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
