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Numerical modeling of the capillary in the Bragg grating area, ensuring uniaxial stress state of embedded fiber-optic strain sensor
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Structural Integrity Procedia 00 (2019) 000–000 Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Structural Integrity 17 (2019) 371–378
ICSI 2019 The 3rd International Conference on Structural Integrity ICSI 2019 The 3rd International Conference on Structural Integrity
Numerical modeling of the capillary in the Bragg grating area, Numerical modeling of the capillary in the Bragg grating area, ensuring uniaxial stress state of embedded fiber-optic strain sensor ensuring uniaxial stress state of embedded fiber-optic strain sensor Grigorii Serovaeva,b* ,Valerii Matveenkobb, Natalia Koshelevaaa, Andrey Fedorovbb a,b* Grigorii Serovaev ,Valerii Matveenko , Natalia Kosheleva , Andrey Fedorov Perm National Research Polytechnic University, 29 Komsomolsky prospekt, Perm, 614990, Russia Research Polytechnic University, Komsomolsky prospekt, InstituteNational of Continuous Media Mechanics UB RAS,29 1, Akademika Koroleva Str,Perm, Perm,614990, 614013,Russia Russia b Institute of Continuous Media Mechanics UB RAS, 1, Akademika Koroleva Str, Perm, 614013, Russia a
b a Perm
Abstract Abstract In this paper, the possibility of providing a uniaxial stress state of FOSS based on the use of a capillary tube in the area of the Bragg In this paper, the possibility of providing a uniaxial stress stateadditional of FOSS external based oncoating the use of tube in the of theand Bragg grating is studied. The capillary tube, which consists of the anda capillary a cavity between thearea coating the grating is studied. The the capillary which of theofadditional and atocavity the coating and the optical fiber, protects Braggtube, grating fromconsists the effects transverseexternal strain. coating This allows use a between direct relation between optical fiber, protects the Bragg grating shift fromand thethe effects of transverse This to use asimulation, direct relation between and the measured value of the Bragg wavelength longitudinal strain. strain. With the helpallows of numerical the geometric measured of the Bragg shift andbeen the longitudinal strain. With the helpshowed of numerical theelastic geometric and mechanicalvalue parameters of thewavelength capillary tube have studied. Numerical calculations a slightsimulation, effect of the modulus mechanical parameters tubeunder have been Numerical calculations showed a slight effectleads of thetoelastic modulus of the capillary coatingofonthe thecapillary cavity size load.studied. However, the presence of a cavity in the capillary an increase in of the concentration, capillary coating on the cavity size underwhen load.designing However,athe presence a cavity in the application. capillary leads an increase in stress which must be considered capillary tubeoffor a particular Thetoobtained results stress concentration, which must considered whenofdesigning a capillary tubeoffor a particular application. The obtained results confirmed the effectiveness of thebe structural scheme the capillary in the area FOSS embedded into the controlled material. confirmed the effectiveness of the structural scheme of the capillary in the area of FOSS embedded into the controlled material. © 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 ICSI organizers. Peer-review under responsibility of the ICSI 2019 2019 organizers. Peer-review under responsibility of the ICSI 2019 organizers. Keywords: Fiber optic strain sensor; fiber Bragg grating; capillary; numerical simulation. Keywords: Fiber optic strain sensor; fiber Bragg grating; capillary; numerical simulation.
1. Introduction 1. Introduction Nowadays, more and more structures are equipped with various sensors, which make it possible to monitor both Nowadays, more and more structures withstate. various sensors, which make it of possible to monitor both important operational characteristics andare theequipped mechanical In the future, the degree integration of sensing important operational characteristics and the mechanical state. In the future, the degree of integration of sensing elements will only increase, which changes the design and development approaches and opens fundamentally new elements will only increase, which changes the design and development approaches and opens fundamentally new
* *
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 Elsevier B.V. Peer-review©under the ICSIby 2019 organizers. Peer-review under responsibility of the ICSI 2019 organizers.
2452-3216 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. 10.1016/j.prostr.2019.08.049
Grigorii Serovaev et al. / Procedia Structural Integrity 17 (2019) 371–378 Author name / Structural Integrity Procedia 00 (2019) 000–000
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opportunities for assessing the state of objects as well as detecting defects at an early stage of their development. Due to the rapid growth of the telecommunications industry based on optical fibers and a lot of researches carried out in this field, the quality of fiber-optic components has significantly increased, while decreasing the production cost. This was one of the reasons for the study of the possibility of using optical fibers as sensitive elements. Fiber-optic sensors (FOSs) have several advantages compared to other sensing elements: they are not sensitive to electromagnetic effects, can operate in a wide range of temperatures, it is possible to place many FOSs on one optical fiber and simultaneously register measurements from all sensors on the line (Udd, (2011)). In this paper, Bragg grating sensors written in a standard single-mode optical fiber are considered. This type of FOSs is widely used to monitor the mechanical state of various objects (Gebremichael et al. (2005); Ghoshal et al. (2015); Hong et al. (2016); Lee et al. (2003); SierraPérez et al. (2016); Wymore et al. (2015)). Due to the small size of the optical fiber, the sensor can be embedded into the structure of the controlled object at the manufacturing stage. Thus, FOSs allow to assess the state of the product not only during its operation, but also to control the technological process of production (Matveenko et al. (2018)). The use of embedded fiber-optic strain sensors (FOSS) based on Bragg gratings, leads to a number of problems. One of which, is the redistribution of stresses in the vicinity of the embedded optical fiber, which can lead to dangerous stress concentrations. When an optical fiber is embedded in the structure of layered composite materials, there is a high probability of forming a technological defect (a resin pocket) in the inclusion region (Shivakumar and Emmanwori (2004)). In addition, an important task is to assess the reliability of the strain values, calculated based on the physical quantity measured by the sensor. Embedded optical fiber operates in a complex stress state, which prevents the direct determination of strain, since the direct correspondence between the measured Bragg wavelength shift and the longitudinal component of the strain tensor exists only for the case of uniaxial stress state of the optical fiber in the Bragg