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Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


Induced Transformation Behavior of a Polycrystalline NiTi
Shape Memory Alloy: Micro and Macromechanical Investigations
via in situ Optical Microscopy

L. Catherine Brinson
, Ina Schmidt
, Rolf Lammering

Mechanical Engineering Department, Northweste
rn University, Evanston IL 60208, USA,
Institute of Mechanics, University of the Federal Armed Forces, D
22043 Hamburg, Germany


An experimental investigation of the micro and macromechanical transformation behavior of
polycrystalline NiTi shap
e memory alloys was undertaken. Special attention was paid to
macroscopic banding, variant microstructure, effects of cyclic loading, strain rate and
temperature effects. Use of an interference filter on the microscope enabled observation of grain
es and martensitic plate formation and growth without recourse to etching or other
chemical surface preparation. Key results of the experiments on the NiTi include observation of
localized plastic deformation after only a few cycles, excellent temperature
and stress relaxation
correlation, a refined definition of “full transformation” for polycrystalline materials, and strain
rate dependent effects. Several of these findings have critical implications for understanding and
modeling of shape memory alloy beh

phase transformations, shape memory, NiTi, microstructure, optical microscopy


Shape memory alloys have been studied intensively for the past two decades with experimental
and theoretical investigations spanning topics from th
ermally induced variant formation

multiaxial prediction of mechanical response
. Much of the experimental work in the
materials literature has focused on the twinning structure of thermally induced martensite (e.g.
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


6, 16
), and on uniaxial thermomechanical r
esponse from the mechanics perspective (e.g.
). Notable macroscale exceptions in recent years include work by Gall et al

l loading states and McDowell et al

on nonproportional tension
torsion loading. Work
with in situ loading and microscopy is found less frequently, but these experiments offer a rich
understanding of the SMA response as they address both microstructural and macromechanical
response simultane
. Some examples of the latter are highlighted below.

The early 1990’s experiments by Abeyaratne, Chu and James

investigated biaxial response
of a CuAlNi single crystal. The specimen was martensitic and oriented such that one variant was
preferred in each of the loading directions. Their work highlights t
he reorientation between these
two martensitic variants when the loading is changed from one axis to another and focuses on the
fine substruture of martensite at the interfaces between variants. Accompanying modeling of the
Landau type was perform
ed to correlate with the experiments.

More recently, Vivet and Lexcellent

considered a similar biaxial loading experiment on
single crystal CuAlNi with the material starting in the austenite state. In addition to sequenced
uniaxial tests (complet
e load
unload cycles in the x
direction, then in the y
direction), they
performed unique nonproportional loading tests. Upon the addition of the y
direction load to a
constant x
direction stress, their results showed the anticipated decrease of the variant

with uniaxial x
loading, followed by increase of the variant preferred by uniaxial y
loading at a
critical stress value in the y

Work by Miyazaki and co
[4, 16, 30

have systematically examined the
crystallography and mechanical behavior of NiTi. In situ o
bservation of single crystal NiTi is
studied in
[4, 16, 30]
. Optical micrographic observations were performed to investigate the self
accommodating morphology during transformation and subsequently, during loading, the
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


ite variant coalescence to form the most favorable variant. Effects of temperature and
strain level on macromechanical behavior of polycrystalline NiTi was investigated in
, while
effects of cycling were examined in
. Cycling was shown to

alter the mechanical behavior
and optical microscopy revealed evidence of residual martensite near grain boundaries.

Polycrystalline NiTi is observed under mechanical loading in several papers using electron
microscopy. For example, stress induced marten
sitic transformation and plastic deformation in
NiTi alloys are investigated in

using transmission electron microscopy (TEM). The
t of the martensite
matrix interface and the formation of dislocations during the reverse
martensitic transformation induced by stress have been studied at low strain rates. In

microstructure of cold
drawn NiTi alloy
s has been investigated using TEM and high
electron microscopy. Of particular interest is the dominant twinning mode appearing in the
martensite variants at different loading stages. The anisotropy due to texture effects in cold
drawn NiTi sheet
s have been examined in
. The differences in stress
strain response for
rolling an
d transverse directions are examined by post
test TEM and identified to be due to
differing dominant detwinning/reorientation modes and dislocation densities.

A more macroscale approach with simultaneous imaging and stress
strain measurement was

by Shaw and Kyriakides
[35, 36]
. Here they used both a standard camera and a
thermal camera to capture the macro
transformation state of the material and
thermal signatures
with loading at different strain rates and under differing isothermal/adiabatic heat transfer
conditions. Their images of the specimen surface used the naturally forming oxide layer as an
indicator of transformation and showed striking m
transformations bands forming and
growing as the loading progressed. The thermal camera supported the results with evidence of
latent heat release during transformation. More recent work
[37, 38]

has examined the effects of
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


cycling on the macro transformation bands and has looked more closely at the evolution of the
band tran
sformation front during loading. The latter is shown to be heavily influenced by
geometric features of the specimens.

Inspired by the papers of Shaw and coworkers, the present study was undertaken to address
similar experiments at a different scale level

to investigate the correlation between the
microstructure of grains and variants and the macromechanical response of the material. Our
loading is uniaxial like their previous work, with load measurement and overall strain
measurement. Unlike Shaw and Kyri
akides, we do not measure localized strains with mini
extensometers, but relate results to the strain of the entire specimen length. For macroscopic
photographs of the transformation surface a digital camera is used, while an optical microscope
is used for

fine scale observations of microstructural changes as a function of loading
parameters. By using an optical microscope and a custom designed loading frame, we are able to
observe microstructures at the habit plane variant level while simultaneously obtain
macroscale transformation images and stress
strain data. While similar to some of the earlier
work by Miyazaki, the current work has yielded unique results on the relationship between
variant formation and macroscopic Lüders
like bands, localized perma
nent deformation and
strain rate effects. In this paper, results for NiTi polycrystalline specimens are given; results for
copper based polycrystals and CuAlNi single crystal can be found in a separate publication

