PSI - Issue 32

Andrey Yu. Fedorov et al. / Procedia Structural Integrity 32 (2021) 194–201 A.Yu. Fedorov et al. / Structural Integrity Procedia 00 (2021) 000–000

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Hong et al. (2016) provides a review of current developments and applications of FBG sensors for health monitoring of key geotechnical structures, including slopes, piles, and soil nail systems. Possible technical di ffi culties with the use of FBG sensors for geotechnical monitoring are discussed. In the article by Anoshkin et al. (2016), the example of a rectangular plate with ”butterfly” shaped cuts made of polymer composite material was concidered to demonstrate that with the use of fiber-optic strain sensors embedded in the material, it is possible to measure the gradient strain field. Matveenko et al. (2020) presented a technique for detecting the onset and development of local material damage based on the strain values measured by a limited number of fiber-optic sensors and the results of numerical simulation of the stress-strain state. Interest in these sensors and their fast-growing applications to di ff erent engineering facilities is due to a number of advantages they o ff er, including small size, resistance to environmental factors and corrosion, insensibility to electromagnetic interference, short response time, in-line location of several sensors and some others. At the same time, a justified commercial application of fiber-optic strain sensors requires solving a number of new problems. One of these problems is related to the evaluation of strain redistribution caused by the incorporation of sensors into the monitored structure. Fiber-optic strain sensors can be embedded in the material of the structure or located on its surface. In the second option, the most common sensor design is that of an optical fiber mounted on a substrate of metallic or polymeric materials, which, in turn, must be rigidly attached to the surface of the controlled structure. In this case, it is natural to expect that the installation of this substrate on the structure surface will lead to a local redistribution of strains near the installation site. In the last decades, there have been dozens of papers dealing with the estimation of strain transfer from the material of the measured structure to the core of the optical fiber. As a rule, these are the analytical studies, in which three- (or more) layer models based on certain assumptions are used to estimate the characteristic features of strain transfer between the host material and the embedded optical fiber. Ansari et al. (1998) developed a simplified analytical three layer concentric model to estimate the actual strain level based on the interpretation of measurements made with the fiber optic sensors (with protective coating) embedded in the material. The mathematical expressions developed in the framework of this model were used to evaluate the level of strain losses within the protective coating of the optical fiber, and the amount of strain transferred to the optical fiber core depending on the mechanical properties of the fiber core and the protective coating, and the gauge length of the optical fiber. A more advanced n -layer concentric model (Li et al. (2009)) makes it possible to estimate the amount of strain transferred to the optical fiber core for a fiber optic sensor placed in a adhesive filled steel tube embedded in a homogeneous material, as well as for a fiber optic sensor embedded in a multilayer composite. The five-layer (Wu et al. (2014); Shen et al. (2018)), six-layer (Wang et al. (2012)), seven-layer (Falcetelli et al. (2020)) analytical models were proposed to analyze the strain transfer from the structure material to the core of the substrate-bonded FBG sensor located on the surface of the structure. These models also provide analytical formulas for estimating the relationship between the strain in the core of the FBG sensor and the strain in the measured structure. More detailed review of these (and other similar) analytical models can be found in the introduction to the article by Falcetelli et al. (2020). The authors of Shen et al. (2018) in order to simplify the analysis of performance a substrate-bonded FBG sensor, split whole process of strain transfer into two parts: 1) strain transfer from the substrate to the fiber core, and 2) strain transfer from the measured structure to the substrate. Thus, the total amount of strain transfer (as %) for a substrate-bonded FBG sensor is evaluated by taking into account the strain transfer ”losses” during the two processes. In present paper, in order to determine the strain changes introduced by the installation of the substrate with fiber optic sensor, we consider only the second process. We propose a mathematical model to estimate changes in the strain fields and present information on changes in the strain tensor components in the zone of substrate location depending on the ratio of the mechanical characteristics of the substrate and the material of the controlled structure for di ff erent dimensions of the structure and under di ff erent loading conditions.

2. Some information about fiber optic sensors based on the fiber Bragg grating

A Bragg grating is a distributed reflector within the core of an optical fiber. When light is allowed to pass from a source with a broadband spectrum through an optical fiber, part of the light wave is reflected from the Bragg grating (Fig. 1). The resonant wavelength of the reflected spectrum λ ∗ depends on the refractive index of the optical fiber n and the length of the period of the the Bragg grating L λ ∗ = 2 nL .