PSI - Issue 17

Grigorii Serovaev et al. / Procedia Structural Integrity 17 (2019) 371–378 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

373

3

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)):

*   

2 1 ( 2 1 (

11 1 n p p

12 2  +  +  (

))

=  −

1

3

3

(2)

2 n p p 11 2

12 1 3  +  +  (

))

=  −

2

3

*

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, 11 12 , p p – strain optic coefficients. These equations are given for low birefringence optical fibers when 1 2 n n n = = . 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 ( ) 2 12 11 12 3 * 1 ( ) 2 n p p p    = − −  +       (3) For silica glass fiber 11 0.113 p = , 12 0.252 p = , 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 3 * 1 k   =   (4)