Experimental Techniques

Specimen Preparation

For the experiments, NiTi specimens of two geometries were machined by wire
EDM from
1.57mm thick plates obtained from the NDC Corporation (SE
508, Ni55.6Ti(wt%)). See Figure
1. Specimen geome
try 1 was used for all tests reported here except those to very large
deformation (only results from figures 9 and 10 use specimen geometry 2). Individual specimens
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


were then heat treated by annealing at 750°C for one hour under low vacuum (approximately
.01mbar) followed by water quench; then heated again to 525°C for 8 minutes and again water
quenched. This heat treatment results in a grain size of approximately 60

m and an A

temperature of

13°C as measured by DSC. The annealed specimens were then p
olished with the
following procedure: as the surface was rough, both sides of the specimens were sanded using
papers of several different roughnesses from 220 to 1000 grit (on the FEPA or P
scale; US
CAMI scale from 220
500); the observation side of the sp
ecimen was then sequentially polished
with fine powder solutions (to 0.25

m) on a Struers Rotomat polishing machine.

Figure 1:

Geometry of two specimens used for experiments

Testing Stage

The testing stage was a custom designed horizontal loading device that holds the specimen for
viewing under a
standard optical microscope (Figure 2). A stepper motor drives a linear rail unit
with two joined ballscrews with opposite rotation direction. This unit controls the displacement
for both grips for the specimen. The maximum speed obtainable with the gear r
atios chosen is 30
mm/s. An LVDT (HBM W10TK) measures grip displacement on one of the grips. Both grips
are driven by the same ballscrew, mounted similarly and therefore assumed to move identically.
Control tests were performed to quantify the uncertainty

in the average strain measurement using
a single LVDT. In the control tests both grip displacements were measured simultaneously and
the error was shown to be less than 1% over the full working range of the LVDT, which is
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


adequate for our results. The as
ymmetric design with a ballscrew on only one side of the
specimen leads to an initial backlash at low stress levels. The set up was carefully calibrated and
results for displacements corrected with a linear approximation of the calibration curve, however
he values at very low stress levels (far below the transformation stress of the specimens) remain

Figure 2:

experimental set
up with loading stage shown in position with the optical microscope.

Special attention was required in design of sev
eral features of the loading device. Due to the
horizontal layout, the grips were supported with brass plates where the frictional resistance was
minimized. The grips were allowed to rotate freely in only one direction to allow for more
precise alignment o
f all the device elements. A movable stage was designed for the microscope
to enable movement of the objectives over any part of the specimen. The entire loading stage is
supported on four columns and is movable in the vertical direction in very fine degr
ees enabling
focus of the microscope even at 1000x magnification. When the microscope was moved or the
stage was moved during tests, very slight imperfections were observed in the load and/or
displacement sensor measurements. However the magnitude was smal
l enough (less than 10 N in
load) not to influence the experimental results. Although care was taken to design the device to
be as stiff as possible, several sources of small inaccuracies exist, in particular the frictional
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


surfaces between grips and brass

supporting plates, and tolerances of the driving screws and all

Optical Microscopy

Microscopy was carried out with a Leica DMRM microscope fitted with a digital video camera
(Canon XLS
1) with output received by a computer with specialized v
ideo card. In most cases
movies were taken of the specimen either at a single location during loading/unloading
sequences to observe variant formation in grains or images were taken at a particular strain level
moving the objective along the length of the
specimen to provide a picture of the transformation
state in different regions of the specimen.

An interference filter (IC objective prism B2 with polarized light) was used on the Leica
microscope which enhances surface relief contours. Even pristinely po
lished specimens, prior to
first loading, revealed most of the grain boundaries under this filter (see Figure 3), eliminating
the need for more elaborate etching treatments of specimens. In addition, as specimens were
cycled through several loading sequenc
es grain boundaries became more distinct. Martensitic
variants due to the surface angle changes were highly visible at all stages with use of the filter.

Figure 3:

Same location on NiTi specimen viewed prior to initial load sequence with (right) an
d without
(left) filter. Without the filter, only an oil mark is visible.

Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


Loading Sequences

Any given specimen was typically subjected to numerous loading cycles to view the evolving
microstructure with cycling. For all the experiments shown, displacemen
t control was used and
tests were performed at room temperature (25°C). Given the low A

temperature of the material,
all specimens were fully austenitic in the original unloaded state and stress
induced phase
transformation to martensite occurred during l
oading. In order to better observe the
microstructure at different states of transformation, in some loading cycles the loading was
temporarily stopped and the specimen held at constant displacement for several minutes while
photos/videos were taken of the

specimen surface, after which loading continued. A
representative stress
strain diagram of this type is shown in Figure 4. Note that the strain (and
strain rates) in this paper are specimen average values, calculated by total grip displacement
divided by
specimen gage length. There are large inhomogeneities in the strain fields along the
specimen length, as demonstrated by Shaw and Kyriakides

and also apparent here by the
localization of variant formation revealed in the microscopy. In Figure 4, the stress relaxation at
the displacement holds during loading (and the “anti stress relaxation” at the hol
ds during
unloading) are due to temperature effects, as discussed later. Some specimens were also tested in
typical ramp load
unload histories, with no pauses for microstructural viewing. Strain rates
ranging from 10

to 10


were used in the investiga
tions. For some specimens, temperature at
one or more locations was measured simultaneously with a thermocouple and correlated to
transformation and stress profiles.

Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


Figure 4:

Typical loading and unloading sequence for specimen allowing microstructural o
bservation at
different states of transformation. Typical location of first observation of martensite notated. Specimen
is NiTi polycrystal loaded at

= 4x10


Although experimental observations of SMA transformation can be found in the references cited
earlier, the simultaneous micro
macro scale observations here are unique and provide both new
results and are able to clarify or confirm h
ypotheses from earlier research. The relation between
macroscopic deformation bands and microstructural martensite will be introduced first. Then we
will discuss formation of “residual martensite”

areas of localized permanent deformation and
their growth

with increasing cycles

and consistency of variants with cycles. Finally, we will
address other observations, including stress relaxation and effect of strain rate.

Macroscopic Bands and Relation to Microstructural Martensite

With reference to the earli
er work of Shaw and Kyriakides
[35, 36]
, we first investigate the
formation of macroscopic transformation bands of martensite at relatively slow strain rat
es (here


and 10


are used) and relate this superstructure to the variants forming in the grains.
Both of these strain rates are slow enough to avoid the dramatic self
heating effects that can lead
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


to more homogeneous transformation behavior
. Consistent with
[35, 36]
, the results here at these
strain rates exhibit macroscopically localized transformation bands that propagate from the
gripped e
nds across the specimen. Although these bands macroscopically have similarities to
Lüders type bands, the deformation mode is quite different and is microscopically far from
homogeneous both inside and outside of the deformation bands as will be seen.

Figure 5:

Macrophotos of NiTi specimen tested at 4x10
. Top image is at 1% strain while lower image
is at 2.5% strain. Width of specimen 3mm. Boxes indicate location of enlarged images shown in
Figure 6, while the arrows indicate the extent of the mac
roscopic transformation band.

While Shaw and Kyriakides used the oxide layer on the specimen surface as a convenient
indication of large scale transformation, our specimens are highly polished and therefore have no
oxide layer. Using careful lighting, ma
croscopic images were obtained and adjusting the contrast
between light and dark regions enabled the macroscopic transformation bands to be seen. Figure
5 shows macrophotos taken at 1% and 2.5% strain and the transformation band forming initially
at the le
ft end of the specimen is distinctly visible. By 2.5% strain, a second band has begun on
the right end of the specimen and the left band has broadened considerably.

Microscopy on the same specimen during transformation reveals several very interesting res
First, for nearly all specimens tested, the first martensite plates appear in the specimen at
approximately 0.7% strain. These plates are isolated from one another and most likely appear in
grains that are optimally oriented for transformation given
the loading direction. In a scan of the
specimen length (covering approximately 10

grains) at 0.7% strain, approximately 10 grains
will be observed with 1
2 variants each. Note from Figure 4 that the formation of these initial
variants is just before the
knee in the stress
strain curve. This direct observation correlating
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


microscopic appearance of the first variants in grains to the macroscopic stress
strain curve
confirms earlier results
[40, 41]

that were based on macroscopic evidence.

At 1% strain, the macrophoto in Figure 5 shows a visible transformation band toward the
left end of the specimen and micrographs of this region (Figure 6, left) also show strong
n. More notable, however, the regions in the specimen center indicated to be pure
austenite in Figure 5, in fact contain significant martensitic variants throughout the grains (Figure
6, right). As the strain is increased, the martensitic variants continue

to form throughout the
specimen, although at a higher rate in the macroscopically observable transformation bands (see
Figure 7). Thus the macroscopic transformation bands seen via disturbance of the oxide layer on
most specimens indeed do denote regions
of high transformation; nevertheless, these results
indicate that transformation occurs outside of these bands to a significant degree.

Figure 6:

Micrographs in the transformation band (left) and toward the center of the specimen (not in
macroband) a
t 1% strain.

Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


Figure 7:

Micrographs at 2.5% strain in the heavily transformed band at left end of specimen (left) and
toward the center of specimen (right) where macrophotos indicate beginnings of transformation.

Returning to the macroscopic images
in Figure 5, in the photos and to the eye, the macroscopic
bands appear on this highly polished surface almost striped, with angled lines closely spaced
together. The striped nature of the surface of the specimen begins even at the first formation of a
roband (1% strain) and remains throughout transformation of the entire specimen. Beyond
strain levels of approximately 3% the distinct striped nature begins to degrade and be replaced by
a more uniform mottled appearance. Microscopy of a transformation ban
d region at 3% strain
reveals a similar striped microstructure (Figure 8). Here it is seen that the grains have
transformed more strongly in small bands approximately 100

m wide, separated from one
another by similarly sized bands where grains have transfo
rmed less and many grains remain
untransformed. This striped morphology may be due to geometric influences of the specimens,
as explained on a macroscale for NiTi strips in

Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


Figure 8:

artensite formation, 3% strain, at medium resolution revealing origin of stripes seen
macroscopically in transformation band.

A final feature of these micro
macro observations is a redefined meaning of 100% or “full”
transformation in a polycrystalline sp
ecimen. Here, tests on two separate specimens are
described, but the results are consistent with observations on all specimens tested. One specimen
was pulled to failure in a standard testing machine (to avoid potential damage to the microscope

while the second specimen was tested with microstructural observation in the load
hold pattern (as in Figure 4) to a high strain level, both at strain rate 10

. The
strain diagram of both tests is shown in Figure 9. Exact data overla
p is not possible due to
the different specimens used and small, but different, inaccuracies in each of the different
machines used. In particular, the specimen tested with microscopy was polished, while the
specimen tested to failure was not; the thin oxi
de layer remaining on the specimen surface for the
latter sample likely carried little load, although contributed to the cross
sectional area. Hence the
stress magnitude for the test to failure is potentially under
calculated. Note that at approximately

strain in both cases, the stress begins to sharply rise as the macroscopic indication of the end
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


of transformation in the specimen. Observation of the surface also revealed that the macroscopic
band traversed the entire specimen at that point. At this slo
west strain rate only one macroband
formed and propagated.

