Model for nondestructive evaluation of hidden defect in arbitrary layers of conductive material using E-core coil sensor

Purpose Eddy current nondestructive testing using ferrite core coil sensors demonstrates superior sensitivity in detecting and locating defects like cracks and corrosion within layered conductive materials compared to air core coil sensors. Developing an accurate mathematical model that captures the relationship between sensor input and output is crucial for both enhancing the understanding of the detection process and facilitating the design of more sensitive sensors. However, current mathematical models using ferrite core sensors for evaluating defects in multilayered conductors are limited to two or three layers, primarily focusing on defects within the first or second layer. A generalized mathematical model capable of addressing defect detection in conductive materials comprising an arbitrary number of layers with concealed defects, using ferrite core coil sensors, has yet to be established. To address this gap, this paper aims to propose and validate a mathematical model specifically for an E-core coil sensor used to evaluate conductors with an arbitrary number of layers containing a hidden hole. Design/methodology/approach First, a model diagram is constructed representing an arbitrary number of conductive layers, with distinct symbols indicating the total number of layers and the location of a defect. A cylindrical coordinate system is used, and the Truncated Region Eigenfunction Expansion method is used to limit the solution domain to a radius of “b.” The magnetic vector potential of each region generated by the filamentary coil is derived. By applying boundary and interface conditions, the impedance of a multi-turn coil is obtained in closed-form using the superposition method, along with corresponding coefficient expressions for defects in any inner layer of the arbitrary number of layers conductor. To validate the model, a specific scenario involving a five-layer conductor with a defect (hole) in the second layer is analyzed using Mathematica and simulated with Ansoft software. The model is then used to investigate the impact of the five-layer conductor with the defect on the impedance change of both E-core and air-core sensors across a frequency range of 100 Hz to 10 kHz. In addition, the influence of a hidden hole on the impedance change of both sensor types is also explored. Findings This paper presents a mathematical model for detecting and evaluating conductive materials with hidden defect. The model uses an E-core coil sensor and incorporates an arbitrary number of layers in the conductive material. It efficiently calculates the impedance change in the E-core coil resulting from both the arbitrary number of layers of conductor and the presence of a defect. The model’s accuracy is validated through finite element analysis and experimental measurement. Originality/value This paper proposes a precise mathematical model for assessing planar conductor with an arbitrary number of layers and potential defect, leveraging a ferrite core coil sensor. This model can be used to analyze how the number of layers of conductor and defect location impact the sensor’s impedance. Furthermore, it enables the design of optimized ferrite core coil sensors and facilitates the direct detection of hidden defect within multilayered conductor.