In this paper, we present an analytical model to represent the 3-D magnetic flux leakage (MFL) field due to the occurrence of a surface-breaking defect in a ferromagnetic specimen. This situation is frequently encountered in the nondestructive evaluation (NDE) of energy pipelines using the MFL technique. The model is derived from first principles, and utilizes the concept of dipolar magnetic charge induction to yield the 3-D MFL field in terms of surface integrals. The magnetic flux density in the specimen is assumed to be in the saturation region, and the permeability is assumed to be locally constant in the vicinity of the defect. The model uses just two geometric parameters and is capable of reproducing results that have been obtained experimentally in the literature. 3-D MFL field simulations obtained from the model facilitate a better understanding of the effect of a surface-breaking defect on the magnetic field in its vicinity. Furthermore, we simulate and analyze the 3-D MFL field in the 3-D space around the defect. This analysis yields numerous properties regarding the spatial characteristics of the three orthogonal components of the MFL field of the defect.

Dipole Modeling of Magnetic Flux Leakage

A 2D mathematical model for the magnetic leakage field of surface-breaking cracks in ferromagnetic materials is developed. The expressions are shown to be valid for 3D defects provided they are at least twenty times as long as they are deep. The model is tested by comparison with measured leakage fields for the range of artificial cracks. The magnetic forces experienced by a small magnetic particle in a leakage field are also calculated and the level of magnetic field strength required for magnetic particle crack inspection is discussed.

https://iopscience.iop.org/article/10.1088/0022-3727/19/4/018/pdf

The magnetic leakage field of surface-breaking cracks

This paper gives a guideline to the literature of magnetic methods for nondestructive evaluation of materials for flaws and defects. This is a sequel to an earlier paper which described magnetic methods for nondestructive evaluation of stress, plastic deformation and microstructure. The present paper discusses magnetic particle inspection, magnetic flux leakage, leakage field calculations and eddy current inspection, including the remote field electromagnetic inspection method. An extensive survey of recent publications in the field is given.

Review of magnetic methods for nondestructive evaluation (Part 2)

One of the largest movers of the world economy is the oil and gas industry. The industry generates billions of barrels of oil to match more than half the world’s energy demands. Production of energ...

https://journals.sagepub.com/doi/pdf/10.1177/1475921719837718

Inspection and monitoring systems subsea pipelines: A review paper:

An analytical model was developed to determine the length of a surface-breaking defect along the direction of the applied field when using the magnetic flux leakage (MFL) non-destructive technique. The theoretical model fits the experimental MFL results from simulated defects. The extreme positions of the normal magnetic leakage field component were subsequently used for a quantitative evaluation of the defect length. Permeability variations were neglected by employing a flux density close to sample saturation. Four different defect geometries were experimentally investigated and the validity of the analytical model was verified. Good agreement between theoretical and experimental results suggests that this method can be used as an inverse MFL data interpretation technique.

https://www.physics.queensu.ca/~lynann/references/research16.pdf

A model for magnetic flux leakage signal predictions

Defect modeling and the prediction of magnetic field/defect interactions is of importance to the further refinement of electromagnetic methods of defect detection and categorization. Finite element methods are particularly suited to the analysis of field distributions within magnetic structures having complex boundary geometries and nonlinear B-H characteristics. This paper describes operational aspects of the finite element technique and shows how such methods can be applied to the analysis of electromagnetic methods of nondestructive testing, by predicting the magnetic field distribution around a rectangular slot in the surface of a circular ferromagnetic bar carrying an axial magnetisation current.

JH Hwang

Papers

Finite Element Modeling of Magnetic Field/Defect Interactions