On grain size dependence of stress hysteresis in shape memory alloy polycrystals: Role of material internal length scales

In this paper, a multiscale continuum model is proposed to study the effect of grain size on the macroscopic dissipative response of shape memory alloy polycrystals during isothermal thermoelastic phase transition. In the simplest one dimensional (1D) heterogeneous structural hierarchy, a series of non-convex and nonlocal 1D continuum elements are employed to model the microinstability and the macroscopic stress hysteresis of the material under uniaxial quasistatic stretching. Three characteristic length scales (specimen size L, grain size l and intrinsic material length g) of a bulk poly crystal are imbedded in the 1D chain model and their important roles in the macroscopic dissipation are quantified. It is shown that that the specific energy dissipation or the width of the stress hysteresis is governed by two nondimensional ratios N (=L/l) and l̄ = (1/g). For a given specimen size L, the hysteresis decreases rapidly at either very large or small values of l̄. In particular, it vanished when the grain size is reduced to the nano-scale where the grain size and the interface thickness become comparable. The above predictions of the 1D model are reproduced in two-dimensional (2D) nonlocal numerical experiment on the energy dissipation during multiple domain evolution in a heterogeneous strip. The predictions of the 1D and 2D models agree qualitatively well with the recent experimental observations on the stress hysteresis in nano-grained superelastic NiTi polycrystals.