SAMPE Journal - May/June 2020 - 29

and foil gage rosettes on both coupons were fitted
with separate linear trendlines. Importantly, it can
be seen that the principal strains calculated from
the fiber varies linearly with the FSG (Figure 10).
Table 2 shows the slope, the zero offset, the R2 values, and the root-mean-square-error (RMSE) for
both Coupons A and B.
The slopes for all comparisons are very similar, within 0.5% of each other, indicating that the
sensors respond repeatably across both coupons.
However, the slope value is not 1. This indicates
that either the gage factor relating spectral shift in
the fiber to strain is incorrect or that the gage factor relating resistance change in the foil rosette to
strain is incorrect. The fiber output has been calibrated using a traceable method, as described
in11. The known sources for foil gage error that are
applicable to this test are signal attenuation due
to lead wires and the interrogator being out of calibration. The FSG rosettes were hooked up in a twowire configuration where a four-wire configuration
would have taken better account of the lead wire
variations. Additionally, the acquisition system was
due for re-calibration. These factors could influence the strain output relationship between fiber
and FSG. However, the linear relationship between
the fiber and foil gage still holds.
In addition to determining the value of the
maximum and minimum strains on the part, the
orientation angle, j, was calculated. Since the
length of the coupon was orthogonal to the applied
moment, it was expected that the orientation angle would be 0°. Figure 11 shows that the calculated angle was indeed close to the anticipated value
once load was applied. Under the zero-load condition there was no consistent orientation (because
there are no principal axes). Under load, the fiber
rosettes calculated the direction of the loading with
+/- 4° accuracy.
Embedded Distributed Strain Rosette
The next step was to determine the distributed
principal strains and orientation angle across both
faces of a composite helicopter tail rotor blade
during load application. The results shown in Figure 12 to Figure 14 were calculated when the base
of the blade (far left) was fixed and the trailing edge
(bottom of picture) was lifted, resulting in torsion
along the length of the blade. A color map of the
strain data as directly measured along the fiber on
the suction side of the blade is shown in Figure 12.
The three measurement axes are clearly visible,
with one axis showing compression, one showing
tension, and the horizontal axis showing a strain
reading near zero.

w w w. s a m p e . o r g

Figure 10. Comparison of the principal strains calculated using the fiber
and foil strain gage rosettes throughout the loading range. The black line is
a linear fit through the data sets.
Slope
Coupon A; Fiber Rosette ε1 1.2801

Intercept (µε)

RMSE (µε)

-6.40

0.9998

3.96

Coupon A; Fiber Rosette ε2 1.2303

-5.29

0.9908

4.09

Coupon B; Fiber Rosette ε1

-5.55

0.9993

8.40

2.55

0.9965

2.62

1.2116

Coupon B; Fiber Rosette ε2 1.3895

Table 2. Trendline slope, intercept, R value, and RMSE for calculated princi2

pal strains on Coupons A and B.

The strain measurements from the suction side
of the blade were then separated into each measurement axes. Data from each measurement axis
was interpolated across the fiber rosette pattern as
shown below in Figure 13. Figure 13a shows the interpolated data from the horizontal measurement
axis, while Figures 13b,c show the interpolations
from the two angled axes.
Using this distributed map of strain measured
along three distinct axes, principal strains and orientation can be calculated at any point along the
blade using Equations 1 and 2 as explained previously. The final output of the software is shown in
Figure 14, where the distributed principal strains
are represented by arrows. The blue (inward point-

M AY/J U N E 2 0 2 0

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SAMPE Journal - May/June 2020

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