###### Abstract
It was found that the SMFD signal around the defect changed depending on the defect types, defect position, and cross-sectional area [17]. Several studies have presented a theoretical equation for the leakage flux generated around a crack using a dipole model [22; 23; 24; 25; 26; 27; 28; 29; 30; 31]. A formula was presented for the magnetization of a specimen by an external magnetic field, assuming that the magnetic dipole moment per unit area occurs at the crack surface. The formula has been used as a model that simulates the qualitative (and partially quantitative) change in MFL based on the presence of defects [22; 23; 24; 25; 26; 27] and sensor designs [28; 29], and is used for quantitative evaluation [22; 23; 24; 25; 26; 27; 29; 30; 31]. However, it is difficult to apply it to very narrow cracks, such as fatigue cracks. In addition, the change in the magnetic flux density (MFD) with the change in stress remains unclear, where conventional studies on MMM states that the magnetic flux density changes when stress changes or fatigue cracks occur, even when no external magnetic field is applied [32; 33; 34; 35; 36]. Therefore, it is uncoherent to use a magnetic dipole that assumes that an external magnetic field is applied which make the specimen in a magnetized state. Therefore, there is a need for a theoretical model to explain the SMFL phenomenon that plays the same role as the magnetic dipole model introduced in the MFLT and SMFL. Furthermore, to formulate the theoretical model of MMM, several phenomena are considered. [PERSON] et al. [32] reported that, for applied stress measurements in the stress region of a steel sample, the magnetic field component parallel to the applied stress has a considerably greater correlation than the normal component. This is because of the magnetic field distribution in the stress region, which is related to the magnetic field distribution generated in the sample after the stress is released, and the pattern was confirmed experimentally. On the other hand, [PERSON] et al. [33] compared the stress analysis using the finite element method (FEM), measured the 3-axial magnetic flux density distribution, and examined the correlation. The stress distribution, which uses the parameter of the 3-axial magnetic flux density, was set as a qualitative relationship in the third polynomial formula. As a result, it was reported that it is possible to examine stress using the MMM. However, a quantitative evaluation of stress is accompanied by a large error. [PERSON] et al. [34] derived a formula in which a change in stress accompanying mechanical deformation causes a change in SMFD. In addition, it was experimentally verified that a change in the SMFD distribution occurred owing to the change in the stress in the weld zone. A system for measuring the residual stress of a wide welding line with a high spatial resolution, using 64 GMR sensor elements arranged at intervals of 0.6 mm, was proposed. In addition to the review of stress performance and its effect on the MFD, the residual magnetic fields have also been considered. [PERSON] et al. [35] investigated the residual magnetic field as a diagnostic signal for the reliable evaluation of the material. Accordingly, the possibility of defining the plastic deformation region of a component, determining the approximate distribution of stresses and strains, and defining the remaining lifespan of the component was presented. Finally, [PERSON] et al. [36] investigated the applicability of the metal magnetic memory (MMM) method for the stress-strain state (SSS) and NDT evaluation of gas and petroleum pipelines. Using the MMM method, it was suggested that the stress concentration zone (SCZ), where the development process of fatigue damage is intensively strengthened, can be detected and used to remove this zone.