PSI - Issue 32

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

199

6

a

b

 

 x , %

 

 x , %   0

5 10 25 50 75 100



E/E 1

1

0.1

0.2

 

 

 

 1

0.3



1

0.4

 

 

 

E/E 1

0.49

 

 

0.01

0.49

0.1 0.2 0.3 0.4  1

Fig. 6. Dependence of ε x on the ratio of elastic moduli E / E 1 and Poisson’s ratio ν of the plate at ν 1 = 0 . 3, t / t 1 = 1 and at the load P x = 1, P y = 0: a) as 3D wireframe; b) as contour plot.

At the first stage of the study we investigated the influence of mechanical characteristics of the plate material on the redistribution of the strain field at fixed mechanical characteristics of the substrate ( E 1 = const , ν 1 = 0 . 3). It was found that in this case, the mechanical characteristics E and ν of the plate material has the greatest e ff ect on ε x at the smallest plate thickness. In this study, we did not consider the plate thicknesses smaller than the substrate thickness ( t / t 1 ≥ 1). Figure 6 shows the dependence of ε x on the ratio of elastic moduli E / E 1 and the Poisson’s ratio of the plate ν at ν 1 = 0 . 3, t / t 1 = 1, and under the load P x = 1, P y = 0. The analysis of these results leads to the following conclusions. The orientation of the sensor with respect to the load has practically no e ff ect on the dependence of the redistribution of strain caused by the attachment of the FBG sensor substrate to the surface of the controlled structure. Poisson’s ratio of the material of the controlled structure also does not a ff ect the dependence of the strain redistribution when the substrate-bonded FBG sensor is pasted to its surface. Therefore, it makes sense to evaluate the changes in the value of ε x as a function of the ratio of the elastic moduli E / E 1 and the ratio of the thicknesses t / t 1 . Figure 7 shows the dependences ε x on the ratio of the moduli E / E 1 and the thicknesses t / t 1 at ν = ν 1 = 0 . 3 for two di ff erent load conditions: a) P x = 1, P y = 0; b) P x = 0, P y = 1. We also evaluated the influence of the substrate width l y at a fixed length l x . Figure 8 shows ε x as a function of the ratios of moduli E / E 1 and thicknesses t / t 1 at ν = ν 1 = 0 . 3 when the aspect ratio of the substrate is l y / l x = 0 . 3 for the same load conditions: P x = 1, P y = 0 and P x = 0, P y = 1. A comparison of the dependencies in Fig. 7 and Fig. 8 demonstrates that the width of the substrate a ff ects the strain redistribution relationship. The range of small values of ε x in Fig. 7 is larger than in Fig. 8. A model has been developed to analyze numerically the strain changes caused by the installation of substrates with fiber optic sensors on the surface of structures. The performed simulation has revealed an insignificant influence of the Poisson’s coe ffi cient of the material of the measured structure on the strain redistribution. The obtained results allow us to estimate changes in the structure strains due to the presence of fiber-optic sensors on its surface in terms of the relationship between the mechanical characteristics and geometrical dimensions of the structure and the contact surface of the sensor. The results obtained make it possible to determine the main characteristics of the structure, at which the installation of the substrate with the selected sensor does not introduce significant errors in the measured 5. Conclusion