SAMPE Journal - May/June 2020 - 24

FEATURE / FIBER OPTIC SENSING
how these basic shapes can be extrapolated to form
distributed rosettes. HD-FOS can be used both to
determine distributed principal strains across a
complex geometry through an extended rosette
pattern and also for structural health monitoring
when embedded in a part. The value of the distributed rosette compared with standard embedded
sensors is that the rosette will allow the user to accurately determine the magnitude and direction of
the maximum and minimum strains anywhere in
the part. In this way, the true strain profile resulting
from a defect can be detected and characterized regardless of the location or orientation of the damage. This would be an extension of current applications where continuous, embedded strain sensing
provides crucial information about the initiation
and growth of mechanical defects4,5. This work culminates with embedding a distributed fiber optic
rosette in a helicopter tail rotor blade. The objective of this paper is to provide engineers, scientists,
and technicians a new and effective way of testing
and analyzing composite parts.
BACKGROUND
Strain Rosette Theory
Measuring principal strains and orientation is often of interest to engineers since these quantities
can be used to predict the onset of failure and
failure location. The orthogonal principal strains,
denoted e1 and e2, are the measure of the maximum and minimum strains existing in the measurement plane at a given point. The orientation,
j, represents the angular rotation of the maximum
and minimum strains from the arbitrary axis along
which the strain measurements were taken. A minimum of three independent strain measurements
are needed to calculate e1, e2, and j. Historically,
these measurements have been taken with foil
strain gage (FSG) rosettes6.

The strain state of an infinitesimal cubic element in 3-dimensional space can be fully described
with no less than 6 independent strain quantities:
3 normal and 3 shear. To simplify the calculation
process, engineers tend to look at the strains on
only one face of the 3-dimensional element. This
2-dimensional view of the strains acting on the
cuboid is referred to as the state of plane strain and
reduces the number of independent strain measurements needed to fully characterize the element
to three, as shown in Figure 1a7.
It is important to keep in mind that the x and
y axes are arbitrary relative to the maximum and
minimum strain values. However, a new set of axes,
x' and y', can be created which do align with the
directions of the maximum and minimum strain
(principal strains) as shown in Figure 1b. Once the
element is aligned with the principal strains, the
shear strain goes to zero. The two principal strains
are perpendicular to each other and offset from the
original x/y coordinate system by angle j. By taking
three independent strain measurements around a
point of interest, the principal strains, e1 and e2, and
the orientation angle, j, can be calculated6,7.
High Definition Fiber Optic Sensing (HD-FOS)
The key technology that has enabled this research
is high-definition fiber optic sensing (HD-FOS).
HD-FOS uses optical frequency domain reflectometry (OFDR) to turn commercially-available optical
fiber into a distributed sensor capable of measuring strain or temperature every 0.65 mm along its
length. A typical optical fiber used for this type of
sensing application is a single-mode fiber consisting of three layers. A germanium-doped fused silica
core is surrounded by a pure fused silica cladding.
The core/cladding strand is often coated with a
polymer (acrylate or polyimide) to improve handleability. A difference in the refractive index be-

Figure 1. (a) Plane strain element showing normal strains, ex and ey, and
shear strain, gxy. (b) Plane strain element showing maximum and minimum
strains, e1 and e2, and the orientation, j.

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SAMPE Journal - May/June 2020

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