<title>Pseudoelastic theory of shape memory alloys</title>

Abstract

This paper presents an extension of the authors' previous analyses on the one-dimensional pseudoelastic theory of shape memory alloys (SMA), in which an interaction energy has been introduced to represent the energy dissipation during the phase transformation. From the equilibrium condition of the two-phase state, we show that the partial derivative of the interaction energy with respect to the phase fraction represents the thermodynamic driving force for the phase transformation. Two functions for the interaction energy are derived from the assumptions about the driving force of the equilibrium transformation. Using these interaction energy, we also examine the stability of equilibrium state and the formation of subloops due to incomplete transformations. Analytical predictions by the proposed theory agree well qualitatively with available experimental observations.

Stress-strain-temperature relationship of shape memory alloys

“…Matsuzaki (1996 and1997a) have concluded that no transformations may proceed in the stress range between a and cr and z is kept constant during the process of unloading and reloading. The stress-strain relationship and the …”

“…In other words, the partial derivative of the interaction energy with respect to the fraction of the martensite, døaM/dZ, represents the TDF during the martensitic transformation. As for the TDF, there exists a positive value, AGOM, at which both the austenitic and the martensitic phase are stable and the phase transformation proceeds along the two-phase equilibrium state Matsuzaki, 1996, and1997a), that is, (*PaM g1 -g2 + ce0 = i\GOM for the martensitic transformation. (13) Similarly, the TDF of the reverse transformation is given by a positive value of AGOA: (1) and (1 1), we obtain (e 2) = 01 -02 (*Pa…”

“…£02 the strain associated with the lattice structure of the martensite. We have introduced the specific interaction energy which is dissipated during the phase transformations Matsuzaki, 1996 and1997a):…”

“…Introducing an interaction energy in the Helmholtz free energy, the first two of the present authors Matsuzaki, 1996 and1997a) proposed a one-dimensional, isothermal pseudoelastic theory which is based on an energy theorem and thermodynamic laws. Deriving equilibrium states in the transformations, they examined stability of the equilibriums during both the transformation and formation of subloops, and theoretically proved that the transformations take place along the stable equilibrium state.…”

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“…In order to make use of the hysteresis of these SMA films or wires, it is important to understand these characteristics of SMAs and to predict their thermomechanical behavior accurately. Therefore, Matsuzaki and co-workers [2][3][4][5][6][7][8][9] have performed analytical studies on SMA's thermomechanical characteristics. Some numerical results will also briefly be described.…”