Multi-layer conductive structures, especially those with features like bolt holes, are vulnerable to hidden corrosion and cracking, posing a serious threat to equipment integrity. Early defect detection is vital for implementing effective maintenance strategies. However, the subtle signals produced by these defects necessitate highly sensitive non-destructive testing (NDT) techniques. Analytical modeling plays a critical role in both enhancing defect-detection capabilities and guiding the design of highly sensitive sensors for these complex structures. Compared to the finite element method (FEM), analytical approaches offer advantages, such as faster computation and high accuracy, enabling a comprehensive analysis of how sensor and material parameters influence defect detection outcomes. This paper introduces a novel T-core eddy current sensor featuring a central air gap. Utilizing the vector magnetic potential method and a truncated region eigenfunction expansion (TREE) method, an analytical model was developed to investigate the sensor’s interaction with multi-layer conductive materials containing a hidden hole. The model yielded closed-form expressions for the induced eddy current density and coil impedance. A comparative study, implemented in Matlab, analyzed the eddy current distribution generated by T-core, E-core, I-core, and air core sensors under identical conditions. Furthermore, the study examined how the impedance of the T-core sensor changed at different excitation frequencies between 100 Hz and 10 kHz when positioned over a multi-layer conductor with a hidden air hole. These findings were then compared to those obtained from E-core, I-core, and air-core sensors. The analytical results were validated through finite element simulations and experimental measurements, exhibiting excellent agreement. The study further explored the influence of T-core design parameters, including the air gap radius, dome radius, core column height, and relative permeability of the T-core material, on the inspection sensitivity. Finally, the proposed T-core sensor was used to evaluate crack and hole defects in conductors, demonstrating its superior sensitivity compared to I-core and air core sensors. Although slightly less sensitive than the E-core sensor, the T-core sensor offers advantages, including a more compact design and reduced material requirements, making it well-suited for inspecting intricate and confined surfaces of the target object. This analytical model provides a valuable tool for designing advanced eddy current sensors, particularly for applications like detecting bolt hole defects or measuring the thickness of non-conductive coatings in multi-layer conductor structures.