grating area. It should also be noted that in order to make reasonable use of fiber-optic strain sensor, it is necessary to evaluate the efficiency of the strain transfer from the host material to the embedded sensor. One approach to solving this problem is to use numerical simulation methods to calculate a strain transfer matrix (Luyckx et al. (2010)). In order to eliminate the effect of transverse strains on the FOSS measurements, the Bragg grating area may be surrounded by a capillary tube. (Voet et al. (2010)) have shown that the encapsulation of the Bragg grating in the capillary ensures the preservation of a single peak in the reflected spectrum after the implementation of the technological process of the composite material manufacturing. Another example of encapsulation of the Bragg grating area into the capillary is presented by (Li et al. (2014)), in which the use of a capillary is aimed at increasing the temperature sensitivity of a fiber-optic sensor. In this paper, the use of a capillary tube in the Bragg grating area to ensure uniaxial stress state of the sensor is studied. This enables the use of a direct relation between the measured value of the Bragg wavelength shift and the longitudinal strain. With the help of numerical simulation methods, geometrical and mechanical parameters of the structural scheme of a capillary tube were investigated. The stress concentration in the vicinity of the embedded optical fiber with a capillary was analyzed. 2. The principle of FBG operation The fiber Bragg grating (FBG) is a periodic change in the refractive index on a specific region of the core of a single-mode optical fiber. Such grating works as a narrowband reflecting optical filter. The light source sends a broadband optical signal through a fiber-optic core. Most of the light passes through the grating without reflection, and only light in a certain narrow wavelength range is reflected from the grating. The central wavelength (Bragg wavelength) λ* of the reflected signal is proportional to the effective refractive index n of the optical fiber core in the region of the grating and the geometric length of the grating period (Othonos (1997)).
* = 2n
(1)
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With a change in temperature or mechanical strain of the optical fiber in the grating region, a linear shift of the central wavelength of the reflected signal Δλ occurs. The principle of operation of fiber-optic Bragg grating sensors is based on the registration of this shift. This approach also allows an easy multiplexing, i.e. writing multiple FBG point sensors in one optical fiber and making simultaneous measurements from all sensors. In this paper, it is assumed that FOSS operates under isothermal conditions and the effect of temperature on FBG readings is not taken into account. In the general case, the relationship between the change in the central wavelength of the reflected spectrum and the strain of the optical fiber in the Bragg grating area is determined by the equations (Measures (2001)): 1 1 = 3 − n 2 ( p111 + p12 ( 2 + 3 )) * 2 2 1 = 3 − n 2 ( p11 2 + p12 (1 + 3 )) 2 *
(2)
where 3 – longitudinal strain component along the fiber, 1 , 2 – principal strains in the plane perpendicular to the optical fiber, 1 = 1 − * , 2 = 2 − * – central wavelength shifts in the current 1 , 2 and initial * moments of time, p11 , p12 – strain optic coefficients. These equations are given for low birefringence optical fibers when n= n= n. 1 2 In the special case when the optical fiber in the region of the Bragg grating is in uniaxial stress state, the following relations between the components of the strain tensor are valid: 1 = 2 = −3 , where – Poisson’s ratio of the
optical fiber. In this case 1 = 2 = and
n 2 = 1 − ( p12 − ( p11 + p12 ) ) 3 * 2 1 3 = * k
(3) (4)
For silica glass fiber p11 = 0.113 , p12 = 0.252 , n =1.458 (Bertholds and Dandliker (1988)), = 0.17. Thus, under the uniaxial stress state of the Bragg grating, the coefficient k~0.798. When the Bragg grating is written in a low-birefringence standard single-mode optical fiber, the original spectrum of the signal reflected from the grating contains only one peak, the wavelength of which is determined by relation (1). It is known that the application of loads in the diametric direction leads to a change in the shape of the spectrum of the reflected signal, and when a certain level of transverse strains is exceeded, two peaks are observed on the reflected spectrum (Wagreich et al. (1996)). When a fiber optic sensor is embedded in a material, a complex stress state will be realized in the sensor as a result of interaction with the material, i.e. the strains 1 , 2 , 3 , will take place in the optical fiber which must be identified on the basis of experimental information, namely values 1 / * and 2 / * . From relations (2) it follows that if 1 2 , there are two equations with three unknowns, and if 1 =2 , one equation with two unknowns, which makes it impossible to unambiguously determine the longitudinal component of the strain tensor in the case of a complex stress state. It is worth noting that the sensitivity of FBG to transverse strains is used for creating sensors that allow to simultaneously measure several strain tensor components (Sonnenfeld et al. (2015)). In such cases, polarization maintaining (PM) optical fibers are used, for which the original spectrum of the signal reflected from the grating contains two separate peaks. This allows to separate the sensitivity of the sensor in the longitudinal and transverse directions. However, due to the substantially different sensitivity of the fast and slow axes of the PM optical fiber to
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transverse strain, very strict adherence to the orientation of the optical fiber is required during embedding process, which is a complex technological problem. Another factor influencing the shape of the reflected Bragg grating spectrum and introducing complexity to the definition of strain is the non-uniform strain distribution along the Bragg grating length (Peters et al. (2001)). The Bragg grating length can vary over a wide range of values. When optical fiber is embedded in the structure of such materials as laminated polymer composites, concretes, etc. consisted of several structural constituents there is a high probability of the occurrence of process-induced strains nonuniformly distributed along the length of the grating at the manufacturing stage. Thus, it is necessary to carry out studies that suggest ways to solve the problems described above for the use of FOSS based on the Bragg gratings embedded in the material. In this paper, we study the possibility of using a capillary in the Bragg grating area, which will provide the uniaxial stress state of the grating and uniform strain distribution along its length. 3. Application of the capillary tube One of the directions for obtaining reliable information about the strains measured by the embedded Bragg grating sensors is associated with a change in the conditions of interaction with the host material in the Bragg grating area. In a constructive implementation, this can be achieved by using a capillary tube around the fiber in the section of the Bragg grating (figure 1).
