A robust macroscopic model for normal-shear coupling, asymmetric and anisotropic behaviors of polycrystalline SMAs

The aim of this article is to develop a robust macroscopic bi-axial model to capture self-accommodation, martensitic transformation/orientation/reorientation, normal-shear deformation coupling and asymmetric/anisotropic strain generation in polycrystalline shape memory alloys. By considering the volume fraction of martensite and its preferred direction as scalar and directional internal variables, constitutive relations are derived to describe basic mechanisms of accommodation, transformation and orientation/reorientation of martensite variants. A new definition is introduced for maximum recoverable strain, which allows the model to capture the effects of tension-compression asymmetry and transformation anisotropy. Furthermore, the coupling effects between normal and shear deformation modes are considered by merging inelastic strain components together. By introducing a calibration approach, material and kinetic parameters of the model are recast in terms of common quantities that characterize a uniaxial phase kinetic diagram. The solution algorithm of the model is presented based on an elastic-predictor inelastic-corrector return mapping process. In order to explore and demonstrate capabilities of the proposed model, theoretical predictions are first compared with existing experimental results on uniaxial tension, compression, torsion and combined tension-torsion tests. Afterwards, experimental results of uniaxial tension, compression, pure bending and buckling tests on rods and tubes are replicated by implementing a finite element method along with the Newton-Raphson and Riks techniques to trace non-linear equilibrium path. A good qualitative and quantitative correlation is observed between numerical and experimental results, which verifies the accuracy of the model and the solution procedure.