Diagnostics of impregnation defects of reinforcing filaments of polymer composite with built-in fibre-optic sensor with distributed Bragg grating

Mathematical model of unidirectional fibrous polymer composite material with optical fiber sensor built into reinforcing fiber (filament of elementary fibers) with distributed Bragg grating is developed in order to diagnoste defects of filament impregnation - finding probability of impregnation defect as relative length of local sections of filament without impregnation, i.e. without filling binder of space between its elementary fibers. The technique of digital processing of reflection spectrum according to the solution of the integral Fredholm equation of the 1st kind is used in order to find the desired informative function of density of distribution of axial strains along the length of the sensitive section of the fibre-optic sensor. The approach assumes that the optical fiber sensor is embedded in the composite material at the stage of its manufacture, wherein the low-reflective nature of the sensitive portion of the optical fiber allows linear summation of reflection coefficients from its various local portions regardless of their mutual positions. Algorithm of numerical processing of strain distribution density function is developed for finding of sought probability of presence of impregnation defects along filament length. It has been revealed that the distribution density function has pronounced informative pulses, from the location and value of which the sought-after values of probability of presence of impregnation defects along the length of the filament can be found. The results of diagnostics of different values of the sought probability of the filament impregnation defect are presented based on the results of numerical simulation of the measured reflection spectra and the sought function of strain distribution density along the length of the sensitive section of the optical fiber sensor at different values of the volume fraction of the filaments, combinations of transverse and longitudinal loads of the representative domain of the unidirectional fibrous composite material in comparison with graphs for the case without load.