The modelling of electromagnetic methods for the nondestructive testing of fatigue cracks
This thesis describes a theoretical and experimental investigation of electromagnetic methods for the detection and measurement of metal fatigue cracks. The available methods are reviewed, with particular attention being paid to mathematical models, and a new model of the electromagnetic field near a metal fatigue crack for small skin-depths is presented which uses a surface impedance boundary condition with the addition of a line source to represent the crack. This leads to a coupled system of two magnetic scalar potentials, one on the crack face which obeys the two-dimensional Laplace equation and one outside the test-piece which obeys the three-dimensional Laplace equation. The behaviour of the field is governed by a parameter m =l/(μ, δ), where l is the size of the field perturbation, μ, is the relative permeability and δ is the skin-depth. When m is small, almost all the flux is concentrated inside the metal and the exterior potential also obeys the two-dimensional Laplace equation, on the test-piece surface. When m is large, the perturbation part of the exterior field has a negligible effect on the field inside the crack so that the crack-face potential may be found by the Born approximation. The general m problem is solved for rectangular and semi-elliptical cracks in flat plates, interrogated by uniform fields, and the solution is verified experimentally. A method for calculating the crack depth from the magnetic field is given, with descriptions of industrial applications. The theory is further developed to find the impedance change in an air-cored circular coil caused by a crack, to find the field near overlapping cracks and to find the field near a crack in an interior corner. Finally, a semi-empirical analysis is presented for a ferrite-cored measuring coil.