A Phenomenological Description on Thermomechanical Behavior of Shape Memory Alloys

Abstract

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

A semi-analytic analysis of shape memory alloy thick-walled cylinders under internal pressure

“…The solution was obtained by the plane stress assumption based on the two-dimensional form of Tanaka's constitutive relations [33]. He presented two different solutions for stress analysis that are called by him "closed-form-solution" and "exact solution".…”

Shape memory alloys as an effective tool to damp oscillations

“…The phase transformation was satisfactorily simulated using the Helmholtz free energy with a dissipative term. Tanaka [47] described the deformation change in terms of the variation of three factors: the stress, the temperature and the martensite volume fraction.…”

An Eulerian Model for Pseudoelastic Shape Memory Alloys

“…In Section 4.5, an isotropic material symmetry is postulated. Then, all quantities may be expressed explicitly in terms of the state variables h e , H, and n. The constants A i , B i , and C i introduced in (70) and (71) are chosen in agreement with [2,42] taking into account subsequent modifications [39,44] …”

“…The functions k a are subject to constraints that may be derived from (68) and (69), noting the implications of definition (64) of p f in terms of the mass fraction of martensite n. Based on [42], where the description of transformation kinetics proposed by Magee is adopted [43], the constants A i > 0, B i and C i ! 0 may be introduced to propose the equations [2] …”