Fig. 1. The scheme of a capillary tube in the Bragg grating area.
The essence of this scheme is that the capillary tube, which represents the additional external coating (capillary coating) and the cavity between the coating and the optical fiber, protects the Bragg grating from the effects of transverse strain. Thus, the sensor region will be under conditions of a uniaxial stress state, under which there is a direct correspondence between the measured value of the Bragg wavelength shift and the longitudinal strain using the relation (4). The interaction of the capillary tube and the optical fiber is provided through the connecting elements (binders) on opposite sides of the tube. In this case, the Bragg grating region can be, as covered by a protective coating or remain without any protective coating. To measure compressive strain, it is necessary to provide the preliminary tension of the optical fiber. The degree of which will determine the maximum possible value of the recorded compressive strain. The geometrical dimensions of the capillary will be determined by the thickness t, the length l, and the size of the cavity tc (figure 2). In addition, it is important to choose the material of the capillary coating, and therefore, to choose the elastic modulus E c and the Poisson’s ratio c (assuming that the coating is made of isotropic material).
Author name / Structural Integrity Procedia 00 (2019) 000–000 Grigorii Serovaev et al. / Procedia Structural Integrity 17 (2019) 371–378
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Fig. 2. Geometric parameters of the capillary tube.
The capillary tube must meet the following conditions: the realization of a uniaxial stress state in the Bragg grating area and the coincidence of the strain values along the fiber directly in the fiber and in the material adjacent to the fiber. Fulfillment of these conditions will provide a reliable measurement of the longitudinal strain with the help of the FOSS. On the other hand, the dimensions of the additional external coating and cavity should ensure a uniform distribution of the strain along the entire length of the Bragg grating and exclude the possibility of touching of the outer coating and the optical fiber in a wide load range. With the help of numerical simulations, the parameters of a capillary tube were estimated on a model problem for a parallelepiped with embedded optical fiber and a capillary in the Bragg grating area (figure 3a). The optical fiber has a diameter of 0.124 mm and a protective coating made of polyimide with a thickness of 0.012 mm. The Bragg grating length is 33 optical fiber diameters (5 mm). The length of the parallelepiped is 8 times longer than the Bragg grating length and in the cross section has the shape of a square with a side equal to 40 diameters of the optical fiber. As an external load, pressure P distributed along the parallelepiped edge in the direction perpendicular to the optical fiber is considered. In this loading case, the greatest difference from the uniaxial stress state takes place in the optical fiber. The calculation of the stress-strain state was carried out by the finite element method in the framework of the linear elastic theory. Perfect contact of all adjacent parts of the model is assumed. Due to symmetry, a quarter of the model with the corresponding boundary conditions was considered. In the finite element method implementation, a mesh with a refinement in the inclusion region was used (figure 3b).
Grigorii Serovaev et al. / Procedia Structural Integrity 17 (2019) 371–378 Author name / Structural Integrity Procedia 00 (2019) 000–000
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Fig. 3. а) calculation scheme for a parallelepiped with embedded optical fiber and a capillary in the Bragg grating area; b) finite element model.
In the numerical simulations the following mechanical properties of materials were used: for an optical fiber made 0.35 ; for controlled material of silica glass Eo = 71.4 GPa, o =0.17 and polyimide coating E p = 2.5 GPa, p =
Eh = 30 GPa, h =0.18 (these properties correspond to concrete). The connecting elements (binders) between the capillary coating and the optical fiber are made of epoxy resin with properties Eb = 3 GPa, b =0.35 . The material properties of the capillary coating may vary. The external pressure P substantially exceeds (10 times) the compressive strength for the material under consideration and is equal to P = 410 MPa. The study of the cavity size tc between the optical fiber and the external coating is carried out on the basis of estimation of the parameter d, corresponding to the relative change in the initial distance between the external coating and the optical fiber t c0 and the minimum distance tc1 after application of the critical load P (figure 4). = d
tc1 − tc0 100% tc0
(5)
Fig. 4. The scheme of deformation of the cavity between the external coating and the optical fiber.
In the performed calculations, the value of the initial cavity size t c0 varied in the range from the size of the optical fiber protective coating, which is equal to 0.012 mm, up to 0.024 mm. The material properties of the external coating coincide with the properties of controlled material. Figure 5 shows the dependence of the parameter d on the cavity size tc under compressive load.
Fig. 5. а) change in parameter d depending on cavity size; b) change in parameter d depending on the modulus of elasticity of the external coating.
Grigorii Serovaev et al. / Procedia Structural Integrity 17 (2019) 371–378 Author name / Structural Integrity Procedia 00 (2019) 000–000
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From the obtained results, it can be concluded that even with a small value of the cavity size and with the load, which significantly exceeds the material strength, the reduction of the gap between the external coating and the optical fiber does not exceed 30%. The change in the elasticity modulus of the external coating with the constant cavity size and thickness of the external coating (0.012 mm) also slightly affects the gap size between the coating and the optical fiber under external load. It should be noted that with the considered parameters of the capillary tube and the material properties, in which the optical fiber is embedded, it is possible to achieve a uniaxial stress state in the Bragg grating area. At this case, the relative difference between the longitudinal strain values in the fiber and in the material zone adjacent to the fiber does not exceed 3%. However, for the anisotropic properties of the host material with a circular section of the additional coating, these conditions are not met. Studies have shown that achieving an acceptable coincidence of strain along the fiber and strain in the material, E= 0.035 , 84.1 GPa, Ez = 10.7 GPa, xy = made of carbon fiber-reinforced plastic with effective properties E= x y
yz = xz =0.45 , Gxy = 4.3 GPa, G= G= 3.5 GPa, is possible with an elliptical cross section of the capillary with yz xz a ratio of ellipse semi-axes equal to a/b = 0.6, where the semi-axis a coincides with the y axis. Embedding into the material such a foreign object as an optical fiber causes a redistribution of the stress-strain state in a certain vicinity around the embedded object and may cause a high stress concentration. As part of the study, analysis of the value K y = y P was made that determines the stress concentration coefficient for the corresponding component of the stress tensor. The stress concentration field Ky for the central along the length cross section of the model for the cases with embedded optical fiber without a capillary tube and with the presence of a capillary tube is presented in figure 6.
