A constitutive mathematical model has been developed that predicts the nonlinear thermomechanical behaviors of shape-memory-alloys (SMAs) and of shape-memory-alloy hybrid composite (SMAHC) structures, which are composite-material structures that contain embedded SMA actuators. SMAHC structures have been investigated for their potential utility in a variety of applications in which there are requirements for static or dynamic control of the shapes of structures, control of the thermoelastic responses of structures, or control of noise and vibrations. The present model overcomes deficiencies of prior, overly simplistic or qualitative models that have proven ineffective or intractable for engineering of SMAHC structures. The model is sophisticated enough to capture the essential features of the mechanics of SMAHC structures yet simple enough to accommodate input from fundamental engineering measurements and is in a form that is amenable to implementation in general-purpose structural analysis environments

Turner, Travis L.

NASA Technical Reports Server

16 NASA Tech Briefs, February 2004
ture enables the growth of 3C-SiC on the
basal plane via nucleation of 3C-SiC is-
lands, followed by lateral step-flow expan-
sion. Well-behaved thermodynamic con-
trol of polytype occurs in the absence of
surface steps, so that the film grows in the
cubic crystal structure rather than a hexag-
onal crystal structure. In experiments, the
step-free interface between the hexagonal
and cubic polytypes was found to elimi-
nate the double-positioning boundary de-
fects commonly found in previous 3C-SiC
heterofilms. However, it was also discov-
ered that the initial 3C-SiC bilayers must
be nucleated slowly to obtain 3C-SiC films
free of stacking-fault defects.
Figure 2 shows two 0.2-by-0.2-mm mesas
topped with 3C-SiC films nearly 2 µm thick
and thermally oxidized to reveal stacking-
fault defects. As indicated in the figure,
the mesas were grown with different initial
island-nucleation rates. It has been sug-
gested that what is needed during the ini-
tial stages of growth to obtain a defect-free
3C-SiC film is the single-island growth
mode, in which a single 3C island nucle-
ates and expands laterally to cover the
mesa before a second interfering 3C is-
land nucleates. It has been further sug-
gested that the multiple-island growth
mode, depicted at the bottom of the fig-
ure, is acceptable after the initial bilayers
of the 3C-SiC film have been grown in the
single-island mode. In experiments, it was
found that 4H-SiC/3C-SiC atomic lattice
spacing mismatch was at least partially re-
lieved, without generating stacking faults
that threaded to the surface of the film.
The step-free surface heteroepitaxy
process is believed to be applicable to
growth of heterofilms of materials other
than 3C-SiC. Further growth and charac-
terization experiments are in progress, in-
cluding experiments on the fabrication of
prototype 3C-SiC devices and attempting
step-free surface heteroepitaxy of GaN
films on 4H- or 6H-SiC substrates.
This work was done by Philip G. Neudeck
and J. Anthony Powell of Glenn Research
Center.  Further information is contained in
a TSP (see page 1).
Inquiries concerning rights for the commer-
cial use of this invention should be addressed to
NASA Glenn Research Center, Commercial
Technology Office, Attn: Steve Fedor, Mail Stop
4–8, 21000 Brookpark Road, Cleveland, Ohio
44135. Refer to LEW-17186.
GROWN WITH HIGH INITIAL
ISLAND-NUCLEATION RATE
GROWN WITH LOW INITIAL
ISLAND-NUCLEATION RATE
Figure 2. 3C-SiC Films were grown on flattened mesas, then thermally oxidized to reveal crystal de-
fects. The defect-free film shown on the right was made by use of step-free surface heteroepitaxy.
A constitutive mathematical model has
been developed that predicts the nonlin-
ear thermomechanical behaviors of shape-
memory alloys (SMAs) and of shape-mem-
ory-alloy hybrid composite (SMAHC)
structures, which are composite-material
structures that contain embedded SMA ac-
tuators. SMAHC structures have been in-
vestigated for their potential utility in a va-
riety of applications in which there are
requirements for static or dynamic control
of the shapes of structures, control of the