Figure 9:

strain curves: loading to failure and loading in a sequenced fashion to observe
microstructural evolution from zero to “full” transformation. Strain rate 10

Micrographs we
re taken along the specimen surface at each strain level yielding similar results to
those already presented (i.e., transformation was dominant in macro transformation band, but
some martensitic plates formed continuously in grains outside of the macro
d). In this
specimen however, loading continued to much higher strain levels. Figure 10 shows the same
location at several strain magnitudes. Note that the last picture is at a strain of 10%, well beyond
the “full transformation” point of this material. Si
milar images were compared at various
locations along the sample and taken together demonstrate that the “complete” transformation
state of this polycrystalline material is not 100% martensite, and likely lies around 60%

transformed. The approximate
volume fraction is determined based on surface metallography
only and is therefore a qualitative value due to possible differences in surface versus bulk
martensitic transformation.

Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


Miyazaki and co

mention remaining parent phase after the main transformation
plateau (stage I) in single and polycrystalline NiTi based on macroscopic evidence. Here, we
provide microstructural evidence for polycrystalline speci
mens that indeed the “full
transformation” corresponds to less than 100% martensite. Grains that are unfavorably oriented
never transform and even grains that are favorably oriented only transform partially, rarely
attaining 100% martensite in a grain. Thi
s latter result can be explained as follows: as
transformation begins in one particular grain, martensitic plates begin to appear in increasing
numbers as the stress is slowly increased; however, as the stress increases, neighboring grains
begin also to tr
ansform changing the local stress state from one favorable to continued
transformation in the original grain, to one unfavorable. Due to this sequenced transformation
behavior, variants become “locked” in each grain in turn and unable to transform fully, i
contrast to what is seen typically in single crystal samples. Figure 10 also demonstrates that the
processes of stress
induced martensite formation and plastic flow are largely sequential, with
very few additional martensite plates forming after the macr
oband has swept the specimen and
large scale plastic flow begins.

Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


Figure 10:

Microscope images at strain levels 0%, 2%, 4%, 10% showing “full transformation”. Note that
in last image, beyond full transformation point, microstructure indicates tha
t the specimen contains at
most 60% martensite due to “locking” of variant structure as sequential grain transformation occurs.

Formation of Residual Martensite with Cycling

With each load
unload cycle, a small amount of residual deformation remains in th
e material,
accumulating with increasing cycles. In our experiments, specimens strained from zero to 4%
strain each cycle (as in Figure 4) accumulated residual strain significantly faster, and thus for the
remaining results, specimens were cycled to a maxi
mum of 2% strain to prolong sample life. The
macroscopic effects of cycling manifest in the stress
strain diagrams similar to other well
documented cases
: the transformation
start stress decreases, the “strain hardening” slope
of the transformation plateau increases and the hysteresis decreases. These effects can be seen in
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


Figure 11, where seve
ral select cycles without the interruption of displacement holds at different
displacement levels are shown. Note that although the hysteresis loops for the three cycles shown
appear substantially different, only a 0.1% residual strain remains in the speci
men after cycle 9.
It is also noted that due to the somewhat large size of the grains in the samples tested, there may
be an increased propensity for slip at the grain boundaries. Results by Saburi


correlation between plastic deformation and grain size on initial pseudoelastic stress cycles.
Although samples with grain size similar to ours (50

m) are shown to exhibit normal
pseudoelasticity without slip in an initial cycle, these results explain the somewhat faster
accumulation of plastic deformation with cycling in our samples.

Figure 11:

Effect of cycling on the stress
strain diagram, showi
ng decreasing transformation stress,
increasing strain hardening, decreasing hysteresis. Symbols indicate approximate location of
macroscopic transformation stress; consistent 0.02% offset of linear portion of loading curve used for


of the micrographs taken at identical locations during different cycles are striking.
Figure 12 shows a compilation of micrographs of the same grains at the end of several loading
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


cycles. Figure 13 shows the same location at the 2% strain level with the m
artensitic variants
active in several cycles. Figure 14 shows a sequence of images in the same area at different strain
levels on two different cycles. Note that in all cycles, the final strain achieved was identical,
although the initial strain varied due

to small accumulating residual deformation. Several
features are notable from these images and are described in the following paragraphs.

First, after the first cycle, no difference is visible between the images in Figure 12. However, by
cycle 5, localiz
ed deformation is clear to see in the lower right grain and several other locations
in the image. This localized deformation increases in magnitude with each cycle, producing a
significant residual martensite image by cycle 15. In contrast to earlier work
by Miyazaki

where residual martensite was confined to the area around the grain boundary, these images
clearly show residual martensite effects spanning across entire grains. These long regions m
ay be
small retained martensite plates, also accompanied by localized slip as suggested by

Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


virgin specimen

after cycle 1

after cycle 5

after cycl

after cycle 15

Figure 12:

Accumulation of localized plastic deformation within the grains upon load cycling. Identical
locations imaged on virgin specimen and after four different cycles, specimen fully unloaded.

Note in comparison between Figures 12
and 13 that the localized deformation occurs in the same
direction and locations as the martensite plates visible at the 2% strain level. Upon unloading, the
plates largely disappear, but in certain grains each cycle results in additional localized permane
deformation near the variants (e.g. the lower right grain in Figure 12). In Figure 12, the grain at
the center
left shows no residual martensite even after many cycles. These results are typical of
image sequences captured at other locations on the spec
imens with respect to the effects of
cycling: the plastic deformation is localized along locations of active variants and occurs in some
grains while not in others.

In addition to the accumulating deformation with cycles, the consistency of variants with
was also examined. It is clear from images in Figure 13 that the active variants in each grain are
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


the same in each cycle (i.e., the same habit plane variant is activated each time), however the
exact spatial position of the variants changes from cy
cle to cycle. This result has important
implications for modeling. It is also seen that in general there is a slight increase in the number
of martensitic plates from cycle 1 to cycle 15.