Fig. 6. The stress concentration field Ky for material with embedded optical fiber: а) without a capillary tube b) with a capillary tube.
The optical fiber embedding causes a stress concentration K y = 1.81 in the vicinity of the fiber, and taking into account in the calculation scheme of the cavity between the optical fiber and the external coating increases the stress concentration to a value of 3.03. A change in the cavity size by 2 times does not significantly affect the stress concentration value. These results are obtained for the studied isotropic material. However in case of composite material with effective mechanical properties described previously, the embedding of the optical fiber leads to a stress concentration K y = 3.87 and introducing the capillary into the model, increases the stress concentration up to the value of 6.31. This means that for anisotropic materials, such as composites, the risk of material failure in the vicinity of the embedded optical fiber and capillary tube is higher compared to the isotropic materials. These results should be taken into account during the design stage of product development.
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4. Conclusions In the paper, the possibility of providing a uniaxial stress state in the vicinity of FOSS based on the use of a capillary tube in the Bragg grating area, was studied. Numerical analysis of the cavity size between the external coating (capillary coating) and the optical fiber showed that for the case of an isotropic material, in which the fiber is embedded, it is possible to ensure the conditions of a uniaxial stress state, uniformity of longitudinal strains along the Bragg grating length, coincidence of longitudinal strains in the optical fiber and in the controlled material, as well as to exclude the contact of the external coating and the optical fiber under the most unfavourable loading case. Numerical calculations showed a slight effect of the elastic modulus of the capillary coating on the cavity size under the load. However, the presence of a cavity in the capillary leads to an increase in stress concentration, which must be taken into account when designing a capillary tube for a particular application. These results confirm the effectiveness of the structural scheme of the capillary in the area of FOSS when embedding optical fiber into the controlled material. Acknowledgements This study was supported by Russian Science Foundation (project No.15-19-00243). References Bertholds, A., Dandliker, R., 1988. Determination of the individual strain-optic coefficients in single-mode optical fibres. Journal of Lightwave Technology 6, 17–20. Gebremichael, Y.M., Li, W., Boyle, W.J.O., Meggitt, B.T., Grattan, K.T.V., McKinley, B., Fernando, G.F., Kister, G., Winter, D., Canning, L., Luke, S., 2005. Integration and assessment of fibre Bragg grating sensors in an all-fibre reinforced polymer composite road bridge. Sensors and Actuators A: Physical 118, 78–85. Ghoshal, A., Ayers, J., Gurvich, M., Urban, M., Bordick, N., 2015. Experimental investigations in embedded sensing of composite components in aerospace vehicles. Composites Part B: Engineering 71, 52–62. Hong, C.-Y., Zhang, Y.-F., Zhang, M.-X., Leung, L.M.G., Liu, L.-Q., 2016. Application of FBG sensors for geotechnical health monitoring, a review of sensor design, implementation methods and packaging techniques. Sensors and Actuators A: Physical 244, 184–197. Lee, J.-R., Ryu, C.-Y., Koo, B.-Y., Kang, S.-G., Hong, C.-S., Kim, C.-G., 2003. In-flight health monitoring of a subscale wing using a fiber Bragg grating sensor system. Smart Materials and Structures 12, 147–155. Li, Y., Wen, C., Sun, Y., Feng, Y., Zhang, H., 2014. Capillary encapsulating of fiber Bragg grating and the associated sensing model. Optics Communications 333, 92–98. Luyckx, G., Voet, E., De Waele, W., Degrieck, J., 2010. Multi-axial strain transfer from laminated CFRP composites to embedded Bragg sensor: I. Parametric study. Smart Materials and Structures 19, 105017. Matveenko, V.P., Kosheleva, N.A., Shardakov, I.N., Voronkov, A.A., 2018. Temperature and strain registration by fibre-optic strain sensor in the polymer composite materials manufacturing. International Journal of Smart and Nano Materials 9, 99–110. Measures, R.M., 2001. Structural monitoring with fiber optic technology. Acad. Press, San Diego, pp. 716. Othonos, A., 1997. Fiber Bragg gratings. Review of Scientific Instruments 68, 4309–4341. Peters, K., Studer, M., Botsis, J., Iocco, A., Limberger, H., Salathé, R., 2001. Embedded optical fiber Bragg grating sensor in a nonuniform strain field: Measurements and simulations. Experimental Mechanics 41, 19–28. Shivakumar, K., Emmanwori, L., 2004. Mechanics of Failure of Composite Laminates with an Embedded Fiber Optic Sensor. Journal of Composite Materials 38, 669–680. Sierra-Pérez, J., Torres-Arredondo, M.A., Güemes, A., 2016. Damage and nonlinearities detection in wind turbine blades based on strain field pattern recognition. FBGs, OBR and strain gauges comparison. Composite Structures 135, 156–166. Sonnenfeld, C., Luyckx, G., Sulejmani, S., Geernaert, T., Eve, S., Gomina, M., Chah, K., Mergo, P., Urbanczyk, W., Thienpont, H., Degrieck, J., Berghmans, F., 2015. Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates. Smart Materials and Structures 24, 055003. Udd, E. (Ed.), 2011. Fiber optic sensors: an introduction for engineers and scientists, 2. ed. ed. Wiley, Hoboken, NJ, pp. 512. Voet, E., Luyckx, G., De Waele, W., Degrieck, J., 2010. Multi-axial strain transfer from laminated CFRP composites to embedded Bragg sensor: II. Experimental validation. Smart Materials and Structures 19, 105018. Wagreich, R.B., Atia, W.A., Singh, H., Sirkis, J.S., 1996. Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre. Electronics Letters 32, 1223. Wymore, M.L., Van Dam, J.E., Ceylan, H., Qiao, D., 2015. A survey of health monitoring systems for wind turbines. Renewable and Sustainable Energy Reviews 52, 976–990.
