Damage detection algorithm based on using surface mounted fiber-optic sensors on Bragg gratings

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Procedia Structural Integrity 18 (2019) 12–19

25th International Conference on Fracture and Structural Integrity 25th International Conference on Fracture and Structural Integrity

Damage detection algorithm based on using surface mounted Damage detection algorithm based on using surface mounted fiber-optic sensors on Bragg gratings fiber-optic sensors on Bragg gratings Valerii Matveenkoa,b , Natalia Koshelevab* , Grigorii Serovaeva,b a,b b* Valerii Matveenko , Natalia Kosheleva , Grigorii Serovaeva,b

Institute of Continuous Media Mechanics UB RAS, 1, Akademika Koroleva Str.,Perm, 614013, Russia a Institute of Continuous Media Mechanics UB 29 RAS, 1, Akademika Koroleva Str.,Perm, 614013, Russia Perm National Research Polytechnic University, Komsomolsky prospekt, Perm, Perm krai, 614990, Russia b Perm National Research Polytechnic University, 29 Komsomolsky prospekt, Perm, Perm krai, 614990, Russia a

b

Abstract Abstract In the paper the problem associated with the use of fiber-optic strain sensors based on Bragg gratings glued to the surface of the In the paper the defects problemregistration associatedand withtheir the development use of fiber-optic strain sensors based gratings glued to to the the numerical surface of and the material for the was studied. The first partonofBragg the work is devoted material for the defects registration was studied. of the work is devoted to the numerical experimental estimation of the errorand of their straindevelopment values calculated on the The basisfirst of part information on physical quantities recordedand by experimental ofofthe of astrain values calculated on the basis of information on physical quantities recorded by sensors. In theestimation second part theerror work, method for defects registration for a given external loads is presented. A background of sensors. In theissecond part of the work, a method for defects registration for aingiven external loads is presented. A background of the technique the Saint-Venant principle, according to which the change the strain values with the appearance of a defect the technique is thedefined Saint-Venant according to sizes. whichBased the change in the straintovalues with the appearance of a defect occurs in the area by 3 – principle, 5 characteristic defect on this, in order register a defect without preliminary occurs in theabout area the defined 3 – 5 characteristic defect sizes. Based this, inobject order atostrains register a defect without information strainby distribution, it is necessary to provide in theon observed measurement by the preliminary sensors that information about the strain distribution, it is necessary to provide in the observed object a strains measurement the sensors form a spatial grid with a step of 3 to 5 sizes of the expected defect. Last can be practically unrealistic. In theby framework of that the form a spatial grid with a based step ofon3 the to 5results sizes of expected defect. Last be practically unrealistic. In the framework of and the considered methodology, of the numerical simulation, thecan sensors are located in stress concentration zones considered methodology, on the results of numerical simulation, the sensors located in stress concentration zones areas with moderate stressbased concentration. Further, in the object without defects on thearebasis of numerical or experimental data,and all areas with stress concentration. in the object without defects on theare basis of numerical or experimental data, all variants ofmoderate the relationships of the strain Further, values obtained by two different sensors recorded. The change in the monitoring variants ofleast the relationships of relationships the strain values obtained bya two differentabout sensors are recorded. The as change in its thelocation monitoring process at of one of these allows to make conclusion the defect appearance well as and process at The leasteffectiveness of one of these relationships allows to make conclusion about thecomposite defect appearance as which well asholes its location and evolution. of the technique is illustrated on aasample of a polymer material, in of different evolution. Themade, effectiveness theappearance technique isand illustrated on a sample of a polymer composite material, in which holes of different diameters are imitatingofthe development of a defect. diameters are made, imitating the appearance and development of a defect. © 2019 The Authors. Published by Elsevier B.V. © 2019 Published by Elsevier B.V. B.V. © 2019The TheAuthors. Authors. Published by Peer-review under responsibility of Elsevier the Gruppo Italiano Frattura (IGF) ExCo. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. Keywords: fiber-optic sensor; Bragg grating; surface mounted sensor; numerical simulation; experiment; damage detection. Keywords: fiber-optic sensor; Bragg grating; surface mounted sensor; numerical simulation; experiment; damage detection.

* *

Corresponding author. Tel.: +7(342)2378308. Corresponding Tel.: +7(342)2378308. E-mail address:author. [email protected] E-mail address: [email protected]

2452-3216 © 2019 The Authors. Published by Elsevier B.V. 2452-3216 2019responsibility The Authors. of Published by Elsevier Peer-review©under the Gruppo Italiano B.V. Frattura (IGF) ExCo. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo.

