On integral equation methods of solution to eddy current interaction problems

Doctoral thesis, 2014

The eddy current method is used for nondestructive evaluation of conducting materials. To achieve a greater knowledge and insure safe and reliable evaluation methods, the use of mathematical models and simulations are needed. In this thesis integral equation methods of solutions are applied to solve the eddy current interaction problem which essentially is a scattering problem. This involves a Green's function technique to generate integral relations between the surface fields and the fields everywhere else. Then the key is to use suitable basis functions to describe the surface fields. In the end numerical integration is used to obtain the solution, the change of impedance due to the scatterer. The scatterer in this case is a model of a defect and the source is a single conductor or a single coil. The solutions are compared to Finite Element solutions with good agreement. This thesis includes four papers where two different methods of solution have been used. In the first paper, the T matrix method is applied on a 2D problem with a subsurface defect. The second paper presents a boundary integral equation method solution to a problem with a surface-breaking flat and infinitely long crack. In the third and fourth papers the 3D problem of a rectangular crack is solved also using a boundary integral method. In the third paper the surface of the material is a plane and in the fourth it is the inside of a cylindrical hole. All papers contain comparisons with finite elements calculations and good agreement is found for all methods presented in the present thesis. The advantage of these methods compared with the finite element method is the numerical efficiency.