Physics-Driven Linear Quantification of Matrix Crack Density in Composites via Continuous Centroid Analysis of FBG Sensors

We proposed a novel continuous centroid analysis method using embedded fiber Bragg grating (FBG) sensors, to linear quantify the density of transverse matrix cracks in fiber-reinforced polymer (FRP) composites. A physics-driven theoretical framework is established, that correlates crack-induced strain fields with spectral energy migration in FBG reflection spectra. Analytical derivations confirm that the wavelength difference of newly-emerged spectral peak is inversely proportional to the crack spacing. Numerical simulations conducted on the conditions of random crack distributions validate the linear quantification capability of the method. Repeatability analyses validate the effectiveness of the method across multiple test scenarios, with a mean value ofR² value approximately equal to 0.88. Experimental results from the characterization of carbon fiber-reinforced polymer laminates demonstrate the efficacy of the method for linear quantification of transverse matrix crack density, yielding anR² value of 0.83 and an RMSE of 0.034nm through the proposed indicator. Furthermore, experiments have demonstrated the insensitivity of this method to external temperature variations. Within the range of 30 °C to 75 °C, the maximum fluctuation of the compensated indicator is only 4.87×10-3nm. The indicator exhibits insensitivity to randomness in crack distribution, establishing the proposed method as an effective approach for quantifying transverse matrix crack density in FRP composites.