Experimental Investigation And Constitutive Modeling For Thermal-Mechanical Properties Of Ni₄₇Ti₄₄Nb₉ SMA

Shape memory alloys(SMAs) have received extensive attention in recent decades for their unique pseudoelasticity and shape memory effect. NiTiNb alloy, as one important member of the NiTi-based SMAs, possesses extremely wide transformation hysteresis and excellent shape memory effect after pre-deformation(about 16%) at a specific temperature(Ms+30oC). With this property, the parts made of such alloy deformed at a lower temperature can conveniently be stored at room temperature, instead of being stored at a lower temperature, before being assembled and recovered by heating, which enables NiTiNb SMA to be used extensively as a kind of pipe-joint material. It has been noticed that it inevitably involves a certain amount of plastic deformation during practical application, while the plastic deformation affects obviously the inverse transformation temperature and the hysteresis of stress.In order to better utilize such kind of material, a lot of efforts have been made in the study of the thermal–mechanical properties of the material and the influencing effects. In this paper, based on the research of the experiment and constitutive models of SMAs in recent years, a systematic experimental study on the thermal-mechanical behavior of Ni47Ti44Nb9 SMAs is made and constitutive model is proposed, which takes into account the effects of plastic deformation and laminar microstructure, a micromechanical model of Ni47Ti44Nb9 SMAs is also built. The main achivements and conclusions in this paper are:(1) A systematic experimental study is made on the thermal-mechanical behavior of Ni47Ti44Nb9. The microstructure and the composition are obtained with the microscopic observations, the critical temperatures for forward and inverse martensitic transformation are measured with a differential scanning calorimetry(DSC), and the textures of the material tested are obtained with X-ray diffraction(XRD). The uniaxial tension and pure torsion at different temperatures and the subsequent heating-induced recovery are studied; the mechanical responses and the subsequent heating recovery of the specimens subjected previously to biaxial straining by various paths are investigated and compared with each other, and the martensite variants activated in the material are measured with XRD. It is shown that, the matrix is composed of different sized acicular austenite at room temperature, the Nb-rich phases are dispersedly distributed in the NiTi matrix; the stress-strain curves as well as the surface morphology of the specimens under uniaxial tension are significantly different from those under pure shear, but the critical transformation stresses are all increased with the temperature rises. The mechanical responses under biaxial straining and the subsequent heating recovery are path-dependent, and recovery of strain develops almost by the shortest path in the strain space. The martensite variants activated during uniaxial tension are different from those during pure torsion, and the variants activated during biaxial tension-torsion loading are the superimposition of those under pure tension and under pure torsion.(2) The constitutive models of the martensite and austenite are formulated based on a non-classical theory of plasticity and the modified phase transformation kinetics. Considering a SMA to be the compound of martensite and austenite, the deformation in the martensite can be considered of elasticity, transformation/reorientation and plasticity, and that in the austenite can be considered as elastoplasticity, then the constitutive model of the martensite and austenite can be built based on a non-classical theory of plasticity. In order to describe the effects of plastic deformation on the inverse transformation stress and temperature, the Tanaka’s transformation kinetics equation is modified.(3) A constitutive model is built for SMAs based on the laminar microstructure of the SMAs observed in experiment. The representative volume element(RVE) of a single SMA crystal is considered to be composed of martensite and austenite lamellas arranged alternatively, and the constitutive relationship of the RVE can be obtained by the consistency of the in-plane strain components, the equilibrium of the out-of-plane stress components, and the composition rules of the other stress and strain components. A SMA is considered as an aggregate of randomly oriented single grains and the constitutive description can be obtained with the conventional self-consistent scheme. The ferroelasticity and pseudoelasticity of some typical SMAs are simulated with the developed model and the results obtained coincide well with the experimental ones. The effects of plastic deformation on the inverse transformation stress can also be well replicated by the developed constitutive model.(4) A constitutive description is developed for NiTiNb SMA by assuming that a NiTiNb SMA is composed of NiTi matrix and dispersedly distributed spherical Nb particulate inclusions. The matrix is composed of martensite and austenite, and the constitutive model is obtained by making use of the constitutive relationships for martensite and that for the austenite, and the Voigt hypothesis. The micromechanical description for NiTiNb SMA can further be obtained with the Mori-Tanaka scheme. The response of NiTiNb SMA under uniaxial tension, under pure torsion and biaxial straining by three typical paths under at different temperatures are simulated, and the comparisons between the computed and experimental results show that the developed constitutive model can satisfactorily describe the main characteristics of the constitutive behavior of the material.