A numerical two-dimensional modelling of eddy-currents: An application to non-destructive test

A way to detect cracks in steam-generator tubes, consists in using probes made of two coils of wire, concentric with the axis of the tube. Alternating currents of the same amount flow in the coils. As the probe is moved inside the tube, eddy currents, circulating in its wall, are created. Then, these eddy currents cause in the coils e.m.f.´s, opposing the initial currents. A crack in the tube offers resistance to the eddy currents circulation, and in so far as the coils are not equidistant from the crack, their corresponding e.m.f.´s are not equal. The e.m.f.´s difference, represented by a complex number, is visualized on a cathodic screen. We decided to build up a mathematical model, allowing us to compute these e.m.f.´s differences in order to get a better knowledge of the relations between crack and visual signals on screens. We had to solve the following problem : knowing Jo, current-density in the coils, determine the induced current density J, in the tube, and then the e.m.f.´s in the coils.