ScienceDirect ScienceDirect
Structural Integrity Procedia 00 (2019) 000–000 Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Structural Integrity 17 (2019) 371–378
ICSI 2019 The 3rd International Conference on Structural Integrity ICSI 2019 The 3rd International Conference on Structural Integrity
Numerical modeling of the capillary in the Bragg grating area, Numerical modeling of the capillary in the Bragg grating area, ensuring uniaxial stress state of embedded fiber-optic strain sensor ensuring uniaxial stress state of embedded fiber-optic strain sensor Grigorii Serovaeva,b* ,Valerii Matveenkobb, Natalia Koshelevaaa, Andrey Fedorovbb a,b* Grigorii Serovaev ,Valerii Matveenko , Natalia Kosheleva , Andrey Fedorov Perm National Research Polytechnic University, 29 Komsomolsky prospekt, Perm, 614990, Russia Research Polytechnic University, Komsomolsky prospekt, InstituteNational of Continuous Media Mechanics UB RAS,29 1, Akademika Koroleva Str,Perm, Perm,614990, 614013,Russia Russia b Institute of Continuous Media Mechanics UB RAS, 1, Akademika Koroleva Str, Perm, 614013, Russia a
b a Perm
Abstract Abstract In this paper, the possibility of providing a uniaxial stress state of FOSS based on the use of a capillary tube in the area of the Bragg In this paper, the possibility of providing a uniaxial stress stateadditional of FOSS external based oncoating the use of tube in the of theand Bragg grating is studied. The capillary tube, which consists of the anda capillary a cavity between thearea coating the grating is studied. The the capillary which of theofadditional and atocavity the coating and the optical fiber, protects Braggtube, grating fromconsists the effects transverseexternal strain. coating This allows use a between direct relation between optical fiber, protects the Bragg grating shift fromand thethe effects of transverse This to use asimulation, direct relation between and the measured value of the Bragg wavelength longitudinal strain. strain. With the helpallows of numerical the geometric measured of the Bragg shift andbeen the longitudinal strain. With the helpshowed of numerical theelastic geometric and mechanicalvalue parameters of thewavelength capillary tube have studied. Numerical calculations a slightsimulation, effect of the modulus mechanical parameters tubeunder have been Numerical calculations showed a slight effectleads of thetoelastic modulus of the capillary coatingofonthe thecapillary cavity size load.studied. However, the presence of a cavity in the capillary an increase in of the concentration, capillary coating on the cavity size underwhen load.designing However,athe presence a cavity in the application. capillary leads an increase in stress which must be considered capillary tubeoffor a particular Thetoobtained results stress concentration, which must considered whenofdesigning a capillary tubeoffor a particular application. The obtained results confirmed the effectiveness of thebe structural scheme the capillary in the area FOSS embedded into the controlled material. confirmed the effectiveness of the structural scheme of the capillary in the area of FOSS embedded into the controlled material. © 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 ICSI organizers. Peer-review under responsibility of the ICSI 2019 2019 organizers. Peer-review under responsibility of the ICSI 2019 organizers. Keywords: Fiber optic strain sensor; fiber Bragg grating; capillary; numerical simulation. Keywords: Fiber optic strain sensor; fiber Bragg grating; capillary; numerical simulation.
1. Introduction 1. Introduction Nowadays, more and more structures are equipped with various sensors, which make it possible to monitor both Nowadays, more and more structures withstate. various sensors, which make it of possible to monitor both important operational characteristics andare theequipped mechanical In the future, the degree integration of sensing important operational characteristics and the mechanical state. In the future, the degree of integration of sensing elements will only increase, which changes the design and development approaches and opens fundamentally new elements will only increase, which changes the design and development approaches and opens fundamentally new
* *
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 Elsevier B.V. Peer-review©under the ICSIby 2019 organizers. Peer-review under responsibility of the ICSI 2019 organizers.
2452-3216 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ICSI 2019 organizers. 10.1016/j.prostr.2019.08.049
Grigorii Serovaev et al. / Procedia Structural Integrity 17 (2019) 371–378 Author name / Structural Integrity Procedia 00 (2019) 000–000
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opportunities for assessing the state of objects as well as detecting defects at an early stage of their development. Due to the rapid growth of the telecommunications industry based on optical fibers and a lot of researches carried out in this field, the quality of fiber-optic components has significantly increased, while decreasing the production cost. This was one of the reasons for the study of the possibility of using optical fibers as sensitive elements. Fiber-optic sensors (FOSs) have several advantages compared to other sensing elements: they are not sensitive to electromagnetic effects, can operate in a wide range of temperatures, it is possible to place many FOSs on one optical fiber and simultaneously register measurements from all sensors on the line (Udd, (2011)). In this paper, Bragg grating sensors written in a standard single-mode optical fiber are considered. This type of FOSs is widely used to monitor the mechanical state of various objects (Gebremichael et al. (2005); Ghoshal et al. (2015); Hong et al. (2016); Lee et al. (2003); SierraPérez et al. (2016); Wymore et al. (2015)). Due to the small size of the optical fiber, the sensor can be embedded into the structure of the controlled object at the manufacturing stage. Thus, FOSs allow to assess the state of the product not only during its operation, but also to control the technological process of production (Matveenko et al. (2018)). The use of embedded fiber-optic strain sensors (FOSS) based on Bragg gratings, leads to a number of problems. One of which, is the redistribution of stresses in the vicinity of the embedded optical fiber, which can lead to dangerous stress concentrations. When an optical fiber is embedded in the structure of layered composite materials, there is a high probability of forming a technological defect (a resin pocket) in the inclusion region (Shivakumar and Emmanwori (2004)). In addition, an important task is to assess the reliability of the strain values, calculated based on the physical quantity measured by the sensor. Embedded optical fiber operates in a complex stress state, which prevents the direct determination of strain, since the direct correspondence between the measured Bragg wavelength shift and the longitudinal component of the strain tensor exists only for the case of uniaxial stress state of the optical fiber in the Bragg grating area. It should also be noted that in order to make reasonable use of fiber-optic strain