Development of a Simplified Mathematical Model for FBG Sensor Bonding: Combining Mechanical Deformation and Thermal Expansion Effects

Fiber Bragg Grating (FBG) sensors, a specialized application of optical fiber technology, have become increasingly popular in aerospace and other demanding fields due to their advantages over traditional electronic sensors. Optical fibers offer immunity to electromagnetic interference, durability under extreme conditions, passive operation, high sensitivity, and multiplexing capabilities. These features make FBG sensors ideal for advanced measurement systems that rely on numerous accurate data points for effective monitoring, diagnostics, and prognostics. A key challenge, however, lies in ensuring the accuracy of measurements, which can be influenced by how sensors are bonded to the components being monitored. This thesis aims to address this issue through the development of a mathematical model for FBG sensor bonding. In the first part of the thesis the base model representing the mechanical interactions between the layers of the bonding was developed. The base model was simplified by introducing specific hypotheses, particularly regarding the geometry of the epoxy resin and the way deformation from the specimen is transmitted through the resin to the sensor. Once the mechanical base model was developed, the deformations caused by the thermal expansion were introduced. The model can be thus used to study the response of the sensors to both strain and temperature variations. In addition, this thesis introduces a preliminary modeling of friction effects within the bonding, providing a foundation for future developments. To test the model's accuracy, a specimen with three FBG sensors was subjected to controlled temperature steps, and data from the sensors were compared with simulated results. This comparison suggests that the model has the potential to enhance the reliability of strain and temperature measurements by accounting for bonding-related discrepancies, thereby supporting more precise applications of FBG sensors in critical monitoring systems.