Figure 13:

Micrographs of activated variants at 2% strain i
n one set of grains at different cycle numbers
(cycle 1, 6 and 10 from left to right). Note that although the same habit plane variants are activated
each loading cycle, the spatial position of the variants within the grains varies from cycle to cycle.

gure 14 also demonstrates that the spatial locations of active variants change from cycle to
cycle. However, here we also see that the first martensite plates to form do not necessarily form
at the site of a visible residual martensite plate, nor even nece
ssarily in a grain with residual
martensite. In both cycles, the first martensite plates to appear are marked with arrows in frame 2
(0.97% strain). Of these, several do occur at the location of residual martensite, while others
occur in grains free of res
idual martensite. In frame 3, the first martensite plates appear in the
outlined grain with significant residual martensite, also marked with arrows. Note that the
location of the first martensite in frame three does not coincide with location of an existi
residual martensite plate. In both cycles, the location of the active martensite plates in the
outlined grain vary significantly and are uncorrelated with the location of residual martensite

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Brinson, Schmidt, Lammering


Figure 14: Micrographs of activated variants at sev
eral strain levels in two different cycles. Location of
residual martensite noted with arrows in the outlined grain at 0% strain level. At higher strain levels,
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


arrows indicate formation of the initial martensite plates. Note that the first martensite plat
es do not
appear in a grain with residual martensite plates visible.

Linking the microstructural observations to the macroscopic response, the decrease of the
threshold stress to begin transformation (seen in Figure 11) is likely due to residual stresses
associated with the localized deformations: the defect sites perturb the local stress field, enabling
variants to form at lower macroscopic loads due to the added residual stress field. Note that due
to the evidence in Figure 14, the local stress states wi
ll be altered in a complex fashion such that
variant formation is not necessarily facilitated at a residual martensite plate. In addition, we
believe that the slight increase in variants with cycling may also be linked to the permanent
deformation that is
visible in the grains: as cycle number increases, the number of variants
needed to achieve the prescribed strain level increases due to the inability of the variants in the
damaged areas to achieve as high a strain as in the first cycle. This hypothesis ma
y also explain
the increasing strain hardening with cycles (Figure 11), as higher stress levels are required to
activate additional variants.

A final feature of transformation that was noted during the microscopy was the negligible impact
of scratches and

other defects on transformation. The NiTi specimens were challenging to polish,
often resulting in some scratching and/or pitting of the samples. We carefully observed such
defect regions during the testing and consistently results proved that these defec
ts had no impact
on transformation behavior. An example is shown in Figure 15, where both scratches and other
surface defects are visible. Note that in some grains, the variants formed pass directly through
the scratch; and in other grains, no transformati
on occurs in spite of the scratch or surface defects
near the grain boundaries. These results turned out to be beneficial to the experiments in that
surface defects could be effectively used to easily locate the same grains on the surface during

Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


Figure 15:

A transformed region of the specimen with scratches (marked by arrows) and other surface
defects due to polishing. Note that transformation is not affected by the surface defects: activated
variants pass through scratches and scratche
s can run through grains that never transform.

Temperature and Strain Rate Effects

All tests reported here were performed at room temperature, however the self
heating and self
cooling of the specimens due to latent heat at various strain rates was examin
ed. During the
loading sequences containing constant displacement holds, a stress
relaxation was observed as
seen earlier in Figure 4 for all tests. The magnitude of the stress relaxation decreased with
decreasing strain rate. The stress relaxation (and an
relaxation for unloading) stems from the
isothermal nature of the experiments due to the latent heat released in the specimen.
Correlation between stress level and latent heat has been reported widely for SMA materials
39, 46, 47]
, and has focused mainly on the increasing strain hardening seen for higher strain rates
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


can be explained by the increase of specimen temperature with transformation due to
latent heat.

In our experiments, we have taken a different approach and have measured the stress and
temperature changes during constant displacement holds during loading.

observations are made simultaneously. A schematic macroscopic stress
strain diagram
commonly found to describe SMA behavior is shown in Figure 16

note that such a
diagram does not reflect local non
monotonic stress
strain behavior, nor does it capture the often
higher initial nucleation stress. A transformation path for the loading case is depicted on Figure
16: as

the specimen heats due to the latent heat of transformation, the loading path diverts from
the isothermal line as indicated. At a constant displacement hold point, the temperature in the
specimen will slowly return to room temperature and simultaneously a

decay of the stress is also
seen, as less load is required to maintain a given transformation level at a lower temperature
(assuming iso
martensite fraction lines are parallel to the transformation zone boundaries).

Figure 16:

Section of a schematic tr
ansformation stress
temperature phase diagram for the loading case.
The nonisothermal loading path due to release of latent heat is shown. Midway through
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


transformation, the loading is stopped and the specimen held at constant displacement. The

and stress decay as indicated.

For several specimens, the temperature decay and stress decay was measured simultaneously.
Figure 17 shows the results of one typical test, performed at a strain rate of 3x10

. Strain rate
is chosen to be higher for
these tests in order to increase the effects of latent heat. Temperature
measurement is from a thermocouple located at the macroband location in this test. Since the
stress and temperature decay in tandem and approach equilibrium values at identical times,

it is
believed that the temperature decay after latent heat release is primarily responsible for the stress
relaxation observed in these specimens. The Clausius
Clayperon slope was measured for one
specimen with a value of 7MPa/K. This value coincides wel
l with other published values for
[46, 47]
. More detailed results of this nature are presented elsewhere

Figure 17:

Temperature and stress decay du
ring a constant displacement hold at 2% strain after loading
at 3x10

. Note that the time to equilibrium for temperature and stress are identical, indicating that
the temperature decay after latent heat release is the primary cause of the stress relax
ation seen.

