Phase diagram based description of the hysteresis behavior of shape memory alloys

Abstract In this paper, we develop a consistent mathematical description of martensite fraction evolution during athermal thermoelastic phase transformation in a shape memory alloy (SMA) induced by a general thermomechanical loading. The global kinetic law is based on an experimentally defined stress–temperature phase diagram, transformation functions for a one-dimensional SMA body and a novel vector hysteresis model. The global kinetic law provides the phase fraction history given a loading path on the stress–temperature phase diagram and an initial value of martensite 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 transformation behaviors depending on the choice of transformation functions and local kinetic law algorithms. The phase fraction evolution is examined for a number of characteristic examples, including cyclic loading resulting in oscillatory transformation paths, and internal loops of partial 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 data.

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