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A constitutive theory, which consists of the constitutive equation and the transformation kinetics, is proposed to describe the thermomechanical behaviors of the shape memory alloys. Simulation in Ti-Ni alloy proves a good applicability of the theory when the overall characteristics of the stress-strain-temperature relation and the recovery stress induced in the heating process are studied in the uniaxial state. IntroductionWhen a specimen in the shape memory alloys is stressed at a temperature, inelastic deformation is observed above a critical stress. The inelastic strain induced in the loading process, however, fully recovers during the subsequent unloading. The stress-strain curve, as a result, forms a hysteresis loop. The same material behaves very differently at lower temperature, since some amount of strain remains even after complete unloading. The residual strain, however, recovers if the specimen is heated. The former behavior is called the transformation pseudoelasticity or the superelasticity, and the latter the shape memory effect [1][2][3]. Intensive metallurgical studies have revealed that such behavior of shape memory alloys was closely connected with the thermoelastic martensitic transformation and its reverse transformation which progress under a certain thermal and/or mechanical circumstances [4-7].As any shape memory devices used under complicated thermomechanical conditions, phenomenological or macroscopic study is more helpful than metallurgical or microscopic study for predicting the behavior of shape memory alloys. Among studies so far carried out along this line, we could list the following pioneering attempts: Falk [8,9] first suggested that Landau's transformation theory [10] could be used to explain the temperature-dependence of stress-strain curves of the shape memory alloys; that is, the stress-strain curve can be derived as a consequence of the thermodynamic considerations if the form of Helmholtz free energy is chosen approximately. The scheme was actually demonstrated in In-Pb alloys by Nittono [11]. Muller and Wilmanski [12,13] established their theory based on the statistical physics, and calculated the stress, strain and temperature changes during the martensitic transformation [14]. Tanaka [15,16], on the other hand, employed the continuum mechanics with an internal variable to describe the transformation pseudoelasticity and the shape memory effect due to the thermoelastic martensitic transformation.In this study, the thermomechanical models of the material

This review article attempts to explain TRIP generally and its appearance in different materials. Continuum mechanics formulations are mainly used to explain this phase change phenomenon. An overview is given of the published literature which is often not very easily accessible. Technological aspects are presented, such as constitutive equations of materials showing TRIP. Aspects of material selection and future material design are also treated. This article contains 315 references.

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