Micromechanical Constitutive Model Of Single Crystal NiTi Shape Memory Alloy

Shape memory alloys (SMAs) are known for the shape memory effect and superelasticity(pseudoelasticity). SMAs have the feature of high work density, high damping coefficient, temperature and stress sensitive and can be employed for vibration isolation, sensation and actuation. For these reasons, SMAs have wide application in fields such as aerospace, automotive and robotics. NiTi-based SMAs have an important position in biomedical field for its good biocompatibility. A well-developed SMA constitutive model is thus indispensable for its application in various fields.A superelastic single crystal model for SMAs is developed in this article assuming that only one martensitic variant is activated during phase transformation. Micromechanics based homogenization method is applied to the phase mixture so that the single crystal can be treated as homogeneous material. The model only considers recoverable martensitic transformation which is determined by the crystallography theory of martensitic transformation. Helmholtz free energy of single crystal is composed of the elastic strain energy, the interaction energy and chemical energy. The interaction energy takes linear form of the martensite volume fraction. Thermodynamic driving force is derived from the Helmholtz free energy. Phase evolution equation is obtained by assuming the thermodynamic driving force to be constant during phase transformation. Martensitic variant is determined according to the maximum transformation work principle. Phase evolution equation in conjunction with the stress-strain relations with internal variables constitute the constitutive equation of SMA single crystal. One-dimensional analytical stress-strain relation for single crystals is also obtained.Stress-strain curves of single crystals under uniaxial loading in different directions are simulated based on the one-dimensional analytical stress-strain relation, results show the characteristic of tension-compression asymmetry, softening and orientation dependence. The single crystal model is extended to polycrystalline materials using Taylor's assumption, simulation results agree well with the experimental data. The model is implemented into finite element code with the ABAQUS user material subroutine UMAT, numerical examples show the ability of simulating the superelastic behavior of structures.