2452-3216  2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Gruppo Italiano Frattura (IGF) ExCo. 10.1016/j.prostr.2019.08.135

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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 nonuniform 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

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3

the expected defect. It is usually impossible to satisfy these conditions. In addition, it is necessary to take into account that a change in the single sensor measurement with varying loads in time does not necessarily indicate the defect appearance. The concept of the proposed method for recording the appearance and development of defects is as follows. Let one of the options of external loads take place for the object under consideration.

pi1  xi , t   k 1 , pi2  xi , t   k 2 , , pij  xi , t   k j , , pin  xi , t   k n .

(1)

Here j  1, 2, , n − external load option, xi − the coordinates components of points on the surface of the body, t − time, pij − the vector components of external forces in the corresponding coordinate system  i  1, 2,3 , k j − constants. It should be noted that in practice a significant number of objects are subject to a limited number of load options. The processes of elastic linear behavior of the material were considered. In this case for each option of external loads a set of ratios of the corresponding components of the strain tensor at a given number of points can be defined.

 pj 

j q

 a pqj , p  1, 2, , s, , k , q p  1, p  2, , s, k

(2)

Here  pj ,  qj – the strain tensor components at points p and q for j – load option, k – number of controlled points,

a pqj – strain ratios. If the integrity of the controlled volume of the material is preserved, then the set of ratios for each of the load options will remain unchanged for different values k j . The defect appearance, the zone of which captures one of the points s, will cause at this point a local change in the strain and a change in the ratios  sj  qj , which will indicate the appearance of a defect in the vicinity of the point s. For the practical application of this technique, it is necessary to limit the amount of sensors for a reasonable number. For this purpose, it is proposed to perform a preliminary numerical simulation of the stress-strain state of the object under study. Based on the simulation results, the scheme of the sensors location is determined with their mandatory placement in the stress concentration zones and moderate stress zones. Further, in the monitoring process for each load option, the initial strain ratio a pqj is recorded based on the data of different sensors. If over time or with changing loads, some of the relationships change, then these changes, tied to a specific sensor, will indicate the appearance and development of defects in the area corresponding to that sensor. 3. Practical implementation of damage detection algorithm The considered object of study was a rectangular glass fiber reinforced plastic (GFRP) plate marked as VPS-48. Sample sizes were 250503 mm. Optical fiber has a diameter 0.124 mm and protective polyimide coating with thickness 0.012 mm. To measure the plate strain, the optical fiber was glued to the plate surface. The mechanical characteristics of GFRP, optical fiber, protective coating and glue are shown in Table 1 and 2. The samples were tested for uniaxial tension on a universal testing machine Shimadzu AG-X Plus. Uniaxial tension was performed in an elastic zone with a load of up to 20 kN with minute holding at loads of 5 kN, 10 kN, 15 kN, 20 kN and subsequent unloading. Loading rate was 2 mm/min. Table 1: Mechanical properties of VPS-48.

E X , GPa

EY , GPa

EZ , GPa

 XY

YZ

 XZ

GXY

22

22

8.7

0.14

0.14

0.14

3

, GPa

GYZ , GPa

GXZ

3

3

, GPa

The deformation control from the machine was driven by an optical extensometer. Three optical fiber lines with fiber Bragg gratings (s1, s2, s3) were glued to the surface of the sample to register transverse strains and one line with

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three sensors (s4, s5, s6) to register longitudinal strains. The scheme of fiber-optic lines mounted on the sample surface is shown in the Fig. 1. Table 2: Mechanical characteristics of optical fiber and epoxy. Material

silica glass

polyimide

epoxy

E, GPa

71.4

2.5

2.9



0.17

0.35

0.36

Fig. 1. Scheme of optical fibers mounted on the sample surface.

To assess the effect of adhesive bonding on sensor data, numerical and experimental studies were performed. The physical quantity that is recorded by FOSS, based on the Bragg grating, is the change in the wavelength of the reflected spectrum. Relationships that establish the link in the wavelength change of the reflected spectrum with the strains of the optical fiber in the Bragg grating zone for a single-mode optical fiber have the following form (Geert Luyckx et al. 2010): 1 1  3  n 2 ( p111  p12 ( 2  3 )) 2 *  2 1  3  n 2 ( p11 2  p12 (1  3 )) * 2 

(3)

where  3 – strain along the fiber, 1 ,  2 – principal strains in the plane perpendicular to the optical fiber,

1  1  * ,  2   2  * – the difference of the resonant wavelengths of the reflected spectrum in the current 1 ,  2 and initial * times, p11 , p12 – Pockels coefficients, n - effective refractive index of optical fiber. The simplest way to use these relations to calculate the strains with the help of experimental information obtained from the sensor is based on the assumption of a uniaxial stress state in the area of the optical fiber and the Bragg grating. At these case: 1   2   and

   n 2  1   p12  ( p11  p12 )   3 * 2    3 

1   k *

Here  - Poisson ratio of optical fiber. For used silica glass fibers k = 0.78.

