SAMPE Journal - March/April 2016 - 51

Feature Article
and can be described by an analytical beam solution;
this solution, however, does involve substrate
properties that are temperature-dependent, and
resin properties that depend on both temperature
and DoC. The shrinkage curvature component is the
difference between these three contributions, and
must be analyzed numerically to obtain the current
cure shrinkage strain, given the temperature, degree
of cure, and curvature-related shrinkage.
Figure 4 shows time histories of individual curvature
contributions during a BMS experiment on a 100 mm
beam with an aluminum substrate 0.50 mm thick, and
a Cycom® 5320-1 resin layer 1.95 mm thick, with an
initial degree of cure of 0.51. The measured curvature
shown is actually the instantaneous curvature less
the initial value, to simplify the plot. The DIC data is
largely free of noise, which suggests that the same
BMS test may be an excellent means of extracting CTE
data, as discussed in the next section. The thermal
contribution to the curvature, computed using resin
and substrate properties based on the instantaneous
temperature, introduces a small amount of oscillation
in the curvature because of fluctuations in the
temperature measurement. The shrinkage-related
curvature (labeled "measured - thermal - initial" in
the figure) inherits this variability.
An additional effect of the temperature
measurement is evident in the sharp peaks occurring
at approximately 8,000, 16,000, and 24,000 seconds.
The temperature record in our early experiments is
known to lag the DIC measurement. As a result, the
temperature-related modulus changes that occur
during the ramps, which are computed using the
lagging temperatures, also lag behind the measured
curvatures. For a brief period, then, the resin modulus
used in the analytical model is artificially high, and
significantly overestimates the magnitude of the CTEinduced curvature. Further experiments are planned
to resolve the timing of the two sets of measurements.
A slight increase in the actual curvature is present
in the measurement at these times, but this actual
change in curvature is an order of magnitude smaller
than that predicted by the model using the recorded
sample temperature. Fortunately, these anomalies
tend to occur at the end of constant-temperature
holds, when the reaction rate is quite small (Figure
5). Since the rate of cure shrinkage is driven by the
reaction rate, the contribution of these brief transients
to the total cure shrinkage strain is quite small. This
behavior does complicate the task of determining the
shrinkage rate coefficients, as discussed below.
SAMPE Journal, Volume 52, No. 2, March/April 2016

Figure 4. Curvature components versus time during BMS
experiment.

The shrinkage-related curvature is used in
conjunction with a detailed finite element model
of the BMS specimen to determine the actual cure
shrinkage strain in the resin versus time. The finite
element model (Figure 6) provides curvature data,
for a given temperature and degree of cure, for known
amounts of volumetric cure shrinkage strain. These
results are used in an inverse interpolation based
on the shrinkage curvature, to give the current total
shrinkage strain.

Figure 5. Time history of reaction rate during BMS
experiment.

Figure 6. Typical finite element model for curvature versus
temperature and shrinkage.

Table of Contents for the Digital Edition of SAMPE Journal - March/April 2016