Shape-memory alloys exhibit strongly nonlinear
thermomechanical response associated with
stress- or temperature-induced transformations of
their crystalline structure. These reversible transformations
lead to the special properties of superelasticity
and shape memory; see (Wayman and
Duerig, 1990; Sun and Hwang, 1993) for a brief
illustrative description of these properties. Nitinol,
a nearly equiatomic NiTi alloy originally brought
into practice by Buehler and Wiley (1965), is one
of very few alloys that are both superelastic and
biocompatible; moreover, the temperature range
within which Nitinol superelasticity is exhibited
includes human body temperature (Duerig et al.,
2000). As a result, Nitinol is now widely used in
* Corresponding author. Tel.: +1-510-486-5798; fax: +1-510-
486-4995.
E-mail address: roritchie@lbl.gov (R.O. Ritchie).
1 Present address: Materials Science and Technology Division,
Lawrence Livermore National Laboratory, University of
California, Berkeley, CA 94720, USA.
0167-6636/$ - see front matter
2002 Elsevier Ltd. All rights reserved.
doi:10.1016/S0167-6636(02)00310-1
Mechanics of Materials 35 (2003) 969–986
www.elsevier.com/locate/mechmat
biomedical devices such as endovascular stents,
vena cava filters, dental files, archwires and guidewires,
etc.
Both the superelasticity and shape-memory
effects are induced in Nitinol by reversible, displacive,
diffusionless, solid–solid phase transformations
from a highly ordered austenitic (simple cubic,
B2) crystal structure to a less ordered martensitic
(B190, monoclinic) structure. The stress-induced
austenite-to-martensite transformation is effected
by the formation of martensitic structures which
correspond to system energy minimizers. Although
24 variants of the less symmetric martensitic phase
can be formed by the same crystal of parent austenite,
it has been experimentally observed that only
a few variants are typically active and fully resolve
the stress/shape change (Miyazaki et al., 1989; Gall
and Sehitoglu, 1999). During the martensiteto-
austenite (reverse) transformation, all variants
transform back to the same parent phase.
Most of the mechanical testing on polycrystalline
Nitinol found in the literature has been performed
on wires and is thus one-dimensional. As a
result, most phenomenological constitutive models
are based on uniaxial data, oftentimes extended to
three-dimensions in an ad hoc fashion. Hence,
there is little confidence that three-dimensional
models can accurately describe the material response
under complex loading experienced in
Nitinol devices. Very little information exists on
the multiaxial loading/unloading of Nitinol and
even less on tubes which are used as the starting
material in the manufacture of critical devices such
as endovascular stents; to our knowledge, only
three previous studies, all on thick-walled tubing,
are available (Miyazaki et al., 1989; Lim and
McDowell, 1999; Helm and Haupt, 2001).
The present work focuses on the biaxial testing
of thin-walled tubes chosen to minimize the gradient
in the torsional strain along the radial direction.
Three distinct biaxial stress-loading paths
are explored under isothermal conditions. The resulting
data are compared to the results obtained
by numerical simulation of polycrystalline Nitinol
response based on an extension to polycrystalline
response and to finite deformations of a threedimensional
single-crystal model by Siredey et al.
(1999).
The organization of the article is as follows: the
experimental protocol and the testing setup are
described in Section 2. The experimental results
are documented in Section 3. These are followed
by discussion and comparison to numerical simulations
in Section 4 and concluding remarks in
Section 5.
2. Experimental procedure
2.1. Materials
Nitinol tubing (Ti 49.2 at.%, Ni 50.8 at.%) was
received from NDC (Fremont, CA), with a 4.64
mm outer diameter and 0.37 mm thickness. The
tubing was cut into 75 mm long specimens and
ground down along the 25 mm long center test
section to an outer diameter of 4.3 mm in order to
obtain an hourglass shape and minimize endeffects
during testing (Fig. 1). Thus, the wall thickness
in the gauge section was reduced to 0.2 mm,
resulting in a thickness-to-radius ratio of approx-
Fig. 1. Schematic illustration of the NiTi specimen (not to
scale).
http://www.lbl.gov/ritchie/Library/PDF/Nitinol_MechMat.pdf

The specimens were subsequently
heat-treated at 485 C in air for 5 min and then
water-quenched to bring the austenite finish temperature
slightly below room temperature. This
treatment produces a complex microstructure
consisting of equiaxed low-angle subgrains of approximately
1 lm in size within irregularly shaped
parent grains of approximately 25 lm in size. The
heat treatment also yields extremely fine Ni-rich
precipitates of Ni4Ti3 and Ni14Ti11 within the NiTi
matrix. The subgrain boundaries and the precipitates
make dislocation movement difficult; thus
they are important in achieving optimum superelasticity.
The precipitates also play an important
role in the ‘‘fine-tuning’’ of the transformation
temperature, which is critical in achieving desired
superelastic properties. Also present in the microstructure
are roughly equiaxed and insoluble
Ti4Ni2O oxide particles of a size up to approximately
1 lm.
The nature of the microstructure makes both
optical and electron microscopy very difficult,
producing complex and difficult to interpret images.
In fact, an additional complicating factor is
that the stresses due to polishing tend to produce
martensite, and, even in electropolished surfaces,
triaxial constraint is lost, leading to a modification
of the hysteresis and thus again, martensite artifacts
are observed. A full microstructural analysis
is deemed to be beyond the scope of this work. For
the present experiments, it is sufficient to note
that optical metallography of the tubing cross
section has confirmed that there are approximately
8–15 grains traversed through the wall thickness
http://www.lbl.gov/ritchie/Library/PDF/Nitinol_MechMat.pdf