thermoelastic responses of structures, or
control of noise and vibrations. The pre-
sent model overcomes deficiencies of
prior, overly simplistic or qualitative mod-
els that have proven ineffective or in-
tractable for engineering of SMAHC struc-
tures. The model is sophisticated enough
to capture the essential features of the me-
chanics of SMAHC structures yet simple
enough to accommodate input from fun-
damental engineering measurements and
is in a form that is amenable to imple-
mentation in general-purpose structural
analysis environments.
SMAs exhibit thermoelastic martensitic
transformations. The interaction of tem-
perature and stress applied to an SMA can
be used to exploit the shape-memory effect.
An SMA can easily be deformed in the low-
temperature (martensitic) state and, if not
mechanically constrained or restrained,
can be returned to its original shape and
size by heating through its reverse-transfor-
mation temperature range; recovery in this
mode is denoted free recovery. If recovery
of the original size and shape is completely
prevented by mechanical constraint, then
the heating results in a large stress and the
recovery is said to be constrained. If the
SMA is neither completely free nor con-
strained but, instead, disposed to perform
work by deforming under load, then the
recovery is said to be restrained.
The model expresses the nonlinear
thermoelastic nature of an SMA in the
form of an effective coefficient of thermal
expansion (CTE). This form enables rep-
resentation of shape-memory behavior, on
the basis of either (1) measurement of the
effective CTE or (2) inference of thermal
strain from measured values of the recov-
ery stress and the modulus of elasticity.
The model captures the thermoelastic
nonlinearity of the SMA implicitly and
provides a simple means of including non-
linear thermoelastic effects of a matrix ma-
terial in an SMAHC structure. The model
can predict constrained and free recovery
implicitly and the combination of this
model with a model of nonlinear elasticity
can predict restrained recovery.
The constitutive equations for a given
SMA, SMAHC, or a larger structure that
incorporates an SMAHC as a substructure
Nonlinear Thermoelastic Model for SMAs and SMA Hybrid
Composites
This model captures essential mechanics with fundamental engineering property input.
Langley Research Center, Hampton, Virginia
https://ntrs.nasa.gov/search.jsp?R=20110016748 2019-08-30T17:42:17+00:00Z
NASA Tech Briefs, February 2004 17
can be derived, using the present model
as a basis, following a mechanics-of-mate-
rials approach or other suitable approach.
The present constitutive model, in combi-
nation with classical lamination theory,
has been incorporated into a finite-ele-
ment mathematical model and computer
code to enable modeling of static and dy-
namic responses of panel-type SMAHC
structures subjected to static and dynamic
thermal and mechanical loads. Loads that
have been considered include acoustic
pressures, acceleration forces, and con-
centrated forces. Phenomena that have
been investigated include control of ther-
mal buckling, thermal post-buckling, ran-
dom vibration, and acoustic transmis-
sion/radiation responses of structures
under constrained recovery. The constitu-
tive model and structural response for-
mulation have been validated against ex-
perimental measurements of thermal
buckling/post-buckling and random vi-
bration responses.
This work was done by Travis L. Turner of
Langley Research Center. For further in-
formation, access the Technical Support Package
(TSP) free on-line at www.techbriefs.com/tsp
under the Materials category.
LAR-16274
One of the major challenges for NASA’s
next-generation reusable-launch-vehicle
(RLV) program is the design of a cryo-
genic lightweight composite fuel tank. Po-
tential matrix resin systems need to exhibit
a low coefficient of thermal expansion
(CTE), good mechanical strength, and ex-
cellent barrier properties at cryogenic
temperatures under load. In addition, the
resin system needs to be processable by a
variety of non-autoclavable techniques,
such as vacuum-bag curing, resin-transfer
molding (RTM), vacuum-assisted resin-
