Zk. Lu et Gj. Weng, A SELF-CONSISTENT MODEL FOR THE STRESS-STRAIN BEHAVIOR OF SHAPE-MEMORY ALLOY POLYCRYSTALS, Acta materialia, 46(15), 1998, pp. 5423-5433
Citations number
34
Categorie Soggetti
Material Science","Metallurgy & Metallurigical Engineering
In spite of the recent progress in the development of constitutive the
ory for shape-memory alloys (SMAs), no micromechanical model has been
developed to calculate the stress-strain behavior of a SMA polycrystal
from the behavior of its constituent grains. A self-consistent model
is developed for such a purpose. Using a recently developed micromecha
nical theory to describe the behavior of single crystals (Lu and Weng,
J. Mech. Phys. Solids, 1997, 45, 1905), the model provides a self-con
sistent relation to connect the stress and phase transformation strain
on the grain level with those on the polycrystal level. This relation
allows the phase transformation strain in each grain to be calculated
in accordance with its stress, and then, by an orientational averagin
g process, the overall phase transformation strain of the polycrystal
is determined. To further test the validity of the single crystal theo
ry, a micromechanical, crystallographic procedure is developed to calc
ulate the anisotropic phase transformation strains of a Ni-Ti crystal
under various directions of tensile loading; the computed results were
found to be in general accord with the experimentally measured values
. The self-consistent model is then applied to derive the stress-strai
n behavior of a Ni-Ti polycrystal at three different levels of tempera
ture, first above A(f), then between A(f) and A(s), and finally betwee
n A(s) and M-s, to illustrate its pseudoelastic behavior, shape-memory
effect and ferroelasticity, respectively. In each case the theoretica
l phase transformation strain of the polycrystal was in very good agre
ement with experiments. The ''work-hardening'' nature of the stress-st
rain curve at the later stage of phase transformation is also vividly
displayed by both theory and experiment. (C) 1998 Acta Metallurgica In
c. Published by Elsevier Science Ltd. All rights reserved.