PSI - Issue 18

Valerii Matveenko et al. / Procedia Structural Integrity 18 (2019) 12–19 Author name / Structural Integrity Procedia 00 (2019) 000–000

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1. Introduction Fiber-optic sensors, possessing a number of unique properties (Majumder et al. 2008), are successfully used in various structures and industries. This paper discusses fiber-optic strain sensors (FOSS) based on Bragg gratings written in a standard single-mode optical fiber. One of the problems with using Bragg grating sensors is the calculation of strains based on the information about the physical quantities recorded by the sensors. The main essence of this problem is that the relations between the physical quantities recorded by the sensor and the components of the strain tensor in the Bragg grating area (Lee 2003) have a unique solution regarding the strain value along the fiber only under the condition of uniaxial stress state in an optical fiber. The most promising applications of FOSS are related to their incorporation into the material at the stage of its technological production, for example, into a polymer composite material, concrete, or by gluing to the surface of the material. In these cases, as a rule, a complex-stressed state takes place in the optical fiber. Usually this issue is discussed for the FOSS embedded in the material. In a review (Kersey et al. 1997) it is noted that the embedded fiber Bragg grating (FBG) is subjected to complex stress state, and when calculating the strains, it is necessary to introduce calibration factors. Problems of calibration are discussed in detail in (Geert Luyckx et al. 2010; Di Sante 2015). Great opportunities for solving the problem associated with the calculation of strains in FBG on the basis of experimental data are associated with mathematical modeling. Various solutions to this problem using the methods of mathematical modeling are given in the works (Fan and Kahrizi 2005; G. Luyckx et al. 2010; Sonnenfeld et al. 2011, 2015). In FOSS, glued to the surface of the material, there may also be a complex stress state in the FBG area. In this paper, a methodology for the numerical evaluation of the error of strain values, calculated on the basis of information on the physical quantities, recorded by FOSS, glued to the material surface, and the experimental results related to the error estimation in calculating the strain values is presented. One of the important results of strain measurement is the possibility of identifying the occurrence and obtaining the quantitative information about the development of a defect in a controlled object. Among the works in this area, a significant place is occupied by studies related to the use of FOSS for recording the occurrence and development of delaminations and cracks in polymer composite materials. These studies are largely based on the analysis of changes in the shape of the spectrum of the reflected signal. For example, in the work (Yashiro et al. 2007) a new approach for monitoring the defect formation in carbon fiber reinforced perforated plastic with an embedded optical fiber with Bragg gratings is proposed. For this purpose, an experimental and numerical study of the process of defect formation and changes in the shape of the spectrum caused by defects was carried out. It was experimentally confirmed that the shape of the spectrum of embedded FBG sensors will change with the growth of defects. The proposed method for modeling the reflected spectrum taking into account defects is consistent with the experiments. Based on the analysis of the spectrum of the signal reflected from the FBG sensor: in (N. Takeda et al. 2005) during four-point bending tests, delaminations were recorded with an increase in their length; in (Okabe, Tsuji, and Takeda 2004) transverse cracks were investigated under the action of tensile loads; in (Yashiro et al. 2005) with quasi-static tensile tests of rectangular samples with side cuts of multilayered carbon plastics, predictions were made for various damage states; in (Jin, Yuan, and Chen 2019) in numerical simulation and experiment, changes in the spectra of sensors with non uniform deformations initiated by generated cracks were considered. It should be noted that in all these studies, the sensors were located in the zone of the defect. In this paper, numerical-experimental technique is considered, which allows, for a single-type loading, to ensure the registration of a defect, and in which the assumed zone of the appearance of a defect is determined as a result of numerical modeling of a stress-strain state. 2. Damage detection algorithm with the use of FOSS data Registration of the appearance and development of defects in materials based on information about the measured components of the strain tensor is associated with the following problem. During quasi-static deformation, the appearance of a defect causes changes in components of the strain tensor in the area defined by 3-5 characteristic defect sizes. This conclusion is confirmed by numerous experimental and numerical results and formulated as the principle of Saint-Venant (Timoshenko and Goodier 1972). Based on this, without preliminary information about the strain distribution, in order to guarantee the defect registration, it is necessary to provide in the observed object a measurement of the main components of the strain tensor by sensors that form a spatial grid with a step of 3-5 sizes of