A relaxed-constraint model for the tensile behavior of polycrystal shape-memory alloy wires
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I. INTRODUCTION
SHAPE -memory alloy (SMA) wires have been used to control robotic arms and are also useful as microactuators and other smart-material applications. As each wire is usually very thin, its axial direction is always the principal direction for any control process. A unique feature of the SMA wire is that it can undergo a very large deformation over a small change of temperature and/or stress. This large strain is produced by the martensitic transformation. In a polycrystalline wire, such a transformation occurs in the constituent grains, and its precise amount is dependent upon the local stress and temperature of the grain. More specifically, transformation in the grain is driven by the reduction of its Gibbs free energy. Under thermomechanical loading, this energy consists of the mechanical-potential energy, which is associated with the internal stress, and the chemical free energy, which is associated with the temperature. While the temperature distribution over a polycrystal can be taken to be uniform (if the rate of temperature variation is sufficiently slow), the stress distribution among the constituent grains is always heterogeneous. Thus, in order to find the change of the Gibbs free energy and the extent of phase transformation in each grain, such a stress heterogeneity must be determined first. Determination of such an internal stress in a wire naturally differs from that in a bulk, for the diameter of the wire is so thin that it cannot possibly retain any significant amount of internal stress in the transverse direction. This is obviously not the case for a bulk material. Due to its large dimension in all three directions, determination of the internal stress of a grain in a bulk polycrystal Y.M. JIN, Graduate Student, and G.J. WENG, Professor, are with the Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, NJ 08903. Manuscript submitted May 25, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
usually can be accomplished by considering the problem of a single inclusion (grain) embedded in an infinitely extended matrix.[1] It is in this light that, in this article, we seek to formulate a micromechanical model to calculate the transformation behavior of a polycrystal SMA wire. The local stress of the constituent grains will be estimated first and then combined with temperature to determine the Gibbs free energy and the thermodynamic driving force for martensitic transformation of the grain. The transformation resistance force will subsequently be established, following consideration of the energy dissipation associated with the movement of the austenite-martensite interface. The balance of these two forces will lead to a kinetic equation that describes the evolution of the martensite phase at a given level of internal stress and temperature. Then, the transformation behavior of the polycrystal SMA wire under a pure thermal loading or a pure mechanical loading, or by a combination of the two, will be determined through an orientational average process over
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