Constitutive model for nanocrystalline NiTi shape memory alloys considering grain size effects and tensile-compressive asymmetry

Mechanical properties of nanocrystalline NiTi shape memory alloys (SMAs) change drastically with grain size. The present contribution develops a constitutive model to reproduce the grain size dependent superelastic behavior and tensile-compressive asymmetry observed in the experiments of nanocrystalline NiTi SMAs. Effects of grain size are incorporated in the developed model by introducing the intrinsic length scale accounting for the transformation hardening as well as the grain-core and grain-boundary phase. In this work, nanocrystalline NiTi SMA is regarded as a two-phase composite material made of inclusions of the grain-core phase dispersed in the grain-boundary phase acting as a matrix. A transformation function allowing for the description of fine-grain strengthening mechanism and tensile-compressive asymmetry is proposed. In the grain-core phase, the evolution law for transformation strain during the forward and reverse transformation is determined. Besides, the constitutive relation of the grain-boundary phase is assumed to be linearly elastic. Based on the equivalent secant bulk and shear modulus of the grain-core and grain-boundary phase, the stress-strain relationship of nanocrystalline NiTi SMAs is derived by using the extended Mori-Tanaka method. Comparisons between experimental and predicted results demonstrate that the proposed model has the ability to reproduce the grain size dependent deformation and asymmetric stress-strain behavior under tension and compression of nanocrystalline NiTi SMAs. In detail, it is found that critical transformation stresses for forward and reverse transformations, dissipation energy density, transformation strain hardening, and maximum transformation strain are sensitive to the grain size and stress states.