diagrams are often serrated. The serrations are accompanied by a nonsmooth, "jerky" motion of the phase boundaries.

In the first part of this talk, we consider two dynamic continuum mechanics models of martensitic phase transitions. In both models, a bar with a nonconvex two-well elastic energy density is subjected to time-dependent displacement boundary conditions. The wells in the elastic energy density represent two different material phases, austenite and martensite. The dynamic models take into account both inertia term and dissipative viscous stresses. The first model also includes the interfacial energy, modeled by a strain-gradient term. In the second model, this term is omitted. Both models predict hysteresis which is caused primarily by metastability of equilibria and phase nucleation. The hysteresis loops persist even when the loading rate is very slow, and viscosity effects are minor. We find that in the model without the interfacial energy term, the hysteresis loops are serrated, and a stick-slip interface motion is observed. We show that for a given loading this solution behavior is a limit of the interface dynamics in the model that includes interfacial energy as the strain-gradient term tends to zero. On the other hand, at fixed strain-gradient coefficient and slow enough (quasi-static) loading the model including the interfacial energy results in a smooth interface motion and smaller, non-serrated hysteresis loops.

In the second part of the talk, we consider placing the viscoelastic bar on an elastic foundation, to mimic interaction of phases in higher dimensions. This model results in tilted hysteresis loops with multiple serrations and reveals an interesting interplay between the foundation-favored step-by-step phase nucleation process and the inertia-favored interface slip and phase annihilation.