Non-destructive testing example : Coil above a crack

The structure consists of a block of austenitic stainless steel which contains a rectangular slot, representing a flaw (see Fig. 1). A differential probe moves across the surface of the block. The probe is a cylinder with an inducing solenoid 44 mm in diameter and two smaller receptive solenoids 10 mm in diameter. Each of these two solenoids is placed in a branch of a Wheatstone's bridge. Therefore, the measured voltage signal is proportional to the difference of the magnetic fluxes in the two receiver solenoids.

Since the benchmark requires results for various relative positions of the coil and crack, the x and y coordinates of the crack were parameterized.

The excitation coil was defined by using the "coil" feature of CST EMS. The receiving coils do not need to be modelled as 3D objects. Instead, the magnetic fluxes at the locations of the receiving coils are calculated in the postprocessing phase.

Since the signal which needs to be detected is very small, it can be affected by large numerical errors. In order to avoid this, the "perturbation" flux in each receiving coil was calculated, by computing the difference between the the magnetic fluxes with and without a crack. The corresponding magnetic flux densities are shown in Figures 2-4.

The difference of the perturbation magnetic fluxes in the two receiving coils, for different positions of the crack, was computed.

The signal trajectory in the Real-Imaginary plane, for a coil placed 28 mm above the plate and moved parallel to the crack is plotted in Figure 5, showing a good agreement with the measured results (Figure 6).