Dipole Modeling of Magnetic Flux Leakage

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.