A micro-macro description for pseudoelasticity of NiTi SMAs subjected to nonproportional deformations

A micro-macro constitutive model is developed and applied to the prediction of the pseudoelasticity (PE) of NiTi shape memory alloys (SMAs) subjected to nonproportional loadings. It is based on the work by Gall et al. and takes into account different elastic properties of the austenite and martensite. In the constitutive model for a single crystal, the activation of forward and inverse martensitic transformations and the volume fraction of each of the 24 martensite variants (MVs), and the interaction between the MVs are considered. The constitutive behavior of polycrystalline NiTi SMAs is obtained by assembling that of single crystals of different orientations with finite element method (FEM). The corresponding numerical algorithm and FEM model are developed, in which an additional step is adopted to get rid of the MVs that may irrationally be activated during transformation calculation, which directly reduces the dimension of the Jacobian and enables the convergence and stability of the numerical implement of the model, especially in the cases of complex multiaxial nonproportional deformation. A thin-walled cylindrical model is suggested for finite element analysis, in which the texture microstructure in the materials formed during the cold-drawn processes can be considered. It is shown that the MVs activated under tension are different from those under compression, and when subjected to shear deformation the MVs activated contain those appearing during tension, and more MVs activated may account for the larger slope in the shear stress-strain curve. The PE of NiTi SMAs subjected to uniaxial strain and nonproportional strain by some paths in ε−γ/3 plane is simulated, and the satisfactory agreement between the simulated and experimental results demonstrates the validity of the approach developed.