transfer molding (VaRTM), resin-film in-
fusion (RFI), pultrusion, and advanced
tow placement (ATP).
To meet these requirements, the Ad-
vanced Materials and Processing Branch
(AMPB) at NASA Langley Research Cen-
ter developed a new family of wholly aro-
matic liquid-crystal oligomers that can be
processed and thermally cross-linked
while maintaining their liquid-crystal
order. All the monomers were polymer-
ized in the presence of a cross-linkable
unit by use of an environmentally benign
melt-condensation technique. This method
does not require hazardous solvents, and
the only side product is acetic acid. The
final product can be obtained as a powder
or granulate and has an infinite shelf life.
The obtained oligomers melt into a ne-
matic phase and do not exhibit isotropiza-
tion temperatures greater than the tem-
peratures of decomposition (Ti > Tdec).
Three aromatic formulations were de-
signed and tested and included esters,
ester-amides, and ester-imides.
One of the major advantages of this in-
vention, named LaRC-LCR or Langley Re-
search Center-Liquid Crystal Resin, is the
ability to control a variety of resin charac-
teristics, such as melting temperature, vis-
cosity, and the cross-link density of the
final part. Depending on the formulation,
oligomers can be prepared with melt vis-
cosities in the range of 10–10,000 poise
(100 rad/s), which can easily be melt-
processed using a variety of composite-
processing techniques. This capability
provides NASA with custom-made matrix
resins that meet the required processing
conditions for the fabrication of textile
composites. Once the resin is in place, the
temperature is raised to 375 °C and the
oligomers are cross-linked into a high-
glass-transition-temperature (Tg) nematic
network without releasing volatiles. The
mechanical properties of the fully cross-
linked, composite articles are comparable
to typical composites based on commer-
cially available epoxy resins.
LaRC-LCR can also be used in thermo-
forming techniques where short holding
times are desired. The resin can be used to
spin fibers, extrude thin films and sheets,
or injection mold complex parts. Al-
though LaRC-LCR has been developed to
meet NASA’s needs towards the develop-
ment of a next-generation launch vehicle,
other applications can be
envisioned as well. The
thermal and mechanical
behavior of this material
are ideally suited for elec-
tronic applications and
may find use in flexible cir-
cuits, chip housings, and
flip-chip underfills. An-
other area where thermal
stability and chemical resis-
tance are highly desirable is
the automotive industry.
Distributor caps, fuel tanks,
air-intake manifolds, rocker
covers, and ignition systems
are among the potential applications. The
low viscosity of this resin makes this mater-
ial ideal for coating applications as well.
Fine powders have been used in plasma-
spray applications, and well-defined thin
coatings were obtained. LaRC-LCR can
also be used as an adhesive. Lap-shear val-
ues of 3,435 psi (22,683 kPa) were easily
obtained. In contrast, these values are ≈20
times higher than those observed in com-
mercially available LCP resins.
This work was done by Theo Dingemans,
Erik Weiser, Tan Hou, Brian Jensen, and
Terry StClair at Langley Research Center
and funded under NASA’s Reusable Launch
Vehicle (RLV) research program.
This invention is owned by NASA, and a
patent application has been filed. An exclu-
sive license for its commercial development
has been granted to TICONA Inc. (Summit,
NJ). For further information, contact Diane
Hope at the Technology Commercialization
Program Office (TCPO), NASA Langley Re-
search Center, 3 Langley Boulevard, Mail
Stop 200, Hampton, VA 23681-2199. 
E-mail: d.l.hope@larc.nasa.gov. 
LAR-16079
Liquid-Crystal Thermosets, a New Generation of High-
Performance Liquid-Crystal Polymers
Liquid-crystal polymers can now be used as resins in textile composites.
Langley Research Center, Hampton, Virginia
Several Products made from LaRC-LCR include films, plaques,
foams, uniaxial carbon-fiber prepregs, and carbon-fiber compos-
ites.


Nonlinear Thermoelastic Model for SMAs and SMA Hybrid Composites

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