ON GRAIN SIZE DEPENDENCE OF STRESS HYSTERESIS IN SHAPE MEMORYALLOY POLYCRYSTALS:ROLE OF MATERIAL INTERNAL LENGTH SCALES

摘要

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 simplestone dimensional (ID) heterogeneous structural hierarchy,a series of non-convex and nonlocal 1D continuum elements are employed to model the micro-instability and the macroscopic stress hysteresis of the material under uniaxial quasistatic stretching.Three characteristic length scales (specimen size L,grain size I and intrinsic material length g) of a bulk polycrystal are imbedded in the I D 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 (l)= (l/g).For a given specimen size L,the hysteresis decreases rapidly at either very large or small values of (l).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 ID 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 ID and 2D models agree qualitatively well with the recent experimental observations on the stress hysteresis in nano-grained superelastic NiTi polycrystals.