Superelastic Constitutive Model Of The Cyclic Behavior Of NiTi Alloy

Because of its unique super elasticity and shape memory effect, NiTi shape memory alloys is widely used in aerospace, transportation, and biomedical and other fields. However, these devices will be inevitably influenced by cyclic loading. In order to improve design of shape memory alloy components and assess its reliability, it is necessary to deeply analysis superelastic deformation characteristics of shape memory alloy under the condition of cyclic loading and the constitutive model which is suitable for engineering application is established.Based on the assumption of laminated micro structure from single crystal martensite phase transformation, the ideal condition of the interface structure is used to build constitutive relation of superelastic of the austenite phase. Using interfacial relations and average relation of two phases, the local stress and strain of representative volume unit can be converted to the overall stress and strain. Helmholtz free energy of two phase is composed of the elastic strain energy and chemical energy. Gibbs free energy is obtained by Legendre transformation, the drive force of phase transformation are obtained by differential expression of Gibbs free energy. Three new state variables are introduced:critical stress, cumulated residual strain, cumulated martensite volume fraction. Using the critical stress, we build the equation between the driving force and cyclic number N. The driving force is used as a material constant which control forward phase transformation and reverse phase transformation in a load for every time. With cumulated residual strain, cumulated martensite volume fraction we obtain single crystal constitutive model under the condition of cycle loading. By Taylor assumption,the polycrystal constitutive model is constructed. In the end this model under the cyclic loading is used for numerical simulation, the simulation results show that we can capture the main superelastic characteristics of the hysteresis loop under the condition of cycle loading, the critical stress and cumulative residual strain changes along with the number N of cycles. So this model can provide certain help for predicting the mechanical properties of NiTi alloy in practical application.