sensor, it is necessary to evaluate the efficiency of the strain transfer from the host material to the embedded sensor. One approach to solving this problem is to use numerical simulation methods to calculate a strain transfer matrix (Luyckx et al. (2010)). In order to eliminate the effect of transverse strains on the FOSS measurements, the Bragg grating area may be surrounded by a capillary tube. (Voet et al. (2010)) have shown that the encapsulation of the Bragg grating in the capillary ensures the preservation of a single peak in the reflected spectrum after the implementation of the technological process of the composite material manufacturing. Another example of encapsulation of the Bragg grating area into the capillary is presented by (Li et al. (2014)), in which the use of a capillary is aimed at increasing the temperature sensitivity of a fiber-optic sensor. In this paper, the use of a capillary tube in the Bragg grating area to ensure uniaxial stress state of the sensor is studied. This enables the use of a direct relation between the measured value of the Bragg wavelength shift and the longitudinal strain. With the help of numerical simulation methods, geometrical and mechanical parameters of the structural scheme of a capillary tube were investigated. The stress concentration in the vicinity of the embedded optical fiber with a capillary was analyzed. 2. The principle of FBG operation The fiber Bragg grating (FBG) is a periodic change in the refractive index on a specific region of the core of a single-mode optical fiber. Such grating works as a narrowband reflecting optical filter. The light source sends a broadband optical signal through a fiber-optic core. Most of the light passes through the grating without reflection, and only light in a certain narrow wavelength range is reflected from the grating. The central wavelength (Bragg wavelength) λ* of the reflected signal is proportional to the effective refractive index n of the optical fiber core in the region of the grating and the geometric length of the grating period (Othonos (1997)).
* = 2n
(1)
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With a change in temperature or mechanical strain of the optical fiber in the grating region, a linear shift of the central wavelength of the reflected signal Δλ occurs. The principle of operation of fiber-optic Bragg grating sensors is based on the registration of this shift. This approach also allows an easy multiplexing, i.e. writing multiple FBG point sensors in one optical fiber and making simultaneous measurements from all sensors. In this paper, it is assumed that FOSS operates under isothermal conditions and the effect of temperature on FBG readings is not taken into account. In the general case, the relationship between the change in the central wavelength of the reflected spectrum and the strain of the optical fiber in the Bragg grating area is determined by the equations (Measures (2001)): 1 1 = 3 − n 2 ( p111 + p12 ( 2 + 3 )) * 2 2 1 = 3 − n 2 ( p11 2 + p12 (1 + 3 )) 2 *
(2)
where 3 – longitudinal strain component along the fiber, 1 , 2 – principal strains in the plane perpendicular to the optical fiber, 1 = 1 − * , 2 = 2 − * – central wavelength shifts in the current 1 , 2 and initial * moments of time, p11 , p12 – strain optic coefficients. These equations are given for low birefringence optical fibers when n= n= n. 1 2 In the special case when the optical fiber in the region of the Bragg grating is in uniaxial stress state, the following relations between the components of the strain tensor are valid: 1 = 2 = −3 , where – Poisson’s ratio of the
optical fiber. In this case 1 = 2 = and
n 2 = 1 − ( p12 − ( p11 + p12 ) ) 3 * 2 1 3 = * k
(3) (4)
For silica glass fiber p11 = 0.113 , p12 = 0.252 , n =1.458 (Bertholds and Dandliker (1988)), = 0.17. Thus, under the uniaxial stress state of the Bragg grating, the coefficient k~0.798. When the Bragg grating is written in a low-birefringence standard single-mode optical fiber, the original spectrum of the signal reflected from the grating contains only one peak, the wavelength of which is determined by relation (1). It is known that the application of loads in the diametric direction leads to a change in the shape of the spectrum of the reflected signal, and when a certain level of transverse strains is exceeded, two peaks are observed on the reflected spectrum (Wagreich et al. (1996)). When a fiber optic sensor is embedded in a material, a complex stress state will be realized in the sensor as a result of interaction with the material, i.e. the strains 1 , 2 , 3 , will take place in the optical fiber which must be identified on the basis of experimental information, namely values 1 / * and 2 / * . From relations (2) it follows that if 1 2 , there are two equations with three unknowns, and if 1 =2 , one equation with two unknowns, which makes it impossible to unambiguously determine the longitudinal component of the strain tensor in the case of a complex stress state. It is worth noting that the sensitivity of FBG to transverse strains is used for creating sensors that allow to simultaneously measure several strain tensor components (Sonnenfeld et al. (2015)). In such cases, polarization maintaining (PM) optical fibers are used, for which the original spectrum of the signal reflected from the grating contains two separate peaks. This allows to separate the sensitivity of the sensor in the longitudinal and transverse directions. However, due to the substantially different sensitivity of the fast and slow axes of the PM optical fiber to
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transverse strain, very strict adherence to the orientation of the optical fiber is required during embedding process, which is a complex technological problem. Another factor influencing the shape of the reflected Bragg grating spectrum and introducing complexity to the definition of strain is the non-uniform strain distribution along the Bragg grating length (Peters et al. (2001)). The Bragg grating length can vary over a wide range of values. When optical fiber is embedded in the structure of such materials as laminated polymer composites, concretes, etc. consisted of several structural constituents there is a high probability of the occurrence of process-induced strains nonuniformly distributed along the length of the grating at the manufacturing stage. Thus, it is necessary to carry out studies that suggest ways to solve the problems described above for the use of FOSS based on the Bragg gratings embedded in the material. In this paper, we study the possibility of using a capillary in the Bragg grating area, which will provide the uniaxial stress state of the grating and uniform strain distribution along its length. 3. Application of the capillary tube One of the directions for obtaining reliable information about the strains measured by the embedded Bragg grating sensors is associated with a change in the conditions of interaction with the host material in the Bragg grating area. In a constructive implementation, this can be achieved by using a capillary tube around the fiber in the section of the Bragg grating (figure 1).
