Thermomechanical characterisation and FEM simulation of the pseudoelastic behaviour of a NiTi alloy

Shape Memory Alloys (SMA) have the unusual property of being able to sustain and recover large strains (about 10%) without inducing irreversible plastic deformation and to remember a previous configuration and restore it with a temperature change. They show features that may not be found in materials traditionally used in engineering; as a consequence, they are a basis for innovative applications. These unusual macrobehaviour is due to a microscopic solid-solid phase transformation front austenite to martensite and vice versa. Due to the variety of potential uses for SMAs and the high interest in developing new applications, the ability to accurately model and analyse structures containing SMA components via a finite element procedure (FEM analysis) would be very attractive. The present dissertation aims to give a contribution to apply the Finite Element Method to design SMA components using 1-D theoretical and experimental models found in literature, in particular the Tanaka model. This model is composed by two equations: A constitutive law and a kinetic law. In the constitutive law the stress depends on deformation and fraction of martensite, in the kinetic law the fraction of martensite depends on stress and temperature. Moreover stress is related to strain by means of the Young Modulus, which is calculated as a weighted mean of austenite and martensite moduli. The model requires detailed material properties of the alloy. So, tensile tests were performed at constant temperatures (17°, 30°, 37° e 42° C), on nitinol (a Ni-Ti Shape Memory Alloy) orthodontic wires (Fig. 1,2,3). Constant temperature was obtained by a thermostatic bath. Water was heated by an electrical resistor (30°, 37°, 42° C) and constantly moved by an electro-mechanical mixer. The FEM software ANSYS was customized to simulate shape memory alloys features (fig. 4,5). The User Programmable Features (UPF) were used to calculate a pseudoelastic truss element. At each iteration the prediction of the stress from the previous step is used to calculate, in a separate iterative subroutine, the values and contribution of the fraction of martensite. In order to verify numerical results, the same equations were solved numerically with a MATLAB routine, not using FEM analysis. The results of the numerical analysis and FEM were coincident. FEM simulation were performed at the temperature of 37° C and 42° C (Fig. 6 and 7). A good correlation between FEM and experimental results were found.