Insight Into the Eddy-Current Reflection Coefficient of Plates and Pipes

The forward model of eddy-current (EC) testing can predict the measurement signals, provided the known measurement conditions and physical properties of test pieces. In the analytical forward model, the test pieces are characterized by the reflection coefficient (RC), which describes the reflection characteristics of test pieces regarding incident electromagnetic (EM) waves and determines the phase of EC signals. The RC is calculated analytically with boundary conditions, which is sophisticated for analyzing complex geometries. In this study, the analytical model of plate and pipe testing using second-order vector potential (SOVP) is investigated. It is found that the numerical RC can be obtained from the source EM field in the air and counterparts in the presence of test pieces. In numerical simulations, the numerical RC is compared with the analytical RC for plate and pipe in a 2-D axisymmetric model. In the 3-D model, the calculated numerical RC corresponds to the dimensions of the measured plate and pipe with defects. In both 2-D and 3-D models, the phase of coil inductance from the numerical RC aligns with the finite-element solutions. It is validated that the RC is a characteristic of test pieces independent of the source field.