An Approximate Analytical Model of Surface Cracks in AC Field Measurement Technique

An appropriate modeling technique is critical for the quick analysis of alternating current (ac) field measurements destined for qualitative or quantitative studies of surface defects in conductive materials. Traditional modeling techniques often use the finite-difference method to solve the governing Laplace equation in the crack region, which gives a closed-form solution in the Fourier domain for regions outside the crack. However, these models are complex and only useful for cracks with extremely narrow openings. This article proposes an approximate analytical model that is based on current shunting of parallel circuits and the Biot–Savart law. We assume that the current induced by a high-frequency current-carrying coil is evenly distributed within a very thin layer at the surface of a conductor. In the presence of a defect, the current flows only along the edges and the bottom of the defect. Under these assumptions, the model simplifies the induced current by treating it as due to many current sources of equal amplitude. The magnetic field above the defect can be mathematically described by the linear superposition of these current sources. The proposed model can thus be used to analyze cracks with wider openings. We compare the magnetic-field signals of flat-bottomed cracks of various sizes as obtained by the proposed model and the finite-element method and also explore cracks with complex bottom profiles. The results show that the proposed model produces accurate quantitative and qualitative results for a wider range of defects.