Fig. 1. The scheme of a capillary tube in the Bragg grating area.
The essence of this scheme is that the capillary tube, which represents the additional external coating (capillary coating) and the cavity between the coating and the optical fiber, protects the Bragg grating from the effects of transverse strain. Thus, the sensor region will be under conditions of a uniaxial stress state, under which there is a direct correspondence between the measured value of the Bragg wavelength shift and the longitudinal strain using the relation (4). The interaction of the capillary tube and the optical fiber is provided through the connecting elements (binders) on opposite sides of the tube. In this case, the Bragg grating region can be, as covered by a protective coating or remain without any protective coating. To measure compressive strain, it is necessary to provide the preliminary tension of the optical fiber. The degree of which will determine the maximum possible value of the recorded compressive strain. The geometrical dimensions of the capillary will be determined by the thickness t, the length l, and the size of the cavity tc (figure 2). In addition, it is important to choose the material of the capillary coating, and therefore, to choose the elastic modulus E c and the Poisson’s ratio c (assuming that the coating is made of isotropic material).
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Fig. 2. Geometric parameters of the capillary tube.
The capillary tube must meet the following conditions: the realization of a uniaxial stress state in the Bragg grating area and the coincidence of the strain values along the fiber directly in the fiber and in the material adjacent to the fiber. Fulfillment of these conditions will provide a reliable measurement of the longitudinal strain with the help of the FOSS. On the other hand, the dimensions of the additional external coating and cavity should ensure a uniform distribution of the strain along the entire length of the Bragg grating and exclude the possibility of touching of the outer coating and the optical fiber in a wide load range. With the help of numerical simulations, the parameters of a capillary tube were estimated on a model problem for a parallelepiped with embedded optical fiber and a capillary in the Bragg grating area (figure 3a). The optical fiber has a diameter of 0.124 mm and a protective coating made of polyimide with a thickness of 0.012 mm. The Bragg grating length is 33 optical fiber diameters (5 mm). The length of the parallelepiped is 8 times longer than the Bragg grating length and in the cross section has the shape of a square with a side equal to 40 diameters of the optical fiber. As an external load, pressure P distributed along the parallelepiped edge in the direction perpendicular to the optical fiber is considered. In this loading case, the greatest difference from the uniaxial stress state takes place in the optical fiber. The calculation of the stress-strain state was carried out by the finite element method in the framework of the linear elastic theory. Perfect contact of all adjacent parts of the model is assumed. Due to symmetry, a quarter of the model with the corresponding boundary conditions was considered. In the finite element method implementation, a mesh with a refinement in the inclusion region was used (figure 3b).
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Fig. 3. а) calculation scheme for a parallelepiped with embedded optical fiber and a capillary in the Bragg grating area; b) finite element model.
In the numerical simulations the following mechanical properties of materials were used: for an optical fiber made 0.35 ; for controlled material of silica glass Eo = 71.4 GPa, o =0.17 and polyimide coating E p = 2.5 GPa, p =
Eh = 30 GPa, h =0.18 (these properties correspond to concrete). The connecting elements (binders) between the capillary coating and the optical fiber are made of epoxy resin with properties Eb = 3 GPa, b =0.35 . The material properties of the capillary coating may vary. The external pressure P substantially exceeds (10 times) the compressive strength for the material under consideration and is equal to P = 410 MPa. The study of the cavity size tc between the optical fiber and the external coating is carried out on the basis of estimation of the parameter d, corresponding to the relative change in the initial distance between the external coating and the optical fiber t c0 and the minimum distance tc1 after application of the critical load P (figure 4). = d
tc1 − tc0 100% tc0
(5)
Fig. 4. The scheme of deformation of the cavity between the external coating and the optical fiber.
In the performed calculations, the value of the initial cavity size t c0 varied in the range from the size of the optical fiber protective coating, which is equal to 0.012 mm, up to 0.024 mm. The material properties of the external coating coincide with the properties of controlled material. Figure 5 shows the dependence of the parameter d on the cavity size tc under compressive load.
Fig. 5. а) change in parameter d depending on cavity size; b) change in parameter d depending on the modulus of elasticity of the external coating.
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From the obtained results, it can be concluded that even with a small value of the cavity size and with the load, which significantly exceeds the material strength, the reduction of the gap between the external coating and the optical fiber does not exceed 30%. The change in the elasticity modulus of the external coating with the constant cavity size and thickness of the external coating (0.012 mm) also slightly affects the gap size between the coating and the optical fiber under external load. It should be noted that with the considered parameters of the capillary tube and the material properties, in which the optical fiber is embedded, it is possible to achieve a uniaxial stress state in the Bragg grating area. At this case, the relative difference between the longitudinal strain values in the fiber and in the material zone adjacent to the fiber does not exceed 3%. However, for the anisotropic properties of the host material with a circular section of the additional coating, these conditions are not met. Studies have shown that achieving an acceptable coincidence of strain along the fiber and strain in the material, E= 0.035 , 84.1 GPa, Ez = 10.7 GPa, xy = made of carbon fiber-reinforced plastic with effective properties E= x y
yz = xz =0.45 , Gxy = 4.3 GPa, G= G= 3.5 GPa, is possible with an elliptical cross section of the capillary with yz xz a ratio of ellipse semi-axes equal to a/b = 0.6, where the semi-axis a coincides with the y axis. Embedding into the material such a foreign object as an optical fiber causes a redistribution of the stress-strain state in a certain vicinity around the embedded object and may cause a high stress concentration. As part of the study, analysis of the value K y = y P was made that determines the stress concentration coefficient for the corresponding component of the stress tensor. The stress concentration field Ky for the central along the length cross section of the model for the cases with embedded optical fiber without a capillary tube and with the presence of a capillary tube is presented in figure 6.
