Analytical Modeling of the Interaction of a Finite Inducer with a Hidden Long Crack in Ferromagnetic Metals

Abstract

This paper proposed a semi-analytical solution for evaluation of field distributions around the surface of a ferromagnetic metallic half space, which contains a hidden long crack and excited by a three-dimensional arbitrary frequency current-carrying inducer. The solution was obtained by using the method of separation of variables in three dimensions. This research assumed that the conductor as a lossy dielectric and used the concept of a rectangular waveguide, which is partially loaded with dielectric to expand all TM and TE field components in the problem. To obtain convergent results, the eigenvalue equation associated with TE modes in the flawed region. By imposing boundary conditions and using the mode matching technique, we obtained a linear system of AX=B was obtained, which is solved to attain the unknown coefficients. The accuracy and efficiency of the modelling technique is confirmed by comparing the results with those obtained by CST finite integration code.