11 July 2002 Inner loops of pseudoelastic hysteresis of shape memory alloys: Preisach approach
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Shape memory alloys (SMA) show very complicated thermomechanical behavior due to phase transformations and rearrangements, including large bounding hysteretic stress-strain loops as well as their inner loops. In our previous analyses, incorporating the phase interaction energy function (PIEF) as a dissipation potential with the free energy of the alloy, we proposed a macroscopic model of SMA for the pseudoelasticity and shape memory effect. Analytical bounding loops derived could accurately model experimental results of a wire subjected to cyclic loads up to 1Hz, including the temperature change. In the present paper, to further extend the concept of the PIEF, we propose a microscopic approach by taking into account the pseudoelastic hysteresis in single crystal grains of polycrystalline SMA. In each grain, we assume that the hysteretic behavior is represented by the Preisach model. Again, incorporating the PIEF with the free energy of the grain, and summing up over the whole material, we have derived the stress-strain relationship in which the Cauchy distribution function is used for the probability of the martensitic and the reverse transformation. We will show that the analytical stress-strain model which has been determined using experimental data of a bounding loop can well describe its inner loops.
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Yuji Matsuzaki, Yuji Matsuzaki, Ken Funami, Ken Funami, Hisashi Naito, Hisashi Naito, } "Inner loops of pseudoelastic hysteresis of shape memory alloys: Preisach approach", Proc. SPIE 4699, Smart Structures and Materials 2002: Active Materials: Behavior and Mechanics, (11 July 2002); doi: 10.1117/12.474993; https://doi.org/10.1117/12.474993

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