One-dimensional pseudoelastic theory of shape memory alloys

Abstract

The one-dimensional isothermal pseudoelastic theory of shape memory alloys which the present authors proposed has been further exploited in order to clarify the thermodynamic meaning of the interaction energy introduced in the theory. From the equilibrium condition of the two-phase state, it is shown that the partial derivative of the interaction energy with respect to the phase fraction represents the thermodynamic driving force of the phase transformation. Functions for the interaction energy are derived from the definition of the driving force of the phase transformation in equilibrium. Analytical results predicted by the present theory agree well qualitatively with available experimental observations. Tanaka's transformation kinetics are also well modelled by the present theory.

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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.…”

“…Therefore, we have carried out a series of thermomechanical analyses of pseudoelastic hysteresis of SMA wires and films subjected to cyclic loading. The analyses are based on the lumped-parameter constitutive model of SMAs which was proposed by Kamita and Matsuzaki [2,3], introducing a general function of dissipation potential called the phase interaction energy function (PIEF). A preliminary analysis of damped oscillation of a simple mass-spring system connected with an SMA wire was presented in [5].…”

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“…To explain those experimental observations, Kamita and Matsuzaki of Nagoya University [80] have proposed a onedimensional pseudoelastic theory from the thermodynamic principle. An energy functional of the SMA is defined by the sum of the potential and an interaction energy which they have introduced to represent the energy dissipated as the work done by an interaction force deforming the lattice structure during the phase transformation.…”

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“…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. To exploit validity of the new pseudoelastic theory, they (Kamita and Matsuzaki, 1997b) also showed that the partial derivative of the interaction energy with respect to the phase fraction of the martensite corresponds to the thermodynamic driving forces for the phase transformation proposed by Patel and Cohen (1953), and how the new theory based on the interaction energy may model Tanaka's transformation kinetics (Tanaka, 1986;Tanaka et al, 1986). In the present paper we will examine the new pseudoelastic theory from a quantitative viewpoint, using experimental data on Ti-Ni shape memory alloy wires obtained for different temperature conditions by Tobushi and his coworkers (Tobushi et al, 1993;Lin et al, 1994).…”