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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. Index Terms--Dipole, magnetic charge, magnetic flux leakage, magnetization, nondestructive evaluation.

In this paper, we present simulation results and analysis of 3-D magnetic flux leakage (MFL) signals due to the occurrence of a surface-breaking defect in a ferromagnetic specimen. The simulations and analysis are based on a magnetic dipole-based analytical model, presented in a previous paper. We exploit the tractability of the model and its amenability to simulation to analyze properties of the model as well as of the MFL fields it predicts, such as scale-invariance, effect of lift-off and defect shape, the utility of the tangential MFL component, and the sensitivity of MFL fields to parameters. The simulations and analysis show that the tangential MFL component is indeed a potentially critical part of MFL testing. It is also shown that the MFL field of a defect varies drastically with lift-off. We also exploit the model to develop a lift-off compensation technique which enables the prediction of the size of the defect for a range of lift-off values. Index Terms--Flaw sizing, lift-off, magnetic flux leakage, nondestructive evaluation, tangential component.