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Previous investigations have shown that the wavelength of the FBG response is closely related to the physical properties of the grating, such as the spacing and the refractive index; the refractive index is affected by the stress, and the Grating Geometry (GG) of the grating is the key factor that influences the stress distribution [15, 16]. Moreover, the high-order mode degeneracy (as the Raman spectral lines) also contributed to the spectral feature [17]. Figure 4b illustrate that with a crack length of 6.0 mm, the number of the subordinate peaks decreased. At a crack length of 9.0 mm, the crack was close to the observation point, and the original peak was completely altered due to the strain gradient field along the grating, as shown in Figure 4c. The behavior of the spectrum is different from the two-component fibers due to the waveguide effect. When the crack reached a length of 12.0 mm, the spectrum was almost completely different as shown in Figure 4d, and the wavelength was longer than that of the tension-compression combination of the initial peak, as shown in Figure 3b.
The strain field was subjected to the stress distribution along the grating, and the grating was stretched out. In addition, it was subjected to the Euler-Bernoulli beam dynamic equations under the cyclic loading. Then, the stress was concentrated into the grating, and the stress concentration is proportional to the strain gradient field along the grating. The strain gradient field ahead of the crack tip along the grating corresponded with the crack tip-FBG distance. A broadening is anticipated due to the strain field, which changes along the grating, leading to a chirp. The wavelength and the spectrum width of the transformation spectrum were increased from 14.3 nm to 25.1 nm and from 1.3 nm to 5.4 nm, respectively. A broadening is anticipated due to the strain field, which changes along the grating, leading to a chirp. Thus, the number of the subordinate peaks increased, the spectrum wavelength enlarged from 1530.7 nm to 1530.9 nm, and the spectrum width broadened from 0.8 nm to 1.2 nm. In addition, the subordinate peaks are more obvious, which are located at a higher wavelength, illustrated by comparing the blue and green curves in Figure 3b.
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