A Simplified Multivariant SMA Model Based on Invariant Plane ...

the original model and simplified models respectively. These results show that both
models are consistent with the main trends of stress-strain relationship in <strong>SMA</strong>s.
However, several significant discrepancies can be seen between the original model
predictions (Figure 6) and the experimental data (Figure 5). The magnitude of the
transformation stresses are nearly three times that of the experimental results; two of the
orientations are unable to recover the strain pseudoelastically upon unloading; and the
moduli differences are clearly missing due to the isotropy assumption. With a move to
the simplified model (Figure 7), the results are strikingly improved and very close to the
experimental results in terms of transformation stresses, strains and moduli. Note that the
parameters F c and B for the model were determined from the experimental result for T3
and there are no other free parameters in the model. Using values from the literature for
the anisotropic elastic constants (see Table 2b), the ratio of maximum to minimum
moduli for the three orientations shown is predicted to be 6.9, while the experimental
value is 5.9.
It should be mentioned that the original <strong>Multivariant</strong> model often predicted appearance of
multiple variants: for the simulations here the variants active in cases T1, T2 and T3 were
(17 & 18), (6 & 15) and (6, 8, 13, 15, 18, & 19) respectively. Experimentally however, a
final product of one variant is expected in most cases, although in directions with special
symmetry several variants are sometimes seen (Lexcellent et al., 1996). With the
simplified <strong>Multivariant</strong> model, the variants predicted in cases T1, T2 and T3 are (17 &
18), (6) and (8) respectively. Since all the materials simulated have 18R structure, the
variant order is same as Saburi and Wayman (Saburi et al., 1980) except here we identify
1(+) as 1, 1(-) as 2, …, and 6'(-) as 24. Angles between the tension direction and the
intersection direction of the habit plane and the sample surface are also measured in the
experiment and compared to prediction based on Type I or Type II twinning for a 2H
system (Shield, 1995). Since the material is at a temperature 17° higher than the Af
(23°C), the CuAlNi material should transform between the parent and a 18R martensite
phase which does not have twinning substructure (Otsuka and Shimizu, 1981; Sun et al.,
1999). Therefore using lattice parameters (table 2b), we calculated the habit plane
16