Evaluation of cracks with different hidden depths and shapes using surface magnetic field measurements based on semi-analytical modelling

In this paper, we present a feasibility study for detecting cracks with different hidden depths and shapes using information contained in the magnetic field excited by a rectangular coil with a rectangular cross section. First, we solve for the eigenvalues and the unknown coefficients of the magnetic vector potential by imposing artificial and natural boundary conditions. Thus, a semi-analytical solution for the magnetic field distribution around the surface of a conducting plate that contains a long hidden crack is formulated. Next, based on the proposed modelling, the influences of the different hidden depth cracks on the surface magnetic field are analysed. The results show that the horizontal and vertical components of the magnetic field near the crack are becoming weaker and that the phase information of the magnetic field can be used to qualitatively determine the hidden depth of the crack. In addition, the model is optimised to improve its accuracy in classifying crack types. The relationship between signal features and crack shapes is subsequently established. The modified model is validated by using finite element simulations, visually indicating the change in the magnetic field near the crack. (paper)