PHASE-DIAGRAM BASED DESCRIPTION OF THE HYSTERESIS BEHAVIOR OF SHAPE-MEMORY ALLOYS

In this paper, we develop a consistent mathematical description of mar tensite fraction evolution during athermal thermoelastic phase transfo rmation in a shape memory alloy (SMA) induced by a general thermomecha nical loading. The global kinetic law is based on an experimentally de fined stress-temperature phase diagram, transformation functions for a one-dimensional SMA body and a novel vector hysteresis model. The glo bal kinetic law provides the phase fraction history given a loading pa th on the stress-temperature phase diagram and an initial value of mar tensite fraction. The phase transformation is considered to occur only within transformation strips on the phase diagram and only on loading path segments oriented in the transformation direction. The developed procedure can be used to model a range of different SMA transformatio n behaviors depending on the choice of transformation functions and lo cal kinetic law algorithms. The phase fraction evolution is examined f or a number of characteristic examples, including cyclic loading resul ting in oscillatory transformation paths, and internal loops of partia l transformation with associated attractor loops. Differences between the various local kinetic law algorithms used in the overall framework are highlighted. The simulation results using a cosine transformation function are found to be in excellent agreement with experimental dat a. (C) 1998 Acta Metallurgica Inc.