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

normal, invariant plane shear direction, magnitude of the shear and transformation strains
for the 18R system, shown in table 2b. The predicted angles between the tension direction
and the intersection direction of the habit plane and the sample surface are shown in table
3. Agreement between prediction and data is quite good with the exception of the highly
symmetric direction T3, where the transformation strain levels of several potential
variants are very close. The variants with largest transformation strain will show up in the
single crystal calculation since we are using a maximum work criterion and all variants
are under same stress state. The model predicts variant 8, with a habit plane angle very
different from the experimentally observed value, note, however, that a minor change in
lattice parameters can cause selections of variants 6,15,18 or19 (with angles very close to
the experiments). For such a symmetric loading direction, it is very likely that a small
amount of misalignment of or imperfection in the specimen may change the observed
variant from one to another, or high resolution microscopy during loading would reveal
presence of several, nearly equivalent variants.
There are only a few triaxial loading experiments which have been performed to
investigate the effect of three dimensional stress states on martensitic transformation in
<strong>SMA</strong>s. Jacobus et al. (Jacobus et al., 1996) investigated the effects of triaxial loading in a
polycrystalline Ni-Ti <strong>SMA</strong>. Lim and McDowell (Lim and McDowell, 1999) investigated
the response of a Ni-Ti <strong>SMA</strong> specimen under axial-torsional proportional and non-
proportional loading. Gall et al. (Gall et al., 1998) investigated triaxial loading in a
polycrystalline Cu71Zn25Al4 (wt%, ∆V/V ≈ -0.3%) <strong>SMA</strong> (shown in figures 8 and 9).
Under uniaxial loading, it was found that the compressive stress level required to
macroscopically trigger the transformation was 34% larger than the required tensile
stress. The triaxial tests produced effective stress-strain curves with critical effective
transformation stress levels in between the tensile and compressive results.
The effective stress-strain plots at a temperature above Af under a loading rate of dε/dt =
10 -4 s are shown in figure 8. Curves for the effective stress at the onset of transformation
vs. the hydrostatic stress at the onset of transformation are shown in figure 9. The
effective stress and effective strain are calculated by:
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