From the simultaneous microscopic observations, it was found that the martensite volume
fraction and the variant structure in the grains remained constant during the time of the stress and
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


temperature decay for the constant displacement holds

during loading. Quite the opposite was
observed in holds during the unloading portions of the curve. Note that during unloading, latent
heat is absorbed by the material causing a decrease in temperature; consequently, during an
unloading pause, the temper
ature of the specimen is seen to rise toward ambient temperature. In
these cases, although again the temperature and stress data are in excellent agreement during
their rise, the number of variants within the grains is observed to decrease simultaneously
Figure 18). The additional conversion of martensitic variants to austenite can also be seen from
more macroscopic views, where it is observed that a macroscopic transformation band
significantly narrows or even disappears during the unloading pause.

Figure 18:

Micrographs of the specimen during a constant displacement hold during unloading, taken at
different times during the hold (identical location): left image at start of hold, right image 60 seconds
later. While the stress slowly increases and the

temperature rises back to room temperature during
the hold, additional martensite also converts back to austensite. These results are in contrast with the
constant martensite state of the specimen during loading pauses.

This asymmetry between loading and
unloading pauses indicates that although the loading
pauses for these specimens appear to be iso
martensite fraction, the unloading pauses follow a
martensite fraction path. A rationale for constant volume fraction results can be made
since the exp
eriments are kinematically driven: upon loading to a given displacement level, a
constant martensite fraction is required to sustain that strain magnitude and is not affected by a
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


relatively small temperature change. However the results from unloading paus
es cannot be
explained in this fashion. One possible mechanism for results in Figure 18 is that upon unloading
as the temperature drops some variants undergo a twin reconfiguration to decrease the strain
magnitude; upon heating in the unloading pause, thes
e twin related variants convert to austenite
with no change in strain. With optical microscopy it is not possible to obtain microstructural
evidence to support such a hypothesis, however. Thus, the reason for the asymmetry is as yet
unclear and warrants fu
rther study, underscoring the complex thermomechanical behavior of
shape memory alloy materials.

During the testing of specimens at different strain rates, typical macroscopic stress
strain curve
differences were seen: increase of transformation stress, i
ncrease of strain hardening and
decrease of hysteresis. These results are all tightly linked to the latent heat released by the
specimen upon transformation, as indicated by the stress relaxation experiments
. The
microstructural observations showed little differences for the various strain rates

the same habit
plane variants were formed in the grains at different strain rates, with spatial location differences
similar to repeat tests at the same st
rain rate. At the highest strain rate achievable in our set
we consistently captured a small amount of variant redistribution within the first 60 seconds after
the final displacement is achieved. The differences were small and usually consisted of a gi
martensitic plate within a grain splitting into two thinner plates. In testing of CuAlNi single

we observed dramatic variant redistribution at the high strain rates. Additional
of the polycrystalline NiTi at higher strain rates to further investigate the phenomenon is
warranted and will be pursued.

Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering



In this paper we examined the microstructural and macroscopic transformation behavior of
polycrystalline NiTi shape memo
ry alloys. The experiments were accomplished with a custom
built loading stage designed to allow simultaneous loading and viewing of transformation
behavior with an optical microscope. The results of the experiments clarify several important
issues regardi
ng the transformation behavior of shape memory alloys under loading at different
strain rates and changes due to cycling.

In contrast to perception that transformation occurs only in the macroscopically visible
transformation bands, the results here show
clearly that martensitic transformation occurs
throughout the material at all strain levels. Macroscopic bands are regions of more intense
transformation, but areas outside the bands are not martensite
free. The bands themselves are
shown to contain striat
ions of higher and lower transformation, especially in the earlier
transformation stages. Even at full transformation of the specimen, our results show that the
polycrystalline NiTi material is approximately 70% martensitic: the sequenced transformation of

grains within the specimen influence the local stress states such that variants become locked
and grains unable to transform further.

Low level cyclic loading of the NiTi specimens was also pursued which revealed significant
microstructural changes in

the material after as few as 10 cycles. Localized plastic deformation
occurs in the vicinity of the martensitic plates that form, with slightly increasing permanent
deformation each cycle. Although the macroscopic “permanent” strain is only 0.1% after 15
cycles, the amount of localized damage is highly visible at the grain level via the microscopy.
The variants activated in each grain were very consistent with cycles, varying only in exact
spatial location from one cycle to the next. However, due to the in
creased localized deformation,
additional variants are formed at each cycle, providing an explanation of the strain hardening
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


seen macroscopically. It was also demonstrated that although residual martensite plates likely
alter the local stress fields facil
itating transformation, the first martensitic plates do not typically
appear at the exact location of the residual martensite.

Strain rate effects were also examined and it was shown that the self
heating of the specimen due
to release of latent heat is t
he primary cause of stress relaxation during constant displacement
holds during testing. Microstructurally, it was observed that the stress relaxation during a loading
pause was iso
martensitic, while an anti
stress relaxation during an unloading pause inv
additional martensite conversion. It was also observed that the variants activated remained the
same at the various strain rates tested, however at the highest strain rate possible in our set
small redistributions of martensitic plates within gra
ins were seen after loading. This latter point
requires further investigation at higher strain rates to elucidate the mechanism.

The results of these experiments are important for understanding shape memory alloy
transformation behavior and some points wi
ll be of particular interest in modeling phase
transformations. Models that account for distributions of grains in a material, such as some
micromechanics models or finite element based approaches, should pay special attention to the
martensite distributio
n within the specimen, with respect to macroscopic banding and actual
grain transformation. The result that “full transformation” of the polycrystal is not 100%
transformed to martensite due to variant locking as the macro transformation band sweeps the
ecimen is also critical to consider in validation of micromechanics models. The almost
immediate presence of residual martensite in some grains will be potentially useful for
understanding and modeling damage accumulation in SMAs. And the confirmation that

rate effects are largely due to the latent heat in the specimen is encouraging and implies that
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Brinson, Schmidt, Lammering


accurate predictions on strain rate effects can be obtained by relatively simple thermo
mechanical coupling with appropriate heat transfer equations.


