Evaluation of a Magnetic Dipole Model in a DC Magnetic Flux Leakage System

One of the most common methods for performing non-destructive testing in steel tank floors is DC magnetic flux leakage (MFL). The magnetic dipole method is the most widely used mathematical technique to predict the MFL from defects in such structures. However, due to the complexity of an exact analytical description of an MFL system, researchers often make coarse approximations for the profile of the magnetic surface charge density sigma(m), orientation of the magnetic field H, and variation of relative permeability mu(r). In this paper, the validity of these approximations is evaluated for 2-D rectangular defects in a steel plate, by comparing model predications with finite element results. The primary sources of deviation between the approximate solutions and true MFL profiles were found to be caused by assumptions that 1) sigma(m) on the specimen surface adjacent to a flaw is zero. This assumption is equivalent to treating the orientation of H to be parallel to the specimen surface, even at locations in close proximity to a flaw and 2) local variation in permeability around the defect can be ignored. This approximation was found to cause an underestimation of sigma(m) and, consequently, the predicted MFL. In contrast, approximating sigma(m) to be zero at the bottom of a flaw, and approximating uniform distribution for sigma(m) on the vertical defect sides of a slot defect was found to generate only minor errors in an estimate of flux leakage.