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Scanning magnetic microscopy model analysis of circular flaws in thin metallic plates
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Image of FIG. 1.
FIG. 1.

Schematic representation of the simulated scanning operation over a flawed metallic plate. The midplane of the plate coincides with the plane.

Image of FIG. 2.
FIG. 2.

The -component of the magnetic field generated by a circular coil of radius at different distances from the coil plane as a function of the radial coordinate . The gray lines illustrate the step function used in this work to approximate the field generated by the coil. For simplicity, we choose . The field is normalized to its value in the center of the coil, .

Image of FIG. 3.
FIG. 3.

Comparison between the solution for the distribution of the eddy current found in this work (solid line) for the unflawed plate and the Dodd and Deeds theory (Ref. 4) (dashed line). Note the linear growth of the current intensity between and

Image of FIG. 4.
FIG. 4.

Current lines in the presence of a circular hole [centered in (0, 0)] calculated as level curves of the magnetic field function derived in this work (arbitrary units). The outer circle sets the extension of the eddy currents.

Image of FIG. 5.
FIG. 5.

Simulated magnetic field profiles for different sensor lift-off values: (a) 5 mm radius hole, (b) 2 mm radius hole. The other parameters used for the simulations are: , , , and . Starting from the top to the bottom curve the scanning distance, in both figures, increase as follows: .

Image of FIG. 6.
FIG. 6.

Comparison between the magnetic field profiles obtained by our analytical model (solid line) and direct numerical simulations (open dots): (a) 5 mm radius hole and (b) 2 mm radius hole. For the comparison, we have chosen the first four curves of Fig. 5 corresponding to scanning heights , respectively.

Image of FIG. 7.
FIG. 7.

Schematic representation of the simulated scanning. The wider circle of radius represents the plate zone in which eddy currents are confined. As this zone moves with the coil (and the sensor), from the left to the right, over the hole, the -component of the magnetic field is calculated at the sensor position (the center of the wider circle ) by an integration over the regions denoted as 1, 2, 3, and 4. During this process, the hole boundary (the smaller circle of radius ) remains confined within the circle of radius , i.e., within the zone of the eddy current extension.


Generic image for table
Table I.

Values of the external magnetic field (nT) at the midplane of the plate ( plane) generated in the center coil for a given lift-off . It is also reported the calculated background signal [Eq. (A3)] for the case of Fig. 5.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Scanning magnetic microscopy model analysis of circular flaws in thin metallic plates