The Mathematical Model of a Built-In Fiber Optic TFBGs Sensor with Tilted Bragg Gratings for Diagnosing a Complex Deformed State in Polymer Composite Structures

The paper presents mathematical models of functioning and numerical values of information transfer coefficients for new built-in fibre-optic TFBGs-sensors (Tilted Fiber Bragg Gratings) with tilted Bragg gratings to diagnose a complex stress-strain state inside loaded polymer composite structures. The fiber optic TFBGs sensors have the form of a continuous structured cable system, in which six unidirectional light guides with the built-in Bragg gratings are placed with a fixed mutual hexagonal arrangement in extended continuous cylindrical polymer sensor housing. Different 3D orientations of reflecting surfaces for different light guides were defined through the coordinates of non-planar normals to these surfaces. Numerical modeling of deformation fields in the elements of the fiber optic TFBGs-sensor was carried out for the calculation area composite material/built-in sensor within the linear theory of elasticity. We present color diagrams of distributions for various components of the strain field along the middle cross-section of the calculation area with corresponding simple cases of its macrostrains. Also we give numerical values of strain tensor components averaged over the area of each light guide. Further, values of strain components averaged over the light guides are used to calculate axial strains along non-planar vectors - normals to reflecting surfaces of the tilted Bragg gratings. As a result, numerical values of the desired information transfer coefficients of the fibre-optic TFBGs sensor were found taking into account given orientations of reflecting surfaces of the tilted Bragg gratings of the sensor light guides. Thus, the task of diagnosing a complex deformed state inside a loaded polymer composite structure in a local neighborhood of a built-in fiber optic TFBGs sensor is reduced to solving a system of linear algebraic equations regarding the desired six independent components of the macrodeformation tensor of this neighborhood from the measured spectra of reflections of the optical fibers of the sensor.