The authors would like to thank the USA National Science Foundation and the Alexander von
Humboldt Foundation (LCB), and the Bundesamt für Wehrtechnik und Beschaffung (RL, IS) for
partial support of this research. All authors express gratitu
de to Prof. Kreye and co
workers for
generous use of their equipment and technical advice during the course of the work.



Adachi, K., J. Perkins, and C.M. Wayman, The Crystallography and Boundary Structure of
oup Combinations of 18r Martensite Variants in Cu
Al Shape Memory
Alloys. Acta Metallurgica, 1988. 36(5): p. 1343


Saburi, T. and S. Nenno. The Shape Memory Effect and Related Phenomena. in International
Conference on Solid
Solid Phase Transform
ations. 1981. Pittsburgh, PA: Metallurgical
Society of AIME.


Saburi, T. and C.M. Wayman, Crystallographic Similarities in Shape Memory Martensites.
Acta Metal., 1979. 27: p. 979.


Miyazaki, S., K. Otsuka, and C.M. Wayman, The Shape Memory Mechanism As
with the Martensitic

Transformation in Ti
Ni Alloys .1. Self
Accommodation. Acta
Metallurgica, 1989. 37(7): p. 1873


Nishida, M., N. Ohgi, I. Itai, A. Chiba, and K. Yamauchi, Electron
Microscopy Studies of
Twin Morphologies in B19' Marten
site in the Ti
Ni Shape
Memory Alloy. Acta Metallurgica
Et Materialia, 1995. 43(3): p. 1219


Madangopal, K., The self accommodating martensitic microstructure of Ni
Ti shape memory
alloys. Acta Materialia, 1997. 45(12): p. 5347


Boyd, J.G.
and D.C. Lagoudas, A Thermodynamic Constitutive Model for the Shape
Memory Materials. Part I. The Monolithic Shape Memory Alloys". Int. J. Plast., 1995. 12: p.


Lagoudas, D.C., Z. Bo, and M.A. Qidwai, A unified thermodynamic constitutive model f
sma and finite element analysis of active metal matrix composites. Mechanics of Composite
Materials and Structures, 1996. 3: p. 153


Huang, M.S. and L.C. Brinson, A Multivariant Model for Single Crystal Shape Memory
Alloys. J. Mech. Phys. Solids,

1998. 46: p. 1379


Goo, B.C. and C. Lexcellent, Micromechanics Based Modeling of Two
way memory effect
of a single crystalline shape memory alloy. acta metall., 1997. 45: p. 727

Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering



Auricchio, F. and R.L. Taylor, Shape
memory alloys: modelli
ng and numerical simulations
of the finite
strain superplastic behavior. Computer Methods Appl. Mech. Engr., 1997. 143:
p. 175


Raniecki, B. and C. Lexcellent, Thermodynamics of isotropic pseudoelasticity in shape
memory alloys. European Journal of

Mechanics a
Solids, 1998. 17(2): p. 185


Siredey, N., E. Patoor, M. Berveiller, and A. Eberhardt, Constitutive equations for
polycrystalline thermoelastic shape memory alloys. Part I. Intragranular interactions and
behavior of the grain. Internati
onal Journal of Solids and Structures, 1999. 36(28): p. 4289


Gao, X., M. Huang, and L.C. Brinson, A Multivariant Micromechanical Model for SMAs:
Part 1: Crystallographic issues for single crystal model. Int. Journal of Plasticity, 2000. 16: p.


Huang, M.S., X. Gao, and L.C. Brinson, A Multivariant Micromechanical Model for SMAs:
Part 2: Polycrystal Model. Int. J. Plasticity, 2000. 16: p. 1371


Miyazaki, S., K. Otsuka, and C.M. Wayman, The Shape Memory Mechanism Associated
the Martensitic

Transformation in Ti
Ni Alloys .2. Variant Coalescence and Shape
Recovery. Acta Metallurgica, 1989. 37(7): p. 1885


Piao, M., K. Otsuka, S. Miyazaki, and H. Horikawa, Mechanism of the a(S) Temperature
Increase by Pre
Deformation i
n Thermoelastic Alloys. Materials Transactions Jim, 1993.
34(10): p. 919


Nishida, M., S. Ii, et al., New deformation twinning mode of B19 ' martensite in Ti
Ni shape
memory alloy. Scripta Materialia, 1998. 39(12): p. 1749


Liang, C. and C
.A. Rogers, One
Dimensional Thermomechanical Constitutive Relations for
Shape Memory Materials. J. of Intell. Mater. Syst. and Struct., 1990. 1(2): p. 207


Ford, D.S. and S.R. White, Thermomechanical Behavior of 55Ni45Ti Nitinol. Acta Mater.,

44: p. 2295


Miller, D.A. and D.C. Lagoudas, Thermomechanical characterization of NiTiCu and NiTi
SMA actuators: influence of plastic strains. Smart Materials & Structures, 2000. 9(5): p. 640


Gall, K., H. Sehitoglu, H.J. Maier, and K. Ja
cobus, Stress
induced martensitic phase
transformations in polycrystalline CuZnAl shape memory alloys under different stress states.
Metallurgical and Materials Transactions a
Physical Metallurgy and Materials Science, 1998.
29(3): p. 765


Lim, T.J
. and D.L. McDowell, Mechanical behavior of an Ni
Ti shape memory alloy under

torsional proportional and nonproportional loading. Journal of Engineering Materials
and Technology
Transactions of the Asme, 1999. 121(1): p. 9


Liu, Y., Z.L. Xie,

J. Van Humbeeck, and L. Delaey, Effect of texture orientation on the
martensite deformation of NiTi shape memory alloy sheet. Acta Materialia, 1999. 47(2): p.