(4)

(5)

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5

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 3exp1 and  3exp 2 are calculated. The difference in the values 1 * and  2 * and respectively 3exp1 and  3exp 2 will demonstrate that the conditions of uniaxial stress state in the optical fiber are not satisfied, while the difference in the values 3exp1 and  3exp 2 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 3exp1 (or  3exp 2 ) 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, 1o ,  o2 , 3o , 1 *

 ,   o

2





* o

are the values of 1 ,  2 , 3 , 1 * and  2 * , divided by the

value of the specified displacement U0. Errors 1 and  2 are determined by the following expressions 1 



exp1 3

 3  3 100% , 2 



exp 2 3

 3  3 100% , where 3exp1 calculated by the formula (5) with   1 ,

while  3exp 2 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.

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Table 3. The calculations results for fiber glued across its length with various parameters of the adhesive layer

 



* o

a/d

b/d

1o

o2

 3o

0.16

4.8

0.26

-0.05

-0.23

-0.236

0.32

4.8

0.21

-0.03

-0.23

0.64

4.8

0.14

0.01

0.16

9.6

0.39

0.32

9.6

0.64

9.6

 



* o

1 %

2 %

-0.186

29.27

1.90

-0.224

-0.186

23.25

2.35

-0.23

-0.208

-0.187

14.31

2.48

-0.08

-0.23

-0.269

-0.194

47.48

6.58

0.36

-0.06

-0.23

-0.261

-0.195

43.10

6.92

0.30

-0.04

-0.23

-0.248

-0.194

35.80

6.29

1



2



To test the defect registration method, the rectangular samples considered in the work with sensor grid (s1-s6) and with holes with a diameter of 2, 4, 6, 8 mm were tested. The scheme of the sample is shown in the Fig. 3. In the experiments under consideration, the holes imitate the appearance and development of damage.

Fig. 3. Rectangular samples with hole.

For plates with different holes, numerical calculations of the stress-strain state based on the finite element method were performed. The difference between the calculation results and the experimental data do not exceed 6%. According to the proposed method, in the problem under consideration there is one loading option, i.e. n=1 in equation (1). For the presented sensor grid, the following 15 strain relations will take place:  1 1  2 2  a a13 ,  , 1 a a a24 ,  , 5 a56 12 , 16 , 23 , 2 3 6 3 4 6

(6)

Here 1 ,  2 , 3 - strain tensor component  y , measured by sensors s1, s2, s3;  4 , 5 , 6 - strain tensor component  x , measured by sensors s4, s5, s6. Fig. 4 shows the dependence of some ratios a pq on the diameter of the hole. In

this case, the hole imitates damage, and an increase in its diameter corresponds to the damage development. It should be noted that the values a pq based on the assumption of a linear elastic behavior, do not depend on the level of load P0 . This proposal was confirmed by the results of the experiment.

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Fig. 4. Calculated dependencies of the ratios

a pq

7

on the hole diameter d.

These results allow to conclude that when a hole appears and its diameter increases, the ratios a pq change. At these case these ratios are: a12 , a15 , a23 , a24 , a25 , a26 , a35 , a45 , a56 . Changes in these ratios indicate the appearance and growth of damage. To indicate the defect location, the ratios, which remained practically unchanged, should be analyzed. In the present problem, these ratios are: a13 , a14 , a46 , a16 , a34 , a36 . These data allow to conclude that in the vicinity of sensors s1, s3, s4, s6 defects did not arise, and the defect occurs in the vicinity of sensors s2 and s5. 4. Conclusions A technique for a numerical estimation of the error in the strain values calculated on the basis of physical quantities recorded by FBG sensors glued to the material surface and based on the assumption of uniaxial stress state in FBG is proposed. Based on the assumption of a uniaxial FBG stress state, experimental estimations of the error in the strain values obtained by mounted to the PCM surface FOSS with different orientations relative to the direction of external loads are given. The concept of a numerical-experimental technique is given, which allows for the given options of external loads to register the appearance and development of defects in stress concentration areas, which are determined as a result of numerical modeling of a stress-strain state. The effectiveness of the technique is illustrated on a rectangular sample of a polymer composite material, in which a defect is simulated by a hole, and the defect development by an increase in the hole diameter. Acknowledgements This study was supported by Russian Science Foundation (project No.15-19-00243). References Fan, Yu., Kahrizi, M., 2005. Characterization of a FBG Strain Gage Array Embedded in Composite Structure. Sensors and Actuators, A: Physical 121(2), 297–305. Xin, J., Yuan, S., Chen, J., 2019. On Crack Propagation Monitoring by Using Reflection Spectra of AFBG and UFBG Sensors. Sensors and Actuators A: Physical 285, 491–500. Kersey, A. D., et al., 1997. Fiber Grating Sensors. Journal of Lightwave Technology 15(8), 1442–63.

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