Theoretical Model of Self-Magnetic Flux Leakage and Its Application in Estimating the Depth Direction of a Fatigue Crack

Abstract

In this study, theoretical models were proposed to explain the changes in self-magnetic flux density (SMFD) due to fatigue cracks in the presence and absence of external magnetic fields. Three theoretical models were proposed: rotation domain model (RDM), concentration domain model (CDM), and vertical domain model (VDM), considering the deformation and non-deformation possibilities. To prove the theoretical model, fatigue cracks with different depth angles were fabricated through fatigue testing and EDM processing on the CT specimens. In addition, tunnel magnetoresistance (TMR) sensors were used to evaluate the 3-axis distribution of SMFD. Comparing the simulation and experimental results, similar tendencies of the occurrence and depth angle of fatigue cracks and their effect on the distribution of SMFD were observed. According to the RDM, the distribution of SMFD occurs in the direction of the crack length (y-direction), while the CDM explains that the SMFD does not occur if the fatigue crack is in a direction perpendicular to the surface. In addition, the VDM shows that SMFDs occur in a direction perpendicular to the crack length (x-direction) and the specimen surface (z-direction). Interestingly, these trends agree with the experimental results, which confirms the validity of the theoretical model and thus can be used to estimate the depth direction of a fatigue crack.