Zheng, Y.F., L.C. Zhao, and H.Q. Ye, High resolution electron microscopy studies on

interface structure of deformed stress induced martensite variants in a Ti
Nb shape
Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering


memory alloy. Materials Science and Engineering a
Structural Materials Properties
Microstructure and Processing, 1999. 275: p. 271


Jost, N., Thermal fatigu
e of Fe
Ti shape
alloys. Materials Science and
Engineering a
Structural Materials Properties Microstructure and Processing, 1999. 275: p.


Fang, D.N., W. Lu, and K.C. Hwang, Pseudoelastic behavior of a CuAlNi single crystal
under u
niaxial loading. Metallurgical and Materials Transactions a
Physical Metallurgy and
Materials Science, 1999. 30(8): p. 1933


Abeyaratne, R., C. Chu, and R.D. James. Kinetics and Hysteresis in Martensitic Single
Crystals. in ASME IMECE. 1994. Chica
go: ASME.


Vivet, A. and C. Lexcellent, Observations and analysis of martensitic phase transformation
on CuZnAl single crystals. J. Phys. IV France, 1998. 9(Pr9): p. 411


Miyazaki, S., S. Kimura, et al., Shape Memory Effect and Pseudoelasticity
in a Ti
Ni Single
Crystal. Scripta Metallurgica, 1983. 17(9): p. 1057


Miyazaki, S., T. Imai, Y. Igo, and K. Otsuka, Effect of Cyclic Deformation on the
Pseudoelasticity Characteristics of Ti
Ni Alloys. Metallurgical Transactions a
urgy and Materials Science, 1986. 17(1): p. 115


Miyazaki, S., K. Otsuka, and Y. Suzuki, Transformation Pseudo
Elasticity and Deformation
Behavior in a Ti
Percent Ni
Alloy. Scripta Metallurgica, 1981. 15(3): p. 287


Jiang, X.P., M. H
ida, et al., In situ observation of stress
induced martensitic transformation
and plastic deformation in TiNi alloy. Materials Science and Engineering a
Materials Properties Microstructure and Processing, 1997. 238(2): p. 303


Zheng, Y.F
., B.M. Huang, J.X. Zhang, and L.C. Zhao, The microstructure and linear
superelasticity of cold
drawn TiNi alloy. Materials Science and Engineering a
Materials Properties Microstructure and Processing, 2000. 279(1
2): p. 25


Shaw, J.A. an
d S. Kyriakides, Thermomechanical aspects of NiTi. J. Mech. Phys. Solids,
1995. 43(8): p. 1243


Shaw, J.A. and S. Kyriakides, On the Nucleation and Propagation of Phase Transformation
Fronts in a NiTi Alloy. Acta mater., 1997. 45(2): p. 683


Iadicola, M.A. and J.A. Shaw, The effect of uniaxial cyclic deformation on the evolution of
phase transformation fronts in pseudoelastic NiTi wire. Journal of Intelligent Material
Systems and Structures, 2002. 13(2
3): p. 143


Shaw, J.A. and S.
Kyriakides, Initiation and propagation of localized deformation in elasto
plastic strips under uniaxial tension. International Journal of Plasticity, 1997. 13(10): p. 837


Brinson, L.C., I. Schmidt, and R. Lammering, Micro and Macromechanical Inves
tigations of
CuAlNi Single Crystal and CuAlMnZn Polycrystalline Shape Memory Alloy. Journal of
Intelligent Material Systems and Structures, 2002. 13(12): p. 761


Sun, Q.P., Z.Q. Li, and K.K. Tse. in Proc. of IUTAM
Symposium. 2001. Magdeburg,
ny: SMIA.

Submitted to JMPS, revised 12/2003

Brinson, Schmidt, Lammering



Liu, Y.N., Y. Liu, and J. Van Humbeeck, Luders
like deformation associated with martensite
reorientation in NiTi. Scripta Materialia, 1998. 39(8): p. 1047


Xie, Z.L., Y. Liu, and J. Van Humbeeck, Microstructure of NiTi shape memory a
lloy due to

compression cyclic deformation. Acta Materialia, 1998. 46(6): p. 1989


Funakubo, H., ed. Shape Memory Alloys. 1987, Gordon and Breach Science Publishers: New


Otsuka, K. and C.M. Wayman, eds. Shape Memory Materials. 1
998, Cambridge University
Press: Cambridge. 284.


Saburi, T., Ti
Ni shape memory alloys, in Shape Memory Materials, K. Otsuka and C.M.
Wayman, Editors. 1998, Cambridge University Press: Cambridge. p. 49


Leo, P.H., T.W. Shield, and O.P. Bruno, Tr
ansient Heat Transfer Effects on the Pseudoelastic
Behavior of Shape
Memory Wires. Acta metall. mater., 1993. 41(8): p. 2477


Lin, P.H., H. Tobushi, K. Tanaka, T. Hattori, and A. Ikai, Influence of strain rate on
deformation properties of TiNi sha
pe memory alloy. Jsme International Journal Series a
Mechanics and Material Engineering, 1996. 39(1): p. 117


Auricchio, F. and E. Sacco, A temperature
dependent beam for shape
memory alloys:
constitutive modelling, finite
element implementation a
nd numerical simulations. COMPUT
METHOD APPL M, 1999. 174: p. 171


Govindjee, S. and E.P. Kasper, Computational aspects of one
dimensional shape memory
alloy modeling with phase diagrams. Computer Methods in Applied Mechanics and
Engineering, 1999.

v 171: p. p 309


Ivshin, Y. and T.J. Pence, A Constitutive Model for Hysteretic Phase Transition Behavior.
Int. J. Eng. Sci., 1994. 32: p. 681


Bekker, A. and L.C. Brinson, Phase Diagram Based Description of the Hysteresis Behavior
of Shap
e Memory Alloys. Acta Mater., 1998. 46: p. 3649


Tanaka, K., S. Kobayashi, and Y. Sato, Thermomechanics of Transformation
Pseudoelasticity and Shape Memory Effect in Alloys. Int. J. Plast., 1986. 2: p. 59