A multiscale analytical model for superelastic deformation of gradient nano-grained NiTi shape memory alloys

A multiscale nonlocal continuum model is proposed to describe the superelastic deformation of gradient nano-grained NiTi shape memory alloys (SMAs). At the mesoscopic scale, the polycrystalline aggregate is regarded as a composite, i.e., the grain-interior (GI) phase is assumed to be a cuboidal inclusion embedded in a matrix of grain-boundary (GB) phase. An intrinsic energetic length and a gradient energy are introduced into the Helmholtz free energy of the GI phase. The criterion of martensite transformation (MT) is derived based on the principle of virtual power and second law of thermodynamics. The hindering effect of GB on MT in GI phase is addressed. By deriving the analytical solution of the proposed model and introducing a scale transition rule, the overall and local stress-strain responses of the specimen at the macroscopic scale are obtained. The prediction capability of the proposed model is verified by comparing the analytical solution with the experiment. The influences of the distribution form for the grain size (GS) on the superelastic deformation of gradient nano-grained NiTi SMAs are further predicted and discussed. The analytical form and low computational cost of the proposed model make it an appropriate theoretical tool to design the gradient nano-grained SMAs with desired mechanical property.