PSI - Issue 54

V.P. Matveenko et al. / Procedia Structural Integrity 54 (2024) 218–224 Matveenko V.P., Serovaev G.S., Kosheleva N.A., Galkina E.B../ Structural Integrity Procedia 00 (2023) 000 – 000

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Strain measurements using FBGs are based on recording the shift of the reflected optical spectrum relative to the initial, unloaded state. The shift of the FBG spectrum is most often determined by its resonant wavelength. When the FBG is subjected to a uniaxial stress state and a uniform strain distribution along the grating's length, the reflected spectrum shifts to one side or another without changing its shape. In this case, determining the resonant wavelength is straightforward and unambiguous. However, the presence of significant transverse strains in the FBG region can induce birefringence and spectrum distortion [5], potentially impacting the accuracy of strain measurements. Another critical factor that influences the shape of the reflected FBG spectrum is the presence of a strain gradient along the length of the grating. In study [6], the influence of the strain gradient on the shape of the FBG spectrum is demonstrated using numerical modeling of the FBG spectrum based on the coupled-mode theory. It is stated that the spectrum broadens as the strain gradient increases. In study [7], the effectiveness of various algorithms for determining the shift of the reflected FBG spectrum was analyzed, considering various scenarios for FBG spectrum shape distortion. An experimental study of the reflected spectra of FBGs with lengths of 2, 5, 10 mm, inscribed using a phase mask and subjected to a strain gradient is given in work [8]. The authors conclude that the spectrum width increases with an increasing strain gradient and suggest the possibility of mitigating the strain gradient's influence by using shorter FBGs. Study [9] presents the results of measuring the strain of a sailboat's composite element during bending using embedded FBGs. The authors attribute the observed error in FBG measurements to the presence of a strain gradient along a 10 mm long FBG. The strain gradient in the area where the FBG is located can arise due to the structural geometry or the presence of defects, such as cracks [10], or due to the structural features of the material. The influence of the material structure on the occurrence of local strain inhomogeneities is most pronounced for composite materials. In study [11], the influence of non-uniform strain distribution in a composite material with twill weaving on the reflected spectrum of FBGs of different lengths is examined. The non-uniform strain field, resulting from the material's structural features, was measured using the Digital Image Correlation (DIC) method. The study demonstrates that the shape of the reflected spectrum of a 1 mm long FBG is minimally affected by the strain gradient in a unit cell of the material. However, the readings from such an FBG are local and do not reflect the averaged strain pattern of the material. Increasing the length of the FBG allows for the acquisition of average material strain readings. However, for such sensors, the presence of a non-uniform strain distribution along the grating length is significantly more pronounced. The solution to the inverse problem of reconstruction a non-uniform strain distribution based on the reflected FBG spectrum using the genetic programming algorithm is given in work [12]. This paper presents a study of the influence of the strain gradient along the length of the FBG on the shape of the reflected spectrum of the grating. Unlike most studies that employ a cantilever clamped beam to implement a strain gradient, a more effective geometric configuration of the samples is proposed to create a strain gradient at the same level of external load. The research was carried out for FBGs with lengths of 5, 10 and 15 mm. FBGs fabricated by using two inscription technologies are considered: the phase mask method (5 and 10 mm), which requires removal of the protective coating in the FBG area with subsequent recoating, and point-by-point inscription with a femtosecond laser, which allows FBGs to be recorded in the core of the optical fiber through the protective coating, maintaining its integrity. The paper highlights the importance of accurate positioning of FBGs when studying the influence of a strain gradient on the FBG spectrum and proposes an approach that employs distributed FOSs based on Rayleigh scattering to precisely determine the location of a point sensor on a sample. 2. Sample manufacturing To implement a strain gradient along the studied FBGs, it is necessary to select the shape of the sample and the type of loading in such a way that the distribution of strains along the sensor is controlled and that such sample allows studying FBGs of different lengths. This research focuses on FBGs with a length of 5, 10 and 15 mm, inscribed in a single-mode germanosilicate optical fiber. The optical fiber has a diameter of 125 μm and is protected by a 12 μm thick polyimide coating. FBGs with a length of 5 and 10 mm were inscribed using a UV source via the phase mask method. This technique involves removing the optical fiber’s protective coating and its subsequent reapplication. A 15 mm long FBG was inscribed with point-by-point method using a femtosecond laser which doesn't require the removal of the protective coating.