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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To estimate the error using relation (5) for calculating the strains, the following scheme of numerical experiments is proposed. The calculation of the stress-strain state in a plate with glued optical fiber is given. One of the results of the calculation is the strains 1 2 3 , ,    in the Bragg grating area. Based on these strains, the values of the change in the wavelengths of the reflected spectrum * 1   and * 2   are calculated by the formula (3). Further, these quantities are taken as experimental data and, based on the relation (5), the strain values along the optical fiber exp1 3  and exp 2 3  are calculated. The difference in the values * 1   and * 2   and respectively exp1 3  and exp 2 3  will demonstrate that the conditions of uniaxial stress state in the optical fiber are not satisfied, while the difference in the values exp1 3  and exp 2 3  from 3  will show the error in the strain calculation based on the relation (5). The simulation was carried out for optical fibers glued to the plate surface along and across its length when the plate was loaded with tensile forces. Fig. 2 shows the cross section of the sample for which numerical calculations were performed. The geometric characteristics of the adhesive bonding are determined by two sizes b and a. For numerical calculations, a finite element method was used.

Fig. 2. Sample cross-section with optical fiber glued to the surface.

In this case, if the optical fiber coincides with the direction of external forces, the numerical experiment gives a difference of values 3  and exp1 3  (or exp 2 3  ) within 1%. Table 3 shows the results of numerical experiments for the optical fiber glued across the external load with various parameters of the adhesive layer. In this table d –diameter of optical fiber, 1 2 3 , , o o o    ,   * 1 o   ,   * 2 o   are the values of 1 2 3 , ,    , * 1   and * 2   , divided by the value of the specified displacement U 0 . Errors 1  and 2  are determined by the following expressions   exp1 1 3 3 3 100%        ,   exp 2 2 3 3 3 100%        , where exp1 3  calculated by the formula (5) with 1    , while exp 2 3  with 2    . The calculations results show that when simulating an experiment with the results of numerical modeling, the error in determining the strain values by the formula (4) can be significant. Along with numerical modeling, experimental studies were carried out, which were performed in two stages. At the first stage, the optical fiber was mounted on the sample surface in such a way that there was glue free area in the vicinity of Bragg grating. This provides a uniaxial stress state on the optical fiber section with FBG, and the reasonable use of relation (5) to determine the strains from experimental data. It should be noted that in the FBG, which does not interact with the material, it is necessary to ensure a preliminary tensile strain. This will allow to register compression strains that do not exceed the preliminary tensile strain in absolute value. At the second stage of the experiment the FBG area was glued. The results showed that the experimental strains values  x  y obtained using relation (5) were different from the calculation results of the sample under tension within 10%. At the same time, the data from sensors glued and not glued to the surface were different by 3.5%. These results, in comparison with the results of a numerical experiment, give good reasons for using relations (5) to calculate strains based on experimental information from FBG sensors mounted on the material surface.