Fig. 6. The stress concentration field Ky for material with embedded optical fiber: а) without a capillary tube b) with a capillary tube.
The optical fiber embedding causes a stress concentration K y = 1.81 in the vicinity of the fiber, and taking into account in the calculation scheme of the cavity between the optical fiber and the external coating increases the stress concentration to a value of 3.03. A change in the cavity size by 2 times does not significantly affect the stress concentration value. These results are obtained for the studied isotropic material. However in case of composite material with effective mechanical properties described previously, the embedding of the optical fiber leads to a stress concentration K y = 3.87 and introducing the capillary into the model, increases the stress concentration up to the value of 6.31. This means that for anisotropic materials, such as composites, the risk of material failure in the vicinity of the embedded optical fiber and capillary tube is higher compared to the isotropic materials. These results should be taken into account during the design stage of product development.
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4. Conclusions In the paper, the possibility of providing a uniaxial stress state in the vicinity of FOSS based on the use of a capillary tube in the Bragg grating area, was studied. Numerical analysis of the cavity size between the external coating (capillary coating) and the optical fiber showed that for the case of an isotropic material, in which the fiber is embedded, it is possible to ensure the conditions of a uniaxial stress state, uniformity of longitudinal strains along the Bragg grating length, coincidence of longitudinal strains in the optical fiber and in the controlled material, as well as to exclude the contact of the external coating and the optical fiber under the most unfavourable loading case. Numerical calculations showed a slight effect of the elastic modulus of the capillary coating on the cavity size under the load. However, the presence of a cavity in the capillary leads to an increase in stress concentration, which must be taken into account when designing a capillary tube for a particular application. These results confirm the effectiveness of the structural scheme of the capillary in the area of FOSS when embedding optical fiber into the controlled material. Acknowledgements This study was supported by Russian Science Foundation (project No.15-19-00243). References Bertholds, A., Dandliker, R., 1988. Determination of the individual strain-optic coefficients in single-mode optical fibres. Journal of Lightwave Technology 6, 17–20. Gebremichael, Y.M., Li, W., Boyle, W.J.O., Meggitt, B.T., Grattan, K.T.V., McKinley, B., Fernando, G.F., Kister, G., Winter, D., Canning, L., Luke, S., 2005. Integration and assessment of fibre Bragg grating sensors in an all-fibre reinforced polymer composite road bridge. Sensors and Actuators A: Physical 118, 78–85. Ghoshal, A., Ayers, J., Gurvich, M., Urban, M., Bordick, N., 2015. Experimental investigations in embedded sensing of composite components in aerospace vehicles. Composites Part B: Engineering 71, 52–62. Hong, C.-Y., Zhang, Y.-F., Zhang, M.-X., Leung, L.M.G., Liu, L.-Q., 2016. Application of FBG sensors for geotechnical health monitoring, a review of sensor design, implementation methods and packaging techniques. Sensors and Actuators A: Physical 244, 184–197. Lee, J.-R., Ryu, C.-Y., Koo, B.-Y., Kang, S.-G., Hong, C.-S., Kim, C.-G., 2003. In-flight health monitoring of a subscale wing using a fiber Bragg grating sensor system. Smart Materials and Structures 12, 147–155. Li, Y., Wen, C., Sun, Y., Feng, Y., Zhang, H., 2014. Capillary encapsulating of fiber Bragg grating and the associated sensing model. Optics Communications 333, 92–98. Luyckx, G., Voet, E., De Waele, W., Degrieck, J., 2010. Multi-axial strain transfer from laminated CFRP composites to embedded Bragg sensor: I. Parametric study. Smart Materials and Structures 19, 105017. Matveenko, V.P., Kosheleva, N.A., Shardakov, I.N., Voronkov, A.A., 2018. Temperature and strain registration by fibre-optic strain sensor in the polymer composite materials manufacturing. International Journal of Smart and Nano Materials 9, 99–110. Measures, R.M., 2001. Structural monitoring with fiber optic technology. Acad. Press, San Diego, pp. 716. Othonos, A., 1997. Fiber Bragg gratings. Review of Scientific Instruments 68, 4309–4341. Peters, K., Studer, M., Botsis, J., Iocco, A., Limberger, H., Salathé, R., 2001. Embedded optical fiber Bragg grating sensor in a nonuniform strain field: Measurements and simulations. Experimental Mechanics 41, 19–28. Shivakumar, K., Emmanwori, L., 2004. Mechanics of Failure of Composite Laminates with an Embedded Fiber Optic Sensor. Journal of Composite Materials 38, 669–680. Sierra-Pérez, J., Torres-Arredondo, M.A., Güemes, A., 2016. Damage and nonlinearities detection in wind turbine blades based on strain field pattern recognition. FBGs, OBR and strain gauges comparison. Composite Structures 135, 156–166. Sonnenfeld, C., Luyckx, G., Sulejmani, S., Geernaert, T., Eve, S., Gomina, M., Chah, K., Mergo, P., Urbanczyk, W., Thienpont, H., Degrieck, J., Berghmans, F., 2015. Microstructured optical fiber Bragg grating as an internal three-dimensional strain sensor for composite laminates. Smart Materials and Structures 24, 055003. Udd, E. (Ed.), 2011. Fiber optic sensors: an introduction for engineers and scientists, 2. ed. ed. Wiley, Hoboken, NJ, pp. 512. Voet, E., Luyckx, G., De Waele, W., Degrieck, J., 2010. Multi-axial strain transfer from laminated CFRP composites to embedded Bragg sensor: II. Experimental validation. Smart Materials and Structures 19, 105018. Wagreich, R.B., Atia, W.A., Singh, H., Sirkis, J.S., 1996. Effects of diametric load on fibre Bragg gratings fabricated in low birefringent fibre. Electronics Letters 32, 1223. Wymore, M.L., Van Dam, J.E., Ceylan, H., Qiao, D., 2015. A survey of health monitoring systems for wind turbines. Renewable and Sustainable Energy Reviews 52, 976–990.