Magnetic Flux Leakage Method: Large-Scale Approximation

We consider the application of the magnetic flux leakage (MFL) method to the detection of defects in ferromagnetic (steel) tubulars. The problem setup corresponds to the cases where the distance from the casing and the point where the magnetic field is measured is small compared to the curvature rad...

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Bibliographic Details
Published in:Mathematical modelling of natural phenomena 2015-01, Vol.10 (3), p.61-70
Main Authors: Pimenova, A. V., Goldobin, D. S., Levesley, J., Ivantsov, A. O., Elkington, P., Bacciarelli, M.
Format: Article
Language:English
Subjects:
78A30
78A55
78M34
Approximation
corrosive defects
Curvature
Defects
Deformation
Ferromagnetism
Inhomogeneity
large-scale approximation
Leakage
Magnetic fields
Magnetic flux
magnetic flux leakage
Magnetism
Mathematical analysis
Steel
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Summary:We consider the application of the magnetic flux leakage (MFL) method to the detection of defects in ferromagnetic (steel) tubulars. The problem setup corresponds to the cases where the distance from the casing and the point where the magnetic field is measured is small compared to the curvature radius of the undamaged casing and the scale of inhomogeneity of the magnetic field in the defect-free case. Mathematically this corresponds to the planar ferromagnetic layer in a uniform magnetic field oriented along this layer. Defects in the layer surface result in a strong deformation of the magnetic field, which provides opportunities for the reconstruction of the surface profile from measurements of the magnetic field. We deal with large-scale defects whose depth is small compared to their longitudinal sizes—these being typical of corrosive damage. Within the framework of large-scale approximation, analytical relations between the casing thickness profile and the measured magnetic field can be derived.
ISSN:0973-5348
1760-6101
DOI:10.1051/mmnp/201510306